Response to Pam: For Fred and/or Rob
Rob Strom
> Okay, guys, if you could help me with this kind of problem I will try very
> hard not to ask any more questions. I figure if I can learn these, I will do
> okay. Last time I took the GRE, believe it or not, I scored in the 60th pr,
> just randomly guessing on most of them -- which just goes to show how little
> most people know about math. I really don't see the point of knowing this
> stuff.
You need to know this stuff to get closer to God
and to understand His handiwork, and build a better world for your
children.
It also helps you understand how the great discoveries were
made and proven, and how to avoid been fooled by nonsense.
>
> The good news is I just solved for x 5/6 times! But although I could just
> figure out #5 by guessing, I don't know what to do mathmatically to solve
> it, and I can't figure out #6:
>
> #5 x^2 + 5x -14 = 0 I know it's 2 but how would I prove that?
Both 2 and -7 are solutions.
Proof: 2*2 + 5*2 -14 = 4 + 10 - 14 = 0.
and (-7)*(-7) + 5*(-7) -14 = 49 - 35 - 14 = 0.
I think you meant to ask: "how would I derive that"?
This is because x^2 + 5x - 14 can be factored into (x + 7)(x - 2).
Since the product of these two expressions is zero,
the equation is solved by setting either one of the expressions
to zero. If x + 7 = 0, x is -7. If x - 2 = 0, then x is 2.
Where do I get (x + 7) and (x - 2) from? Well, it's because 7*(-2) =
-14,
and 7 + (-2) = 5. That is, I'm looking for a pair of numbers that
multiply to -14, and add to 5.
Why is that so? Because that's how the distributive
law works when I multiply (x + a) * (x + b).
Watch.
Remember from the last post that P * (Q + R) is P*Q + P*R.
So put (x+a) for P, x for Q and b for R:
(x+a) * (x+b) = (x+a)*x + (x+a)*b.
In for a penny, in for a pound, so let's apply the distributive law
again,
this time to (x+a)*x.
This is x*x + a*x (that is, x^2 + ax).
And similarly (x+a)*b is bx + ab. So altogether,
we get:
x^2 + ax + bx + ab.
Applying the distributive law in reverse, the second and third terms
ax + bx
are the same as (a+b)x, hence:
(x+a)*(x+b) = x^2 + (a+b)x + ab.
In short, whenever you have
x^2 + something x + somethingelse,
you can factor it into (x + a)(x + b)
where the "something" is a+b and the "somethingelse" is a*b.
>
>
> #6 3x^2 + 10x -8 = 0
>
> I looked up the answer and it is 2/3 or -4, but I don't have any idea how
> you get this. I followed the formula for solving quadratic equations but it
> doesn't work.
This is harder, because you have a 3x^2 instead of simply an x^2,
but you can either do it the factoring way I showed above, or by the
formula.
Try it both ways:
Divide everything by 3. 0/3 is still 0 on the right side.
The equation is now:
x^2 + (10/3)x - (8/3) = 0.
So now I have to find two numbers that multiply to -8/3 and add to
10/3
(that is 3 1/3)
Obviously one is positive and the other is negative. Since 3 is
prime, one
of them has to be some number of thirds and the other an integer.
Here's all the ways to factor -8/3:
(-8)*(1/3) (8)*(-1/3) (-4)*(2/3) (4)*(-2/3) (-2)*(4/3) (2)*(-4/3)
(-1)*(8/3) (1)*(-8/3)
The only pair of factors that adds to 3 1/3 is : (4) plus (-2/3).
So the equation is
(x + 4)(x - 2/3) = 0, yielding the solutions -4 and 2/3
The quadratic formula always works.
For ax^2 + bx + c = 0, the roots are: (-b +- sqrt(b^2 - 4ac))/2a
Here a=3, b=10, c=-8, so we have:
(-10 +- sqrt(100 - (4)(3)(-8)) / 6, which is
(-10 +- sqrt(100 - (-96)) / 6, which is
(-10 +- sqrt(196)) / 6, which is
(-10 +- 14)/6, which is
(-10 + 14)/6 = 4/6 = 2/3 and
(-10 - 14)/6 = -24/6 = -4.
Baruch Hashem, the same answer as we got the other way.
>
> One example of a solution of this kind of problem they gave using factoring
> is
>
> 2x^2 - x - 6 = (2X + 3) (x-2) = 0
>
> I don't see how they got to the second expression. What happened to the -X
> in the middle?
Let's say you didn't know how to factor 2x^2 - x - 6.
You know (hopefully) that it has to be (2x + something) * (x +
somethingelse), right?
OK. Call the two unknowns a and b.
(2x + a)(x + b).
By our wonderful distributive law, this is
(2x+a)x + (2x+a)b, which is
2x^2 + ax + 2bx + ab, which is
2x^2 + (a+2b) x + ab.
So now I need to find two numbers a and b such that a*b = -6, and a+2b
= -1.
There aren't a lot of ways to factor -6
-1*6 1*-6 -2*3 2*-3 6*-1 -6*1 3*-2 -3*2
Which of these has the first plus twice the second equal to -1?
The next to the last, because 3 plus twice -2 is 3 plus -4, which is
-1.
So it's (2x + 3)(x - 2) = 0. So therefore x is 2 or -3/2.
Rob
Pam
st...@watson.ibm.com on 6/19/03 12:28 AM said:
> "Pam" <pst...@sbcglobal.net> wrote in message
> news:BB169E76.12F6E%pst...@sbcglobal.net...
>> Okay, guys, if you could help me with this kind of problem I will try very
>> hard not to ask any more questions. I figure if I can learn these, I will do
>> okay. Last time I took the GRE, believe it or not, I scored in the 60th pr,
>> just randomly guessing on most of them -- which just goes to show how little
>> most people know about math. I really don't see the point of knowing this
>> stuff.
>
>
> You need to know this stuff to get closer to God
> and to understand His handiwork, and build a better world for your
> children.
But not to teach history, which is my own means of accomplishing the above.
>
> It also helps you understand how the great discoveries were
> made and proven, and how to avoid been fooled by nonsense.
Um, maybe at more rarified levels, but I don't think these little puzzle
things enlighten me much about how great discoveries are made, though of
course it will come in hand next time someone springs some bogus equation on
me - I won't be fooled again (to quote Who).
>> The good news is I just solved for x 5/6 times! But although I could just
>> figure out #5 by guessing, I don't know what to do mathmatically to solve
>> it, and I can't figure out #6:
>>
>> #5 x^2 + 5x -14 = 0 I know it's 2 but how would I prove that?
>
> Both 2 and -7 are solutions.
> Proof: 2*2 + 5*2 -14 = 4 + 10 - 14 = 0.
> and (-7)*(-7) + 5*(-7) -14 = 49 - 35 - 14 = 0.
>
> I think you meant to ask: "how would I derive that"?
>
> This is because x^2 + 5x - 14 can be factored into (x + 7)(x - 2).
Let me see:
x*x + 5x - 14
Now I'm stuck. Never mind, I see you explain it below.
> Since the product of these two expressions is zero,
> the equation is solved by setting either one of the expressions
> to zero. If x + 7 = 0, x is -7. If x - 2 = 0, then x is 2.
That's the way I figured out it was 2.
>
> Where do I get (x + 7) and (x - 2) from? Well, it's because 7*(-2) =
> -14,
> and 7 + (-2) = 5. That is, I'm looking for a pair of numbers that
> multiply to -14, and add to 5.
Well then this is hopeless, because I would never in a million years look
for two such numbers.
>
> Why is that so? Because that's how the distributive
> law works when I multiply (x + a) * (x + b).
>
> Watch.
>
> Remember from the last post that P * (Q + R) is P*Q + P*R.
Right.
> So put (x+a) for P, x for Q and b for R:
>
> (x+a) * (x+b) = (x+a)*x + (x+a)*b.
Okay, this makes sense to me but to sink in I am going to have to study it a
while.
>
> In for a penny, in for a pound, so let's apply the distributive law
> again,
> this time to (x+a)*x.
> This is x*x + a*x (that is, x^2 + ax).
> And similarly (x+a)*b is bx + ab. So altogether,
> we get:
>
> x^2 + ax + bx + ab.
Okay.
>
> Applying the distributive law in reverse, the second and third terms
> ax + bx
> are the same as (a+b)x, hence:
>
> (x+a)*(x+b) = x^2 + (a+b)x + ab.
Okay.
>
> In short, whenever you have
> x^2 + something x + somethingelse,
> you can factor it into (x + a)(x + b)
> where the "something" is a+b and the "somethingelse" is a*b.
Okay let me try this step by step:
x^2 + 5x -14 = 0
x*x + 5*x - 14 = 0
x*x + 5*x + (-2)*7 = 0
x*(x + 5) + (-2)*7 = 0 I think I got off track.
Now what do I do?
I will do (or more likely, fail to do) the next one in another post -- it's
after 2:00. I take the test 7-17, but I have 10 days of two sets of house
guests coming next week, and extensive preparations before then. I'm going
to print up all these posts and study them whenever I can.
Thank you; this is all such a huge help. I really don't know anybody IRL who
can explain this to me.
Rob Strom
> in article abea7612.03061...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/19/03 12:28 AM said:
>
> > "Pam" <pst...@sbcglobal.net> wrote in message
> > news:BB169E76.12F6E%pst...@sbcglobal.net...
> >> Okay, guys, if you could help me with this kind of problem I will try very
> >> hard not to ask any more questions. I figure if I can learn these, I will do
> >> okay. Last time I took the GRE, believe it or not, I scored in the 60th pr,
> >> just randomly guessing on most of them -- which just goes to show how little
> >> most people know about math. I really don't see the point of knowing this
> >> stuff.
> >
> >
> > You need to know this stuff to get closer to God
> > and to understand His handiwork, and build a better world for your
> > children.
>
> But not to teach history, which is my own means of accomplishing the above.
You can't get away with being ignorant of math any more than
I can get away with being ignorant of history. I might just
as well say "I'm a computer researcher, so why do I need to
know that there was a Civil War or a Roman Empire?"
God didn't say just study what you need for your job.
That's why He gave you a sabbath.
>
> >
> > It also helps you understand how the great discoveries were
> > made and proven, and how to avoid been fooled by nonsense.
>
> Um, maybe at more rarified levels, but I don't think these little puzzle
> things enlighten me much about how great discoveries are made, though of
> course it will come in hand next time someone springs some bogus equation on
> me - I won't be fooled again (to quote Who).
I don't know any Who, except, of course, the Time Lord
known as the Doctor.
The distributive law illustrates a basic fact of nature, as
I said in another post. That is, that units like dollars vs. pounds
or inches vs. meters aren't intrinsic parts of nature, and therefore
adding up something in inches and then converting to meters
has to produce the same result as converting to meters first
and then adding up in meters, because a length is a length is a length
regardless of how you measure it. This notion of finding
out which things are invariants in nature and which things
are relative to your perspective or how you measure it is
a fundamental idea without which you can't understand
Relativity or any of the other great discoveries of the 20th
century which transformed our world.
...
> >
> > This is because x^2 + 5x - 14 can be factored into (x + 7)(x - 2).
>
> Let me see:
>
> x*x + 5x - 14
>
> Now I'm stuck. Never mind, I see you explain it below.
>
>
> > Since the product of these two expressions is zero,
> > the equation is solved by setting either one of the expressions
> > to zero. If x + 7 = 0, x is -7. If x - 2 = 0, then x is 2.
>
> That's the way I figured out it was 2.
No it wasn't because you didn't factor the expression into two expressions.
If you had, you would have found x=-7 as well.
> >
> > Where do I get (x + 7) and (x - 2) from? Well, it's because 7*(-2) =
> > -14,
> > and 7 + (-2) = 5. That is, I'm looking for a pair of numbers that
> > multiply to -14, and add to 5.
>
> Well then this is hopeless, because I would never in a million years look
> for two such numbers.
But the explanation below explains why you want to
look for two such numbers.
>
>
> >
> > Why is that so? Because that's how the distributive
> > law works when I multiply (x + a) * (x + b).
> >
> > Watch.
[... steps omitted]
> >
> > (x+a)*(x+b) = x^2 + (a+b)x + ab.
>
> Okay.
OKAY??? Then please keep this in your head for
the next 3 paragraphs of this post where you will use it!!
>
>
> >
> > In short, whenever you have
> > x^2 + something x + somethingelse,
> > you can factor it into (x + a)(x + b)
> > where the "something" is a+b and the "somethingelse" is a*b.
>
>
> Okay
You need to remember this, too.
> let me try this step by step:
>
>
> x^2 + 5x -14 = 0
>
> x*x + 5*x - 14 = 0
>
> x*x + 5*x + (-2)*7 = 0
Oops, you seem to have forgotten what I just said above,
and which you said OK to. That is, if you have
x^2 + something x + somethingelse, look for a and b
such that a+b is something and a*b is somethingelse,
and you will find that x^2 + (a+b)x + ab = (x + a)(x + b).
So we write this as
x^2 + (-2 + 7)x + (-2)(7) = 0
which we know factors into
(x - 2)(x + 7) = 0
>
> x*(x + 5) + (-2)*7 = 0 I think I got off track.
>
> Now what do I do?
The track was finding two numbers that multiplied to -14 and added to 5.
>
>
> I will do (or more likely, fail to do) the next one in another post -- it's
> after 2:00. I take the test 7-17, but I have 10 days of two sets of house
> guests coming next week, and extensive preparations before then. I'm going
> to print up all these posts and study them whenever I can.
>
> Thank you; this is all such a huge help. I really don't know anybody IRL who
> can explain this to me.
What about the math teacher at the school where you teach???
--
Rob
Pam
>>
>> Thank you; this is all such a huge help. I really don't know anybody IRL who
>> can explain this to me.
>
> What about the math teacher at the school where you teach???
>
Everyone teaches math, and even a little simple algebra (I demonstrate it
using this balance thing -- hang weights on different numbers on one side,
then hang weights on some numbers on the other and ask 1) how to write the
equation, and 2) what number do I need to add to make it balance?)
Anyway, as you can see, from what you, Fred, and Joe have given me, if I
will study, study, study, and try to absorb it deep into my bones, I'll have
more than enough to keep me busy for a while.
It's frustrating for me to understand something -- for about 60 seconds --
then it slips away. This is a good experience for me when I feel like
beating my head against a wall trying to get kids to learn something.
Imagine trying to teach math to a classful of people, half a dozen of which
are learning disabled like me and have to have something
explained/demostrated/drawn/sung/acted out/mimed to them ten different ways
a hundred different times (and another half dozen get it before the words
are out of your mouth) -- while constantly being interrupted by people
asking you to repeat instructions you just gave, or finishing your sentences
for you, or chatting with people around them, etc. -- and you can just
barely begin to have an idea of what my job is. And you want to be a teacher
when you "retire"! Well, you'd probably be good at it anyway. (And
fortunately these people are terribly cute, and no matter how many times you
bang your head on the overhead, look up at you with big adoring eyes.)
Rob Strom
Pam wrote:
>
> in article abea7612.03061...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/19/03 10:44 AM said:
>
> >>
> >> Thank you; this is all such a huge help. I really don't know anybody IRL who
> >> can explain this to me.
> >
> > What about the math teacher at the school where you teach???
> >
> Everyone teaches math, and even a little simple algebra
That's a scandal.
They should not allow people who don't know how to
add, subtract, multiply, and divide simple algebraic formulas
to teach math. If you still don't grok the distributive
law, you should not be allowed to teach math, or anything
else (like science) that depends upon knowing this kind of reasoning.
That's why I'm for raising the standards for teachers,
and paying them something commensurate with their skill.
If you pay a teacher less than an auto mechanic, don't
be surprised if your teachers don't have the skills.
> (I demonstrate it
> using this balance thing -- hang weights on different numbers on one side,
> then hang weights on some numbers on the other and ask 1) how to write the
> equation, and 2) what number do I need to add to make it balance?)
>
That's OK if they already know that the torque equals
the weight times the distance, but usually they learn
that *after* they've learned basic algebra.
I would use a problem that uses concepts clear to a 5-year-old:
If I can ride my bike at 20 feet per second and my little
brother can ride his at 15 feet per second and I give him
a head start of so many feet or so many seconds, how
long or how far before I catch up with him?
The poor kid has to learn algebra, which is hard enough --
why make it worse by having him apply it to this torque problem
that he might not understand? At least everybody understands
what it means to run a race with a faster/slower kid
where the slower kid gets a head start.
> Anyway, as you can see, from what you, Fred, and Joe have given me, if I
> will study, study, study, and try to absorb it deep into my bones, I'll have
> more than enough to keep me busy for a while.
>
> It's frustrating for me to understand something -- for about 60 seconds --
> then it slips away. This is a good experience for me when I feel like
> beating my head against a wall trying to get kids to learn something.
> Imagine trying to teach math to a classful of people, half a dozen of which
> are learning disabled like me and have to have something
> explained/demostrated/drawn/sung/acted out/mimed to them ten different ways
> a hundred different times (and another half dozen get it before the words
> are out of your mouth) -- while constantly being interrupted by people
> asking you to repeat instructions you just gave, or finishing your sentences
> for you, or chatting with people around them, etc. -- and you can just
> barely begin to have an idea of what my job is.
Yes, but how much harder is it to *learn* math in the same
classroom, when the *teacher* doesn't really understand
what she's talking about, but is desperately trying to
remember something she was told once but isn't at all sure
why it works!!!
> And you want to be a teacher
> when you "retire"!
It's because my kids learned lots of subjects, but
especially science, from teachers who understood
their subject far less well than you understand math!
--
Rob Strom
Pam
> Yes, but how much harder is it to *learn* math in the same
> classroom, when the *teacher* doesn't really understand
> what she's talking about, but is desperately trying to
> remember something she was told once but isn't at all sure
> why it works!!!
What we are discussing here is the GRE! Not 4th grade. I'm applying for
graduate school, not to teach elementary math. Last time I scored in the
60th pr, 600 out of 800 -- above average for all people who take the GRE, if
that has not occurred to you. And I haven't had algebra since I was 14! I am
practically a math genius.
It so happens that I am quite a superb teacher of elemary math. My
evaluator, who was the district elementary math coordinatior, observed me
teach math twice and told me what I did was extraordinary and very rare
among teachers. (She kept asking me if I _knew_ how good I was, so I finally
said, well, yes.) No parent has ever complained that his gifted child was
not sufficiently challenged. I have a very specific curriculum to teach.
Teaching the distributive, associative, and commutative properties are
simply not part of the curriculum for this age group. Maybe it should be but
it's not. Even so, there are plenty of opportunities for gifted kids to do
math that challenges their little 150 IQs.
Here's a scenario I can see: You, like some other dads I've encountered,
waltz in at open house to meet the dumb bunny teacher and tell me how to do
my job. With consummate professionalism I chew you up, spit you out, and
send you out the door with your tail between your legs. :-) How sweet it
is.
don't spam me]@slater.net Joe Slater
>But the explanation below explains why you want to
>look for two such numbers.
One thing occurred to me last night; the diagram that a teacher drew
for me once. This shows two things - why we call it a quadratic
equation, and where the numbers come from.
You know how you work out the area of a rectangle by multiplying the
length and the width? Let's describe the sides of the rectangle in
terms of _x_. One side is x+something and the other side is
x+somethingelse.
Well call these two "somethings" _a_ and _b_ so we end up with a
diagram like this: (you need a fixed-width font to make sense of the
diagram, sorry)
x + a
--------
| |
| |
x| |
| |
+| |
| |
b| |
| |
--------
Now let's divide the width of the diagram into the part that's "x"
wide and the part that's "a" wide:
x a
--------
| | |
| | |
x| | |
| | |
+| | |
| | |
b| | |
| | |
--------
And let's do the same horizontally - draw a line marking the bit
that's "x" high and the bit that's "b" high:
x a
--------
| | |
| | |
x| | |
| | |
|--------|
| | |
b| | |
| | |
--------
Now, from what we know about the area of rectangles we can see that
the areas of the little sections are as follows:
x a
--------
| | |
| | |
x|x*x |x*a|
| | |
|--------|
| | |
b|x*b |a*b|
| | |
--------
If you add up all the areas you get:
x^2 + x*(a+b) + a*b
Which is the form that a quadratic equation takes. And now you can see
why the equations have two answers - if the area of the rectangle is
zero then it means that either the height is equal to zero or the
width is equal to zero, and that only happens if "x" is either equal
and opposite to "a" (for instance, like + 2 and -2) or if "x" is equal
and opposite to "b".
And this is why it's called a quadratic equation - because it's based
on a rectangle, which is a four-sided shape and "quadra" means "four".
jds
Pam
joe[please don't spam me]@slater.net on 6/19/03 7:42 PM said:
> On 19 Jun 2003 08:44:18 -0700, st...@watson.ibm.com (Rob Strom) wrote:
>> But the explanation below explains why you want to
>> look for two such numbers.
>
> One thing occurred to me last night; the diagram that a teacher drew
> for me once. This shows two things - why we call it a quadratic
> equation, and where the numbers come from.
Oh, wow, this is brilliant! Now it makes sense to me -- plus I really like
knowing what it has to do with "quadratic". Now, this is the kind of thing
that a good teacher does -- and you remembered it all these years. BTW, Fred
sent me your "lesson" and I emailed you but it bounced because I forgot to
take out the nospam thing. Thanks so much for your help; I really appreciate
it. I am going to go try solving these things using the diagram.
don't spam me]@slater.net Joe Slater
>Oh, wow, this is brilliant! Now it makes sense to me -- plus I really like
>knowing what it has to do with "quadratic". Now, this is the kind of thing
>that a good teacher does -- and you remembered it all these years.
The complicating thing is that the equation might be something like
(x+a)*(x-b)=0. That is, the height of the rectangle is x PLUS a and
the width is x MINUS b. So take the diagram:
x a
--------
| | |
| | |
x|x*x |x*a|
| | |
|--------|
| | |
b|x*b |a*b|
| | |
--------
And what you need to do is take the top half which is x*(x+a) and
subtract the bottom half which is b*(x+a) like this:
x a
--------
| | |
| | |
x|x*x |x*a|
| | |
--------
minus
--------
| | |
b|x*b |a*b|
| | |
--------
and this is because if you worked out the equation it would be
written:
(x+a)*(x-b)= 0
x^2 -bx +ax -ab = 0
Group the negative bits together so it makes more sense and you have
x^2 + ax (the top bit) -bx - ab (the bottom bit) = 0
And if BOTH "a" AND "b" are negative then you're left with x^2 being
positive, ax and bx both being negative, and ab being positive because
two negative numbers multiplied by eachother make a positive one, so
it becomes
x^2 -ax -bx +ab = 0
Hope this helps,
jds
Pam
joe[please don't spam me]@slater.net on 6/19/03 9:31 PM said:
>
> And if BOTH "a" AND "b" are negative then you're left with x^2 being
> positive, ax and bx both being negative, and ab being positive because
> two negative numbers multiplied by eachother make a positive one, so
> it becomes
> x^2 -ax -bx +ab = 0
>
> Hope this helps,
> jds
Yes indeed. If I had come across an example w/o this explanation I would
have been flummoxed. I really appreciate the effort that you've gone to to
make these little diagrams. It's amazing how much more illuminating these
diagrams are than just verbalization.
You know, these days there are algebra manipulative kids can use -- concrete
objects that you can manipulate so that you can see what you are really
doing when you use the expressions. I have no idea how they work, but when I
teach math I always start with the manipulatives and then help the kids make
the connection between what they are doing and whatever algorithm they are
learning. Another thing I do is teach them to multiply large numbers not
with the standard algorithm (which was designed to conserve space when
writing) but with a diagram not unlike the one you showed me. It takes up
much more space but it's much easier to do and the kids can understand the
math behind what they are doing more easily.
Thanks again!
vince garcia
Mordecai!
"John F. Nixon" wrote:
> On Fri, 20 Jun 2003 06:37:22 -0700, vince garcia
> <vgga...@ix.netcom.com> wrote:
>
> >hey joe could you take a crack at my question?
>
> 42.
Is that the radio version - what do you get if you multiply eight by six? or the book version? Which ran out
of scrabble letters?
>
>
> --
> regards, Fred
>
> "Verbing weirds language." -- Calvin
----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==----
http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 Newsgroups
---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =---
Rob Strom
Pam wrote:
>
> in article abea7612.03061...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/19/03 5:16 PM said:
>
> > Yes, but how much harder is it to *learn* math in the same
> > classroom, when the *teacher* doesn't really understand
> > what she's talking about, but is desperately trying to
> > remember something she was told once but isn't at all sure
> > why it works!!!
>
> What we are discussing here is the GRE! Not 4th grade. I'm applying for
> graduate school, not to teach elementary math. Last time I scored in the
> 60th pr, 600 out of 800 -- above average for all people who take the GRE, if
> that has not occurred to you. And I haven't had algebra since I was 14! I am
> practically a math genius.
The principles involved are certainly taught in 7th grade, and I still
think that someone who teaches math to 4th graders should
know 7th grade math, especially because the algebraic rules
of 7th grade math tend to explain *why* this particular sequence of
operations solves a particular 4th grade problem while
this other similar sequence of operations doesn't.
>
> It so happens that I am quite a superb teacher of elemary math. My
> evaluator, who was the district elementary math coordinatior, observed me
> teach math twice and told me what I did was extraordinary and very rare
> among teachers. (She kept asking me if I _knew_ how good I was, so I finally
> said, well, yes.) No parent has ever complained that his gifted child was
> not sufficiently challenged. I have a very specific curriculum to teach.
You're being too thin-skinned. I'm sure you're a superb
teacher. But you are unskilled in math, since you can
nod your head when some algebraic rule is explained to you,
and 3 paragraphs down you're not able to see that this very
same rule is applicable to the problem you're faced with.
In the evolution threads, it was clear that elementary
probability and statistics was confusing to you as well.
> Teaching the distributive, associative, and commutative properties are
> simply not part of the curriculum for this age group. Maybe it should be but
> it's not. Even so, there are plenty of opportunities for gifted kids to do
> math that challenges their little 150 IQs.
These properties are not taught *formally*, but they're
taught operationally nevertheless.
Fourth grade certainly involves learning how to read maps
and convert units, and therefore it involves understanding
that you can manipulate things in any units you wish
as long as they're common units, which is
the principle underlying the distributive law. And I think
that when I was in fourth grade, we learned about fractions,
where we had problems like adding 1/2 + 1/3. This is
a similar skill to your quadratic factoring problem.
You have to find a number that simultaneously meets two
properties: in this case,
it must divide 2 evenly and also divide 3 evenly. Then
you have to realize that it's 6, and that 1/2 is 3/6
and that 1/3 is 2/6. Then you have to realize
that 3/6 + 2/6 is the same as (3+2)/6 which is *explicitly*
an application of the distributive law!! The geometric
explanation of why it works is essentially the same
kind of thing of chopping up rectangles that Joe showed you
for the other problem.
The only thing about the distributive law that
was not taught is its *abstract* formalization ---
A*(B+C) = A*B + A*C.
That is because it is generally perceived that
children that age deal better with concrete operations
than with formal ones. But you as the teacher
need to understand the formal principles, because
they explain why it's OK to add the tops of the fractions
but not the bottoms. And somehow the kids have
to get an intuition of why it's OK to add the tops
and not the bottoms otherwise they're just doing magic
tricks not mathematics.
I stand by my position that they should pay teachers
more, and they should make sure that anyone who is going to teach
4th grade math to kids is solidly conversant in 7th grade math.
