The Calculator!
Jason
again and I'll be taking Trigonometry. My question is, should i get a
graphing calculator for the class? If it will be of any help of all, I
would strongly consider buying one soon, and if you know of certain
makes/models that you find pretty efficient and easy to use, let me
know. Thanks for the help in advance.
The Denlingers
Well this may not be what you want to hear but I would suggest that you
learn how to do the work by hand (if possible) before using the
calculator.
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Nathaniel Silver
>Well, I'm an incoming Junior in High School when school get's going
>again and I'll be taking Trigonometry. My question is, should i get a
>graphing calculator for the class? If it will be of any help of all, I
>would strongly consider buying one soon, and if you know of certain
>makes/models that you find pretty efficient and easy to use, let me
>know. Thanks for the help in advance.
Recommendation: Buy the TI-89.
The TI-83 is good enough but the 89
is great for the next level and nice here too.
You will be at a great disadvantage without it
regardless if you are a strong student or not.
Quill
>Recommendation: Buy the TI-89.
>The TI-83 is good enough but the 89
>is great for the next level and nice here too.
>You will be at a great disadvantage without it
>regardless if you are a strong student or not.
>
>
>
Remember the good old days when all you needed to do Advanced Calculus was a
pencil a textbook and a slide rule.
Where I went to High School, graphing calcs were not allowed before Elem
Calculus.
When I got to college I watched my struggling classmates fumble around with
them during lecture because they couldn't remember what an arcsin function
looked like....
Something to think about...
da...@nospam.com
wrote:
>Well, I'm an incoming Junior in High School when school get's going
>again and I'll be taking Trigonometry. My question is, should i get a
>graphing calculator for the class? If it will be of any help of all, I
>would strongly consider buying one soon, and if you know of certain
>makes/models that you find pretty efficient and easy to use, let me
>know. Thanks for the help in advance.
Weeelll.... if your teacher decides that a course can be taught
without it, and proceeds to set up problems with that in mind, you are
OK. If, however, like hockey-players who wear suits of armour and
then decide to bash each other into the boards iinstead of showing
their skill with the puck, the teacher decides to use degrees,
minutes, seconds, radians, transformations, and the whole shebang
right from square one (foolish in my humble opinion), a graphing
calculator might be an asset. I like to be able to do the stuff
without, and then use a calculator only if absolutely necessary. It
is most useful *after* you have mastered the basics by manual labour.
It really depends upon the planned course, I suppose. Technique is
really more important than the arithmetic. Some problems of an
advanced nature are difficult not because it takes a long time to
graph them. Best ask your prospective teacher what the expectation is
for the course.
David.
Sean Manning
and understand fully your high school algebra. Graphics calculators are
designed for people who study complex math at university, for engineers and
for scientists etc, not for high school students!
The Denlingers wrote:
> Jason wrote:
> >
> > Well, I'm an incoming Junior in High School when school get's going
> > again and I'll be taking Trigonometry. My question is, should i get a
> > graphing calculator for the class? If it will be of any help of all, I
> > would strongly consider buying one soon, and if you know of certain
> > makes/models that you find pretty efficient and easy to use, let me
> > know. Thanks for the help in advance.
>
da...@nospam.com
wrote:
>Remember the good old days when all you needed to do Advanced Calculus was a
>pencil a textbook and a slide rule.
First of all, I'll agree with you.
Now, it might be wise to let this discussion end. Anyone who takes a
peek now and then in the alt.sci conference with see threads like this
going on endlessly with no resolution whatsoever, and essentially no
math or conclusive direction whatsoever. It is in fact a form of
spam. Anyone sincerely interested in this discussion though can find
endless comments in dejanews.
Just a thought.
David.
Stan Brown
rang...@sprynet.com (Jason) wrote in alt.algebra.help:
>Well, I'm an incoming Junior in High School when school get's going
>again and I'll be taking Trigonometry. My question is, should i get a
>graphing calculator for the class? If it will be of any help of all, I
>would strongly consider buying one soon, and if you know of certain
>makes/models that you find pretty efficient and easy to use, let me
>know. Thanks for the help in advance.
When I studied (and taught) trig, a calculator would be very helpful but
a graphing calculator would be useful very very seldom. I've never owned
one, and only rarely felt the need. A plain ordinary "scientific"
calculator, of course, is almost a necessity these days (since there are
no more slide rules to look up trig functions with).
On the other hand, if you're going on to calculus you may as well make
the investment now. Graphing calculators had not been invented when I
studied calculus, but I definitely would have welcomed one.
