Calculator Dependence.
Mark
world where calculators are ubiquitous, read William Kohl's guest essay on
calculator dependence.
http://irascibleprofessor.com/comments-06-07-06.htm
Sincerely,
Dr. Mark H. Shapiro
Editor and Publisher
The Irascible Professor
http://irascibleprofessor.com
Dave L. Renfro
> Before you tell your students that learning arithmetic is
> unnecessary in a world where calculators are ubiquitous,
> read William Kohl's guest essay on calculator dependence.
>
> http://irascibleprofessor.com/comments-06-07-06.htm
Do you *really* believe any teachers tell their students
this? I'm sure some students may say that their teachers
tell them this, but that's a different issue altogether.
Dave L. Renfro
Mark
Some schools introduce calculators as early as the third grade, well before
students have mastered the basics of arithmetic.
Dr. S.
"Dave L. Renfro" <renf...@cmich.edu> wrote in message
news:1149778409.8...@i40g2000cwc.googlegroups.com...
Bob LeChevalier
>Some schools introduce calculators as early as the third grade, well before
>students have mastered the basics of arithmetic.
They also introduce dictionaries, and spell-checking on the computer,
before students have mastered the basics of spelling. That does not
mean that they are telling kids that learning spelling is unnecessary.
Students may come up with the idea that it is unnecessary, but the
teachers aren't telling them so.
lojbab
Cary Kittrell
> Dave,
>
> Some schools introduce calculators as early as the third grade, well before
> students have mastered the basics of arithmetic.
>
BRING BACK THE SLIDE RULE!!
No, I'm serious. Or at least semi-serious:
One of my main complaints, not only with calculators but
with the teaching of arithmetic in general, is that
one learns to crank out results without having to
develop an intuition as to the approximate magnitude
of the correct result -- we're not taught to estimate,
to guess order-of-magnitude, to develop that intuition
that allows you to look at an answer and realize
"That cannot be right; I must have made some
mistake". Although I am definitely of the
pre-calculator generation, I often wonder if
today's kids realize when they've made some
mistake in punching the buttons, resulting
in a silly answer.
A virtue of the slide rule was that it gave you
only the digits; you had to keep track of the
decimal place for yourself. Perhaps there
ought to be some kind of teaching calculator,
one where the student would similarly be relived
of the burden of the mechanics of arithmetic
operations, but where the result would always be
presented with an arbitrary decimal placement --
or even with no decimal point -- and the
student required to provide the magnitude
of the answer on his own. For example:
13 X 252 => 3.276
I don't think it would be too much to ask
the kids to learn to estimate whether
the correct answer is 32.76, 327.6, 3276
or 32,670.
-- cary
Gray Shockley
(in article <e6c9us$ceo$1...@onion.ccit.arizona.edu>):
> In article <KeKdnUa4JqNtYRXZ...@adelphia.com> "Mark"
> <mshapiro2@nospam -adelphia.net> writes:
>> Dave,
>>
>> Some schools introduce calculators as early as the third grade, well before
>> students have mastered the basics of arithmetic.
>>
>
> BRING BACK THE SLIDE RULE!!
>
> No, I'm serious. Or at least semi-serious:
>
> One of my main complaints, not only with calculators but
> with the teaching of arithmetic in general, is that
> one learns to crank out results without having to
> develop an intuition as to the approximate magnitude
> of the correct result -- we're not taught to estimate,
> to guess order-of-magnitude, to develop that intuition
> that allows you to look at an answer and realize
> "That cannot be right; I must have made some
> mistake". Although I am definitely of the
> pre-calculator generation, I often wonder if
> today's kids realize when they've made some
> mistake in punching the buttons, resulting
> in a silly answer.