(Same with any other subject --- people who teach
4th grade reading should themselves be able to read
at at least a 7th grade level!)
>
> Here's a scenario I can see: You, like some other dads I've encountered,
> waltz in at open house to meet the dumb bunny teacher and tell me how to do
> my job. With consummate professionalism I chew you up, spit you out, and
> send you out the door with your tail between your legs. :-) How sweet it
> is.
I'm not going to disrupt your fantasies.
--
Rob Strom
CL
<8736fv4npglo0et8p...@4ax.com>:
> On Fri, 20 Jun 2003 06:37:22 -0700, vince garcia
> <vgga...@ix.netcom.com> wrote:
>
>>hey joe could you take a crack at my question?
>
> 42.
You forgot to carry a 1.
--
Please visit http://www.jtf.org
Pam
st...@watson.ibm.com on 6/20/03 12:01 PM said:
> Sent by Google just in case:
>
> Pam wrote:
>>
>> in article abea7612.03061...@posting.google.com, Rob Strom at
>> st...@watson.ibm.com on 6/19/03 5:16 PM said:
>>
>>> Yes, but how much harder is it to *learn* math in the same
>>> classroom, when the *teacher* doesn't really understand
>>> what she's talking about, but is desperately trying to
>>> remember something she was told once but isn't at all sure
>>> why it works!!!
>>
>> What we are discussing here is the GRE! Not 4th grade. I'm applying for
>> graduate school, not to teach elementary math. Last time I scored in the
>> 60th pr, 600 out of 800 -- above average for all people who take the GRE, if
>> that has not occurred to you. And I haven't had algebra since I was 14! I am
>> practically a math genius.
>
> The principles involved are certainly taught in 7th grade, and I still
> think that someone who teaches math to 4th graders should
> know 7th grade math,
What you think really doesn't matter, to me or the state of Texas, because
it's merely an assertion without any basis. There is no research that says
one cannot teach elementary math if all one knows is elementary math.
> especially because the algebraic rules
> of 7th grade math tend to explain *why* this particular sequence of
> operations solves a particular 4th grade problem while
> this other similar sequence of operations doesn't.
If the state told me to teach 7th grade math to 9 year olds, I'd do it. But
I guarantee it's absolutely impossible for most of them to learn 4th, 5th,
6th, and 7th grade math in 10 months.
>
>
> You're being too thin-skinned. I'm sure you're a superb
> teacher. But you are unskilled in math, since you can
> nod your head when some algebraic rule is explained to you,
> and 3 paragraphs down you're not able to see that this very
> same rule is applicable to the problem you're faced with.
Thosw were problems on the GRE. They are not problems given to people with a
foundation in 3rd grade math.
> In the evolution threads, it was clear that elementary
> probability and statistics was confusing to you as well.
Yet I can teach them perfectly well at the elementary level. If I had to,
Rob, I could learn and teach high school algebra. It would take more than a
couple of weeks to learn it, but I could. However, it would be a complete
waste of time to do it in order to teach elementary kids what they need to
know.
>
>
>> Teaching the distributive, associative, and commutative properties are
>> simply not part of the curriculum for this age group. Maybe it should be but
>> it's not. Even so, there are plenty of opportunities for gifted kids to do
>> math that challenges their little 150 IQs.
>
> These properties are not taught *formally*, but they're
> taught operationally nevertheless.
That's what I do.
>
> Fourth grade certainly involves learning how to read maps
> and convert units,
They do not have to convert units in 4th. They do that in 5th.
> and therefore it involves understanding
> that you can manipulate things in any units you wish
> as long as they're common units, which is
> the principle underlying the distributive law.
But not at the level of complexity of the problems on the GRE!
> And I think
> that when I was in fourth grade, we learned about fractions,
> where we had problems like adding 1/2 + 1/3.
Because you went to genius school, no doubt. It is not taught in 4th grade.
They only convert fractions by looking at models -- they can look at two
pictures and identify 3/4 as equal to 6/8. They don't have to know how to
perform the operation, although some figure it out: I have them use
manipulates and record all the equivalent fractions -- many of them see the
pattern and figure out how to generated equivalent fractiosn or reduce them.
But this is not tested (I only give these as bonus questions on the tests I
make.)
They do not add or subtract fractions in 4th grade except by looking at
models.
Now, in 5th grade they do have to learn how to add & subtract fractions with
different denominators. I teach it using cuisenaire rods. For example they
would lay down one half rod and one third rod; then they would find the rod
that they could evenly line up beside the half and the third rod, which
would be the one sixth rod. They can then understand why it makes sense to
multiply the two denominators to find a common one. They also have to learn
to reduce fractions. No one taught me to use manipulatives in this way -- I
had to figure out a way to concretely represent the process to make it
easier for kids to understand. This is the part of teaching that you don't
know a thing in the world about -- and why we teachers get annoyed that
everyone who's ever been through school thinks they know something about
teaching.
> This is
> a similar skill to your quadratic factoring problem.
Speaking of which, did you notice the simple elegance of Joe's diagram,
learned from a real teacher? This is the sort of thing that real teachers
do. You can't just call people stupid when they have trouble seeing what's
obvious to you. You have to get inside their heads, figure out how they
think, what it is that is confusing them, and devise a way to help them
understand. You evidently didn't do a very good job, since I didn't
understand it immediately. (I have yet to find time to study it carefully
because I am here writing these stupid posts instead.) See, in the real
world these days, if a student doesn't learn, you are responsible. It's YOUR
responsibility to find a way to explain it so he does understand; or find a
way to get him to pay attention so he can learn; or motivate him to want to
learn. When we are told "Leave No Child Behind" there are no excuses. I am
responsible for making sure every single child passes the test, even though
last year he didn't, and therefore came to me lacking the foundation for 4th
grade math, and his IQ is only 85. But every year, this is what I do. 100%
passing rate.
> You have to find a number that simultaneously meets two
> properties: in this case,
> it must divide 2 evenly and also divide 3 evenly. Then
> you have to realize that it's 6, and that 1/2 is 3/6
> and that 1/3 is 2/6. Then you have to realize
> that 3/6 + 2/6 is the same as (3+2)/6 which is *explicitly*
> an application of the distributive law!!
Oh, you would do a bang up job teaching this to elementary school kids, Rob.
Telling them they "have to" realize it's 6 won't get you very far.
> The geometric
> explanation of why it works is essentially the same
> kind of thing of chopping up rectangles that Joe showed you
> for the other problem.
Right -- which you didn't think to present. THAT'S what's essential in an
elementary teacher -- not knowing higher math, but knowing how to teach
elementary math in a way that kids can learn.
>
> The only thing about the distributive law that
> was not taught is its *abstract* formalization ---
> A*(B+C) = A*B + A*C.
> That is because it is generally perceived that
> children that age deal better with concrete operations
> than with formal ones. But you as the teacher
> need to understand the formal principles, because
> they explain why it's OK to add the tops of the fractions
> but not the bottoms. And somehow the kids have
> to get an intuition
"Somehow" the kids have to "get an intuition"??? <wild laughter> Don't hold
your breath.
> of why it's OK to add the tops
> and not the bottoms otherwise they're just doing magic
> tricks not mathematics.
I'll make sure to tell them they must "somehow get an intuition" about these
things.
>
> I stand by my position that they should pay teachers
> more, and they should make sure that anyone who is going to teach
> 4th grade math to kids is solidly conversant in 7th grade math.
Well, they are not going to pay teachers more any time soon, at least not
here. I've been teaching 17 years and will make $43K next year. Out of that
I have to pay all but $250 of health insurance for my family, disability,
life insurance, and teacher retirement (no social security). The state for
the first time contributed $1000 per annum last year -- which the district
did not pass along, since they only gave us a $1000 pay increase -- but this
session took that away, because if they are going to balance the budget it
is always going to be on teachers' backs.
> (Same with any other subject --- people who teach
> 4th grade reading should themselves be able to read
> at at least a 7th grade level!)
Actually, that's not even true. We must be able to analyze exactly why it
is, for example, that a kid can read every word on a page perfectly and not
be able to tell you one single thing about what it said. And then devise a
range of strategies to help him do so.
Teaching is a real skill, a terribly difficult one, esp when you have more
than one student, and half the battle with some is just getting them to pay
attention and want to learn (because if they don't want to learn something
they are not going to do it). You really do not need to know one element of
content beyond that which the students are required to learn. I am far more
literate than most elementary teachers, but that gives me absolutley no
advantage in teaching children to understand what they read, and make
inferences, predictions, draw conclsions, identify cause and effect,
identify fact and opinion, understand character motives, identify author's
purpose, and a ton of other stuff.
Thin skinned? No, just tired of people devaluing what we do because they
have not the tiniest clue what it is we do. We are tired of being ground
into exhaustion for little pay, and then having people like you come along
and tell us we aren't doing it right, and that we must make sure that
"somehow" the kids must just "intuit" how do things.
Rob Strom
>...
> > especially because the algebraic rules
> > of 7th grade math tend to explain *why* this particular sequence of
> > operations solves a particular 4th grade problem while
> > this other similar sequence of operations doesn't.
>
> If the state told me to teach 7th grade math to 9 year olds, I'd do it.
You have misunderstood nearly everything I've said here.
I didn't say you should teach 7th grade math to 9 year olds.
I said that if you want to teach 4th grade math to 9 year olds,
it helps having learned 7th grade math because the 7th grade
math explains why the "rules" of 4th grade math work. I am
raising the conjecture that it is easier to teach something well
if you know how it works, because knowing how it works enables
you to know when to vary the procedure and when not. Just like
when I first learned to cook, I cooked my mother's recipes by
rote. I was a pretty bad cook, because I didn't really understand
why I was doing any of the steps I was doing, and therefore
if the slightest thing went wrong I didn't have any basis for
adjusting.
> But
> I guarantee it's absolutely impossible for most of them to learn 4th, 5th,
> 6th, and 7th grade math in 10 months.
This isn't what I argued so it's not the point.
>
> >
> >
>
> > You're being too thin-skinned. I'm sure you're a superb
> > teacher. But you are unskilled in math, since you can
> > nod your head when some algebraic rule is explained to you,
> > and 3 paragraphs down you're not able to see that this very
> > same rule is applicable to the problem you're faced with.
>
> Thosw were problems on the GRE. They are not problems given to people with a
> foundation in 3rd grade math.
Same thing here.
>
> > In the evolution threads, it was clear that elementary
> > probability and statistics was confusing to you as well.
>
> Yet I can teach them perfectly well at the elementary level. If I had to,
> Rob, I could learn and teach high school algebra. It would take more than a
> couple of weeks to learn it, but I could. However, it would be a complete
> waste of time to do it in order to teach elementary kids what they need to
> know.
We're just going to have to disagree about this.
Every time my kids were taught by somebody who just knew the
curriculum and nothing else beyond they had a real problem. Sometimes
my kid even would answer a question correctly and intelligently
and the teacher would complain because it wasn't the way she was
taught to do it. Or if my child didn't get it, the teacher would
just keep repeating the original instructions until she did, because
the teacher couldn't come up with an equivalent alternative method
on the fly. Once, the geography teacher had a map
(made by the official materials-makers) where for
reasons of space, Kampuchea was abbreviated as "Kam", but of course
she had never heard of either Kampuchea or "Kam" so kept making up
tests getting her students to identify where "Kam" was. Yuck.
She had her curriculum, she had her materials, she had her tests,
and in her mind, she was all prepared to go.
> ...
> > Fourth grade certainly involves learning how to read maps
> > and convert units,
>
> They do not have to convert units in 4th. They do that in 5th.
>
> > and therefore it involves understanding
> > that you can manipulate things in any units you wish
> > as long as they're common units, which is
> > the principle underlying the distributive law.
>
> But not at the level of complexity of the problems on the GRE!
The problem you were having was with the distributive law.
The only difference between that law as you had to do it for
the GRE and how you have to do it for 4th (or 5th) grade is
that you have to perform this operation on formulas with variables,
rather than with specific numbers.
>
> > And I think
> > that when I was in fourth grade, we learned about fractions,
> > where we had problems like adding 1/2 + 1/3.
>
> Because you went to genius school, no doubt. It is not taught in 4th grade.
In my generation, it was taught in 4th grade. And in Europe
stuff way beyond this level is taught in 4th grade. All
my European, Indian, and Far-Eastern colleagues, while they
praise US higher education as the best in the world, are shocked
at how far behind the rest of the world US primary education is.
My French colleague, on a 2-year assignment to the US, took care
to enroll his kids in French schools here, not because they
couldn't speak English, but because they'd otherwise be dangerously behind
in subjects like math and science when they went back.
And even if it's done in 5th grade, it's much better to teach
them that adding fractions of different denominators is exactly
like adding quantities of different units --- the principle
that you convert things to a common unit is the same. They
have certainly learned to add mixtures of dollars, dimes and cents.
> ... This is the part of teaching that you don't
> know a thing in the world about -- and why we teachers get annoyed that
> everyone who's ever been through school thinks they know something about
> teaching.
>
Huh???
You forget that my family consists of 3 generations of teachers,
and that I have sat in classrooms, graded papers, observed
and assisted with lessons,
browsed through the teaching manuals, and manipulated the manipulatives.
My father taught shop, my mother taught remedial reading, 3rd grade elementary
school, and later 7th grade English and French, my brother taught
elementary school on Navajo reservations, my wife taught
first grade regular and special education, my son teaches violin
and orchestra, and
my daughter teaches homebound students
in all subjects at a variety of grade levels. And I direct 4th and 5th
grade schoolmusicals.
My father, mother, wife, and son all had specific certifications,
and my daughter is a few credits from obtaining hers.
Spare me the lectures on what I don't know about teaching.
>
> > This is
> > a similar skill to your quadratic factoring problem.
>
> Speaking of which, did you notice the simple elegance of Joe's diagram,
> learned from a real teacher? This is the sort of thing that real teachers
> do. You can't just call people stupid when they have trouble seeing what's
> obvious to you. You have to get inside their heads, figure out how they
> think, what it is that is confusing them, and devise a way to help them
> understand. You evidently didn't do a very good job, since I didn't
> understand it immediately.
You're not going to understand it immediately; you have to practice.
Joe's diagram is good because it moves the law to another modality,
in this case areas of geometrical figures. I gave yet another modality,
in this case, converting pounds to dollars.
> (I have yet to find time to study it carefully
> because I am here writing these stupid posts instead.) See, in the real
> world these days, if a student doesn't learn, you are responsible. It's YOUR
> responsibility to find a way to explain it so he does understand; or find a
> way to get him to pay attention so he can learn; or motivate him to want to
> learn. When we are told "Leave No Child Behind" there are no excuses. I am
> responsible for making sure every single child passes the test, even though
> last year he didn't, and therefore came to me lacking the foundation for 4th
> grade math, and his IQ is only 85. But every year, this is what I do. 100%
> passing rate.
As you know, I don't agree with these methods. When my son teaches
violin, he doesn't start with a group of beginners and expect to
have everyone finishing Book I at the same time, or Book II or whatever.
If a child is having trouble with Book I, he isn't "passed on" to
Book II merely because he gets xxx% of the notes right.
>
> > You have to find a number that simultaneously meets two
> > properties: in this case,
> > it must divide 2 evenly and also divide 3 evenly. Then
> > you have to realize that it's 6, and that 1/2 is 3/6
> > and that 1/3 is 2/6. Then you have to realize
> > that 3/6 + 2/6 is the same as (3+2)/6 which is *explicitly*
> > an application of the distributive law!!
>
> Oh, you would do a bang up job teaching this to elementary school kids, Rob.
> Telling them they "have to" realize it's 6 won't get you very far.
And if you think I suggested any such thing, you need to
take the reading test again.
> ...
> > The only thing about the distributive law that
> > was not taught is its *abstract* formalization ---
> > A*(B+C) = A*B + A*C.
> > That is because it is generally perceived that
> > children that age deal better with concrete operations
> > than with formal ones. But you as the teacher
> > need to understand the formal principles, because
> > they explain why it's OK to add the tops of the fractions
> > but not the bottoms. And somehow the kids have
> > to get an intuition
>
> "Somehow" the kids have to "get an intuition"??? <wild laughter> Don't hold
> your breath.
If you just tell the kids to add the tops and not the bottoms
they'll obey, but if they don't know why it works, they'll
be in trouble later. Some will forget, and they'll add
the bottoms and not the tops. Others will not be able to generalize
it to other situations where the "bottoms" don't happen to be on the
bottom, but where the principle is the same (e.g. adding whole
numbers and percents).
>
> > of why it's OK to add the tops
> > and not the bottoms otherwise they're just doing magic
> > tricks not mathematics.
>
> I'll make sure to tell them they must "somehow get an intuition" about these
> things.
If you do, don't expect me to support you.
> >
> > I stand by my position that they should pay teachers
> > more, and they should make sure that anyone who is going to teach
> > 4th grade math to kids is solidly conversant in 7th grade math.
>
...
> > (Same with any other subject --- people who teach
> > 4th grade reading should themselves be able to read
> > at at least a 7th grade level!)
>
> Actually, that's not even true. We must be able to analyze exactly why it
> is, for example, that a kid can read every word on a page perfectly and not
> be able to tell you one single thing about what it said. And then devise a
> range of strategies to help him do so.
>
> Teaching is a real skill, a terribly difficult one, esp when you have more
> than one student, and half the battle with some is just getting them to pay
> attention and want to learn (because if they don't want to learn something
> they are not going to do it). You really do not need to know one element of
> content beyond that which the students are required to learn.
I just don't accept this last statement.
...>
> Thin skinned? No, just tired of people devaluing what we do because they
> have not the tiniest clue what it is we do. We are tired of being ground
> into exhaustion for little pay, and then having people like you come along
> and tell us we aren't doing it right, and that we must make sure that
> "somehow" the kids must just "intuit" how do things.
I agree. If I meet any such people who devalue what you do,
don't have a clue, and tell you that you aren't doing it right,
I'll give them a piece of my mind. In the meantime, I still believe
that teachers teaching chapter 6 of the book had better know
way beyond chapter 7 or their students are going to be in trouble.
--
Rob Strom
Pam
> Pam <pst...@sbcglobal.net> wrote in message
> news:<BB18E804.131EF%pst...@sbcglobal.net>...
>> ...
I am
> raising the conjecture that it is easier to teach something well
> if you know how it works,
Well, gee, Rob, you think so? In 17 years that never dawned on me. Maybe
that's why my kids have so much trouble learning, since I'm up there
bumbling around without a clue. Do you think I should try to get them to
understand how it works, too?
Just like
> when I first learned to cook, I cooked my mother's recipes by
> rote. I was a pretty bad cook, because I didn't really understand
> why I was doing any of the steps I was doing, and therefore
> if the slightest thing went wrong I didn't have any basis for
> adjusting.
I can make spaghetti perfectly well without knowing how to make lasagne.
>
> Every time my kids were taught by somebody who just knew the
> curriculum and nothing else beyond they had a real problem. Sometimes
> my kid even would answer a question correctly and intelligently
> and the teacher would complain because it wasn't the way she was
> taught to do it. Or if my child didn't get it, the teacher would
> just keep repeating the original instructions until she did, because
> the teacher couldn't come up with an equivalent alternative method
> on the fly.
> Once, the geography teacher had a map
> (made by the official materials-makers) where for
> reasons of space, Kampuchea was abbreviated as "Kam", but of course
> she had never heard of either Kampuchea or "Kam" so kept making up
> tests getting her students to identify where "Kam" was. Yuck.
> She had her curriculum, she had her materials, she had her tests,
> and in her mind, she was all prepared to go.
So, you think I should not be like that teacher, huh? I'll give it a try but
old habits die hard.
>>
>> Because you went to genius school, no doubt. It is not taught in 4th grade.
>
> In my generation, it was taught in 4th grade. And in Europe
> stuff way beyond this level is taught in 4th grade.
Well guess what? Times have changed, and this is not Europe.
>
> And even if it's done in 5th grade, it's much better to teach
> them that adding fractions of different denominators is exactly
> like adding quantities of different units --- the principle
> that you convert things to a common unit is the same. They
> have certainly learned to add mixtures of dollars, dimes and cents.
Did you understand my explanation of how I teach them to use manipulatives
to actually see with their own eyes that this is what they are doing?
>
>> ... This is the part of teaching that you don't
>> know a thing in the world about -- and why we teachers get annoyed that
>> everyone who's ever been through school thinks they know something about
>> teaching.
>>
>
> Huh???
>
> You forget that my family consists of 3 generations of teachers,
> and that I have sat in classrooms, graded papers, observed
> and assisted with lessons,
> browsed through the teaching manuals, and manipulated the manipulatives.
>
> My father taught shop, my mother taught remedial reading, 3rd grade elementary
> school,
A different universe.
> and later 7th grade English and French, my brother taught
> elementary school on Navajo reservations, my wife taught
> first grade regular and special education,
How long ago?
> my son teaches violin
> and orchestra,
Oh, _violin_. And _orchestras_. Those wouldn't be elective courses, would
they? When he is held responsible for teaching every child to play the
violin regardless of talent or inclination, let me know.
? and
> my daughter teaches homebound students
> in all subjects at a variety of grade levels.
And what's the teacher - student ratio?
> And I direct 4th and 5th
> grade schoolmusicals.
Oh, school musicals! How did they do on the state test?
> My father, mother, wife, and son all had specific certifications,
> and my daughter is a few credits from obtaining hers.
A veteran, hun? Let me know when she's stuck it out 5 years.
> Spare me the lectures on what I don't know about teaching.
All this is like saying you know how to drive 18 wheelers because you come
from a long line of car drivers, and you have ridden in them all your life.
If anyone nees to spare someone lectures on what they don't know about
teaching, it's you.
>>
>>> This is
>>> a similar skill to your quadratic factoring problem.
>>
>> Speaking of which, did you notice the simple elegance of Joe's diagram,
>> learned from a real teacher? This is the sort of thing that real teachers
>> do. You can't just call people stupid when they have trouble seeing what's
>> obvious to you. You have to get inside their heads, figure out how they
>> think, what it is that is confusing them, and devise a way to help them
>> understand. You evidently didn't do a very good job, since I didn't
>> understand it immediately.
>
> You're not going to understand it immediately; you have to practice.
> Joe's diagram is good because it moves the law to another modality,
> in this case areas of geometrical figures. I gave yet another modality,
> in this case, converting pounds to dollars.
You don't get it -- the teacher who showed him that did not make an analogy;
she showed him a model.
>
>
>> (I have yet to find time to study it carefully
>> because I am here writing these stupid posts instead.) See, in the real
>> world these days, if a student doesn't learn, you are responsible. It's YOUR
>> responsibility to find a way to explain it so he does understand; or find a
>> way to get him to pay attention so he can learn; or motivate him to want to
>> learn. When we are told "Leave No Child Behind" there are no excuses. I am
>> responsible for making sure every single child passes the test, even though
>> last year he didn't, and therefore came to me lacking the foundation for 4th
>> grade math, and his IQ is only 85. But every year, this is what I do. 100%
>> passing rate.
>
> As you know, I don't agree with these methods. When my son teaches
> violin, he doesn't start with a group of beginners and expect to
> have everyone finishing Book I at the same time, or Book II or whatever.
Exactly.
> If a child is having trouble with Book I, he isn't "passed on" to
> Book II merely because he gets xxx% of the notes right.
Right. That's not how my job is. I am told to squeeze blood from turnips. So
that's what I do. As a consequence, Texas minorities are at the top of the
nation. We didn't used to have this No Child Left Behind gun pointed to our
heads, and our jobs were a lot easier. But now we do, and it's a huge amount
of pressure, but the truth is that a lot of kids who otherwise would fail
are now passing, each year at a higher rate.
>
>
>>
>> "Somehow" the kids have to "get an intuition"??? <wild laughter> Don't hold
>> your breath.
>
> If you just tell the kids to add the tops and not the bottoms
> they'll obey, but if they don't know why it works, they'll
> be in trouble later. Some will forget, and they'll add
> the bottoms and not the tops. Others will not be able to generalize
> it to other situations where the "bottoms" don't happen to be on the
> bottom, but where the principle is the same (e.g. adding whole
> numbers and percents).
Duh.
>
>
>>
>>> of why it's OK to add the tops
>>> and not the bottoms otherwise they're just doing magic
>>> tricks not mathematics.
>>
>> I'll make sure to tell them they must "somehow get an intuition" about these
>> things.
>
> If you do, don't expect me to support you.
You said it, not me.
>>
>> Teaching is a real skill, a terribly difficult one, esp when you have more
>> than one student, and half the battle with some is just getting them to pay
>> attention and want to learn (because if they don't want to learn something
>> they are not going to do it). You really do not need to know one element of
>> content beyond that which the students are required to learn.
>
> I just don't accept this last statement.
So? The fact is that I can make spaghetti without having the faintest idea
how to make lasagne, or even ever heard of lasagne. Your son doesn't need to
know how to play the harp to teach violin.
>
> ...>
>> Thin skinned? No, just tired of people devaluing what we do because they
>> have not the tiniest clue what it is we do. We are tired of being ground
>> into exhaustion for little pay, and then having people like you come along
>> and tell us we aren't doing it right, and that we must make sure that
>> "somehow" the kids must just "intuit" how do things.
>
> I agree. If I meet any such people who devalue what you do,
> don't have a clue, and tell you that you aren't doing it right,
> I'll give them a piece of my mind. In the meantime, I still believe
> that teachers teaching chapter 6 of the book had better know
> way beyond chapter 7 or their students are going to be in trouble.
Look, different subjects have different requirements. Take the geography
example. If I am teaching world geography, I better be an expert on it,
prepared to answer any question. But if I am teaching US geography, I can
actually do that perfectly well without knowing where India is. It would be
odd, but that's really how it is.
When it comes to teaching history, I always have a bunch of little history
buggs (and kids who become buffs by virtue of being in my class). Now, I am
certified to teach history through grade 12 (the qualifying test has only a
64% passing rate, but even though I took it on the spur of the moment I only
missed 4/100). And I think in order to teach elementary history really well,
I need to be able to answer (ie tell stories) about anything having to do
with American or Texas history, which is what's taught in elementary. If all
I did was teach from the incredibly boring and dumbed down textbook (even
the kids develop scorn for it), I would hardly be doing justice to the
subject.
That's not the case with math. I don't need to know one thing about 7th
grade math to thoroughly understand elementary math. I don't need to have
even heard of the commutative property in order to teach them to convert
inches to feet.
Okay, you have so thoroughly imugned my ability to teach that I am going to
tell you a teaching story, and no matter how boring you find it, you have to
read the whole thing.
About once a week I put a "story problem" on the overhead, and I have a
rubric that I use to score student solutions. The scale is 1-4. The criteria
are 1) effectiveness of strategies -- for example, in a 4 part problem, how
many of the steps did they correctly identify and solve 2) use of
appropriate models, tables, etc. 3) how fully elaborated a written
explanation is given of how each step was solved 4) the solution is extended
in some way -- for example, showing more than one way to solve the problem.
One such problem asked, if Miss Jones has 50 ft of fencing, what are some
dimensions of pens she could make for her puppy? And which way would give
the puppy the most space?