As several others have mentioned, you will profit most from trig if you
first do any graphing by hand, with paper and pencil, at least in rough
form. Use the graphing calculator to check your work, not to substitute
for it (except where speed is of the essence). By doing the rough work
with pencil and paper you will reinforce your understanding of how the
trig functions behave, and that will help you not only in trig but even
more in calculus.
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Steven Bradshaw
I ask because I have and graphing calculators are a valuable tool if used
correctly. There are lots of things that can be done with them that cannot
be accomplished with paper and pencil. In seconds, students can explore
what happens when the slope of line is changed or when intercepts change.
They can use the calculators to collect data and "discover" slope intercept
for themselves.
I am not suggesting that pencil and paper be done away with. I insist that
my students be able to graph without them, but their learning is enhanced
with the use of the graphing calculator.
Sean Manning <se...@nmd.ebina.fujixerox.co.jp> wrote in message
news:3797DE8A...@nmd.ebina.fujixerox.co.jp...
Elizabeth Stapel
>...graphing calculators are a valuable tool if used
>correctly...
And there's the rub: "if used correctly".
I worked at a tutoring service, and had to deal with
so many students who knew all about their calculators,
and didn't have a clue about the math. About the
worst experience was with a high-school senior: in
the course of working some problem, I asked him to
multiply 4 and 1/4. He stared at me like I was insane
and told me, "I can't; this calculator doesn't have a
fraction key!"
I am a tutor on an Internet tutoring service, and
recently dealt with a student who had zero clue how to
graph a simple quadratic function. She had to use her
graphing calculator, and even then had no idea what
was going on, because all she'd been taught was "punch
the buttons and look at the magic picture".
Yes, graphing calculators can be great (I've got one
myself, and use it preferentially), but there's a lot
to be said for teaching the students the math, too.
And, just so you know, that =was= a reactionary
statement that I just made. Here's was the bleeding
edge prefers:
"[W]e recommend introducing these [graphing calculator]
techniques as the primary methods for solving new types
of equations and inequalities. In other words, REQUIRE
students to rely on these methods for each new type of
equation and inequality that is presented in a
precalculus course, by simply not describing any other
means of solving the problem."
--from PRIMUS, Volume IX, Number 2, June 1999 issue
(emphasis in the original)
In other words: "Stop teaching the students the math.
Just tell them what buttons to push. It's the only
way they'll do it the politically-correct way."
And don't tell me that the students all prefer the
calculators. They've told me different.
Eliz. Stapel
(remove *nospam* to reply privately)
For math (mostly algebra) links, go to:
http://home.earthlink.net/~stapel
Nathaniel Silver
Where would these math-challenged students
be before the advent of powerful graphic calculators?
Calculators always help talented student the most.
I believe that most of the particular ludicrous
cases, described below, would be failures under
most any education system.
Elizabeth Stapel wrote
Raymond E. Griffith
----------
In article <7nl8ji$9pn$1...@bgtnsc03.worldnet.att.net>, "Nathaniel Silver"
<mat...@worldnet.att.net> wrote:
> The question one must ask is:
> Where would these math-challenged students
> be before the advent of powerful graphic calculators?
> Calculators always help talented student the most.
> I believe that most of the particular ludicrous
> cases, described below, would be failures under
> most any education system.
>
is that they would either
1) fail
2) be forced to cope and learn something.
Frankly, I agree with both Steven and Elizabeth's respective points of view:
>>Steven Bradshaw wrote:
>>
>>>...graphing calculators are a valuable tool if used
>>>correctly...
> Elizabeth Stapel wrote
>>
>>And there's the rub: "if used correctly".
<clip>
>>but there's a lot
>>to be said for teaching the students the math, too.
>>
>>And, just so you know, that =was= a reactionary
>>statement that I just made. Here's was the bleeding
>>edge prefers:
>>
>>"[W]e recommend introducing these [graphing calculator]
>>techniques as the primary methods for solving new types
>>of equations and inequalities. In other words, REQUIRE
>>students to rely on these methods for each new type of
>>equation and inequality that is presented in a
>>precalculus course, by simply not describing any other
>>means of solving the problem."
>>
>>--from PRIMUS, Volume IX, Number 2, June 1999 issue
>>(emphasis in the original)
>>
>>In other words: "Stop teaching the students the math.
>>Just tell them what buttons to push. It's the only
>>way they'll do it the politically-correct way."
Elizabeth's spin on the PRIMUS article is probably correct. There are a lot
of "educators" that are trying to respond to lower achievement by lowering
the barrier to success. By requiring students to rely on a tool they hope
that more students will achieve success in algebra and algebra-based math.
The attempt will be seen as a significant failure later, when many students
will have been sacrificed on the altar of expediency.