After months and months of number-crunching and "homework" ("barracks' work?)
where the constant refrian was, "You're not here to learn to design circuits
but . . . ", we finally got to Mr Paul's class where he stated: "I don't even
want to see a calculator in this class; I want you to learnhow to see a
figure and - in a couple of seconds - know that it is the wrong answer. You
can be off by 50% nearly all the time and you can spot the error. The
calculator works for you - you work for your sergeant and your lieutenant and
not that breakable under stress calculator."
> A virtue of the slide rule was that it gave you
> only the digits; you had to keep track of the
> decimal place for yourself. Perhaps there
Dad and I were talking about calculators one time and he, offhandedly,
mentioned that many people were against students using slide rules (this was
in the early 1930s) because (1) they were so expensive and (2) they kept
students from learning to do the math.
> ought to be some kind of teaching calculator,
> one where the student would similarly be relived
> of the burden of the mechanics of arithmetic
> operations, but where the result would always be
> presented with an arbitrary decimal placement --
> or even with no decimal point -- and the
> student required to provide the magnitude
> of the answer on his own. For example:
>
> 13 X 252 => 3.276
>
> I don't think it would be too much to ask
> the kids to learn to estimate whether
> the correct answer is 32.76, 327.6, 3276
> or 32,670.
Mr Paul would have said multiply 10 x 252 which is 2,520
so the answer is 3,276.
In the 1950's Dad was doing something or anudder (not a cow college) and I
was looking at his slide rule. I asked him why the rule was yellowish and the
slide was a perfect white. He laughed and said that the slide wore out and he
had to get a new one from Keuffel & Esser and that the new slide was
something like ten times what he had, originally, paid for the slide rule.
Interesting enuff, "K&E" is nowhere on the slide rule; that musta come later.
The other thing stamped in is, "PAT.APRIL 1'24". In these 50 years, the slide
is now almost the shade of the rule. But one can still "tickle the ivories"
with it. <dux>
> -- cary
++ gray
Gary Schnabl
> On Fri, 9 Jun 2006 12:08:44 -0500, Cary Kittrell wrote
> (in article <e6c9us$ceo$1...@onion.ccit.arizona.edu>):
>
>> In article <KeKdnUa4JqNtYRXZ...@adelphia.com> "Mark"
>> <mshapiro2@nospam -adelphia.net> writes:
>>> Dave,
>>>
>>> Some schools introduce calculators as early as the third grade, well before
>>> students have mastered the basics of arithmetic.
>>>
>> BRING BACK THE SLIDE RULE!!
>>
>> No, I'm serious. Or at least semi-serious:
I still remember those big trig and log tables in high school/college
(and beyond) and am glad to not need them short of a power failure for
my computer or missing my "solar" powered scientific calculator.
But again, I was schooled in an era when we really learned arithmetic
and reading text-based material, when phonetics education was universal,
when being taught axiomatic geometry and calculus courses in high
school/college were the norm, and when we were actually taught our non
dumbed-down courses by competent teachers who weren't constantly
bitching about not being overpaid enough (and, fortunately for those
teachers, were not universally dissed).
Gary
Dave L. Renfro
Gary Schnabl wrote:
http://groups.google.com/group/misc.education/msg/bed857ef919e3d8f
> I still remember those big trig and log tables in
> high school/college (and beyond) and am glad to not
> need them short of a power failure for my computer
> or missing my "solar" powered scientific calculator.
I've always thought it was interesting that texts
continued to include these tables throughout the 1980's
(and maybe even into the early 1990's), long after
no one was ever using them. Well, *almost* no one.
I sometimes used them to help students understand
certain concepts in a more concrete fashion. For
example, properties of logarithms such as
log(ab) = log(a) + log(b) and log(a^b) = b*log(a)
become more personalized when you spend a few
minutes using log tables to perform a numerical
computation such as the fifth root of 3500 times
the cube root of 260. Also, the rule that
10^log(a) = a gets reinforced when you're using
the antilog tables.