Simple, hun? I thought it would be, but no. Most of them came up with just
one way, and ignored the second part of the problem. Only one student --
gifted -- thought to make a table to show every possible configuration, evne
though everyone knew how to make tables. (Knowing how to do something isn't
good enough for the new state test -- you have to know when to do it.) She
said the largest space would be a 12 * 13 pen. She drew the table on the
overhead to show the class. But a gifted boy said he knew a square wauld be
the largest area, so his answer was 12 1/2 * 12 1/2. (I asked him how he
knew that, and he said he just figured it out -- typical gifted behavior). I
then said "Hmm, I wonder what the area of that would be? And I wonder how
much larger that square would be than the 12 * 13 rectangle?" The gifted
kids were intrigued, but they had no idea how to multiply mixed numbers. I
didn't drop any hints, just told them there was a way to do it. Someone
suggested converting 1/2 ft to 6 inches but that didn't do them any good. At
last someone figured out that they could convert everything to inches, and
find the area in inches. Then they figured out they needed to convert the
rectangle into inches so they could compare area. Now, all this last part
was an extension -- I had given the rest of the class something else to work
on while I capitalized on the gifted kids' interest.
Can't believe I'm actually missing teaching and it's only June.
Rob Strom
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/21/03 9:38 PM said:
>
> > Pam <pst...@sbcglobal.net> wrote in message
> > news:<BB18E804.131EF%pst...@sbcglobal.net>...
> >> ...
> I am
> > raising the conjecture that it is easier to teach something well
> > if you know how it works,
>
> Well, gee, Rob, you think so? In 17 years that never dawned on me.
Uh, gee Pam. You're the one who said you don't believe that you
don't need to know anything about 7th grade math to teach 4th grade math.
....
> >> Because you went to genius school, no doubt. It is not taught in 4th grade.
> >
> > In my generation, it was taught in 4th grade. And in Europe
> > stuff way beyond this level is taught in 4th grade.
>
> Well guess what? Times have changed, and this is not Europe.
>
And times can change again.
....
> >
> > My father taught shop, my mother taught remedial reading, 3rd grade elementary
> > school,
>
> A different universe.
>
Third grade elementary school is a different universe from
4th grade elementary school?????
>
> > and later 7th grade English and French, my brother taught
> > elementary school on Navajo reservations, my wife taught
> > first grade regular and special education,
>
> How long ago?
Back in the dark ages when teaching school had no connection
with what teaching school is about now.
>
> > my son teaches violin
> > and orchestra,
>
> Oh, _violin_. And _orchestras_. Those wouldn't be elective courses, would
> they? When he is held responsible for teaching every child to play the
> violin regardless of talent or inclination, let me know.
He's responsible for teaching every child to play the violin
regardless of talent, but not inclination.
>
> ? and
> > my daughter teaches homebound students
> > in all subjects at a variety of grade levels.
>
> And what's the teacher - student ratio?
>
> > And I direct 4th and 5th
> > grade schoolmusicals.
>
> Oh, school musicals! How did they do on the state test?
100% of the students possessed 60% or more of the
fundamental school musical tasks, so I guess they all passed.
>
>
> > My father, mother, wife, and son all had specific certifications,
> > and my daughter is a few credits from obtaining hers.
>
> A veteran, hun? Let me know when she's stuck it out 5 years.
My father taught for about 45 years, my mother for about 20,
my brother about 25. My son and daughter are still young.
...
>
> You don't get it -- the teacher who showed him that did not make an analogy;
> she showed him a model.
Models are analogies and vice versa. Having 10 rectangles in a row
is one model of multiplying by 10. Converting a dime to ten pennies
is another.
....
>
> > If a child is having trouble with Book I, he isn't "passed on" to
> > Book II merely because he gets xxx% of the notes right.
>
> Right. That's not how my job is. I am told to squeeze blood from turnips. So
> that's what I do. As a consequence, Texas minorities are at the top of the
> nation. We didn't used to have this No Child Left Behind gun pointed to our
> heads, and our jobs were a lot easier. But now we do, and it's a huge amount
> of pressure, but the truth is that a lot of kids who otherwise would fail
> are now passing, each year at a higher rate.
Fortunately, political fads are just that, and we will try to reverse this one.
...
> >> ...You really do not need to know one element of
> >> content beyond that which the students are required to learn.
> >
> > I just don't accept this last statement.
>
> So? The fact is that I can make spaghetti without having the faintest idea
> how to make lasagne, or even ever heard of lasagne. Your son doesn't need to
> know how to play the harp to teach violin.
My son needs to know how to play the Mendelssohn concerto in order
to teach kids how to play "Go Tell Aunt Rhody".
There are various ways of lifting fingers and balancing the bow
that if done wrong, don't affect the sound of "Go Tell Aunt Rhody"
very much (except to an expert teacher), but the wrong way won't
generalize to the Mendelssohn concerto and the right way will. To
a teacher who doesn't play the Mendelssohn concerto, these differences
won't seem to matter.
...
> That's not the case with math. I don't need to know one thing about 7th
> grade math to thoroughly understand elementary math. I don't need to have
> even heard of the commutative property in order to teach them to convert
> inches to feet.
Really???
Suppose you want to convert inches to kilometers.
You can convert inches to miles and miles to kilometers,
or inches to millimeters, and millimeters to kilometers.
Which do you do? If it doesn't make a difference, why?
...>
> One such problem asked, if Miss Jones has 50 ft of fencing, what are some
> dimensions of pens she could make for her puppy? And which way would give
> the puppy the most space?
>
> Simple, hun? I thought it would be, but no. Most of them came up with just
> one way, and ignored the second part of the problem. Only one student --
> gifted -- thought to make a table to show every possible configuration, evne
> though everyone knew how to make tables.
There are an infinite number of possible configurations, so I'm sure
you meant to say something else, like every possible configuration
with integer dimensions.
> (Knowing how to do something isn't
> good enough for the new state test -- you have to know when to do it.) She
> said the largest space would be a 12 * 13 pen. She drew the table on the
> overhead to show the class. But a gifted boy said he knew a square wauld be
> the largest area, so his answer was 12 1/2 * 12 1/2. (I asked him how he
> knew that, and he said he just figured it out -- typical gifted behavior).
Boy, did you just shoot your argument in the foot with this problem!!!
How do *you* know that the square is the largest area, without knowing
any 7th grade math, huh?????
Hint: It's the same factoring rule that you had on your GRE!!!!
See, suppose I have a square x by x. (In your example x was 12 1/2.)
Then its area is x^2. Now a rectangle of the same perimeter would have to
be x minus something by x plus the same something, that is:
(x-a)*(x+a). This, by the rules that Fred and Joe and I have
been trying to teach you, is the same as x^2 + (a-a)x + (a)*(-a),
that is, x^2 - a^2. Since a^2 is always a positive number, x^2 - a^2
is always less than x^2, and thus the rectangle's area is less than
the square's.
>I
> then said "Hmm, I wonder what the area of that would be? And I wonder how
> much larger that square would be than the 12 * 13 rectangle?" The gifted
> kids were intrigued, but they had no idea how to multiply mixed numbers.
Actually, if they knew how to multiply 12*13, they were *already*
multiplying mixed numbers, since 12 is one ten and 2 ones and
13 is one ten and 3 ones, so these numbers are already mixed.
So they could have a tens column, a ones column, and a "halfs" column
and do the same thing they did in multiplying two numbers with 3 columns each.
--
Rob Strom
Pam
> Pam <mr...@io.com> wrote in message news:<BB1A9EEF.13245%mr...@io.com>...
>>
>> Well guess what? Times have changed, and this is not Europe.
>>
>
> And times can change again.
That's not under discussion. I just finished reading Diane Ravitch's Left
Back, the history of education in the 20th c., with all its disastrous fads.
I can discuss how things would be if I were queen, but that's beside the
point.
>
> ....
>>>
>>> My father taught shop, my mother taught remedial reading, 3rd grade
>>> elementary
>>> school,
>>
>> A different universe.
>>
>
> Third grade elementary school is a different universe from
> 4th grade elementary school?????
School a generation ago (like almost everything else socially) is so
different from now it might as well have taken place in one of Fred's
parallel universes. The difference is so extreme that we teachers never
quite get used to it. For many of these kids, their teacher is the only
stable non-addict adult in their lives. These are kids who never had a
single story read to them in their homes. They have never met their fathers,
but live with a succession of mom's boyfriends, or with grandparents. Their
parents have zero interest in their child's schoolwork or behavior -- I ask
for conferences and am ignored. The kids are allowed to watch any R rated
movie or TV show they want -- what's the difference when they live in an R
rated home? Even kids from more stable homes are unlikely to live with both
parents.
When I was in school, no one threw their chairs across the room. No one
called the teacher a f****** b****, no one stabbed his teacher with
scissors, no one bit the principal, no one exposed himself during music
class, elementary boys didn't proposition girls, and parents did not come to
school to beat the teacher up.
>>> and later 7th grade English and French, my brother taught
>>> elementary school on Navajo reservations, my wife taught
>>> first grade regular and special education,
>>
>> How long ago?
>
> Back in the dark ages when teaching school had no connection
> with what teaching school is about now.
That's right. School in many places now is a war zone and teachers are on
the front lines.
>>> my son teaches violin
>>> and orchestra,
>>
>> Oh, _violin_. And _orchestras_. Those wouldn't be elective courses, would
>> they? When he is held responsible for teaching every child to play the
>> violin regardless of talent or inclination, let me know.
>
> He's responsible for teaching every child to play the violin
> regardless of talent, but not inclination.
Right. Ask him how easy it would be to teach children to play the violin who
didn't want to play the violin but would rather whack each other with it.
>>
>> Right. That's not how my job is. I am told to squeeze blood from turnips. So
>> that's what I do. As a consequence, Texas minorities are at the top of the
>> nation. We didn't used to have this No Child Left Behind gun pointed to our
>> heads, and our jobs were a lot easier. But now we do, and it's a huge amount
>> of pressure, but the truth is that a lot of kids who otherwise would fail
>> are now passing, each year at a higher rate.
>
>
> Fortunately, political fads are just that, and we will try to reverse this
> one.
You want to reverse the trend of kids passing who have historically failed?
Listen, it makes my job a thousand times more difficult, but seeing these
kids pass is hugely rewarding. I would do things differently, but the idea
that we will not give up on the hardest to teach is a good one.
>> So? The fact is that I can make spaghetti without having the faintest idea
>> how to make lasagne, or even ever heard of lasagne. Your son doesn't need to
>> know how to play the harp to teach violin.
>
> My son needs to know how to play the Mendelssohn concerto in order
> to teach kids how to play "Go Tell Aunt Rhody".
That's just ridiculous. I could teach someone to play 3 Blind Mice on the
recorder even if that's all I knew.
> ...
>> That's not the case with math. I don't need to know one thing about 7th
>> grade math to thoroughly understand elementary math. I don't need to have
>> even heard of the commutative property in order to teach them to convert
>> inches to feet.
>
> Really???
>
> Suppose you want to convert inches to kilometers.
>
> You can convert inches to miles and miles to kilometers,
> or inches to millimeters, and millimeters to kilometers.
> Which do you do? If it doesn't make a difference, why?
Talk about a non sequitor.
>
>> (Knowing how to do something isn't
>> good enough for the new state test -- you have to know when to do it.) She
>> said the largest space would be a 12 * 13 pen. She drew the table on the
>> overhead to show the class. But a gifted boy said he knew a square wauld be
>> the largest area, so his answer was 12 1/2 * 12 1/2. (I asked him how he
>> knew that, and he said he just figured it out -- typical gifted behavior).
>
> Boy, did you just shoot your argument in the foot with this problem!!!
>
> How do *you* know that the square is the largest area, without knowing
> any 7th grade math, huh?????
Same way I know the sky is blue without knowing why. Next.
>
> Actually, if they knew how to multiply 12*13, they were *already*
> multiplying mixed numbers, since 12 is one ten and 2 ones and
> 13 is one ten and 3 ones, so these numbers are already mixed.
A mixed number is defined as a whole number plus fraction.
To sum up: I drive an 18 wheeler; your family members drive or have driven
cars; you have ridden in cars all your life; and you personally drive a
tricycle.
vince garcia
But I got As-Bs in reading and vocabulary :)
Pam
vgga...@ix.netcom.com on 6/22/03 1:58 PM said:
> well, pam, in my school days I always got Ds and Fs in math.
> But I got As-Bs in reading and vocabulary :)
Yeah, Vince, you and I are at such a disadvantage when in social settings
everyone is sitting around discussing quadratic equations. Don't you just
feel SO left out? I guess we are stuck with the crowd that talks about
literature, history, culture, art, and politcs. Oh, well...
Pam
jfn...@ieee.org on 6/22/03 6:47 PM said:
> On Sun, 22 Jun 2003 13:26:03 -0500, Pam <mr...@io.com> wrote:
>
>>> My son needs to know how to play the Mendelssohn concerto in order
>>> to teach kids how to play "Go Tell Aunt Rhody".
>>
>> That's just ridiculous. I could teach someone to play 3 Blind Mice on the
>> recorder even if that's all I knew.
>
> If all you ever want is for them to play Three Blind Mice, then your
> statement is correct. If you expect them to progress beyond Three
> Blind Mice, you should teach them so they will not have to unlearn
> skills when they get to Flight of the Bumblebee. And that is Rob's
> point, AIUI. The best way to teach elementary skills must be
> compatible with intermediate skills, which in turn should be taught in
> a way that is compatible with advanced skills. A teacher will likely
> not understand how to do this properly without having mastered the
> next few steps up.
>
A teacher can certainly teach elementary skills in a way that is compatible
with intermediate ones, if the elementary skills are taught properly, in a
way that is conducive to understanding of mathmatical principles.
I know y'all think I am an idiot, but when I did take algebra and geometry
in high school, it was the first time I liked math, and I made an A average
the first semester in both classes. (Unfortunately, I was disinclined to do
homework so got behind in the second semesters.) I must have retained
something in order to score better than 60% of everyone who takes the GRE,
ie college graduates seeking to do graduate study, not the general
population, or even the SAT population. Plus I just looked up my score on
the California teacher test, and I was in the 90th pr in math. Rob acts like
I am a moron because I am not picking this up on a first read-through -- in
only my third time in over 30 years to even look at math.
To further suggest that I am incompent to do my job is really rather beyond
the pale.
don't spam me]@slater.net Joe Slater
I don't think I saw it, would you mind reposting?
jds
Pam
jfn...@ieee.org on 6/22/03 6:48 PM said:
> On Sun, 22 Jun 2003 15:59:03 -0500, Pam <mr...@io.com> wrote:
>
>> I guess we are stuck with the crowd that talks about
>> literature, history, culture, art, and politcs. Oh, well...
>
> Most technically gifted people are able to talk about literature,
> history, culture, art, and politics. So why are most socially gifted
> people unable to talk about mathematics and science?
>
People do talk about science some. I just never hear anyone talk about math.
The only math discussions I've read here, for example, are those I've
initiated. BTW, technically I AM technically gifted in mechanical and
spatial reasoning. I can't say I've used these much, though, except maybe
spatial reasoning in decorating my house.
Rob Strom
> >> ... As a consequence, Texas minorities are at the top of the
> >> nation. We didn't used to have this No Child Left Behind gun pointed to our
> >> heads, and our jobs were a lot easier. But now we do,
> >> and it's a huge amount
> >> of pressure, but the truth is that a lot of kids who otherwise would fail
> >> are now passing, each year at a higher rate.
> >
> >
> > Fortunately, political fads are just that, and we will try to reverse this
> > one.
>
> You want to reverse the trend of kids passing who have historically failed?
I want to reverse the trend of teaching kids to a test and
passing them when they've learned to spew out the responses
for the test.
> Listen, it makes my job a thousand times more difficult, but seeing these
> kids pass is hugely rewarding. I would do things differently, but the idea
> that we will not give up on the hardest to teach is a good one.
No. It is not rewarding to see a kid apparently play
"Go Tell Aunt Rhody" and move on to "O Come Little Children"
so he won't be "left behind" when his technique is going to
cause him many problems down the road.
> >> So? The fact is that I can make spaghetti without having the faintest idea
> >> how to make lasagne, or even ever heard of lasagne. Your son doesn't need to
> >> know how to play the harp to teach violin.
> >
> > My son needs to know how to play the Mendelssohn concerto in order
> > to teach kids how to play "Go Tell Aunt Rhody".
>
> That's just ridiculous. I could teach someone to play 3 Blind Mice on the
> recorder even if that's all I knew.
I will do whatever in my power to keep you from teaching recorder.
>
> > ...
> >> That's not the case with math. I don't need to know one thing about 7th
> >> grade math to thoroughly understand elementary math. I don't need to have
> >> even heard of the commutative property in order to teach them to convert
> >> inches to feet.
> >
> > Really???
> >
> > Suppose you want to convert inches to kilometers.
> >
> > You can convert inches to miles and miles to kilometers,
> > or inches to millimeters, and millimeters to kilometers.
> > Which do you do? If it doesn't make a difference, why?
>
> Talk about a non sequitor.
Let's not talk about a non sequitur; let's instead talk about
this example, which shows that in order to know how to do
conversions, you need to know the commutative property.
>
> >
> >> (Knowing how to do something isn't
> >> good enough for the new state test -- you have to know when to do it.) She
> >> said the largest space would be a 12 * 13 pen. She drew the table on the
> >> overhead to show the class. But a gifted boy said he knew a square wauld be
> >> the largest area, so his answer was 12 1/2 * 12 1/2. (I asked him how he
> >> knew that, and he said he just figured it out -- typical gifted behavior).
> >
> > Boy, did you just shoot your argument in the foot with this problem!!!
> >
> > How do *you* know that the square is the largest area, without knowing
> > any 7th grade math, huh?????
>
> Same way I know the sky is blue without knowing why. Next.
I didn't realize that you know the sky is blue by comparing
with an infinite number of alternatives, which is what you
have to do if you are comparing the square with all possible
rectangles, and you don't have the algebraic basis to rule
the others out.
>
> >
> > Actually, if they knew how to multiply 12*13, they were *already*
> > multiplying mixed numbers, since 12 is one ten and 2 ones and
> > 13 is one ten and 3 ones, so these numbers are already mixed.
>
> A mixed number is defined as a whole number plus fraction.
It also means (at least outside of Texas) numbers with mixed
*units*, like 2 pounds 3 ounces. The usual way of teaching
multiplication or even addition of multi-digit numbers is to teach it as
if the ones, tens, and hundreds were themselves diverse units.
What was called in my day "carrying" is now called "regrouping",
and is in effect a conversion from one unit to the next.
Regrouping works because of the distributive law, even if
you don't explicitly tell the kids that.
Oh, and by the way, I would point out to you
that in various non-Texas public and private schools,
(e.g. http://www.hanover.k12.va.us/Instruction/ESInstruction/GRADE4.pdf,
www.stjohntheevangelist.org/school/MATHEMATICS.PDF)
the math curriculum *does* require students in 4th grade to
add and subtract with fractions with denominators less that 12,
both with pencil and paper, and with manipulatives, as well
as illustrate mathematical laws and
invariants with expressions like (15 + 13) + 12
= 15 + (13 + 12), so I think that the commutative and associative
principles are discussed explicitly and the distributive
implicitly in the matter of converting units and/or reducing
fractions to a common denominator.
>
>
> To sum up: I drive an 18 wheeler; your family members drive or have driven
> cars; you have ridden in cars all your life; and you personally drive a
> tricycle.
Well you may consider that because you live in Texas your
30-odd years of teaching experience is to my father's 40-plus
as an 18-wheeler is to a car. I don't happen to think so.
I also forcefully disagree with the philosophy that the teacher
doesn't need to know a stitch of material beyond what's on the test
and in the syllabus.
I think it harms students.
--
Rob Strom
Mordecai!
Rob Strom wrote:
<clipped>
>
>
> I also forcefully disagree with the philosophy that the teacher
> doesn't need to know a stitch of material beyond what's on the test
> and in the syllabus.
> I think it harms students.
>
> --
> Rob Strom
Whilst I happen to agree with you, I have some slight quandary with all this.
One of the math's units I did at university included proving things. I was a proper whiz - knew math's well -
was always top few of class etc. ... but this course stretched me.
It stretched me as it went into formal proof methods -and the teaching I had had in mathematics over many
years had left me ill equipped to deal with the subject.
This was expected in the course BTW - as it was beyond the sort of proofs that have been quoted on this NG -
and that level of "proofs" is taught perfectly by the curriculum in the schools.
Yet, none of what I had been taught up til then was up to the standard ... and as you said with your musical
analogy - it was fine for simple tunes but unacceptable for the devote - and in later years they have to
"unlearn" what they had been taught.
But few indeed go to that level of mathematics.
Engineers and the like do not go into the level of math's taught to me and others.
Many school teachers are not able to teach such things - or even be able to understand them. Just as some
cannot hear or appreciate music, arts or any other subject.
So there are all sorts of questions .. and one is "how far in advance do you need to understand?"
Do we need mathematical genius's teaching six year olds?
Are we supposed to get specialists in every subject?
OTOH - we also need generalists. Generalists are as important and more important than specialists. You need
someone with a wide breadth of experience to head - say - a school. A head master, principle, dean or whatever
- is far more than a teacher and needs to be. He or she needs to have many skills outside of teaching.
Diplomacy skills, accountancy skills and so on.
Why can't there be generalists teaching something?
This is a case where I fully accept your POV and support it - and then say ... but ....
Perhaps it is better to have someone with a love of the subject to enthuse the students - rather than a
specialist? I do not know.
Relearning this subject taught me far more than having the right answers - and that applied to every aspect of
my life, not merely mathematics.
But seeing I have no answers, and seeing you are of a certainty correct - I still maintain every choice in
this field is less than perfect, and there are no right answers.
vince garcia
sure:
I have a question I wonder if you can help me with: The Catholic
and orthodox faiths affirm that prayers for the dead are efficacious.
Obviously this came from Judaism, and perhaps from the JEwish apostles.
Can you tell me if there is anything in the torah or tanakh that refers
to praying for the dead? Perhaps an idiom we gentiles miss (ala "wash
their clothes" referring to immersion as an example)? Is there any
SCRIPTURE that supports the notion?
Thanx for any help!
Pam
> Pam <mr...@io.com> wrote in message news:<BB1B5EE9.1325A%mr...@io.com>...
>>
>> You want to reverse the trend of kids passing who have historically failed?
>
> I want to reverse the trend of teaching kids to a test and
> passing them when they've learned to spew out the responses
> for the test.
What we teach are the TEKS -- Texas Essential Knowledge and Skills. I don't
see what having a clearly defined set of TEKS has to do with "spewing out
responses", if by that you mean memorization without understanding. See
below for an example of some TEKS that you do not find in most states (those
that have standards at all).
>> Listen, it makes my job a thousand times more difficult, but seeing these
>> kids pass is hugely rewarding. I would do things differently, but the idea
>> that we will not give up on the hardest to teach is a good one.
>
> No. It is not rewarding to see a kid apparently play
> "Go Tell Aunt Rhody" and move on to "O Come Little Children"
> so he won't be "left behind" when his technique is going to
> cause him many problems down the road.
Evidently you assume that successfiully teaching the hardest to teach equals
bad teaching. The fact is that until I was told I could and would see to it
that every child in my class would pass every test, I had not had my ability
to teach fully tested. This is the toughest, most intensive teaching
possible.
>
> Oh, and by the way, I would point out to you
> that in various non-Texas public and private schools,
> (e.g. http://www.hanover.k12.va.us/Instruction/ESInstruction/GRADE4.pdf,
> www.stjohntheevangelist.org/school/MATHEMATICS.PDF)
> the math curriculum *does* require students in 4th grade to
> add and subtract with fractions with denominators less that 12,
The only relevant question is, in which state do 4th grade students do
better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
Furthermore, compare the demographics below, esp WRT large differences in
poverty and ethnicity -- and note that VA spends several hundred more
dollars a year per student and has a lower teacher student ratio -- and you
will see that Texas is dealing with a far more challenging demographic. And
while we're at it, we'll look at CT, coming in at #4:
This is VA:
Student Characteristics
Percent in Title I schools: 30.6%
With Individualized Education Programs (IEP): 14.1%
Percent in limited-English proficiency programs: 3.7% ***
Percent eligible for free/reduced lunch: 29.3% ***
Racial/Ethnic Background
White: 62.8% ***
Black: 27.1%
Hispanic: 5.5%
Asian/Pacific Islander: 4.3%
American Indian/Alaskan Native: 0.3%
Per-pupil expenditures: $6,8411
Pupil/teacher ratio: 13.0
__________________________________________________
And this is Texas:
Student Characteristics
Percent in Title I schools: 57.7%
With Individualized Education Programs (IEP): 11.9%
Percent in limited-English proficiency programs: 14.5% ***
Percent eligible for free/reduced lunch: 45.4% ***
Racial/Ethnic Background
White: 40.9% ***
Black: 14.4%
Hispanic: 41.7% ***
Asian/Pacific Islander: 2.8%
American Indian/Alaskan Native: 0.3%
Per-pupil expenditures: $6,2881
Pupil/teacher ratio: 14.7
And this is CT, which spends several thousand dollars a year more than Texas
per student, and note the 40% vs 13% Hispanic population:
Student Characteristics
Percent in Title I schools: 36.9%
With Individualized Education Programs (IEP): 13.0%
Percent in limited-English proficiency programs: 3.8% ***
Percent eligible for free/reduced lunch: -- (not available)
Racial/Ethnic Background
White: 69.2% ***
Black: 13.8%
Hispanic: 13.7%
Asian/Pacific Islander: 3.0%
American Indian/Alaskan Native: 0.3%
Per-pupil expenditures: $9,7531
Pupil/teacher ratio: 13.7
These are the percentage of students in each state scoring at or above these
levels:
Basic Profient Advanced
Texas 77 27 2
VA 73 25 2
CT 77 32 3
And keep in mind that while CT teachers make the highest avg salary in the
nation, Texas teacher salaries rank #27.
Also, since you seem to find Texas standards not up to par, here are the
last two sections of the 4th grade TEKS which show the emphasis placed on
the understanding of mathmatical principles and reasoning. If you look at
the VA standards, there are no TEKS like these -- the emphasis remains
mostly on computaton rather than higher level thinking skills. There are
also _many_ fewer algebra related items than Texas has, if you check the
TEKS at http://www.tea.state.tx.us/rules/tac/chapter111/ch111a.html. With
the institution of these new TEKS, tested for the first time this year, you
can expect to see Texas students do even better on future NAEP tests.:
(14) Underlying processes and mathematical tools. The student applies Grade
4 mathematics to solve problems connected to everyday experiences and
activities in and outside of school. The student is expected to:
(A) identify the mathematics in everyday situations;
(B) use a problem-solving model that incorporates understanding the
problem, making a plan, carrying out the plan, and evaluating the solution
for reasonableness;
(C) select or develop an appropriate problem-solving strategy, including
drawing a picture, looking for a pattern, systematic guessing and checking,
acting it out, making a table, working a simpler problem, or working
backwards to solve a problem; and
(D) use tools such as real objects, manipulatives, and technology to solve
problems.
(15) Underlying processes and mathematical tools. The student communicates
about Grade 4 mathematics using informal language. The student is expected
to:
(A) explain and record observations using objects, words, pictures,
numbers, and technology; and
(B) relate informal language to mathematical language and symbols.
(16) Underlying processes and mathematical tools. The student uses logical
reasoning to make sense of his or her world. The student is expected to:
(A) make generalizations from patterns or sets of examples and nonexamples;
and
(B) justify why an answer is reasonable and explain the solution process.
So much for the state of Virginia's superior math program. Texas elementary
teachers do more with less, and with more difficult demographics, compared
to any teachers in any state, except maybe NC. Can you imagine what Texas
teachers would do with CT's resources and demographics -- a piece of cake!
Adjusted for differences in demographics and money, Texas has the most
successful elementary math program and the most effective teachers in the
nation. And you don't even have to pay us well to get that kind of
performance.