Please note: I am a calculator user and fanatic. I have taught its uses and
secrets to other instructors in statewide organizations. But you cannot use
a tool when you do not understand the problem, and this is what I am seeing
in a lot of students.
The problem may be summed up like this: many students do not have the
ability to generalize. Generalization is the ability to infer general rules
from specific facts. That is, to take a section of knowledge and push it
forward.
I have never seen a student who had trouble performing basic arithmetic on
paper ever perform well in algebra. The calculator does not help these
students. Oh they can multiply large numbers more accurately, but they
cannot seem to understand WHY they should multiply. There is an intrinsic
barrier of thought that separates arithmetic from algebra. Algebra
generalizes. Arithmetic is specific. Algebra recognizes classes of problems.
Arithmetic does not.
By not requiring students to be able to perform basic computations in
arithmetic (including fractions) quickly and accurately both mentally and on
paper, these students are being deprived of the ability to know a subject
well enough to generalize it. Generalization is a result of a fairly
complete knowledge. Whenever gaps in the background appear, the ability to
generalize fades.
And no tool can overcome that barrier. The calculator only helps those who
understand what it is doing to begin with.
My students are all required to have calculators. The calculators do not
overcome their basic deficiencies. I try to teach them to visualize, but
they are unable to do so if the requisite thought processes of
generalization do not exist.
Just my 2 cents worth.
Raymond E. Griffith
Stan Brown
>There are lots of things that can be done with them that cannot
>be accomplished with paper and pencil. In seconds, students can explore
>what happens when the slope of line is changed or when intercepts change.
That *can* be done with paper and pencil -- not in seconds, maybe, but in
a reasonable time.
The problem with doing it the easy way from the beginning is that I fear
students will not really understand slope and intercept if it just means
punching buttons on a calculator. I think working examples with pencil
and paper forces you to focus on them in a way that punching buttons does
not.
A more mundane example: multiplying 6.4 times 4.3 and getting 2.752. A
student who works with pencil and paper might make the same errors, but I
think she would be less likely to do so. When you do arithmetic by pencil
and paper, you learn to think "the answer should be upwards of 6x4 = 24,
but less than 7x5 = 35." When you have always depended on the calculator,
you are much less likely to develop an "unreasonableness detector".
Two notes: (1) I can't prove any of the above; it's my feeling. (2) I am
*not* advocating dispensing with calculators; they have their place as
long as they are used for mechanical work after understanding has been
acquired.
>They can use the calculators to collect data and "discover" slope intercept
>for themselves.
I know it is periodically the fashion for students to "discover" things
for themselves. I am firmly convinced -- based on wide reading and on my
own experience teaching classes in several different ways -- that that
fashion serves all or almost all students very badly. It is simply hugely
inefficient to let them blunder about making "discoveries" that the
teacher wants them to make. They can do much better much faster with the
guidance of a decent textbook and a decent teacher (preferably both). And
the good students will discover things for themselves anyway, but they
will be real discoveries, made because they enjoy playing with number and
symbol. We've seen examples on a.a.h from time to time. I remember how
pleased I was to discover, before I knew any algebra, that the squares of
integers increase by an amount that itself increases as double the
integer. I was only a bit crestfallen to discover the following year that
that's simply (x+1)^2 = x^2 + 2x + 1.
--
I don't need e-mail copies of posted follow-ups, but if you send
Stan Brown
alt.algebra.help:
>I worked at a tutoring service, and had to deal with
>so many students who knew all about their calculators,
>and didn't have a clue about the math.
Every couple of weeks we get a query from some student who thinks that
because it comes out of the calculator it must be correct. Think about
0^0 and i^i, for instance.
Elizabeth Stapel
>alt.algebra.help:
>>I worked at a tutoring service, and had to deal with
>>so many students who knew all about their calculators,
>>and didn't have a clue about the math.
bra...@mindspring.com (Stan Brown) wrote:
>Every couple of weeks we get a query from some student
>who thinks that because it comes out of the calculator
>it must be correct. Think about 0^0 and i^i, for instance.
No need to get fancy! Think about 2*3. My husband was
tutoring a student, and spent twenty minutes trying to
convince the student that he had pushed the wrong button,
and that 2*3 really truly honestly wasn't 5.
Stan Brown
>tutoring a student, and spent twenty minutes trying to
>convince the student that he had pushed the wrong button,
>and that 2*3 really truly honestly wasn't 5.
Twenty minutes?
Why didn't he just have him work the problem again, and see that he came
up with 6? I can think of few better ways to convince a student that "the
calculator is always right" is an error.