>> To sum up: I drive an 18 wheeler; your family members drive or have driven
>> cars; you have ridden in cars all your life; and you personally drive a
>> tricycle.
>
> Well you may consider that because you live in Texas your
> 30-odd years of teaching experience is to my father's 40-plus
> as an 18-wheeler is to a car. I don't happen to think so.
Your Dad taught an elective course, back in the Good Olde Days.
I have "only" 16 years experience -- stayed home with my kids (and subbed)
until Dan entered K.
>
> I also forcefully disagree with the philosophy that the teacher
> doesn't need to know a stitch of material beyond what's on the test
> and in the syllabus.
As I said, it depends on the subject.
> I think it harms students.
That's what we teachers love best about our jobs -- we knock ourselves out
trying to help kids succeed, and feel really good about it, but if we get
any feedback from the public, it's to tell us what a lousy -- even harmful
-- job we are doing.
Emma
"Pam" <mr...@io.com> wrote in message news:BB1C7EEB.1327F%mr...@io.com...
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/23/03 12:11 AM said:
>
> > Pam <mr...@io.com> wrote in message
news:<BB1B5EE9.1325A%mr...@io.com>...
>
> >>
> >> You want to reverse the trend of kids passing who have historically
failed?
> >
> > I want to reverse the trend of teaching kids to a test and
> > passing them when they've learned to spew out the responses
> > for the test.
>
> What we teach are the TEKS -- Texas Essential Knowledge and Skills. I
don't
> see what having a clearly defined set of TEKS has to do with "spewing out
> responses", if by that you mean memorization without understanding. See
> below for an example of some TEKS that you do not find in most states
(those
> that have standards at all).
>
>
Pam, I think that anyone should think twice before picking a fight with you
:-) You fight your corner so well :-)
Do children stab their teachers with scissors and throw chairs around the
room in the school that you teach at??
Pam
on 6/23/03 11:45 AM said:
>
> "Pam" <mr...@io.com> wrote in message news:BB1C7EEB.1327F%mr...@io.com...
>> in article abea7612.03062...@posting.google.com, Rob Strom at
>> st...@watson.ibm.com on 6/23/03 12:11 AM said:
>>
>>> Pam <mr...@io.com> wrote in message
> news:<BB1B5EE9.1325A%mr...@io.com>...
>>
>>>>
>>>> You want to reverse the trend of kids passing who have historically
> failed?
>>>
>>> I want to reverse the trend of teaching kids to a test and
>>> passing them when they've learned to spew out the responses
>>> for the test.
>>
>> What we teach are the TEKS -- Texas Essential Knowledge and Skills. I
> don't
>> see what having a clearly defined set of TEKS has to do with "spewing out
>> responses", if by that you mean memorization without understanding. See
>> below for an example of some TEKS that you do not find in most states
> (those
>> that have standards at all).
>>
>>
>
> Pam, I think that anyone should think twice before picking a fight with you
> :-) You fight your corner so well :-)
Coming from you, Emma, I am humbled. :-) Sometimes you just have to drive a
stake through their tiny black hearts, ya know?
>
> Do children stab their teachers with scissors and throw chairs around the
> room in the school that you teach at??
That very person was in my room this year, but it was his first grade
teacher he stabbed. He did call me the name and threw his chair, threw
tantrums, etc. But by the end of the year he was pretty much okay, and often
hugged me and often told me I was the nicest teacher he ever had. He could
turn on a dime. A gifted kid -- the one who said he knew a square would have
the largest area. I'll really miss him.
Pam
jfn...@ieee.org on 6/23/03 12:58 PM said:
> Maybe the teachers should fire their unions, and start fresh.
We don't have any unions in Texas (except in name only). We can't strike. We
have no power to negotiate. Our "unions" are just lobbyists. When we do get
a raise, it's only because lawmakers take pity on us, or feel guilty, not
because we have any power. All the legislators know Texas teachers are doing
a spectacular job, but Texas has no income tax, property taxes are at the
state mandated cap, and Texas is running a deficit. Everyone knows that
"born" teachers will teach for pennies if they can possibly afford it, and
it's a female dominated profession.
I hate to say it, but because we have no power, it's easy to fire bad
teachers, and bad administrators are yanked as soon as a school gets in
trouble. Schools are ranked according to test scores, and each minority and
low income population must score at the required level, and aren't just
averaged in. A school can have fabulous scores, but if just one demographic
group doesn't excel, the school doesn't get the highest rating. I was in a
school where if one minority kid had answered one more math question right,
the school would have been rated a notch higher. Therefore the quality of
the people I've always worked with is very high - I didn't realize how high
until I joined a Usenet educator group for a while and heard the nightmre
tales of incompetency. Unions can have the effect of protecting incompetent
teachers and administrators. And as difficult and high pressure it is to
have these high-stakes tests, we know who those incompetent people are.
Pam
> On Mon, 23 Jun 2003 09:54:53 -0500, Pam <mr...@io.com> wrote:
>
>> The only relevant question is, in which state do 4th grade students do
>> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
>
> Is the difference statistically significant? And why is the NAEP the
> be-all arbiter of "doing better in math?"
It's the only nationwide test of its kind I know of, and has been considered
The Nation's Report Card for a long time. Whenever you see news reports
about state rankings, they are quoting from the NAEP.
>
>> Furthermore, compare the demographics below, esp WRT large differences in
>> poverty and ethnicity -- and note that VA spends several hundred more
>> dollars a year per student and has a lower teacher student ratio
>
> Are the salaries adjusted for cost of living differences? Are the per
> pupil ratios skewed by special programs in VA that are not present in
> Texas?
I don't know anything but the data I gave you.
>
>> This is VA:
>> Percent in Title I schools: 30.6%
>> Per-pupil expenditures: $6,8411
>> Pupil/teacher ratio: 13.0
>
>> And this is Texas:
>> Percent in Title I schools: 57.7%
>
> What does this mean exactly?
A xhool is designated Title I when a certain percentage of students in a
school are on free lunch. Then the school gets some govt money to hire an
aide or teacher to work with failing kids. Texas has almost twice as many of
these schools as VA. We have a lot of kids who start school not speaking
English. We have a lot of migrant kids who go to school only between Ovt
and Apr.
> Is there no teacher's
> union that is looking into why teaching gets such a bad rap with the
> public at large?
In Texas, the public at large has a quite favorable view of its teachers, as
well they should. It's individual members of the public who can be jerks to
the very people who are moving heaven and earth to help their children
suceed.
>
> What taxpaying citizens see is that education taxes always go up,
the
> results of standardized tests do not appear to be correlated with
> higher expenditures, the HS kids we interact with can't make change
> without a register that does it for them,
In Texas, no student graduates without passing the state test. It's been a
conundrum because school and district rates are based in part on attendance
and drop out rate. Some kids who don't pass the test wil want to drop out.
It's tricky motivating them to stay in school so they can be given intensive
remedial help and try again. If a kid has no confidence he can pass a test,
he won't try.
Starting this past year, no third grader was promoted unless he passed the
reading test. Year after next when they are in fifth grade, this same group
will not be promoted unless they pass both reading and math -- and so on.
The tests have always been high-stakes for schools and teachers, but now
they are for the students as well. Up till now, I have had to rely on my
kids' desire to please me in order to get them to do their very best on
these tests (bless their little hearts), but now they will have added
incentive.
> and the teachers union is
> unable to learn a new tune to the annual "Leave No Dollar Behind"
> campaign. If politicians try to offer a tradeoff of
> pay-for-performance or changing tenure policies in return for
> additional resources, and the union says "give us the money, but keep
> your filthy hands off the current seniority and tenure scheme."
I agree. I would certainly like to be paid well, but if the price is to have
to work with incompetent colleages under incompetent administrators in
schools that are not committed to excellence, then I'll pass.
Rob Strom
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/23/03 12:11 AM said:
>
> > Pam <mr...@io.com> wrote in message news:<BB1B5EE9.1325A%mr...@io.com>...
>
> >>
> >> You want to reverse the trend of kids passing who have historically failed?
> >
> > I want to reverse the trend of teaching kids to a test and
> > passing them when they've learned to spew out the responses
> > for the test.
>
> What we teach are the TEKS -- Texas Essential Knowledge and Skills. I don't
> see what having a clearly defined set of TEKS has to do with "spewing out
> responses", if by that you mean memorization without understanding. See
> below for an example of some TEKS that you do not find in most states (those
> that have standards at all).
What you listed sounds little different from what was shown on the
curricula I posted earlier.
>
>
> >> Listen, it makes my job a thousand times more difficult, but seeing these
> >> kids pass is hugely rewarding. I would do things differently, but the idea
> >> that we will not give up on the hardest to teach is a good one.
> >
> > No. It is not rewarding to see a kid apparently play
> > "Go Tell Aunt Rhody" and move on to "O Come Little Children"
> > so he won't be "left behind" when his technique is going to
> > cause him many problems down the road.
>
> Evidently you assume that successfiully teaching the hardest to teach equals
> bad teaching.
No. I state that having someone play the notes of Go Tell Aunt Rhody
at the right pitches for the right times doesn't constitute
"successfully teaching" that person if his technique is wrong.
By analogy, if he can multiply two 3-digit numbers by following an
algorithm but hasn't had the opportunity to see the patterns that
would enable him to generalize to multiplying two 2-digit numbers
plus a half, then I think he hasn't learned what he should even
if by using this algorithm he's able to get all the questions
right on the test.
> The fact is that until I was told I could and would see to it
> that every child in my class would pass every test, I had not had my ability
> to teach fully tested. This is the toughest, most intensive teaching
> possible.
Some kids will need an extra year.
Or they will need a different
class with a different approach. Making everybody march in lockstep
and using the tests as the criterion is not good. Tougher doesn't
equal better.
>
> >
> > Oh, and by the way, I would point out to you
> > that in various non-Texas public and private schools,
> > (e.g. http://www.hanover.k12.va.us/Instruction/ESInstruction/GRADE4.pdf,
> > www.stjohntheevangelist.org/school/MATHEMATICS.PDF)
> > the math curriculum *does* require students in 4th grade to
> > add and subtract with fractions with denominators less that 12,
>
> The only relevant question is, in which state do 4th grade students do
> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
That's by average scores; if you compare the percentages scoring
"proficient" or above, then Texas is #10.
I'm not surprised that they do better than VA. If the test
doesn't test adding fractions with unequal denominators, then
clearly a curriculum that does spend time teaching these things
will not directly benefit their score, unless solving these
problems has the side effect at making students more proficient
at other problems that are tested.
But you are still thin-skinned, believing that I am trying
to argue that Texans are stupid or that you are an incompetent
teacher, while neither of these things is the case.
I was just responding to your crack that only in "genius schools"
do they teach 4th graders to add fractions of unequal denominators.
And this was part of a larger context saying that when this
kind of thing is taught, it should be taught in such a way as
to facilitate generalizations to other applications of the
distributive law, thereby making the 7th grader's life easier later
on. I ventured a hypothesis that such facilitating would be
easier if the teacher actually were proficient in the sort of
7th or 8th grade math that is tested on the SAT and the GRE.
...
>
> And keep in mind that while CT teachers make the highest avg salary in the
> nation, Texas teacher salaries rank #27.
I thought you were the one arguing that paying teachers more doesn't
make for better teachers. Now you seem to be arguing that the
difference accounts for Connecticut's better math scores (32% proficient
and above vs. 27% for Texas, the gap widening to 34% vs. 25% by 8th grade,
with Virginia at 26%).
>
>
> Also, since you seem to find Texas standards not up to par,
I didn't say that!!! I just said that some places outside
of Texas teach 4th graders to add 1/2 + 1/3!
...
> >> To sum up: I drive an 18 wheeler; your family members drive or have driven
> >> cars; you have ridden in cars all your life; and you personally drive a
> >> tricycle.
> >
> > Well you may consider that because you live in Texas your
> > 30-odd years of teaching experience is to my father's 40-plus
> > as an 18-wheeler is to a car. I don't happen to think so.
>
>
> Your Dad taught an elective course, back in the Good Olde Days.
No!!!! My Dad did *not* teach an elective course!
You're confusing him with my son the violin teacher.
These were *vocational* schools --- shop was *core* curriculum!
These were people who had already been placed outside
of the college prep track of the public schools, either
because of low IQs, poor English skills, dyslexia, or whatever.
*Lots* of these kids were only in school because the
truancy laws forced them to be there.
And my Mom taught remedial reading (before she had us), and
English and French (after she had us). French was an elective
in some NYC schools only in the sense that you could have chosen
Spanish or Hebrew instead
(or Latin in some places), but you *had* to take a language.
In the parochial school where my mother taught, everybody in 7th grade
took both Hebrew and French, because the school was too
small to separate the groups into French and Spanish.
>
> I have "only" 16 years experience -- stayed home with my kids (and subbed)
> until Dan entered K.
Oh --- then you've hardly taught at all.
>
> >
> > I also forcefully disagree with the philosophy that the teacher
> > doesn't need to know a stitch of material beyond what's on the test
> > and in the syllabus.
>
> As I said, it depends on the subject.
I can't think of a subject where that isn't true.
Certainly that's true for music, math, and science.
The science teachers at my kids' school who only knew the curriculum were
positive disasters --- if there was a smudge on the dittos telling
them what to teach, they wouldn't be able to
figure it out. Extemporizing
about some current events in the news relating to science was
out of the question.
They *loved* repeating standard experiments, putting the results
in specific rows and columns, and having the kids memorize
long lists of definitions or fact sheets. God forbid a kid
should define a word slightly differently from the way it
was defined on the word list.
I can't imagine a successful 4th grade English teacher who could
only read at the 4th grade level, either.
>
> > I think it harms students.
>
> That's what we teachers love best about our jobs -- we knock ourselves out
> trying to help kids succeed, and feel really good about it, but if we get
> any feedback from the public, it's to tell us what a lousy -- even harmful
> -- job we are doing.
I'm not talking about *you*!!!!! There you are being thinskinned again!
It's clear that you *do* teach beyond the curriculum and exploit
numerous creative methods based upon outside knowledge. My problem
isn't with your teaching; it's with your policies on who should
be allowed to teach.
--
Rob Strom
Rob Strom
> Rob Strom wrote:
>
> <clipped>
>
> >
> >
> > I also forcefully disagree with the philosophy that the teacher
> > doesn't need to know a stitch of material beyond what's on the test
> > and in the syllabus.
> > I think it harms students.
> >
[I'm reformatting your lines that are longer than 80 characters]
We don't need mathematical geniuses teaching 6 year olds math.
I didn't intend to imply that. I just don't want adults who
don't know any math beyond 6-year-old to teach 6-year-old math.
>
> Are we supposed to get specialists in every subject?
>
> OTOH - we also need generalists. Generalists are as important
> and more important than specialists.
Absolutely!! I don't *want* specialists, especially for
the young grades. I want teachers who have a broad liberal
education, meaning that they understand the history of
ideas, and know enough of the techniques of how these ideas
were worked out. That means that they not only know about
the US Constitution, but also about earlier forms of government,
in medieval and ancient times. They not only know that the
earth is 93 million miles from the sun, but how we first learned
that, and what are different ways to find out how far away something
is that's too far to see. They know how we extended our view
of the universe from a flat earth to a round one, to a solar system,
to a galaxy-universe, to a universe of multiple galaxies.
They know how we discovered about the bits of the world too small
to see, those hidden within the earth, and those so old that
they leave but scant traces.
They
know about the great ancient nations, and the great empires, and
how they rose and fell, and changed. They know about the great
works of visual art, music, and literature. They know about
the economic network of production and
distribution, how it changed from early times
to now. They know about the history of technology and about
the technologies on the brink of being developed, and how they
may change daily life, economic life, and the set of ethical
problems we will face. They know about moral and ethical principles,
about human psychology, about philosophy. They model what it
means to be curious, how to discover things that others have
discovered, and how to discover new things that haven't. They
model how to live harmoniously with others.
You couldn't want any more of a generalist than an elementary
schoolteacher.
> You need
> someone with a wide breadth of experience to head - say - a school.
> A head master, principle, dean or whatever
> - is far more than a teacher and needs to be.
> He or she needs to have many skills outside of teaching.
> Diplomacy skills, accountancy skills and so on.
>
> Why can't there be generalists teaching something?
>
> This is a case where I fully accept your POV and support it
> - and then say ... but ....
>
> Perhaps it is better to have someone with a love of the
> subject to enthuse the students - rather than a
> specialist? I do not know.
I never intended to argue for specialists. The fact that
in today's world, any adult who actually remembers how to
factor x^2 - 8x + 12 is considered a "specialist" or
a "math whiz" is to me a scandal!!!
That would be like considering someone who knew who
Job was a "Bible scholar" and a specialist.
--
Rob Strom
don't spam me]@slater.net Joe Slater
>I never intended to argue for specialists. The fact that
>in today's world, any adult who actually remembers how to
>factor x^2 - 8x + 12 is considered a "specialist" or
>a "math whiz" is to me a scandal!!!
How often does the average adult need to factor a quadratic equation? I
think it's enough that they know what the equation is, and that it *can* be
factored. I had to look the formula up, and I consider myself better at
maths than most.
jds
don't spam me]@slater.net Joe Slater
wrote:
>I have a question I wonder if you can help me with: The Catholic
>and orthodox faiths affirm that prayers for the dead are efficacious.
What's a "prayer for the dead"? Is it something like "Lord, have mercy upon
this woman's soul"? And efficacious in what way?
>Obviously this came from Judaism, and perhaps from the JEwish apostles.
I don't see how this is obvious at all.
jds
Pam
jfn...@ieee.org on 6/23/03 9:21 PM said:
> On Mon, 23 Jun 2003 16:24:04 -0500, Pam <mr...@io.com> wrote:
>
>>> Maybe the teachers should fire their unions, and start fresh.
>>
>> We don't have any unions in Texas (except in name only).
>
> You aren't represented by the NEA at the federal level?
I don't know -- we have various "unions", but they have no power. Zero.
>
>> We can't strike.
>
> You can vote. There are lots of teachers. Politicians listen to
> numbers. That is the usual formula.
We vote, but Texas is a big state. It's less politically risky to hurt
teachers than some other groups, so that's why the budget this year was
balanced by cutting the $1000 for benefits the state gave us last year.
>
>> We have no power to negotiate.
>
> In Georgia, we elected a Republican governor for the first time in
> over a century because the previous governor tried to reform the
> educational system. He touched the third rail of state government;
> and he paid the price. Of course, it wasn't the only reason, but the
> teachers seemed mightily pleased they had a hand in the result.
Maybe there's a lower ratio of teachers in Texas -- all I know is that we
have little political power.
>
>> I hate to say it, but because we have no power, it's easy to fire bad
>> teachers,
>
> I've lived in four states, and in each the power of the state
> educational system was immense, due to the sheer amount of money at
> stake. The teacher's union was able to claim a portion of this power
> by careful lobbying, and the teacher's lobbyists had a few well known
> nonnegotiable points. One was tenure. It was next to impossible to
> fire tenured teachers, unless they were caught on videotape selling
> crack to first graders on the schoolhouse steps, and even then they
> received five chances to reform.
We dopn't have tenure in Texas. I just read an article on how to fix
education in Atlantic, and it said that getting a tenured teacher fired can
cost hundreds of thousands of dollars. Doesn't cost anything to fire bad
teachers here. I've seen it done at four different schools. In each case the
teachers were not horribly derelict, but they just were not very good, and
that's not good enough any more.
>
> I had an English class in HS in which the teacher was totally zoned
> out, the bullies ran the class, and it was a rare day that a chair or
> three wasn't tossed out the windows of the third floor classroom.
> What I learned in that class did not involve English at all. Was the
> teacher penalized in any way for the complete and total failure of the
> class? Not to my knowledge.
>
> I also had a tremendous Physics teacher who was sharp, worked hard at
> presenting material to keep the class challenged, maintained excellent
> order -- and he had to work nights at a pharmacy to make ends meet.
> Was he rewarded for his excellence in teaching? Not to my knowledge.
He wasn't paid for it, but you can be sure he was richly rewarded.
>
> This is what I despise about public education. I refuse to send my
> children to a system that perpetuates such idiocy; yet I have to pony
> up a full share of tax money for the maw of public education, then pay
> for my children's education with after-tax dollars.
>
> Texas may be different, of course.
A large percentage of teachers have to have other jobs. The man on my team
mowed lawns and coached volleyball.
I taught in a Christian school for three years when I went back to teaching
-- took my kids with me and had to pay tuition. My students were incredibly
brilliant -- a differnt universe from public school. I was teaching them
pretty complicated algebra in second grade. But I prefer public school
because I feel I make a bigger difference there, and both my children
prefered public school. There is somewhat of a hothouse atmosphere in
private school that they did not like.
>> A school can have fabulous scores, but if just one demographic
>> group doesn't excel, the school doesn't get the highest rating.
>
> That's the way things work in the Real World, too. One can excel in
> many categories, yet be dinged for weak performance in one area.
>
>> I was in a
>> school where if one minority kid had answered one more math question right,
>> the school would have been rated a notch higher.
>
> The cutoff has to fall somewhere. There is probably a school that
> would have been rated a notch lower if one majority kid had missed one
> additional History question, too.
It certainly has had the effect of making sure minority kids get lots of
extra help.
Rob Strom
news:2n6ffvg8ophpu951i...@4ax.com...
Let's see: my daughter is taking an exam tomorrow on American History,
and another one on literature.
How often does the average adult need to know about the Smoot Hawley
tariffs? Isn't it enough to know that there are taxes and the
experts know when to raise and lower them? Why not?
Or how often does the average
adult need to recite anything from Macbeth? Or know who Wordsworth was?
Or care whether Picasso lived before or after Renoir?
Isn't it enough to know that there are poets and playwrights and artists and
that
the names of their works and stuff like when
and where they lived can be looked up on the Internet? Why not?
Why should a farmer or a lathe operator or a receptionist
or even a banker, loan officer, or medical doctor need to
know *anything* other than how to get to work, operate the
equipment and execute the
correct procedures there, and get home to eat, watch TV and go to sleep?
This isn't just about math. It's about what's the point of being educated
at all.
Why shouldn't just professional art critics or art historians learn about
Picasso?
--
Rob Strom
Mordecai!
Rob Strom wrote:
I was not actually making to great a point - merely finding the discussion of teaching - and (from my point
of view) learning - of interest.
So perhaps we can ask the outcome we desire?
You see - I am still a student - I hope. That is I am still learning what life has to teach me - and I hope
I am still open and learning till my dying day. Some people stop learning and think they have learned the
lessons.
The goal to me is not to get the right answer - but to think. I hope I get right answers - but unfortunately
life's questions always have many answers.
So if I am selfish, my answers are based on selfishness and the outcomes are the "fruit" of a selfish heart.
In good times, this is enough. In hard times when the only way to survive is to share - then I am up the
creek without a paddle.
To me, the art of learning is the ability to think for oneself. I am well aware you have mentioned this as
your goal - so I doubt I will be arguing this point with you in any way.
The way I learned to think (which is personal to me) was the ability to reason - and this was taught
indirectly through mathematics. Proofs as I said before ...
It allowed me to look at my own assumptions - including my religion of the time - Christianity (which could
not stand my scrutiny) and my political system, and the economic system - and the desire for wealth and many
other things given to me by society. None of these stood up to scrutiny. Sometimes I did not understand what
was taught. Mostly the equations failed to work.
Few people will use mathematics the way I did ... but many become students in life. The ability to think
for yourself is difficult and few actually achieve it. Some of those who do become the Einstein's of the
earth. Others become guru's sitting on mountains - some become ... destitute. That is their value system
sets things which others consider unimportant as important. I was hearing of a man who saw a problem with
penguins getting fish hooks in them - and dedicated his life to this goal. He became poor ... but he set up
things to help a serious problem - and now others have joined him.
Or a woman who dedicated her life to stop the proliferation of nuclear armaments. A doctor who says that a
nuclear winter killing all mankind is the worst health risk that she saw ... and some indirect results of
her work are the nuclear armament agreements between the USA and the old USSR.
Both those people left the normal paths for their desires and dreams - and there was a price in economic and
social terms.
They may not be "genius" level IQ but they could think for themselves and responded to the situations they
found themselves confronted with. Many do so within the society - but it manifest itself in going beyond
expectations ...
My Christian friend who I spoke of a lot is a generalist and also genius level ... he was sent to a school
for the gifted in Australia. His education was set not only to getting right answers but to think. I do not
know if this is still being taught - but I am aware that you can teach people to think. Not merely get right
answers.
Tools such as good teachers, a good training system - and families and society can enhance this learning.
With children, the equation is "how do we teach this" and there are so many factors - such as proficient
teachers - they would help.
But Pam has also added in many other factors which are more important.
I will add one from one state in Australia, giving the children a decent breakfast!
They found many children were undernourished (working poor) and this was a the cause of much education
problems.
This state provides breakfast to any school child who asks (no means test or anything - they have a
rationale for their choice) and just this single action increased attendance, plus the ability of the
children to learn and pay attention. It also increased health and well being.
Pam has spoken that she is defecto parent ... because the social system has collapsed. Families are
breaking down and the demands of work give them no time ...
On the scale of things - the competency of the teachers in one field or another is rather small. There are
so many larger problems out there.
Sure, I would prefer competent teachers ...
If you can do 90% of the job well - and ten percent competantly - that is more than enough!
Training the young is hard. Training the old is harder, and I am one of the old.
There would need to be a radical overturn of just about every institution and goal of society to set in
place the love of the learned ... rather than the use of them as a commodity in an economic system.
Imagine - to applaud the wise and not the rich! What a radical concept.
Emma
> in article bd7aq...@enews2.newsguy.com, Emma at emmas...@yahoo.co.uk
> on 6/23/03 11:45 AM said:
>
> >
> > "Pam" <mr...@io.com> wrote in message news:BB1C7EEB.1327F%mr...@io.com...
> >> in article abea7612.03062...@posting.google.com, Rob Strom at
> >> st...@watson.ibm.com on 6/23/03 12:11 AM said:
> >>
> >>> Pam <mr...@io.com> wrote in message
> news:<BB1B5EE9.1325A%mr...@io.com>...
>
> >>>>
> >>>> You want to reverse the trend of kids passing who have historically
> failed?
> >>>
> >>> I want to reverse the trend of teaching kids to a test and
> >>> passing them when they've learned to spew out the responses
> >>> for the test.
> >>
> >> What we teach are the TEKS -- Texas Essential Knowledge and Skills. I
> don't
> >> see what having a clearly defined set of TEKS has to do with "spewing out
> >> responses", if by that you mean memorization without understanding. See
> >> below for an example of some TEKS that you do not find in most states
> (those
> >> that have standards at all).
> >>
> >>
> >
> > Pam, I think that anyone should think twice before picking a fight with you
> > :-) You fight your corner so well :-)
>
> Coming from you, Emma, I am humbled. :-)
I have learnt all my techniques from you lot! I now argue my poor
husband into the ground. He agrees with everything I say before I am
anywhere near finished. Perfect!
> Sometimes you just have to drive a
> stake through their tiny black hearts, ya know?
Absolutely!
> >
> > Do children stab their teachers with scissors and throw chairs around the
> > room in the school that you teach at??
>
> That very person was in my room this year, but it was his first grade
> teacher he stabbed. He did call me the name and threw his chair, threw
> tantrums, etc. But by the end of the year he was pretty much okay, and often
> hugged me and often told me I was the nicest teacher he ever had. He could
> turn on a dime. A gifted kid -- the one who said he knew a square would have
> the largest area. I'll really miss him.
I don't know how you cope! I think it's wonderful that you persevere
with these children.
Your schools break up for the summer very early, btw. Our children
don't finish until the middle of July. By that time, most of the good
weather has gone!
vince garcia
>
> On Mon, 23 Jun 2003 04:54:22 -0700, vince garcia <vgga...@ix.netcom.com>
> wrote:
> >I have a question I wonder if you can help me with: The Catholic
> >and orthodox faiths affirm that prayers for the dead are efficacious.
>
> What's a "prayer for the dead"? Is it something like "Lord, have mercy upon
> this woman's soul"? And efficacious in what way?
I don't know it can be defined that simply. In Judaism you say various
prayers for the dead, and I presume you must somehow believe that
"helps" a dead person's soul somehow. In catholicsm they say prayers for
the dead and/or hold masses for them in the belief it "helps" their soul
go to heaven sooner after death. So do both groups think the dead gain a
benefit from our prayers? I suspect they do. My question is whether the
old testament shows any precedence for the belief
>
> >Obviously this came from Judaism, and perhaps from the JEwish apostles.
>
> I don't see how this is obvious at all.
>
> jds
since catholics say the teaching is justified from the book of 2nd
maccabees, which is about as jewish a work as you can get, I don't see
why you question the statement
Pam
> Pam <mr...@io.com> wrote in message news:<BB1C7EEB.1327F%mr...@io.com>...
>> in article abea7612.03062...@posting.google.com, Rob Strom at
>>
>> What we teach are the TEKS -- Texas Essential Knowledge and Skills. I don't
>> see what having a clearly defined set of TEKS has to do with "spewing out
>> responses", if by that you mean memorization without understanding. See
>> below for an example of some TEKS that you do not find in most states (those
>> that have standards at all).
>
> What you listed sounds little different from what was shown on the
> curricula I posted earlier.
Well, you can check for yourself -- there's a big difference, since those
last two sections are not included in the VA standards. They are more like
the standards we had 3 yrs ago.
>
>
>>
>>
>>>> Listen, it makes my job a thousand times more difficult, but seeing these
>>>> kids pass is hugely rewarding. I would do things differently, but the idea
>>>> that we will not give up on the hardest to teach is a good one.
>
>> The fact is that until I was told I could and would see to it
>> that every child in my class would pass every test, I had not had my ability
>> to teach fully tested. This is the toughest, most intensive teaching
>> possible.
>
> Some kids will need an extra year.
> Or they will need a different
> class with a different approach. Making everybody march in lockstep
> and using the tests as the criterion is not good. Tougher doesn't
> equal better.
The point is that they did not need an extra year, and did not need to be
put in a dummy class. They ALL passed! Who said anything about everyone
marching in lockstep? I am expected to meet the unique needs of each of my
students -- even though there's a 70 pt IQ spread. It's certainly not easy.
Tougher teaching certainly does mean better, because it means I am trying so
hard it hurts. And they are trying just as hard to learn, if I am doing my
job of motivating and encouraging them, and esp getting them to believe that
if they try, if they practice the strategies I have taught them (like I am
practicing the strategy Joe taught me) they will succeed.
>
>
>>
>>>
>>> Oh, and by the way, I would point out to you
>>> that in various non-Texas public and private schools,
>>> (e.g. http://www.hanover.k12.va.us/Instruction/ESInstruction/GRADE4.pdf,
>>> www.stjohntheevangelist.org/school/MATHEMATICS.PDF)
>>> the math curriculum *does* require students in 4th grade to
>>> add and subtract with fractions with denominators less that 12,
>>
>> The only relevant question is, in which state do 4th grade students do
>> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
>
> That's by average scores; if you compare the percentages scoring
> "proficient" or above, then Texas is #10.
But it's still better than VA, even though they supposedly teach these
advanced concepts you recommend. Turns out it doesn't mean they turn out
better math students.
> I ventured a hypothesis that such facilitating would be
> easier if the teacher actually were proficient in the sort of
> 7th or 8th grade math that is tested on the SAT and the GRE.
And I'm telling you, your hypothesis is faulty because you are making a
false assumption. You need to know something about subtraction in order to
teach that division is repeated subtraction of the divisor. But the converse
is not true -- in order to teach subtraction, a person doesn't need to have
even heard of division.
>>
>> Also, since you seem to find Texas standards not up to par,
>
> I didn't say that!!! I just said that some places outside
> of Texas teach 4th graders to add 1/2 + 1/3!
So what's your point then in bringing it up at all, if not that Texas has a
dummy curriculum?
> No!!!! My Dad did *not* teach an elective course!
> You're confusing him with my son the violin teacher.
>
> These were *vocational* schools --- shop was *core* curriculum!
> These were people who had already been placed outside
> of the college prep track of the public schools, either
> because of low IQs, poor English skills, dyslexia, or whatever.
> *Lots* of these kids were only in school because the
> truancy laws forced them to be there.
Okay, then he drives a pickup truck, but not an 18 wheeler because when he
was teaching kids were NOT like they are today. He would be astonished if he
spent a week in vocational school today (not there is such a thing in Texas
any more).
>
> And my Mom taught remedial reading (before she had us), and
> English and French (after she had us). French was an elective
> in some NYC schools only in the sense that you could have chosen
> Spanish or Hebrew instead
> (or Latin in some places), but you *had* to take a language.
Then she drives a truck too.
>> I have "only" 16 years experience -- stayed home with my kids (and subbed)
>> until Dan entered K.
>
> Oh --- then you've hardly taught at all.
Feels like 160 some days. :-)
>>
>>> I think it harms students.
>>
>> That's what we teachers love best about our jobs -- we knock ourselves out
>> trying to help kids succeed, and feel really good about it, but if we get
>> any feedback from the public, it's to tell us what a lousy -- even harmful
>> -- job we are doing.
>
> I'm not talking about *you*!!!!! There you are being thinskinned again!
Right -- you are talking about all these teachers who are exactly like me,
but aren't specifically me. But even if I was a math whiz, I would still be
offended on behalf of the superb, deeply dedicated teachers who aren't, yet
are highly successful in teaching elementary kids elementary subjects about
as well as it's possible to teach them. The truth is that few of the people
I teach with are as self-educated as I am, but that's not what makes the
difference in teaching ability. It's not knowing concepts that you don't
have to teach that matters, or even your depth of understanding of what you
teach -- it's the latter combined with a gift for teaching. Understanding is
useless unless you have a gift for being able to find ways to make that it's
these kids, plus the gifted kids, both of which groups have different
learning styles and intellectual needs that regular students, that separate
the good from the great teachers.
> It's clear that you *do* teach beyond the curriculum and exploit
> numerous creative methods based upon outside knowledge.
I only teach beyond the TEKS on the fly, such as quickly showing the gifted
kids how to use decimals or fractions instead of remainders. District policy
is to differentiate horizontally rather than vertically. I don't formally
teach gifted kids advanced skills, but give them problem solving
opportunities than enable them to use grade level skills in higher level
problem solving. Sometimes they can extrapolate above grade level skills
simply from understand concepts well. For example, one page I gave them
asked them, among other things, to divide 100 by 1/2. All of them came up
with 50, of course, but I just told them it was wrong, didn't tell them why
-- I take fiendish satisfaction in stumping them because until they got in
my class they always got the same work as everyone else, and it's always
been easy for them. They don't believe me when I tell them no, ther's no
mistake, their answer is wrong. After a long time looking befuddled, finally
one of them thought more carefully about what division means, and got the
right answer. The others were dumbfounded, but that only made them think
harder. Finally one by one they figured it out. Now dividing by fractions
isn't an elementary skill but just using the conepts they knew, they figured
it out.
BTW, when I first introduce mult & div I put some disks on the overhead and
invite them to come up and arrange them to show 5 x 3. Someone comes up and
makes a group of 5 and a group of 3. Everyone agrees this is correct. I ask
them how much 5 x 3 is, and they say 15, and I ask if that's how many disks
there are. Befuddlement. After a good while, a gifted kid will come up and
make 5 groups of 3, I push them together into one group of 15, and everyone
goes Ah ha! We do that several times THEN I ask someone to show me a
divison problem, and they do exactly the same thing -- make groups and push
them together into one large group. I tell them nope. Finally someone
figures out that they have to START with the total and separate it into
groups. Mind you, this includes the gifted kids. At this age their
understanding of basic concepts, even of place value, is pretty superficial.
It's essential that a strong foundation of understanding is laid in
elementary. To waste time traing them to find common denominators is like
training parrots to recite poetry -- they might be able to do it, but the
time is better spent grounding them in number concepts and problem solving
strategies.
> My problem
> isn't with your teaching; it's with your policies on who should
> be allowed to teach.
That's just elitist garbage. Fellow teachers and I may not know much math
above the elementary level, but we do know a very great deal about teaching
kids what they actually need to understand, and that alone is what counts.
don't spam me]@slater.net Joe Slater
>> think it's enough that they know what the equation is, and that it *can*
>>be factored. I had to look the formula up, and I consider myself better at
>> maths than most.
On 23 Jun 2003 21:45:25 -0700, st...@watson.ibm.com (Rob Strom) wrote:
>Let's see: my daughter is taking an exam tomorrow on American History,
>and another one on literature.
>
>How often does the average adult need to know about the Smoot Hawley
>tariffs?
Never, I suspect. I have heard of them, vaguely, but most people in the
world haven't.
>Isn't it enough to know that there are taxes and the
>experts know when to raise and lower them? Why not?
No, I think you should know the purpose of taxes and that taxes have
consequences. I don't think you need to know about the Smoot Hawley Act,
except insofar as it is a particular instance relevent to your own country.
That's a historical note, not a practical one. Knowing about taxes is
practical because it helps you understand political arguments. This is all
said because where I live people are obliged to vote. In countries where
you don't have to vote I suppose you can live just fine without knowing
about taxes.
>Or how often does the average
>adult need to recite anything from Macbeth?
Never. Why is _Macbeth_ privileged over _The Iliad_?
>Or know who Wordsworth was?
That's entirely useless. What's the point of knowing he was a poet if you
don't know any of his poetry? Better you should know the poems and not the
poet. How much Wordsworth do *you* know? Tennyson? Dryden? Masefield?
Motion? Where does it end?
>Or care whether Picasso lived before or after Renoir?
I don't especially. I don't care for Picasso. But should you know whether
Li Po or Li Bai lived earlier?
>Isn't it enough to know that there are poets and playwrights and artists and
>that the names of their works and stuff like when
>and where they lived can be looked up on the Internet? Why not?
I think it's nice to know and care about some particular pieces of art, and
you don't need to have a head stuffed with boring dead facts about dates
and so forth.
>Why should a farmer or a lathe operator or a receptionist
>or even a banker, loan officer, or medical doctor need to
>know *anything* other than how to get to work, operate the
>equipment and execute the
>correct procedures there, and get home to eat, watch TV and go to sleep?
Because he chooses to?
>This isn't just about math. It's about what's the point of being educated
>at all.
>Why shouldn't just professional art critics or art historians learn about
>Picasso?
Because other people may want to do so. But if they don't, then so what?
You're privileging a tiny part of the world's culture above all others and
demanding that people must recite a quotation from Shakespeare, correctly
place several French Impressionists in chronological order, identify the
occupations of some writers and artists, and (I presume) whistle the theme
from the Mikado. This is sterile and pointless. Culture is a living thing
and being a rounded person means discovering your own loves, finding your
own plays to recite or songs to sing. You can't put art in a box, because
when you do it's already dead.
jds
don't spam me]@slater.net Joe Slater
>> What's a "prayer for the dead"? Is it something like "Lord, have mercy upon
>> this woman's soul"? And efficacious in what way?
On Tue, 24 Jun 2003 05:10:02 -0700, vince garcia <vgga...@ix.netcom.com>
wrote:
>I don't know it can be defined that simply. In Judaism you say various
>prayers for the dead,
I'm not sure that we do. The only one I can think of offhand (and I may
well be wrong) is Yizkor, and all that is, is a request that G-d
"remember" them.
>and I presume you must somehow believe that
>"helps" a dead person's soul somehow. In catholicsm they say prayers for
>the dead and/or hold masses for them in the belief it "helps" their soul
>go to heaven sooner after death. So do both groups think the dead gain a
>benefit from our prayers? I suspect they do. My question is whether the
>old testament shows any precedence for the belief
The Jewish scriptures document people praying for other people, and having
their prayers answered. So, are dead people to be considered "people" in
this sense? I would say yes, because even if they don't have a *present*
existence they have a potential *future* existence. Would the mother of the
child raised by Elisha have been wrong to pray for him while he was dead?
>> >Obviously this came from Judaism, and perhaps from the JEwish apostles.
>> I don't see how this is obvious at all.
>since catholics say the teaching is justified from the book of 2nd
>maccabees, which is about as jewish a work as you can get, I don't see
>why you question the statement
Maccabees is not part of the Jewish canon. It's not even studied as a book
dealing with our faith, any more than Jubilees or Enoch is.
jds
Pam
joe[please don't spam me]@slater.net on 6/24/03 9:18 PM said:
> Culture is a living thing
> and being a rounded person means discovering your own loves, finding your
> own plays to recite or songs to sing.
Amen -- THIS is what people gain from a liberal education -- it opens up a
world to them in which they can discover what it is that they have a passion
for. Some people have a passion for Picasso and Smoot Hawley, some don't --
so what? I am a rather low brow person: I don't care for Shakespeare, but I
love Thornton Wilder. I find James Joyce tedious, but love Jane Austen and
Elmore Leonard. Don't like Picasso, love good movies. Not interested in
Smoot Hawley, love military history, politics, and the Bible.*
I really don't think that makes me too ill equipped to teach elementary
school, which is Rob's whole point.
* I have my own prejudices -- IMO, all those people who know about all those
things Rob mentioned, but are ignorant of the Bible, which is the most
influential piece of literatue in history, and has had the greatest
influence on Western Civilization, simply cannot be considered well
educated. That would be the vast majority of them.
Rob Strom
Pam wrote:
>
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/23/03 6:17 PM said:
> ...
> >> The fact is that until I was told I could and would see to it
> >> that every child in my class would pass every test, I had not had my ability
> >> to teach fully tested. This is the toughest, most intensive teaching
> >> possible.
> >
> > Some kids will need an extra year.
> > Or they will need a different
> > class with a different approach. Making everybody march in lockstep
> > and using the tests as the criterion is not good. Tougher doesn't
> > equal better.
>
> The point is that they did not need an extra year, and did not need to be
> put in a dummy class. They ALL passed!
They all passed the NAEP, or what? The same test that only about
70-odd percent pass in your state?
I still disagree. I believe in ability-grouped classes, I dislike
the disparaging term "dummy class" for the lower groups, and I think
that 20-odd percent reaching proficiency which the NAEP designers
defined as truly being comfortable with the concepts means that
a lot more folks should get an extra year.
> Who said anything about everyone
> marching in lockstep? I am expected to meet the unique needs of each of my
> students -- even though there's a 70 pt IQ spread.
If everybody has to pass the same test at the end of the same
year, that's lockstep. And it's not obvious to me that
people who pass only at the basic level should be moving on.
...
> >>
> >> The only relevant question is, in which state do 4th grade students do
> >> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
> >
> > That's by average scores; if you compare the percentages scoring
> > "proficient" or above, then Texas is #10.
>
> But it's still better than VA, even though they supposedly teach these
> advanced concepts you recommend. Turns out it doesn't mean they turn out
> better math students.
The margin is closer, and by 8th grade VA has caught up
and surpassed Texas.
>
> > I ventured a hypothesis that such facilitating would be
> > easier if the teacher actually were proficient in the sort of
> > 7th or 8th grade math that is tested on the SAT and the GRE.
>
> And I'm telling you, your hypothesis is faulty because you are making a
> false assumption. You need to know something about subtraction in order to
> teach that division is repeated subtraction of the divisor. But the converse
> is not true -- in order to teach subtraction, a person doesn't need to have
> even heard of division.
In order to teach it properly, in a way that they're
prepared to learn more advanced concepts later, yes they do.
It's the same argument as whether someone who
can't play the Bach Double Concerto can teach
Go Tell Aunt Rhody. The good violin teachers
find that they want to go back in time and fix
the way that kid learned Go Tell Aunt Rhody.
>
> >>
> >> Also, since you seem to find Texas standards not up to par,
> >
> > I didn't say that!!! I just said that some places outside
> > of Texas teach 4th graders to add 1/2 + 1/3!
>
> So what's your point then in bringing it up at all, if not that Texas has a
> dummy curriculum?
You need to stop assuming hostility, and start remembering
who I am --- someone who is not only intelligent, but
also kind, patient, and helpful. Also following
the thread from one posting to the next would help.
The history of the exchange was:
Me: "And I think
that when I was in fourth grade, we learned about fractions,
where we had problems like adding 1/2 + 1/3."
You: "Because you went to genius school, no doubt.
It is not taught in 4th grade. ...
They do not add or subtract fractions in 4th grade
except by looking at models. "
Me: (The above is false. Here are some ordinary US
schools that are not "genius schools" that
do teach 1/2 + 1/3 in 4th grade.)
Not to bad-mouth Texas, but to rebut your
blanket statement with its jibe about
"genius schools" and its overweaning
pontification about what just isn't taught
in 4th grade. The subject of Texas never
came up.
>
> > No!!!! My Dad did *not* teach an elective course!
> > You're confusing him with my son the violin teacher.
> >
> > These were *vocational* schools --- shop was *core* curriculum!
> > These were people who had already been placed outside
> > of the college prep track of the public schools, either
> > because of low IQs, poor English skills, dyslexia, or whatever.
> > *Lots* of these kids were only in school because the
> > truancy laws forced them to be there.
>
> Okay, then he drives a pickup truck, but not an 18 wheeler because when he
> was teaching kids were NOT like they are today. He would be astonished if he
> spent a week in vocational school today (not there is such a thing in Texas
> any more).
I would say about 70% of his kids were Hispanic, and
almost all of the rest had other problems just reading English.
Several times I helped grade his tests for him.
It seemed that everybody's name was Rodriguez!
Don't know about chair-throwing.
...
> > I'm not talking about *you*!!!!! There you are being thinskinned again!
>
> Right -- you are talking about all these teachers who are exactly like me,
> but aren't specifically me. But even if I was a math whiz, I would still be
> offended on behalf of the superb, deeply dedicated teachers who aren't, yet
> are highly successful in teaching elementary kids elementary subjects about
> as well as it's possible to teach them. The truth is that few of the people
> I teach with are as self-educated as I am, but that's not what makes the
> difference in teaching ability. It's not knowing concepts that you don't
> have to teach that matters, or even your depth of understanding of what you
> teach -- it's the latter combined with a gift for teaching. Understanding is
> useless unless you have a gift for being able to find ways to make that it's
> these kids, plus the gifted kids, both of which groups have different
> learning styles and intellectual needs that regular students, that separate
> the good from the great teachers.
I didn't say that knowing advanced concepts was *sufficient*,
only that it was *necessary*!
I don't agree that you can demonstrate that elementary
kids have learned their subjects "as well as it's possible
to teach them" if 4 years down the road they start having
trouble. Sometimes the reason that these kids have
trouble with algebra later is that even though they
could pass the tests of 4th grade, they didn't become
sufficiently familiar with the patterns that they
would have to manipulate formally 4 years later.
And it is not beyond the realm of possibility that
a reason for that is that *some* of the teachers
of 4th grade weren't aware of these patterns because
of the philosophy that "if the kids don't have to
know it, I don't have to know it either."
Just as students can get stuck at a plateau in
Violin Book III, and the fault is not the
Book III teacher, but rather the Book I teacher
who passed them on, it is very likely that the
same thing can happen with 4th grade math.
And it happens even worse in science, because
(a) the standards are so crummy in 4th grade
and (b) even where the standards are good
the tests can be passed by memorizing
fact sheets without having acquired *any*
of the skills that the curriculum claims to require!
>
> > It's clear that you *do* teach beyond the curriculum and exploit
> > numerous creative methods based upon outside knowledge.
>
> I only teach beyond the TEKS on the fly, such as quickly showing the gifted
> kids how to use decimals or fractions instead of remainders. District policy
> is to differentiate horizontally rather than vertically. I don't formally
> teach gifted kids advanced skills, but give them problem solving
> opportunities than enable them to use grade level skills in higher level
> problem solving.
But that's exactly what most "advanced skills" are.
Your example of dividing 100 by 1/2 is just such an
illustration --- something kids in one grade
aren't "supposed to know" how to do, that
kids an a higher grade are required to learn.
My example of multiplying 12 1/2 by 12 1/2 for kids
who can multiply any number of digits,
generalizing place value notation to handle "mixed" numbers
is the same thing:
Tens Place Ones Place Half's Place
1 (10s) 2 (1s) 1 (half)
x 1 (10s) 2 (1s) 1 (half)
--------------------------------------------------
1 (5s) 2 (halfs) 1 (quarter)
2(10s) 4 (1s) 2 (halfs)
1 (100s) 2(10s) 1 (5s)
-------------------------------------------------------------------------
1 (100s) 4(10s) 2 (5s) 4 (1s) 4 (halfs) 1 (quarter)
"Regrouping", 2 5's = a ten, 4 halfs = 2, therefore:
1 (100s) 5 (10s) 6 (1s) + 1/4 = 156 1/4
So is this "horizontal" differentiation, or vertical???
...
>
> > My problem
> > isn't with your teaching; it's with your policies on who should
> > be allowed to teach.
>
> That's just elitist garbage.
I love how you use elitism as a pejorative when you attack
others, and take pride in elitism when you condemn
liberals who lower standards or demand more
diversity in the literature or arts curriculum.
Elitism is *good* --- it's another way of saying
I want the standards to be high.
>Fellow teachers and I may not know much math
> above the elementary level, but we do know a very great deal about teaching
> kids what they actually need to understand, and that alone is what counts.
I'd be surprised if you generalized that to other subjects.
Do you really want someone who can't read above 4th grade
level to teach 4th grade reading?
--
Rob Strom
Chris
<BB1E4529.132D3%mr...@io.com>:
> The point is that they did not need an extra year, and did not need to be
> put in a dummy class. They ALL passed! Who said anything about everyone
> marching in lockstep? I am expected to meet the unique needs of each of my
> students -- even though there's a 70 pt IQ spread. It's certainly not
> easy. Tougher teaching certainly does mean better, because it means I am
> trying so hard it hurts. And they are trying just as hard to learn, if I
> am doing my job of motivating and encouraging them, and esp getting them
> to believe that if they try, if they practice the strategies I have taught
> them (like I am practicing the strategy Joe taught me) they will succeed.
What about the advanced kids? Do they get the opportunity to move ahead at
their own pace? I remember when I moved from Wisconsin to Illinois when I
was in 4th grade. In Wisconsin schools I was allowed to advance to 7th or
8th grade level materials. That year, mid-year, I moved to this tiny
little town in the middle of nowhere in Illinois. My parents tried to
explain but there was nothing they could do. I was forced to go back to
doing material that I had covered in 2nd grade if not earlier. I got
extremely bored in school after that and developed terrible study habits. I
moved again (to IN) and they were even further behind. By the time I got to
high school I refused to even bring home a book.
How does this "Leave no child behind" affect the ones who werent behind to
begin with?
--
Please visit http://www.jtf.org
Pam
dont...@none.net on 6/25/03 8:50 AM said:
> On Tuesday 24 June 2003 18:13 Pam(mr...@io.com) wrote in
> <BB1E4529.132D3%mr...@io.com>:
>> The point is that they did not need an extra year, and did not need to be
>> put in a dummy class. They ALL passed! Who said anything about everyone
>> marching in lockstep? I am expected to meet the unique needs of each of my
>> students -- even though there's a 70 pt IQ spread. It's certainly not
>> easy. Tougher teaching certainly does mean better, because it means I am
>> trying so hard it hurts. And they are trying just as hard to learn, if I
>> am doing my job of motivating and encouraging them, and esp getting them
>> to believe that if they try, if they practice the strategies I have taught
>> them (like I am practicing the strategy Joe taught me) they will succeed.
>
> What about the advanced kids? Do they get the opportunity to move ahead at
> their own pace?
They can take a test and move up. I've recommended it several times to
parents, but they don't do it. I've studied the advantages and disadvantages
of grade skipping and IMO the advantages are substantially greater.
>
> How does this "Leave no child behind" affect the ones who werent behind to
> begin with?
As with everything else, it depends on how the teacher, the district, and
school handle the gifted and the remedial programs. There is no question
that the high-stakes testing, with its focus on bringing the bottom kids up,
causes more focus to be put on lower kids, often at the expense of the top
ones. Gifred kids' needs are often ignored, even though they are just as
much "special needs" kids as the special education ones, and suffer as much
if their needs are not met. They need many opportunities to excercise
leadership, have maximum autonomy and choices, less direct teach and
structure, and real intellectual challenge.
Pam
>
> I still disagree. I believe in ability-grouped classes, I dislike
> the disparaging term "dummy class" for the lower groups, and I think
> that 20-odd percent reaching proficiency which the NAEP designers
> defined as truly being comfortable with the concepts means that
> a lot more folks should get an extra year.
There are things such as "developmental" first grade which is an extra year
between K and 1st. Otherwise in elementary, the only option is retention.
The problem with that is that research shows that kids who are retained,
compared with a control group who are not, show no benefit. Some kids may,
but most kids I have my classes who have been retained are still at the
bottom of the class. Have you studied the research on ability grouping? The
top and bottom kids do need differentiation/modification, but the bottom
kids benefit by not being placed in a separate track. I have taught tracked
classes before and hate them. In the low classes there is little modeling of
the kind of thinking and attitudes toward learning that they need. For
example, when the low kids here the others begging "Can we write? Can we
read? Can we do social studies? Yay, math!" they start looking for what's
fun about these things, and next thing you know they are all enthusiastic,
too. It's not just lip service -- they really are working and learning.
>
>
>> Who said anything about everyone
>> marching in lockstep? I am expected to meet the unique needs of each of my
>> students -- even though there's a 70 pt IQ spread.
>
> If everybody has to pass the same test at the end of the same
> year, that's lockstep.
> And it's not obvious to me that
> people who pass only at the basic level should be moving on.
You know, the things you say are so totally ill-informed I am tired of
responding to them. You know about as much about education as I do about
calculus.
>>>> The only relevant question is, in which state do 4th grade students do
>>>> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
>>>
>>> That's by average scores; if you compare the percentages scoring
>>> "proficient" or above, then Texas is #10.
>>
>> But it's still better than VA, even though they supposedly teach these
>> advanced concepts you recommend. Turns out it doesn't mean they turn out
>> better math students.
>
> The margin is closer, and by 8th grade VA has caught up
> and surpassed Texas.
Could that have anything to do with, say, the culture of poverty, and
Hispanic culture which tends not to value education highly? The demographics
really do make things more difficult, esp when the kids are teens.
Otherwise, I assume it must be the inferior teaching at elementary school
that gives them the edge.
>
>
>>
>>> I ventured a hypothesis that such facilitating would be
>>> easier if the teacher actually were proficient in the sort of
>>> 7th or 8th grade math that is tested on the SAT and the GRE.
>>
>> And I'm telling you, your hypothesis is faulty because you are making a
>> false assumption. You need to know something about subtraction in order to
>> teach that division is repeated subtraction of the divisor. But the converse
>> is not true -- in order to teach subtraction, a person doesn't need to have
>> even heard of division.
>
> In order to teach it properly, in a way that they're
> prepared to learn more advanced concepts later, yes they do.
No.
>
> I don't agree that you can demonstrate that elementary
> kids have learned their subjects "as well as it's possible
> to teach them" if 4 years down the road they start having
> trouble. Sometimes the reason that these kids have
> trouble with algebra later is that even though they
> could pass the tests of 4th grade, they didn't become
> sufficiently familiar with the patterns that they
> would have to manipulate formally 4 years later.
> And it is not beyond the realm of possibility that
> a reason for that is that *some* of the teachers
> of 4th grade weren't aware of these patterns because
> of the philosophy that "if the kids don't have to
> know it, I don't have to know it either."
In general, elementary teachers in Texas are doing their jobs, and doing it
better than anyone else. We are teaching what the state has said needs to be
taught, and the kids are learning. If the upper grade levels lose the edge
we give them, don't blame it on us. Over half the kids fail something in 9th
grade -- I don't know if this is everywhere, or just Texas.
> Do you really want someone who can't read above 4th grade
> level to teach 4th grade reading?
>
If she is a great 4th grade reading teacher, why would I care about her own
reading level?
vince garcia
> >> >Obviously this came from Judaism, and perhaps from the JEwish apostles.
>
> >> I don't see how this is obvious at all.
>
> >since catholics say the teaching is justified from the book of 2nd
> >maccabees, which is about as jewish a work as you can get, I don't see
> >why you question the statement
>
> Maccabees is not part of the Jewish canon. It's not even studied as a book
> dealing with our faith, any more than Jubilees or Enoch is.
>
> jds
Today that is true, but in the 1st century it was accepted by many if
not most jews. So i see no problem believeing Jews would have drawn
theology from it, since the hanukkah one could argue might come out of
it. But this, in and of itself, doesn't convince me that the doctrine as
practiced by the Catholic and Orthodox is truly scriptural
Chris
<BB1F1DBD.13305%mr...@io.com>:
> in article OMhKa.1953$Vx2.1...@newssvr28.news.prodigy.com, Chris at
> dont...@none.net on 6/25/03 8:50 AM said:
>
>> On Tuesday 24 June 2003 18:13 Pam(mr...@io.com) wrote in
>> <BB1E4529.132D3%mr...@io.com>:
>>> The point is that they did not need an extra year, and did not need to
>>> be put in a dummy class. They ALL passed! Who said anything about
>>> everyone marching in lockstep? I am expected to meet the unique needs of
>>> each of my students -- even though there's a 70 pt IQ spread. It's
>>> certainly not easy. Tougher teaching certainly does mean better, because
>>> it means I am trying so hard it hurts. And they are trying just as hard
>>> to learn, if I am doing my job of motivating and encouraging them, and
>>> esp getting them to believe that if they try, if they practice the
>>> strategies I have taught them (like I am practicing the strategy Joe
>>> taught me) they will succeed.
>>
>> What about the advanced kids? Do they get the opportunity to move ahead
>> at their own pace?
>
> They can take a test and move up. I've recommended it several times to
> parents, but they don't do it. I've studied the advantages and
> disadvantages of grade skipping and IMO the advantages are substantially
> greater.
Funny, I had teachers recommending it for me, I think it was 2nd grade or
something. The principal at my school wouldn't allow it because she thought
that when I got to HS I would smaller than everyone else and wouldn't fit
in. Turned out to be 6'4 and most years taller than pretty much everyone
else.
>
>>
>> How does this "Leave no child behind" affect the ones who werent behind
>> to begin with?
>
> As with everything else, it depends on how the teacher, the district, and
> school handle the gifted and the remedial programs. There is no question
> that the high-stakes testing, with its focus on bringing the bottom kids
> up, causes more focus to be put on lower kids, often at the expense of the
> top ones. Gifred kids' needs are often ignored, even though they are just
> as much "special needs" kids as the special education ones, and suffer as
> much if their needs are not met. They need many opportunities to excercise
> leadership, have maximum autonomy and choices, less direct teach and
> structure, and real intellectual challenge.
That is a shame. Perhaps their slogan should be "Make all children the
same".
Rob Strom
...
> >How often does the average adult need to know about the Smoot Hawley
> >tariffs?
>
> Never, I suspect. I have heard of them, vaguely, but most people in the
> world haven't.
>
> >Isn't it enough to know that there are taxes and the
> >experts know when to raise and lower them? Why not?
>
> No, I think you should know the purpose of taxes and that taxes have
> consequences. I don't think you need to know about the Smoot Hawley Act,
> except insofar as it is a particular instance relevent to your own country.
> That's a historical note, not a practical one. Knowing about taxes is
> practical because it helps you understand political arguments. This is all
> said because where I live people are obliged to vote. In countries where
> you don't have to vote I suppose you can live just fine without knowing
> about taxes.
But that's the point. The better educated you are, the better
prepared you are to exercise critical judgement. Should we
favor tariffs or free trade? Should we finance the SuperCollider?
How can we judge the effects of this or that change to the
flow of goods in the economy? How can we judge the value of
detecting the Higgs Boson? What is the Higgs Boson? What
similar discoveries of fundamental principles of nature in
the past have had dramatic, life-changing effects?
>
> >Or how often does the average
> >adult need to recite anything from Macbeth?
>
> Never. Why is _Macbeth_ privileged over _The Iliad_?
I didn't say it was. Our schools teach both, but
that's not the point. They take a sampling of
literature, traditionally favoring Western, but
more recently being more eclectic. It's still
the case that any particular item on the reading
list can be disdained as irrelevant, in exactly
the same way you appeared to disdain applying
factoring to solve quadratic equations.
No one item is essential, but what is essential
is that children get a sampling of the
accumulated knowledge of the culture, and
of the different styles of creativity and
their most prominent fruits.
>
> >Or know who Wordsworth was?
>
> That's entirely useless. What's the point of knowing he was a poet if you
> don't know any of his poetry? Better you should know the poems and not the
> poet. How much Wordsworth do *you* know? Tennyson? Dryden? Masefield?
> Motion? Where does it end?
Most of my generation knows at least about
Wordsworth's wandering lonely as a cloud,
and Tennyson's view of nature "red in tooth and claw".
>
> >Or care whether Picasso lived before or after Renoir?
>
> I don't especially. I don't care for Picasso. But should you know whether
> Li Po or Li Bai lived earlier?
>
> >Isn't it enough to know that there are poets and playwrights and artists and
> >that the names of their works and stuff like when
> >and where they lived can be looked up on the Internet? Why not?
>
> I think it's nice to know and care about some particular pieces of art, and
> you don't need to have a head stuffed with boring dead facts about dates
> and so forth.
The reason for the boring dead facts about dates is so that
you can imagine that you're the person being talked about
and you can get an image of what that person might have
known about and not known about when he was creating the things.
>
> >Why should a farmer or a lathe operator or a receptionist
> >or even a banker, loan officer, or medical doctor need to
> >know *anything* other than how to get to work, operate the
> >equipment and execute the
> >correct procedures there, and get home to eat, watch TV and go to sleep?
>
> Because he chooses to?
But the topic under debate seemed to be whether (1)
they should be *required* to be exposed to this stuff
in school, before we know what they're going to become,
and whether (2) we should as a culture value
the fact that stockbrokers have read Wordsworth and Tennyson and
maybe remember a few of their metaphors, and that
lathe operators had a glimpse of how Aggasiz figured out
that there were Ice Ages long before there were historical records,
and yes, that 4th grade math teachers should have a
premonition of the fact that in 4 years their kids should
have to know something about quadratic equations or the
binomial distribution.
> >This isn't just about math. It's about what's the point of being educated
> >at all.
> >Why shouldn't just professional art critics or art historians learn about
> >Picasso?
>
> Because other people may want to do so. But if they don't, then so what?
> You're privileging a tiny part of the world's culture above all others and
> demanding that people must recite a quotation from Shakespeare, correctly
> place several French Impressionists in chronological order, identify the
> occupations of some writers and artists, and (I presume) whistle the theme
> from the Mikado. This is sterile and pointless. Culture is a living thing
> and being a rounded person means discovering your own loves, finding your
> own plays to recite or songs to sing. You can't put art in a box, because
> when you do it's already dead.
>
The only way they will discover their own loves in adulthood is
to be exposed to a smorgasbord of them in childhood.
--
Rob Strom
Pam
> Joe Slater <joe[please don't spam me]@slater.net> wrote in message
> news:<7k0ifvsk5i25a868g...@4ax.com>...
>
> No one item is essential, but what is essential
> is that children get a sampling of the
> accumulated knowledge of the culture, and
> of the different styles of creativity and
> their most prominent fruits.
For the record, your original point was not that people are better off with
a liberal education than not, which no one disagrees with. YOUR point was
that elementary teachers cannot properly teach elementary skills unless they
know quadratic equations and all this other unnecessary stuff elementary
school, which you list below:
Rob wrote:
> I want teachers who have a broad liberal
> education, meaning that they understand the history of
> ideas, and know enough of the techniques of how these ideas
> were worked out. That means that they not only know about
> the US Constitution, but also about earlier forms of government,
> in medieval and ancient times. They not only know that the
> earth is 93 million miles from the sun,
I hadn't a clue how far away the sun is.
> but how we first learned
> that, and what are different ways to find out how far away something
> is that's too far to see.
I don't have a clue.
> They know how we extended our view
> of the universe from a flat earth to a round one, to a solar system,
> to a galaxy-universe, to a universe of multiple galaxies.
> They know how we discovered about the bits of the world too small
> to see, those hidden within the earth, and those so old that
> they leave but scant traces.
> They
> know about the great ancient nations, and the great empires, and
> how they rose and fell, and changed. They know about the great
> works of visual art, music, and literature. They know about
> the economic network of production and
> distribution, how it changed from early times
> to now. They know about the history of technology and about
> the technologies on the brink of being developed, and how they
> may change daily life, economic life, and the set of ethical
> problems we will face. They know about moral and ethical principles,
> about human psychology, about philosophy.
All very nice to know, and I've even discussed a few of these things with
kids on the fly, but these are all things that will be studied in depth
beginning in middle school, where teachers are all specialists. It's
ridiculous to think that because elem teachers teach all subjects, that
means they absolutely must "know about the great ancient nations and how
they rose and fell". Only a very tiny minority of kids has the ability even
to conceptualize historical time. I ask them how long ago they think
Columbus discovered America, and even the gifted ones will say something
like "50 years". Most kids know absolutely nothing about history. The first
day of school I ask everyone to put their heads down and point to planet
earth. Most of them point to the sky. They really and truly have not made
the connection that this "planet earth" they have studied about, which is
somehow "our planet" is what they are standing on! I ask them to point North
and most of them point to the ceiling; South is toward the ground. (This
necessitates a discussion of the definition of "up" and "down".)
They model what it
> means to be curious, how to discover things that others have
> discovered, and how to discover new things that haven't. They
> model how to live harmoniously with others.
Well, without knowing quadratic equations, I don't know how they could
possibly do that. BTW, we *are* very conscious of ourselves as moral and
ethical models. (We are shocked that secondary teachers will say "damn" in
class.) I see the subject matter as the medium through which we teach the
values of perseverance, honesty, fairness, kindness, forgiveness, patience,
sharing, the value and pleasure of learning, how to identify and produce the
elements that make for quality work, etc. That's our specialty.
>
> You couldn't want any more of a generalist than an elementary
> schoolteacher.
Everyone agrees. We just don't believe that if elementary teachers don't
remember their algebra or ancient history, they are unfit to teach.
Pam
PM said:
> I ask them how long ago they think
> Columbus discovered America,
BTW, lest I be accused of child abuse, I do teach them that Columbus was not
the first discoverer. I tell them about some probable early migrations, and
show them the evidence for those, then the Norse settlement of Vinland.
don't spam me]@slater.net Joe Slater
>> Maccabees is not part of the Jewish canon. It's not even studied as a book
>> dealing with our faith, any more than Jubilees or Enoch is.
On Wed, 25 Jun 2003 08:53:19 -0700, vince garcia <vgga...@ix.netcom.com>
wrote:
>Today that is true, but in the 1st century it was accepted by many if
>not most jews.
Have you any basis for saying this?
>So i see no problem believeing Jews would have drawn
>theology from it, since the hanukkah one could argue might come out of
>it.
No, Chanuka comes out of the events, not out of this particular text. The
miracle we celebrate isn't even mentioned in the text.
jds
Rob Strom
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/25/03 8:39 AM said:
>
> >
> > I still disagree. I believe in ability-grouped classes, I dislike
> > the disparaging term "dummy class" for the lower groups, and I think
> > that 20-odd percent reaching proficiency which the NAEP designers
> > defined as truly being comfortable with the concepts means that
> > a lot more folks should get an extra year.
>
> There are things such as "developmental" first grade which is an extra year
> between K and 1st. Otherwise in elementary, the only option is retention.
Actually, that's not the only option.
When I was in school, they had ability groups within the class
without retention.
That went out of fashion later, but like a lot of things in
education, new fashions don't necessarily mean better research.
Just like phonics went out of fashion for several years and
now is coming back.
> The problem with that is that research shows that kids who are retained,
> compared with a control group who are not, show no benefit. Some kids may,
> but most kids I have my classes who have been retained are still at the
> bottom of the class. Have you studied the research on ability grouping? The
> top and bottom kids do need differentiation/modification, but the bottom
> kids benefit by not being placed in a separate track. I have taught tracked
> classes before and hate them. In the low classes there is little modeling of
> the kind of thinking and attitudes toward learning that they need. For
> example, when the low kids here the others begging "Can we write? Can we
> read? Can we do social studies? Yay, math!" they start looking for what's
> fun about these things, and next thing you know they are all enthusiastic,
> too. It's not just lip service -- they really are working and learning.
There are too many variables here. The slower moving students
are not necessarily less able to think, they need a different
set of presentations to motivate them, and possibly more
time to make the connections. The enthusiasm of the brighter
kids won't always be contagious to them, it could also be frightening
to them.
>
>
> >
> >
> >> Who said anything about everyone
> >> marching in lockstep? I am expected to meet the unique needs of each of my
> >> students -- even though there's a 70 pt IQ spread.
> >
> > If everybody has to pass the same test at the end of the same
> > year, that's lockstep.
> > And it's not obvious to me that
> > people who pass only at the basic level should be moving on.
>
>
> You know, the things you say are so totally ill-informed I am tired of
> responding to them. You know about as much about education as I do about
> calculus.
Well, since you are an educator, educate me, instead of just giving
up. But I don't take your conclusions at face value. After all,
I think I know quite a bit about music education, and your
conclusions definitely don't apply there, so if you claim they
apply to math, you must overcome my skepticism by citing some studies.
And your difficulties following scientific reasoning makes
me doubt whether you can critically derive the correct conclusions
from these studies. But you're welcome to try.
>
>
> >>>> The only relevant question is, in which state do 4th grade students do
> >>>> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
> >>>
> >>> That's by average scores; if you compare the percentages scoring
> >>> "proficient" or above, then Texas is #10.
> >>
> >> But it's still better than VA, even though they supposedly teach these
> >> advanced concepts you recommend. Turns out it doesn't mean they turn out
> >> better math students.
> >
> > The margin is closer, and by 8th grade VA has caught up
> > and surpassed Texas.
>
> Could that have anything to do with, say, the culture of poverty, and
> Hispanic culture which tends not to value education highly? The demographics
> really do make things more difficult, esp when the kids are teens.
> Otherwise, I assume it must be the inferior teaching at elementary school
> that gives them the edge.
Look, there are lots of hypotheses for why one group performs
well in 4th grade and falls behind in 8th grade. (Even assuming
that 30% of the class being "proficient" constitutes performing well.
It may be well relative to other states, but it seems that if
most of the students aren't proficient in the subject, that
there's lots of room for improvement.)
H1: The lower-grade teachers are just better at doing their
jobs than the upper-grade teachers.
H2: The standards for what should be accomplished in the lower
grades are suboptimal, encouraging strategies that are going to
have to be unlearned later on because they interfere with these
later concepts.
H3: The standards for what should be accomplished in the lower
grades are OK, but the tests don't actually test for these skills,
and therefore teachers are able to prepare students for these
tests via various shortcuts that cause them to do well on the
tests despite not having all the skills.
H4: The teachers are qualified, the standards are correct,
and the tests are appropriate, but the student body contains
a higher proportion of students from cultures that devalue
higher education beyond a certain level.
Or various mixtures of these hypotheses can all be true.
To discriminate among the different hypotheses, I'd want
either a carefully reasoned theoretical model of how learning works,
or empirical studies that control precisely for these effects.
I don't think we have that. If you're going to state categorically
that H2 can never occur, or that the tests measure the skills by
definition, I am going to need more than just your bald
assertion that you're an experienced teacher and you just *know*
so much more than I do.
...
> > And it is not beyond the realm of possibility that
> > a reason for that is that *some* of the teachers
> > of 4th grade weren't aware of these patterns because
> > of the philosophy that "if the kids don't have to
> > know it, I don't have to know it either."
>
> In general, elementary teachers in Texas are doing their jobs, and doing it
> better than anyone else.
I don't know that. I don't know that they have been given
the right jobs, I don't know that even if they have, that
the existing tests accurately measure whether they have
been doing these jobs, so I can't just agree.
> We are teaching what the state has said needs to be
> taught, and the kids are learning.
All you know is that 30% of the kids are scoring proficient
or above on the tests. You haven't proven either that these
tests actually test the skills that your curriculum says
kids are supposed to learn, nor that these skills are the
optimum skills 4th graders should learn so that passage
from 4th grade to 8th grade will be easier than it would
had different skills been taught.
> If the upper grade levels lose the edge
> we give them, don't blame it on us.
I don't know whom to blame it on yet. Maybe the
designers of the syllabus, maybe the designers
of the tests, maybe the 4th grade teachers, maybe the 8th grade teachers.
...
>
> If she is a great 4th grade reading teacher, why would I care about her own
> reading level?
So that kids get exposed to things that they can't do now that
people they respect are able to do?
--
Rob Strom
Rob Strom
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/25/03 11:45 AM said:
>
> > Joe Slater <joe[please don't spam me]@slater.net> wrote in message
> > news:<7k0ifvsk5i25a868g...@4ax.com>...
>
> >
> > No one item is essential, but what is essential
> > is that children get a sampling of the
> > accumulated knowledge of the culture, and
> > of the different styles of creativity and
> > their most prominent fruits.
>
> For the record, your original point was not that people are better off with
> a liberal education than not, which no one disagrees with. YOUR point was
> that elementary teachers cannot properly teach elementary skills unless they
> know quadratic equations and all this other unnecessary stuff elementary
> school, which you list below:
Huh??? Quadratic equations is *part* of a liberal education.
If I don't have to know quadratic equations or how history is done
or how the economic system works, or anything about art or music,
because it's not something a 4th grader is going to be tested on,
then you *are* disagreeing that elementary teachers need a liberal education.
You're saying they're "better off" in the abstract with
a liberal education, but it doesn't help them to be better teachers????
>
> Rob wrote:
>
> > I want teachers who have a broad liberal
> > education, meaning that they understand the history of
> > ideas, and know enough of the techniques of how these ideas
> > were worked out. That means that they not only know about
> > the US Constitution, but also about earlier forms of government,
> > in medieval and ancient times. They not only know that the
> > earth is 93 million miles from the sun,
>
> I hadn't a clue how far away the sun is.
This is actually taught in 4th grade. What I'm suggesting
is that the teacher not only should know this, but should
also know how we found out in case, God forbid, some kid
should ask how do we know it's 93 million and not thousand
or billion.
>
>
> > but how we first learned
> > that, and what are different ways to find out how far away something
> > is that's too far to see.
>
> I don't have a clue.
Then it's dangerous to be telling people authoritatively
that the stars are very far away. It comes out sounding
like revealed truth rather than something anybody can
figure out.
...,
> All very nice to know, and I've even discussed a few of these things with
> kids on the fly, but these are all things that will be studied in depth
> beginning in middle school, where teachers are all specialists.
Sad to say, they aren't taught in any more depth in middle school.
In fact, they have more "facts" to cram into these poor kids' heads
then, so they don't have time to spend a month or two actually
trying to measure the distance to anything in a number of different ways.
And just because middle school teachers teach a single subject
rather than all subjects does not mean that they should be specialists.
They need to be generalists precisely so that they can relate
the formal stuff they teach to lots of different applications.
A perfect example is to get the math, science, and history teachers
to coordinate so that they can get across the point of why it
was important in the Age of Exploration to be able to have
accurate clocks that could be carried on board ships, so much
so that the government offered an enormous prize to someone who
could demonstrate such a clock. (The reason is that while you
can measure your latitude or north-south position by measuring the
altitude of the pole star, which doesn't move, there's no way to measure your
longitude or east-west position except by noting the absolute time of
day when a particular meridian is at the due south position. Since
you can only guess your east-west velocity, and it can be confused
by winds and currents, it is very easy to be way off course in
the east-west direction.) To tell the story properly, you need
someone who knows how to relate the necessary geometry, astronomy,
and history together --- not a "specialist".
> It's
> ridiculous to think that because elem teachers teach all subjects, that
> means they absolutely must "know about the great ancient nations and how
> they rose and fell". Only a very tiny minority of kids has the ability even
> to conceptualize historical time. I ask them how long ago they think
> Columbus discovered America, and even the gifted ones will say something
> like "50 years". Most kids know absolutely nothing about history. The first
> day of school I ask everyone to put their heads down and point to planet
> earth. Most of them point to the sky. They really and truly have not made
> the connection that this "planet earth" they have studied about, which is
> somehow "our planet" is what they are standing on! I ask them to point North
> and most of them point to the ceiling; South is toward the ground. (This
> necessitates a discussion of the definition of "up" and "down".)
>
The more the teacher knows about the universe, the more likely
they are to ask their kids this kind of challenging question.
You should read Feymann's books which discuss exactly this issue ---
teachers who have learned formulas, and can manipulate all the
symbols that they're expected to teach their kids but who can't
relate it to even the most basic things.
>
>
> They model what it
> > means to be curious, how to discover things that others have
> > discovered, and how to discover new things that haven't. They
> > model how to live harmoniously with others.
>
> Well, without knowing quadratic equations, I don't know how they could
> possibly do that. BTW, we *are* very conscious of ourselves as moral and
> ethical models. (We are shocked that secondary teachers will say "damn" in
> class.) I see the subject matter as the medium through which we teach the
> values of perseverance, honesty, fairness, kindness, forgiveness, patience,
> sharing, the value and pleasure of learning, how to identify and produce the
> elements that make for quality work, etc. That's our specialty.
>
If you do that, then you have conceded my point, because none of
these things you've listed is on the curriculum, and therefore by
your earlier logic, the teacher doesn't have to have any of them.
> >
> > You couldn't want any more of a generalist than an elementary
> > schoolteacher.
>
> Everyone agrees. We just don't believe that if elementary teachers don't
> remember their algebra or ancient history, they are unfit to teach.
It's not any particular subject, it's rather that they should have
a broad general education about the universe and humanity,
and they should draw on this general education both to
give examples of their teaching, and to give them
concrete examples of patterns they're going to have to
learn about later. Whereas
you argued earlier that if they're teaching chapters 1-6, they
don't need to know even chapter 7,
much less something totally irrelevant like
what country they're living in.
--
Rob Strom
Pam
>> Well, without knowing quadratic equations, I don't know how they could
>> possibly do that. BTW, we *are* very conscious of ourselves as moral and
>> ethical models. (We are shocked that secondary teachers will say "damn" in
>> class.) I see the subject matter as the medium through which we teach the
>> values of perseverance, honesty, fairness, kindness, forgiveness, patience,
>> sharing, the value and pleasure of learning, how to identify and produce the
>> elements that make for quality work, etc. That's our specialty.
>>
>
> If you do that, then you have conceded my point, because none of
> these things you've listed is on the curriculum, and therefore by
> your earlier logic, the teacher doesn't have to have any of them.
Okay, Rob, as one of my teammates says, you would argue with a dead dog.
Taking showers is not in the curriculum, either, and we know how to do that,
so I guess your logic is unassailable: elementary teachers are just
incompetent if they don't know how to spell Richard Feynman's name correctly
when they advise other people to read him.
vince garcia
>
> >Joe Slater wrote:
> >> Maccabees is not part of the Jewish canon. It's not even studied as a book
> >> dealing with our faith, any more than Jubilees or Enoch is.
>
> On Wed, 25 Jun 2003 08:53:19 -0700, vince garcia <vgga...@ix.netcom.com>
> wrote:
> >Today that is true, but in the 1st century it was accepted by many if
> >not most jews.
>
> Have you any basis for saying this?
i have never heard anyone deny this. Josephus used part of the
maccabbees (genealogy) in his history of the jews, as one example, and
I think he alludes to 2 macabbes 7 elsewhere. if these books were really
obscure and not used by anyone i doubt they would have survived to be a
part of the early christian canon
>
> >So i see no problem believeing Jews would have drawn
> >theology from it, since the hanukkah one could argue might come out of
> >it.
>
> No, Chanuka comes out of the events, not out of this particular text. The
> miracle we celebrate isn't even mentioned in the text.
>
> jds
well, here's a jewish web site that ties hannukkah to the books in
question:
http://www.ijn.com/archive/2001arch/chanfoods2001.htm
Plus, since the story of the oil being replenished is in maccabees, why
do you say it has nothing to do with the events portrayed in it?
Rob Strom
Good grief! This is my reward for giving you a bye on your
post two years ago, the relevant bit of which I excerpt below!
'BTW, I got a very nice e-mail from William (it's "Bill" to me) Demski.'
Does Dembski still let you call him Bill after that???
--
Rob Strom
Pam
As I recall, there was no bye. And at least I spelled it like it sounds!
Do you have several notebooks filled with my posts that you read before
going to bed every night? Or have you just committed them all to memory?
don't spam me]@slater.net Joe Slater
>> >> Maccabees is not part of the Jewish canon. It's not even studied as a book
>> >> dealing with our faith, any more than Jubilees or Enoch is.
>> On Wed, 25 Jun 2003 08:53:19 -0700, vince garcia <vgga...@ix.netcom.com>
>> wrote:
>> >Today that is true, but in the 1st century it was accepted by many if
>> >not most jews.
>Joe Slater wrote:
>> Have you any basis for saying this?
On Thu, 26 Jun 2003 06:13:35 -0700, vince garcia <vgga...@ix.netcom.com>
wrote:
>i have never heard anyone deny this. Josephus used part of the
>maccabbees (genealogy) in his history of the jews, as one example, and
>I think he alludes to 2 macabbes 7 elsewhere. if these books were really
>obscure and not used by anyone i doubt they would have survived to be a
>part of the early christian canon
The reason I asked that was because your statement presumes two things.
Firstly, it presumes that there was the very concept of a canon. This is by
no means clear. Even in Talmudic times they made a strong differentiation
between the books of The Prophets and The Writings, with the latter having
a distinctly secondary place. Furthermore, we know that different people
had different ideas of what should be in the canon. For instance, the Book
of Jubilees has been found in multiple copies among the Dead Sea Scrolls,
in multiple locations. This indicates that it was popular - but it isn't
part of the mdoern Jewish canon. Since it contradicts what we know was
common Jewish practice on things like the calendar it must have been
popular among sectarians.
Josephus himself doesn't list a canon per se, but he does state that there
is a certain number of books which Jews find sufficient. I read that it
comes to about the same number as the present Jewish canon, but we can't
really tell - did he divide up Kings, did he include a deuterocanonical
book, did he exclude Song of Songs and so forth.
The fact is that nobody really knows definitively what people read in those
days. However I can assure you that Maccabees may have been a popular book
(and it may not) but there was never any hope of a history book set in
Second Temple times being included in a canon which terminated rather
earlier. Even the historians who argue for late dates of Biblical texts
would acknowledge that those texts were believed to be early and therefore
fit into the canon.
>> No, Chanuka comes out of the events, not out of this particular text. The
>> miracle we celebrate isn't even mentioned in the text.
>well, here's a jewish web site that ties hannukkah to the books in
>question:
>
>http://www.ijn.com/archive/2001arch/chanfoods2001.htm
>
>Plus, since the story of the oil being replenished is in maccabees, why
>do you say it has nothing to do with the events portrayed in it?
Can you tell me where the story of the oil appears?
jds
Rob Strom
>
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/26/03 11:26 AM said:
>
> >>
> >> Okay, Rob, as one of my teammates says, you would argue with a dead dog.
> >> Taking showers is not in the curriculum, either, and we know how to do that,
> >> so I guess your logic is unassailable: elementary teachers are just
> >> incompetent if they don't know how to spell Richard Feynman's name correctly
> >> when they advise other people to read him.
> >
> > Good grief! This is my reward for giving you a bye on your
> > post two years ago, the relevant bit of which I excerpt below!
>
> As I recall, there was no bye. And at least I spelled it like it sounds!
>
At 1:26AM, which is when I wrote the "Feynman/Feymann" post,
you should be grateful that I at least put in all the letters
of his name, if not in the all the right positions.
As for your bye, you can look it up in Google yourself.
Your "Demski" post was made on July 27, 2000, and my
reply on July 31. You can see that I made no allusion
to either your gratuitous assertion of friendship to
Dembski, or to your misspelling of his name.
You can also use Google to check that in December 1999,
I actually *did* know how to spell Richard
(as you might say, it's "Dick" to me)
Feynman's name on Usenet.
> Do you have several notebooks filled with my posts that you read before
> going to bed every night? Or have you just committed them all to memory?
You mean I forgot to tell you that I needed these notebooks as input
for compiling my collection "Logical Brilliancies and Fallacies
in Real Life" for my tutees?
Sorry, now you know.
--
Rob Strom
vince garcia
> >Plus, since the story of the oil being replenished is in maccabees, why
> >do you say it has nothing to do with the events portrayed in it?
>
> Can you tell me where the story of the oil appears?
>
> jds
You got me on that one; my memory was bad. I could have sworn it was in
there!
Jewish redaction must be responsible for its disappearance :)
Pam
> Pam <mr...@io.com> wrote in message news:<BB1F23A7.13307%mr...@io.com>...
>
> There are too many variables here. The slower moving students
> are not necessarily less able to think, they need a different
> set of presentations to motivate them, and possibly more
> time to make the connections.
That's because they are less able to think. The thought processes that most
people figure out almost automatically, they don't do. But they can be
directly taught them -- for example, when they read they do not visualize
anything -- they just say words. But they can be taught to visualize. They
don't use logic to find and evaluate the reasonableness of an answer, but
they can be taught. They do need different presentations to some extent, but
mostly they need more repetitions. 14 is average; gifted kids need only one
or two. These kids need a huge number. And just as the gifted kids need less
structure and direct teach, they need a lot of structure and maximum direct
teach, with me interacting with them constantly. They don't do well working
in a group trying to discover math principles for themselves -- they have an
astonishing capacity for doing something over and over and not seeing a
pattern, like the other kids do. I have to guide them into these
"discoveries".
> The enthusiasm of the brighter
> kids won't always be contagious to them, it could also be frightening
> to them.
No, sadly, it's not always contagious -- but most of the time it is. When
you are in a class of people who are enthusiastic and diligent about
learning, your natural desire to fit in with the group comes into play. They
just naturally develop a positive attitude toward learning. Research has
shown this benefit to be measureable -- there is measurable benefit to the
gifted kids, though.
>>>
>>>> Who said anything about everyone
>>>> marching in lockstep? I am expected to meet the unique needs of each of my
>>>> students -- even though there's a 70 pt IQ spread.
>>>
>>> If everybody has to pass the same test at the end of the same
>>> year, that's lockstep.
>>> And it's not obvious to me that
>>> people who pass only at the basic level should be moving on.
>>
>>
>> You know, the things you say are so totally ill-informed I am tired of
>> responding to them. You know about as much about education as I do about
>> calculus.
>
> Well, since you are an educator, educate me, instead of just giving
> up. But I don't take your conclusions at face value. After all,
> I think I know quite a bit about music education, and your
> conclusions definitely don't apply there, so if you claim they
> apply to math, you must overcome my skepticism by citing some studies.
> And your difficulties following scientific reasoning makes
> me doubt whether you can critically derive the correct conclusions
> from these studies. But you're welcome to try.
Okay, I'll try one last time. What you want to do in each grade level is
identify the skills you want children to learn at that grade level, and make
those the standard. The test and all curriculum materials are perfectly
aligned with the standards (since Texas and CA call the shots on textbook
contents). All of our textbooks have little notes in the margins saying
which TEKS they correlate with.
Now, the standard is an ideal. We know all children, or even most children
will not meet the ideal. I had only one perfect total score on the three
test. There was one other in another class. Several kids did make perfect
scores on individual tests, and some missed only one or two. Now in Texas
when we started this testing many years ago, the tests were very easy -- I
think the first one was the TEAMS, which tested minimum skills. Every year
the average scores went up, and with it the score necessary to pass; then
they created a more difficult test, TAAS, which followed the same pattern.
Over the years scores improve a great deal. This year we instituted the
TAKS, which focuses much more on the highest level skills. It will no doubt
follow the same pattern.
In any case, the curriculum is spiral -- you don't start with all new
materical each year -- you review, reteach, and then add on. One of the
most-missed items on the 5th grade test every year is something as simple as
subtracting across a middle zero, which they were introduced to in 2nd
grade. Of course, the items involving higher reasoning are missed most
often, too (We give three benchmark math and reading tests, two writing; I
have to score each test and identify how many items each child missed of
each objective; then I make all these graphs so I can analyze the data.)
So even if the kids don't make a perfect or near perfect score, they can
still be considered to have the basic skills they need to be successful in
the next grade.
Now, as you know, I teach the gifted kids at a higher level, but they are
not always really, really careful on the tests (which take some kids all
day, for each test) so they make careless errors and may not do as well as
more conscience but less talented kids. When I say all my kids passed --
when last year several of them didn't -- it is certainly significant for me,
and a great confidence-builder for them.
>
>
>>
>>
>>>>>> The only relevant question is, in which state do 4th grade students do
>>>>>> better in math? According to the 2000 NAEP, Texas is #6, and VA is #14.
>>>>>
>>>>> That's by average scores; if you compare the percentages scoring
>>>>> "proficient" or above, then Texas is #10.
>>>>
>>>> But it's still better than VA, even though they supposedly teach these
>>>> advanced concepts you recommend. Turns out it doesn't mean they turn out
>>>> better math students.
>>>
>>> The margin is closer, and by 8th grade VA has caught up
>>> and surpassed Texas.
>>
>> Could that have anything to do with, say, the culture of poverty, and
>> Hispanic culture which tends not to value education highly? The demographics
>> really do make things more difficult, esp when the kids are teens.
>> Otherwise, I assume it must be the inferior teaching at elementary school
>> that gives them the edge.
>
> Look, there are lots of hypotheses for why one group performs
> well in 4th grade and falls behind in 8th grade. (Even assuming
> that 30% of the class being "proficient" constitutes performing well.
> It may be well relative to other states, but it seems that if
> most of the students aren't proficient in the subject, that
> there's lots of room for improvement.)
>
> H1: The lower-grade teachers are just better at doing their
> jobs than the upper-grade teachers.
There's no question that we are. But this is going to have to change. In the
past, high school kids were only tested in 10th grade, if they passed. Then
they had more chances to pass. Now they have to take it every year up to
senior year, if they pass. Otherwise they keep trying, because they can't
graduate without it. In all seconary schools, teachers have seen themselves
as more imparters of content than analysts of children's learning problems
-- if they didn't get it, oh, well. We elementary teachers, OTOH, are told
that we are respnsible for student learning. If they don't pay attention,
well, we have to find a way to get them to. If the parents don't care, then
it's up to us to get the kids to care anyway. If the kids' homelife is
devoid of enrichment, then we better make up the difference. We simply never
give up on them.
>
> H2: The standards for what should be accomplished in the lower
> grades are suboptimal, encouraging strategies that are going to
> have to be unlearned later on because they interfere with these
> later concepts.
Nope.
>
> H3: The standards for what should be accomplished in the lower
> grades are OK, but the tests don't actually test for these skills,
> and therefore teachers are able to prepare students for these
> tests via various shortcuts that cause them to do well on the
> tests despite not having all the skills.
Nope.
>
> H4: The teachers are qualified, the standards are correct,
> and the tests are appropriate, but the student body contains
> a higher proportion of students from cultures that devalue
> higher education beyond a certain level.
This makes it harder as they grow older, and less interested in pleasing
their teachers. The world outside the classroom has more influence than it
did, and if that world is part of a culture that does not value eduation
highly, it will be more difficult to convince them that they ought to.
>
> Or various mixtures of these hypotheses can all be true.
>
> To discriminate among the different hypotheses, I'd want
> either a carefully reasoned theoretical model of how learning works,
> or empirical studies that control precisely for these effects.
> I don't think we have that.
We certainly have an abudance of research on how learning works -- what do
you think it is we are doing, if not basing our teaching on research. For
example, studies have shown the value of a certain schedule and duration of
review of new skills to produce optimum retention. Or, many studies have
shown that kids are demotivated by extrinsic rewards when the task has the
potential to be intrinsically rewarding. Or did you know that the average
"wait time" after asking a question before calling on someone is one second?
(You have to give a long wait time and have many hands waving in the air).
This year I took a workshop that presented many studies about, among other
things, how slower learners train the teacher not to call on them because
they will not answer, and she will not want to waste time and will move on -
eventually she shys away from calling on them as often. When I began
practicing the techniques I learned, the slower kids expected to be called
on, so when I told the class to think about a question, they did it, and
were ready with an answer, quite often a good one. Soon they were
volunteering much more often, and because I have learned to dignify
incorrect responses (That's a good guess! or Good, that's exactly the right
answer to this other question I was going to ask, which is...) Kids learn
best when they get immediate feedback, so mine have little whiteboards that
they write answers on all day long -- they show them to me and I either nod
or shake my head. They keep trying until they get it, or, when most have, a
kid comes up to the overhead and explains it.
Carefully reasoned theoretical models are worthless -- it's what's cause the
cycling fads of this century. Research has certainly shown that phonics is
extremely beneficial to young readers -- it was only tossed out because of
someone's' "carefully reasoned theory".
> If you're going to state categorically
> that H2 can never occur, or that the tests measure the skills by
> definition, I am going to need more than just your bald
> assertion that you're an experienced teacher and you just *know*
> so much more than I do.
Well, that will have to do, unless you want to do the research. I don't know
why, if I was going to lie about something, I would decide to say that TEKS
and TAKS were perfectly aligned (well, as much as they can be -- the TAKS
doesn't test how well the kids use manipulative, for example, just pictoral
models).
>>> And it is not beyond the realm of possibility that
>>> a reason for that is that *some* of the teachers
>>> of 4th grade weren't aware of these patterns because
>>> of the philosophy that "if the kids don't have to
>>> know it, I don't have to know it either."
>>
>> In general, elementary teachers in Texas are doing their jobs, and doing it
>> better than anyone else.
>
> I don't know that. I don't know that they have been given
> the right jobs, I don't know that even if they have, that
> the existing tests accurately measure whether they have
> been doing these jobs, so I can't just agree.
For years the states along the Canadian border, which have comparatively few
minorities, have been at the top. Those with high numbers of minorities
have not. If you just look at the raw data, figure out some ratios, and
adjust every state's fourth grade scores, Texas (and maybe NC, because of
it's stong standards) would be at the top.
Also, many studies have shown that students from low income homes do much
more poorly than others, and Texas has a lot of them.
>> We are teaching what the state has said needs to be
>> taught, and the kids are learning.
>
> All you know is that 30% of the kids are scoring proficient
> or above on the tests.
I'm not talking about the NAEP. I don't imagine most teachers have even
heard of it, though I am always interested in it. All we care about is the
test that test the things we teach. The NAEP can't be aligned with any
particular state's standards, esp since many states just don't have any.
It's hard to imagine going back to the days when there were no standards.
And don't expect union states to get them very easily, either, because they
make teachers' jobs much more difficult, and make identification of poor
educators and administrators easy.
> You haven't proven either that these
> tests actually test the skills that your curriculum says
> kids are supposed to learn, nor that these skills are the
> optimum skills 4th graders should learn so that passage
> from 4th grade to 8th grade will be easier than it would
> had different skills been taught.
Well, they probably aren't optimum -- evidently the idea is to keep raising
the bar until teachers drop dead of exhaustion. I keep asking "Has anyone at
TEA ever sat down and calucated exactly how long it would take for the
slowest kid in the class to learn every one of these TEKS?"
Pam
AM said:
I just read over this, something I rarely do. I would like to say that it is
late and I am apparently half asleep, judging from all the misspellings,
typos, and half finished sentences. Some of it doesn't even make sense. Oh,
well.
moshe
> > Now, as you know, I teach the gifted kids at a higher level, but they are
> > not always really, really careful on the tests (which take some kids all
> > day, for each test) so they make careless errors and may not do as well as
> > more conscience but less talented kids.
...
***************
Very true.
In first grade my IQ test showed only an IQ of 121, which is not much
above the average of something like 110 nowadays.
But because I concentrated so completely on every word that the
teacher was saying in class, I almost never had to study at home, and
I got straight A's in college.
And I always checked my answers again before turning in a test.
One time in college I discovered that I had missed one line on one of
those "Use a pencil to mark A or B or C on the computer-graded answer
card".
So I had listed my correct answers on the wrong lines.
The computer would have said that I missed 95 per cent of the answers
and would have given me an "F" if I hadn't caught the mistake before
turning in the test.
But a teacher did show me once why I had a tendency to miss one
question on each test:
She said that I was reading too much into what she intended as simple
questions, so that I was thinking up rare exceptions to rules and
marking "False" what most people would immediately mark as "True".
"All poodles are dogs" should be "False".
Because some poodles are skirts :^)
Or I was noticing a slight mis-wording of her question which would
technically change the required answer from what she intended.
Even teachers need occasional reminding that there is a huge
difference between "Not all dogs are poodles" and "All dogs are not
poodles".
I sure feel sorry for any student who has diabetes or epilepsy.
Recent research proves what my last 5 years of experience had already
shown: Diabetes ruins a person's memory.
Hence, my increasing difficuly spelling and memorizing numbers and
remembering to do little tasks.
And my wife's epilespy medicine is infamous for ruining a person's
memory.
- moshe
randy
has diabetes or epilepsy.
> Recent research proves what my last 5 years of experience had already
> shown: Diabetes ruins a person's memory.
> Hence, my increasing difficuly spelling and memorizing numbers and
> remembering to do little tasks.
> And my wife's epilespy medicine is infamous for ruining a person's
> memory.
ahem, I'm gonna say the obvious. you may just be aging a bit. lol
randy
don't spam me]@slater.net Joe Slater
>> >Plus, since the story of the oil being replenished is in maccabees, why
>> >do you say it has nothing to do with the events portrayed in it?
>>
>> Can you tell me where the story of the oil appears?
On Fri, 27 Jun 2003 05:48:40 -0700, vince garcia <vgga...@ix.netcom.com>
wrote:
>You got me on that one; my memory was bad. I could have sworn it was in
>there!
I didn't think it was in there, but I could have been wrong and was
interested in finding out if I was.
>Jewish redaction must be responsible for its disappearance :)
Hardly likely, since we didn't even both keeping a copy of the (presumably
Hebrew/Aramaic) original.
jds
moshe
***************
A story I read many years ago:
An 85-year-old woman goes to the doctor and says, "My right arm is
hurting something terrible."
Without even looking at the arm the doctor says, "It's just old age".
The old woman replies, "My left arm is just as old and it doesn't
hurt."
Doctors have finally started to realize that any significant loss of
memory in old people is due to disease rather than old age.
Age itself only causes minor deterioration of memory.
Anything worse than that is due to stroke, Alzheimers, fatty blockage
of carotid artery, etc.
I was young at age 42, but now I'm old at age 47?
Then at this rate I'd be mulch by age 50.
- moshe
Rob Strom
> in article abea7612.03062...@posting.google.com, Rob Strom at
> st...@watson.ibm.com on 6/26/03 12:02 AM said:
>
> > Pam <mr...@io.com> wrote in message news:<BB1F23A7.13307%mr...@io.com>...
> >
> > There are too many variables here. The slower moving students
> > are not necessarily less able to think, they need a different
> > set of presentations to motivate them, and possibly more
> > time to make the connections.
>
> That's because they are less able to think. The thought processes that most
> people figure out almost automatically, they don't do.
But there's a difference between people who have trouble because
they use different modalities and people who have trouble because
they just can't make generalizations. My daughter teaches
a kid with non-verbal learning disability and another kid who
has trouble with diagrams. They're both bright kids. Their
problems are different from those who have mental retardation
and who actually learn more slowly.
...
> >
> > Well, since you are an educator, educate me, instead of just giving
> > up. But I don't take your conclusions at face value. After all,
> > I think I know quite a bit about music education, and your
> > conclusions definitely don't apply there, so if you claim they
> > apply to math, you must overcome my skepticism by citing some studies.
> > And your difficulties following scientific reasoning makes
> > me doubt whether you can critically derive the correct conclusions
> > from these studies. But you're welcome to try.
>
> Okay, I'll try one last time. What you want to do in each grade level is
> identify the skills you want children to learn at that grade level, and make
> those the standard. The test and all curriculum materials are perfectly
> aligned with the standards (since Texas and CA call the shots on textbook
> contents). All of our textbooks have little notes in the margins saying
> which TEKS they correlate with.
How do you know that the test is aligned with the standards?
The standards talk about things like manipulatives and very few
tests actually require students to manipulate manipulatives, just
to cite one example.
...
>
> Now, as you know, I teach the gifted kids at a higher level, but they are
> not always really, really careful on the tests (which take some kids all
> day, for each test) so they make careless errors and may not do as well as
> more conscience but less talented kids. When I say all my kids passed --
> when last year several of them didn't -- it is certainly significant for me,
> and a great confidence-builder for them.
Going back to my earlier point. One way to teach the kids
at a higher level is to pose examples that might come in handy
later on. Like, for instance, those problems where you make
up a symbol (like *!@) to mean "take the first number and subtract
twice the second number". Now you ask them to calculate
things like 10 !*@ 4. For your younger kids, it's just another
way to get them to do a sequence of calculations, so it's
effective as an exercise in multi-step calculations, which is
on the objectives for some grade. But unbeknownst to them, it
also is something that's going to show up on the PSAT, so you're
simultaneously given them an exercise they need now *and* preparing
them for something that they're going to need later. To do that,
the teacher needs to be aware that they *are* going to need this later,
which was my point about why the teacher has to look ahead.
> ...
> > Look, there are lots of hypotheses for why one group performs
> > well in 4th grade and falls behind in 8th grade. (Even assuming
> > that 30% of the class being "proficient" constitutes performing well.
> > It may be well relative to other states, but it seems that if
> > most of the students aren't proficient in the subject, that
> > there's lots of room for improvement.)
> >
> > H1: The lower-grade teachers are just better at doing their
> > jobs than the upper-grade teachers.
>
> There's no question that we are.
I was hoping for something more like evidence than just an assertion
that this was true.
,,,
>
> >
> > H2: The standards for what should be accomplished in the lower
> > grades are suboptimal, encouraging strategies that are going to
> > have to be unlearned later on because they interfere with these
> > later concepts.
>
> Nope.
I was looking for something more like evidence than an assertion
that this was false.
>
> >
> > H3: The standards for what should be accomplished in the lower
> > grades are OK, but the tests don't actually test for these skills,
> > and therefore teachers are able to prepare students for these
> > tests via various shortcuts that cause them to do well on the
> > tests despite not having all the skills.
>
> Nope.
>
Ditto.
> >
> > H4: The teachers are qualified, the standards are correct,
> > and the tests are appropriate, but the student body contains
> > a higher proportion of students from cultures that devalue
> > higher education beyond a certain level.
>
> This makes it harder as they grow older, and less interested in pleasing
> their teachers. The world outside the classroom has more influence than it
> did, and if that world is part of a culture that does not value eduation
> highly, it will be more difficult to convince them that they ought to.
Nobody's arguing against the idea that H4 *could* explain
the results. I was asking you what was the evidence that
somebody had structured an experiment to determine that
H4 *did* explain the results better than H2 or H3 did.
...
> Carefully reasoned theoretical models are worthless -- it's what's cause the
> cycling fads of this century.
Exactly!!! That's why they have to be backed up by
*empirical data*!!!! And that's why I was asking
you whether *empirical data* had shown that more of
the decline in performance from 4th grade to 8th
grade was accounted for by H4 than by H2 or H3.
...
> > If you're going to state categorically
> > that H2 can never occur, or that the tests measure the skills by
> > definition, I am going to need more than just your bald
> > assertion that you're an experienced teacher and you just *know*
> > so much more than I do.
>
> Well, that will have to do, unless you want to do the research. I don't know
> why, if I was going to lie about something, I would decide to say that TEKS
> and TAKS were perfectly aligned (well, as much as they can be -- the TAKS
> doesn't test how well the kids use manipulative, for example, just pictoral
> models).
It isn't an issue of lying, it's an issue of stating
something as fact because it sounds nice to you, rather
than because it's been demonstrated empirically --- exactly
what you complain the look-and-say folks were doing.
If it has been empirically tested, show me.
Given a test and a skill set, how does a school
district evaluate the test to determine that
the test correctly measures the skills in the skill set?
Given alternative possible skill-sets 4a and 4b for
4th grade, and a skill set 8c for 8th grade, how
does a school district determine whether teaching
4a or 4b provides kids with a better head start
to reach 8c four years later?
--
Rob Strom
don't spam me]@slater.net Joe Slater
>Going back to my earlier point. One way to teach the kids
>at a higher level is to pose examples that might come in handy
>later on. Like, for instance, those problems where you make
>up a symbol (like *!@) to mean "take the first number and subtract
>twice the second number". Now you ask them to calculate
>things like 10 !*@ 4.
This is really stupid. It's like the "new math" we had when I was at school
where we were asked to calculate things in base 5. Base 5! This will
*never* be useful. There is a *small* benefit in being able to calculate in
other bases, but *only* in powers of 2. Even there, the benefit is pretty
low.
There is an accepted way to describe functions, and making up funny symbols
is not it. By all means ask kids to calculte f(10,4), where f(a,b)=a-2b.
Don't make up silly symbols - it's aggravating and pointless and leads to
mistakes like where I presumed that Pam's question about (x)^1 means ""x
raised to the first power".
If you really do get this sort of question on your exams then the
curriculum designers should be dismissed.
jds
Rob Strom
I disagree with almost everything you say here.
First of all, in real life, mathematicians define new names
and new symbols all the time. When you go to college,
and take math you
learn about the div and the curl and the dot product and
the cross product and all these things. Or they would
just come up and say "A *Cauchy* interval is one that ...."
or "A *Hausdorff* space is a space that has this property ..."
Second of all, telling them f(a, b) = a - 2b is at least as obscure
for a 4th grader (who isn't used to letters) as is telling them
I'm making up a symbol that means multiply the thing on the
right by two and subtract it from the thing on the left.
Third of all, kids at that age are just learning about how
names are arbitrary, and not an intrinsic part of the way
things are. So driving home the point in another way by
deliberately making up kooky names for things is actually
a way to reinforce a message they need to learn anyway.
> If you really do get this sort of question on your exams then the
> curriculum designers should be dismissed.
And another point is a very pragmatic one, namely that
in HS they will have to take SAT tests that have *exactly*
this sort of problem on it, so why not combine testing
them on computing a - 2b with giving them a skill that
will be useful in later life?
--
Rob Strom
don't spam me]@slater.net Joe Slater
>> is not it. By all means ask kids to calculte f(10,4), where f(a,b)=a-2b.
>> Don't make up silly symbols - it's aggravating and pointless and leads to
>> mistakes like where I presumed that Pam's question about (x)^1 means ""x
>> raised to the first power".
>I disagree with almost everything you say here.
>
>First of all, in real life, mathematicians define new names
>and new symbols all the time. When you go to college,
>and take math you
>learn about the div and the curl and the dot product and
>the cross product and all these things.
They don't define new names and symbols all the time. Mathemetians invent a
new symbol when there is a new class of operation to be performed, and one
which will be useful over a range of problems. Any mathemetician who
invented a symbol for "x+1" would be a fool. Furthermore, these kids are
studying arithmetic, not "how do I become a mathemetician". They need to
know math skills, not how to extend the frontiers of mathematical research.
>Second of all, telling them f(a, b) = a - 2b is at least as obscure
>for a 4th grader (who isn't used to letters) as is telling them
>I'm making up a symbol that means multiply the thing on the
>right by two and subtract it from the thing on the left.
Perhaps this teaches you that 4th graders shouldn't be doing this
nonsense.
>And another point is a very pragmatic one, namely that
>in HS they will have to take SAT tests that have *exactly*
>this sort of problem on it, so why not combine testing
>them on computing a - 2b with giving them a skill that
>will be useful in later life?
The SAT tests shouldn't have it either. To whatever extent there is a pont
in them having it, it should follow a substantial knowledge of other
functions.
jds
randy
> Doctors have finally started to realize that any significant loss of
> memory in old people is due to disease rather than old age.
> Age itself only causes minor deterioration of memory.
> Anything worse than that is due to stroke, Alzheimers, fatty blockage
> of carotid artery, etc.
>
> I was young at age 42, but now I'm old at age 47?
> Then at this rate I'd be mulch by age 50.
Really, I know how serious our physical problems can be. I hope you
know I was kidding. The only way I deal with pain myself is through
forcing a smile and weak jokes. :)
Incidently, I'm about to turn 50. Lots of people I work around are all
around 50. We all are beginning to go to seed....
randy
Mordecai!
Rob Strom wrote:
You might have noticed me playing patty cake with Christians about Trinity ... and explaining logic to them.
Logic is not confined to mathematics.
Now - in the "real world" most people including very intelligent people, professionals and engineers and scientists and
whatever - cannot create or understand very, VERY simple ideas like theories - or apply them. Most would not know a
philosophy as opposed to a religion. I had that argument with an atheist who wanted me to think every atheist had to
accept the philosophy of "rationalism" to be an atheist - but atheism at the same time was not a religion and had no
philosophical basis!
You say teaching children the tools they need later in life - how about teaching the children the tools they need later in
life!
They know how to regurgitate facts.
They know how to apply a formulae given to them by someone else to something that they know it applies to ...
But they cant figure out how to apply something from maths or science into a religious setting - or philosophy to a moral
question.
I remember trying to apply "proof by negation" to bob Felts who "I am an engineer and have been doing this since high
school" and left him spluttering how JtB came teaching JC ... (the contradiction was so blatant - I think he left the NG
because of it.) I did not kick him out ... I did not rub his nose in the problem. But he was not trained to think - despite
his brilliance.
You want to teach children an education. Damn I wish I had a better education - one that helped me prepare for life.
But what do you think I am doing HERE? Same thing you are doing - teaching adults how to think!
Now for the real problems with the education system.
Consider a place where the road system is handling twice the design capacity - so that the roads are clogged.
Think of the costs of road accidents ... of fuel, of time in transport - of resources in transport ... and the
infrastructure of roads.
The obvious solution? provide public transport which is cheap - or free for goodness sake - so convenient you keep the car
for local transport only.
How much would a PERSON save - if 20% of the car accidents did not occur - the cost on your health fund and insurance - how
much would you save?
In building new roads if the old ones were suddenly within design capacity? If the transportation costs were minimal in the
overall household budget?
If the time going to and from work became a time of rest rather than a time of stress.
Now - I postulated that the transportation of individuals was free - and paid for in tax payers dollars.
Can such a solution be sold to the general public?
Why not? It is in their interests - they would pay less overall each year ... Don't tell me? They would be paying a bigger
tax bill. Yeah - right!
That is the problem with the education system.
If people were educated - then how come they succumb to the sweet words of the advertisers and the politicians and the
others with invested interests?
If people could think ...
There is the education system applied to the real world. You have people able to be scientists or fill jobs - but you do
not have people able to think.
Thus the education system has been hijacked into a public service to provide skilled workers to industry - rather than
create a human resource of brilliance in their citizens. You do not have a politically - emotionally and morally astute
population.
Judaism teaches these things. Why the hell do you think Jews have such material success in the world?
Because these things pay off - BIG time.
----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==----
http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 Newsgroups
---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =---
Chris
<3F017FD7...@ace.net.au>:
<snip>
> There is the education system applied to the real world. You have people
> able to be scientists or fill jobs - but you do not have people able to
> think. Thus the education system has been hijacked into a public service
> to provide skilled workers to industry - rather than create a human
> resource of brilliance in their citizens. You do not have a politically -
> emotionally and morally astute population.
A politically, emotionally, and morally astute population would certainly
not keep voting to maintain the status quo now would they? How else do the
politicians keep their jobs?
> Judaism teaches these things. Why the hell do you think Jews have such
> material success in the world? Because these things pay off - BIG time.
--
Please visit http://www.jtf.org
Mordecai!
Chris wrote:
> On Tuesday 01 July 2003 07:34 Mordecai!("mldavis<pleasenospam) wrote in
> <3F017FD7...@ace.net.au>:
> <snip>
> > There is the education system applied to the real world. You have people
> > able to be scientists or fill jobs - but you do not have people able to
> > think. Thus the education system has been hijacked into a public service
> > to provide skilled workers to industry - rather than create a human
> > resource of brilliance in their citizens. You do not have a politically -
> > emotionally and morally astute population.
>
> A politically, emotionally, and morally astute population would certainly
> not keep voting to maintain the status quo now would they? How else do the
> politicians keep their jobs?
Israel?
>
>
> > Judaism teaches these things. Why the hell do you think Jews have such
> > material success in the world? Because these things pay off - BIG time.
>
> --
> Please visit http://www.jtf.org
----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==----
Rob Strom
> >Joe Slater <joe[please don't spam me]@slater.net> wrote in message news:<t3r1gvkenda7bf8dt...@4ax.com>...
> >> There is an accepted way to describe functions, and making up funny symbols
> >> is not it. By all means ask kids to calculte f(10,4), where f(a,b)=a-2b.
> >> Don't make up silly symbols - it's aggravating and pointless and leads to
> >> mistakes like where I presumed that Pam's question about (x)^1 means ""x
> >> raised to the first power".
>
> On 30 Jun 2003 21:51:08 -0700, st...@watson.ibm.com (Rob Strom) wrote:
> >I disagree with almost everything you say here.
> >
> >First of all, in real life, mathematicians define new names
> >and new symbols all the time. When you go to college,
> >and take math you
> >learn about the div and the curl and the dot product and
> >the cross product and all these things.
>
> They don't define new names and symbols all the time. Mathemetians invent a
> new symbol when there is a new class of operation to be performed, and one
> which will be useful over a range of problems.
And that happens frequently. This is an exercise in
understanding the concept of "introducing a definition".
That's not just math. It could be history: "An ex post facto
law means blah blah blah" (something that was just litigated in the USSC).
It could be law: "In this document 'the company' shall mean
Greaseball Insurance Company, Inc., their heirs and/or assignees".
> Any mathemetician who
> invented a symbol for "x+1" would be a fool. Furthermore, these kids are
> studying arithmetic, not "how do I become a mathemetician". They need to
> know math skills, not how to extend the frontiers of mathematical research.
First of all, you never know who is going to be extending
frontiers in the future.
Second of all, the are two fundamental concepts that are useful for
the future:
(1) the notion that the association between names and things
is both arbitrary and extensible. If you read Piaget's studies
of children, they don't know this at first. They think that
you couldn't add a rule to the game of marbles even if all
the players agreed ahead of time, and they think that you couldn't
change the names of things.
(2) the notion of composition. That not only are +, -, and * operators,
but you can also make new operators by putting them together.
Later on they can learn that sometimes you can exploit this fact
and even reverse the roles of primitive and derived operators.
In high school, we learned that you could define a new operator,
the "stroke" out of AND and NOT. And furthermore that if you
started with "stroke" instead of AND and NOT, you could actually
derive all logical operators just from stroke. In geometry (10th grade), we
learned that you could give the name "line" and "point" to other
things besides the things we ordinarily called "line" and "point"
and Euclid's axioms would still hold. And then the theorems
we proved would apply equally well to the other lines and points.
All of this couldn't have taken place without the foundation
having been laid earlier that you can make up definitions.
And you never know when introducing a symbol makes reasoning
easier. I seem to recall a great leap forward when somebody
decided that it was useful to introduce the operator that
turned v into sqrt(1 - v^2/c^2) and it really made a revolution.
>
> >Second of all, telling them f(a, b) = a - 2b is at least as obscure
> >for a 4th grader (who isn't used to letters) as is telling them
> >I'm making up a symbol that means multiply the thing on the
> >right by two and subtract it from the thing on the left.
>
> Perhaps this teaches you that 4th graders shouldn't be doing this
> nonsense.
>
It doesn't teach me this at all.
Trust me: there's a lot more nonsensical stuff 4th graders
are made to do that has a lot less to do with real life than this.
> >And another point is a very pragmatic one, namely that
> >in HS they will have to take SAT tests that have *exactly*
> >this sort of problem on it, so why not combine testing
> >them on computing a - 2b with giving them a skill that
> >will be useful in later life?
>
> The SAT tests shouldn't have it either. To whatever extent there is a pont
> in them having it, it should follow a substantial knowledge of other
> functions.
The SAT tests are (supposedly) tests of reasoning, not of
knowledge. And the concept being tested is exactly the
opposite of the one you're trying to convey. They want
to get across the idea that the set of functions you can
have is unlimited and open-ended because you can always
define new ones. You are arguing that someone should
decide the fixed set of functions that are age-appropriate
for someone to know, and stop there.
I'm not a fan of the SAT test, but in this case I would imagine
that the test designers have discovered that being good at doing these
make-up-a-symbol problems is correlated with future success
in math, engineering, or law, and since they are good
predictors they will keep using them.
--
Rob Strom
Chris
<3F019D7C...@ace.net.au>:
>
>
> Chris wrote:
>
>> On Tuesday 01 July 2003 07:34 Mordecai!("mldavis<pleasenospam) wrote in
>> <3F017FD7...@ace.net.au>:
>> <snip>
>> > There is the education system applied to the real world. You have
>> > people able to be scientists or fill jobs - but you do not have people
>> > able to think. Thus the education system has been hijacked into a
>> > public service to provide skilled workers to industry - rather than
>> > create a human resource of brilliance in their citizens. You do not
>> > have a politically - emotionally and morally astute population.
>>
>> A politically, emotionally, and morally astute population would certainly
>> not keep voting to maintain the status quo now would they? How else do
>> the politicians keep their jobs?
>
> Israel?
No, the good ole USA. No one seems to have a memory longer than the date on
the last newspaper when it comes to voting.
Pam
st...@watson.ibm.com on 6/30/03 7:18 PM said:
> Pam <mr...@io.com> wrote in message news:<BB22A2D3.133E1%mr...@io.com>...
>> in article abea7612.03062...@posting.google.com, Rob Strom at
>> st...@watson.ibm.com on 6/26/03 12:02 AM said:
>>
>>> Pam <mr...@io.com> wrote in message news:<BB1F23A7.13307%mr...@io.com>...
>>>
>>> There are too many variables here. The slower moving students
>>> are not necessarily less able to think, they need a different
>>> set of presentations to motivate them, and possibly more
>>> time to make the connections.
>>
>> That's because they are less able to think. The thought processes that most
>> people figure out almost automatically, they don't do.
>
> But there's a difference between people who have trouble because
> they use different modalities and people who have trouble because
> they just can't make generalizations. My daughter teaches
> a kid with non-verbal learning disability and another kid who
> has trouble with diagrams. They're both bright kids. Their
> problems are different from those who have mental retardation
> and who actually learn more slowly.
I am not talking about kids with learning disabilities per se -- those kids
get special services from special education. Sp ed is ONLY for kids who show
a 15 pt difference between their expected level of achievement based on IQ
tests, and the actual level of achievement. The slow kids I am talking about
are those who simply have low IQs -- they are not retarded, but they are
also not "bright kids" who have learning disabilities. Mostly they are kids
who either are not developmentally ready to learn something at the same
time, or same rate, as most kids, or who must be directly taught thinking
skills and strategies that come naturally to most kids. Here's an example:
when I was a kid I figured out the "make it simpler" strategy, in which you
substitute smaller numbers in a word problem so that you can more easily
visualize and/or draw a diagram of (another strategy) the problem. This does
not occur to slow kids, but they can be trained to do it.
>
> ...
>>>
>>> Well, since you are an educator, educate me, instead of just giving
>>> up. But I don't take your conclusions at face value. After all,
>>> I think I know quite a bit about music education, and your
>>> conclusions definitely don't apply there, so if you claim they
>>> apply to math, you must overcome my skepticism by citing some studies.
>>> And your difficulties following scientific reasoning makes
>>> me doubt whether you can critically derive the correct conclusions
>>> from these studies. But you're welcome to try.
>>
>> Okay, I'll try one last time. What you want to do in each grade level is
>> identify the skills you want children to learn at that grade level, and make
>> those the standard. The test and all curriculum materials are perfectly
>> aligned with the standards (since Texas and CA call the shots on textbook
>> contents). All of our textbooks have little notes in the margins saying
>> which TEKS they correlate with.
>
> How do you know that the test is aligned with the standards?
>
> The standards talk about things like manipulatives and very few
> tests actually require students to manipulate manipulatives, just
> to cite one example.
I did cite that example of an exception below. The test deals only with
pictoral models. Other than these things, I know that the test is aligned
with the standards because you can put them side by side and look at them.
>>
>> Now, as you know, I teach the gifted kids at a higher level, but they are
>> not always really, really careful on the tests (which take some kids all
>> day, for each test) so they make careless errors and may not do as well as
>> more conscience but less talented kids. When I say all my kids passed --
>> when last year several of them didn't -- it is certainly significant for me,
>> and a great confidence-builder for them.
>
> Going back to my earlier point. One way to teach the kids
> at a higher level is to pose examples that might come in handy
> later on. Like, for instance, those problems where you make
> up a symbol (like *!@) to mean "take the first number and subtract
> twice the second number". Now you ask them to calculate
> things like 10 !*@ 4. For your younger kids, it's just another
> way to get them to do a sequence of calculations, so it's
> effective as an exercise in multi-step calculations, which is
> on the objectives for some grade. But unbeknownst to them, it
> also is something that's going to show up on the PSAT, so you're
> simultaneously given them an exercise they need now *and* preparing
> them for something that they're going to need later. To do that,
> the teacher needs to be aware that they *are* going to need this later,
> which was my point about why the teacher has to look ahead.
My gifted kids could do that, but I don't see how that involves higher level
thinking skills. They would find it boring to do that. They must know how to
do multiple step calculations, but usually in the context of a word problem,
where they must identify the steps. I give them lots of training in this. I
also give them ordered pairs in an "in-out machine" like this:
5, 17
8, 26
3, 11
9, ?
They have to solve for the ? and write the "rule" on their white boards.
They like to make these up and see if others can solve them, too.
We don't use letters for variables, but empty boxes. They understand empty
boxes, and it's easy enough later on to substitute letters or weird symbols.
>>>
>>> H2: The standards for what should be accomplished in the lower
>>> grades are suboptimal, encouraging strategies that are going to
>>> have to be unlearned later on because they interfere with these
>>> later concepts.
>>
>> Nope.
>
> I was looking for something more like evidence than an assertion
> that this was false.
Look at the continuum. You have people vertically aligning the curriculum --
you don't have some people deciding what 4th graders are to learn, and some
other people deciding what 8th graders (and every intervening grade) will
learn.
>>> H3: The standards for what should be accomplished in the lower
>>> grades are OK, but the tests don't actually test for these skills,
>>> and therefore teachers are able to prepare students for these
>>> tests via various shortcuts that cause them to do well on the
>>> tests despite not having all the skills.
>>
>> Nope.
>>
>
> Ditto.
Like I say -- all you have to do is look at TEKS and TAKS and see that they
are aligned. Our textbooks are aligned. Everything is aligned.
>
> ...
>> Carefully reasoned theoretical models are worthless -- it's what's cause the
>> cycling fads of this century.
>
> Exactly!!! That's why they have to be backed up by
> *empirical data*!!!! And that's why I was asking
> you whether *empirical data* had shown that more of
> the decline in performance from 4th grade to 8th
> grade was accounted for by H4 than by H2 or H3.
You don't need to conduct a study to see that the TAKS tests the TEKS.
>>> If you're going to state categorically
>>> that H2 can never occur, or that the tests measure the skills by
>>> definition, I am going to need more than just your bald
>>> assertion that you're an experienced teacher and you just *know*
>>> so much more than I do.
>>
>> Well, that will have to do, unless you want to do the research. I don't know
>> why, if I was going to lie about something, I would decide to say that TEKS
>> and TAKS were perfectly aligned (well, as much as they can be -- the TAKS
>> doesn't test how well the kids use manipulative, for example, just pictoral
>> models).
>
> It isn't an issue of lying, it's an issue of stating
> something as fact because it sounds nice to you, rather
> than because it's been demonstrated empirically --- exactly
> what you complain the look-and-say folks were doing.
> If it has been empirically tested, show me.
<shrug> I don't know how much more obvious it could be either that TEKS is
aligned with TAKS, or that the TEKS are vertically aligned. All you have to
do is look at them side by side. If one of the TEKS is ordered pairs, and
the TAKS tests ordered pairs, that's alignment.
>
> Given a test and a skill set, how does a school
> district evaluate the test to determine that
> the test correctly measures the skills in the skill set?
By looking at them and seeing that everything that can be tested on a paper
& pencil test, is tested.
> Given alternative possible skill-sets 4a and 4b for
> 4th grade, and a skill set 8c for 8th grade, how
> does a school district determine whether teaching
> 4a or 4b provides kids with a better head start
> to reach 8c four years later?
There are no alternative skill sets. Texas tells us what to teach, and we do
it. The standards are carved in stone. They may get new stone tablets every
now and then, but whatever is carved on them is what we teach.
Pam
joe[please don't spam me]@slater.net on 6/30/03 9:10 PM said:
> On 30 Jun 2003 17:18:59 -0700, st...@watson.ibm.com (Rob Strom) wrote:
>> Going back to my earlier point. One way to teach the kids
>> at a higher level is to pose examples that might come in handy
>> later on. Like, for instance, those problems where you make
>> up a symbol (like *!@) to mean "take the first number and subtract
>> twice the second number". Now you ask them to calculate
>> things like 10 !*@ 4.
>
> This is really stupid.
It's stupid and it's boring. This would only fruitlessly confuse most kids,
and would bore the gifted ones who understood it.
Pam
joe[please don't spam me]@slater.net on 7/1/03 12:38 AM said:
>> Joe Slater <joe[please don't spam me]@slater.net> wrote in message
>> news:<t3r1gvkenda7bf8dt...@4ax.com>...
>>> There is an accepted way to describe functions, and making up funny symbols
>>> is not it. By all means ask kids to calculte f(10,4), where f(a,b)=a-2b.
>>> Don't make up silly symbols - it's aggravating and pointless and leads to
>>> mistakes like where I presumed that Pam's question about (x)^1 means ""x
>>> raised to the first power".
>
> On 30 Jun 2003 21:51:08 -0700, st...@watson.ibm.com (Rob Strom) wrote:
>> I disagree with almost everything you say here.
>>
>> First of all, in real life, mathematicians define new names
>> and new symbols all the time. When you go to college,
>> and take math you
>> learn about the div and the curl and the dot product and
>> the cross product and all these things.
>
> They don't define new names and symbols all the time. Mathemetians invent a
> new symbol when there is a new class of operation to be performed, and one
> which will be useful over a range of problems. Any mathemetician who
> invented a symbol for "x+1" would be a fool. Furthermore, these kids are
> studying arithmetic, not "how do I become a mathemetician". They need to
> know math skills, not how to extend the frontiers of mathematical research.
Yep -- it's ridiculous to say that this sort of thing should be gratuitously
introduced when most kids find it plenty challenging just to develop a solid
foundation in pretty basic math and arithmetic.
>
>> Second of all, telling them f(a, b) = a - 2b is at least as obscure
>> for a 4th grader (who isn't used to letters) as is telling them
>> I'm making up a symbol that means multiply the thing on the
>> right by two and subtract it from the thing on the left.
>
> Perhaps this teaches you that 4th graders shouldn't be doing this
> nonsense.
And the reason is that the curriculum is designed in large part to teach
children to identify which operations, steps, and strategies are needed to
solve real-world problems. Practical stuff that they really do need to know
and will use, not some useless parlor trick they might see on a college
entrance exam.
Rob Strom
>
> Yep -- it's ridiculous to say that this sort of thing should be gratuitously
> introduced when most kids find it plenty challenging just to develop a solid
> foundation in pretty basic math and arithmetic.
>
It's not at all gratuitous. I gave numerous examples of
the importance of the concept of definitions and introducing
definitions, and of disabusing them of the notion that
names are intrinsic properties of things and that things
are divided up into concepts in only one way.
> >
> >> Second of all, telling them f(a, b) = a - 2b is at least as obscure
> >> for a 4th grader (who isn't used to letters) as is telling them
> >> I'm making up a symbol that means multiply the thing on the
> >> right by two and subtract it from the thing on the left.
> >
> > Perhaps this teaches you that 4th graders shouldn't be doing this
> > nonsense.
>
> And the reason is that the curriculum is designed in large part to teach
> children to identify which operations, steps, and strategies are needed to
> solve real-world problems. Practical stuff that they really do need to know
> and will use, not some useless parlor trick they might see on a college
> entrance exam.
So many fallacies here. Start with the last first.
First of all, it's very odd for you not to consider something
that is needed for an entrance exam "impractical".
Second, your glib dismissal of the idea as a "parlor trick" implies
that you don't think that college entrance exams test things
that will actually be useful in college. A funny position to take for
someone who thinks that it's virtually axiomatic that Texas
tests the right skills, and that Texas skills prepare students for
what they need to learn the next set of Texas skills.
Finally, I totally disagree with the premise. We don't
limit our teaching to what is needed to solve a delimited
set of real-world problems. We don't even know what kinds
of real-world problems will exist when today's 4th graders grow up.
And even if we did, it's clear that we teach them
an appreciation of the world way beyond what they might
face in their possibly dull jobs. Otherwise, what use
are Shakespeare's sonnets or Steinbeck's novels
or Magellan's voyages or Churchill's slogans or
the electrochemical series? Will they help balance their
checkbook? Will they be writing their interoffice memos
in iambic pentameter? Will they get their next promotion
thanks to impressing their boss with their knowledge of
Ferenc Jozsef's imperial policy? Will a stockbroker
apply his knowledge of how to measure the heat of vaporization?
Will a physicist apply his knowledge of the causes of
the collapse of the gold standard? Will anybody but
classics teachers apply their knowledge of classics?
We don't teach kids parlor tricks. We teach them the history,
the mechanics, and the aesthetics of the world they live in,
and how it got that way and how to think and imagine
future worlds and how to get there. For some it will
inspire some thought, for others, it will shape their
moral viewpoint, and for others, it will just give them
a richer aesthetic experience.
Maybe after doing a few made-up operations, the kid
will have fun making up some operations of his own. You
never know what the result will be.
Cynics can make fun of anything.
--
Rob Strom
don't spam me]@slater.net Joe Slater
>> invented a symbol for "x+1" would be a fool. Furthermore, these kids are
>> studying arithmetic, not "how do I become a mathemetician". They need to
>> know math skills, not how to extend the frontiers of mathematical research.
On 1 Jul 2003 08:41:17 -0700, st...@watson.ibm.com (Rob Strom) wrote:
>First of all, you never know who is going to be extending
>frontiers in the future.
I presume that that will be after they have learned and grasped other
mathematic notation.
>Second of all, the are two fundamental concepts that are useful for
>the future:
>
>(1) the notion that the association between names and things
>is both arbitrary and extensible.
I commend this story to you:
http://www.sacred-texts.com/neu/eng/eft/eft43.htm
>The SAT tests are (supposedly) tests of reasoning, not of
>knowledge. And the concept being tested is exactly the
>opposite of the one you're trying to convey. They want
>to get across the idea that the set of functions you can
>have is unlimited and open-ended because you can always
>define new ones. You are arguing that someone should
>decide the fixed set of functions that are age-appropriate
>for someone to know, and stop there.
No. I argue that they should spend their time learning useful functions and
*proceed* from there.
>I'm not a fan of the SAT test, but in this case I would imagine
>that the test designers have discovered that being good at doing these
>make-up-a-symbol problems is correlated with future success
>in math, engineering, or law, and since they are good
>predictors they will keep using them.
I imagine as many as three impossible things before breakfast, but even so
I am unable to place quite so much faith in the SAT designers. They do this
because it's fashionable, just as they once favored Venn diagrams over
arithmetic or modular arithmetic over long division.
jds
Suzanne
"vince garcia" <vgga...@ix.netcom.com> wrote in message
news:3EFAF...@ix.netcom.com...
> Joe Slater wrote:
> >
> > >Joe Slater wrote:
> > >> Maccabees is not part of the Jewish canon. It's not even studied as a
book
> > >> dealing with our faith, any more than Jubilees or Enoch is.
> >
<vgga...@ix.netcom.com>
> > wrote:
> > >Today that is true, but in the 1st century it was accepted by many if
> > >not most jews.
> >
>
> maccabbees (genealogy) in his history of the jews, as one example, and
> I think he alludes to 2 macabbes 7 elsewhere. if these books were really
> obscure and not used by anyone i doubt they would have survived to be a
> part of the early christian canon
>
to be the same as Hannukah. It's located in these
verses, one from the Old Testament, and one from the
New Testament.
2 Ch. 7:9:
"And in the eigth day they made a solemn assembly:
for they kept the dedication of the altar seven days,
and the feast seven days."
John 10:22:
"And it was at Jerusalem the feast of the dedication,
and it was winter."
It is also in...
1 Macc. 4:52-59; 2 Macc. 10:5-8
Of course, Maccabees is Apocryphal, but the
verses about the Feast of Dedication is in the Bible
and is Chanukah. : )
>
Suzanne
don't spam me]@slater.net Joe Slater
<suzan...@altavista.remove.net> wrote:
>In the Bible the term "feast of dedication" is supposed
>to be the same as Hannukah. It's located in these
>verses, one from the Old Testament, and one from the
>New Testament.
>2 Ch. 7:9:
>"And in the eigth day they made a solemn assembly:
>for they kept the dedication of the altar seven days,
>and the feast seven days."
This isn't Chanuka, or at elast is not the modern Chanuka. Chanuka does
indeed mean "dedication", but the festival mentioned here was a single
event marking Solomon's dedication of the First Temple, not an annual
festival celebrating the defeat of Antiochus' forces by the Maccabees.
Solomon's festival took place in the week before Succos (the Feast of
Tabernacles) while the Maccabean one took place two months later.
jds
Suzanne
Hannukah. So that's all that I know. I am not a Ph.D. in
Hebrew. It's also in some Bible Dictionaries that way.
That's all I can tell you. If you say that's wrong, I leave
that with you as I can't quarrel with you, since I don't know
any more than that about it.
>
Suzanne
don't spam me]@slater.net Joe Slater
>> indeed mean "dedication", but the festival mentioned here was a single
>> event marking Solomon's dedication of the First Temple, not an annual
>> festival celebrating the defeat of Antiochus' forces by the Maccabees.
>> Solomon's festival took place in the week before Succos (the Feast of
>> Tabernacles) while the Maccabean one took place two months later.
On Mon, 21 Jul 2003 04:44:34 GMT, "Suzanne"
<suzan...@altavista.remove.net> wrote:
>According to a professor of Hebrew with a Ph.D., this is
>Hannukah.
As I said: the word itself is "Chanuka" but it's not the modern festival
known as Chanuka. What did your professor say?
>So that's all that I know. I am not a Ph.D. in
>Hebrew. It's also in some Bible Dictionaries that way.
>That's all I can tell you. If you say that's wrong, I leave
>that with you as I can't quarrel with you, since I don't know
>any more than that about it.
Fortunately I do. I bet that the Bible dictionaries do not in fact say that
it's the mdoern festival of Chanuka. WHy not tell me which ones and what
they say?
jds
Suzanne
professor of Hebrew and Old Testament studies, and who
got his degree from Johns Hopkins. He is the author of
many books in cluding Unger's Bible Handbook, and
Archaeology in the Old Testament (and - New Testament).
In Macc. 4:52-59 it is called "the dedication of the altar,"
and by Josephus (Ant. 12.7.7) "the feast of lights." He says
"it was a popular and joyous festival commemorating the
purifying of the Temple, the removal of the old polluted
altar, and the restoration of the worship of Jehovah by
Judas Maccabeus, 164 B.C."
>
He continues to explain it: "This feast began on the
25th Chisleu (December) and lasted eight days but
did not require attendance at Jerusalem. Assembled
in the Temple or in the synagogues of the places
where they resided, the Jews sang 'Hallel,' carrying
palm and other branches; and there was a grand
illuimination of the Temple and private houses. The
origin of the illumination of the Temple is unknown,
although tradition says that when the sacred
'lampstands' of the restored Temple were to be
lighted only one flagon of oil, sealed with the signet
of the high priest, was found to feed the lamps. This
was pure oil, but only sufficient for one day---when
by a miracle the oil increased, and the flagon
remained filled for eight days, in memory of which
the Temple and private houses were ordered to be
illuminated for the same period. No public mourning
or fast was allowed on account of calamity or
bereavement. The festival did not require anyone
to abstain partially or completely from his ordinary
occupation, and unlike some other celebrations it
was not marked by a holy assembly at the beginning
and the end. The celebration was always of a
joyous, exuberant character which commemorated
the restoration of the worship of the Temple
(1 Macc. 4:41-49). The similarty between this
festival and the 'feast of Booths' would seem to
indicate some intended connection between the two.
Without doubt, our Lord attended this festival at
Jerusalem (John 10:22). It is still observed by the
Jews." It says in this also that the word in Hebrew
for "Dedication, Feast of," is "hanukkah."
(New Unger's Bible Dictionary, page 422.)
>
I don't know what you mean by a modern celebration
of this festival, since it is rooted in something from
long ago. Please explain.
>
Kindest regards,
Suzanne