I once gave a talk at a T^3 (Teachers Teaching
with Technology) conference whose theme was a
little antithetical to the party line. One part
of my talk dealt with the topic "What has Technology
Subtracted?", and before giving a number of examples
(such as logarithm tables), I said:
Technology has made a number of previously taught
topics obsolete. Some of these obsolete topics were
useful for their reinforcement of facts that we
wanted students to know very well, some of these
topics were useful for their development of mathematical
thinking, and some of these topics do not appear
to have any significant merit beyond their necessity
before present technology.
I focused on these two areas:
A. Topics that Reinforce Certain Facts
There are several topics that once reinforced certain
mathematical facts, but no longer do so in the presence
of current technology. The impact of these omissions
has less effect on the teaching of gifted students
than on the teaching of average ability students,
since the former require less drill and practice.
Nonetheless, I often encounter very talented students
who display some striking weaknesses. I suspect that
these weaknesses are primarily caused by less drill
due to the omission of these topics.
I discussed "Numerical calculations with logarithm
tables", "Calculating square roots", "Arithmetic
operations with rational numbers", "Estimation,
consistency, and exact values", and then posed
the question: "Do we want students to be as proficient
with these skills as they once were? For those
skills in which the answer is "YES", what should
we include in the curriculum to give our students
the necessary drill?"
B. Topics that Develop Mathematical Thinking Skills
The presence of graphing and symbolic calculators has
turned some problems whose solution once involved higher
order thinking skills into drill problems.
I discussed "Curve sketching" and "Algebraic and numerical
computations". In the latter, I discussed the re-enforcement
of algebraic facts in simplifying numerical computations,
such as rewriting 5*7*11*2 as (5*2)*(7*11) and (3.8 x 10^-7)/5
being evaluated via (380 x 10^-9)/5 = (10)(38)/5 x 10^-9
= (2)(38) x 10^-9 = [(2)(30) + (2)(8)] x 10^-9
= 76 x 10^-9 = 7.6 x 10^-8). Then I posed the question:
"How do we compensate for the absence of topics
that once required higher order thinking skills,
but no longer do so?"
> But again, I was schooled in an era when we really
> learned arithmetic and reading text-based material,
> when phonetics education was universal, when being
> taught axiomatic geometry and calculus courses in
> high school/college were the norm, and when we were
> actually taught our non dumbed-down courses by
> competent teachers who weren't constantly bitching
> about not being overpaid enough (and, fortunately
> for those teachers, were not universally dissed).
Without getting into the other things you said,
I disagree with the part about calculus. In the
last 10 or 20 years many, many more U.S. high school
students (as a percentage of the population, even)
have taken calculus than in the decades before this.
My high school didn't even offer calculus (well into
the early 1980's, I think), but they do now. I think
you'll find the number of high school students taking
AP-calculus is far higher in recent years than it
was 30 or more years ago, before calculators were
in general use. Now, the question of whether this is
a good thing or not is another issue, one that is
often brought up by college faculty who have to
deal with students that took calculus in high school
and then wind up not_even_placing_into_precalculus.
By the way, I thought Cary Kittrell's idea (in this
thread) of a calculator that forces students to
determine the power-of-ten order of a computation was
a great idea. I think it has significant potential
(financial and educational), and she should
consider approaching a calculator company about it.
Dave L. Renfro
Dave L. Renfro
> One part of my talk dealt with the topic "What has
> Technology Subtracted?", and before giving a number
> of examples (such as logarithm tables), I said:
>
> Technology has made a number of previously taught
> topics obsolete. Some of these obsolete topics were
> useful for their reinforcement of facts that we
> wanted students to know very well, some of these
> topics were useful for their development of mathematical
> thinking, and some of these topics do not appear
> to have any significant merit beyond their necessity
> before present technology.
>
> I focused on these two areas:
>
> A. Topics that Reinforce Certain Facts
[snip]
> B. Topics that Develop Mathematical Thinking Skills
For completeness, I should add that I also discussed
C. Topics that can be left out
and then I went through the same three areas in the second
part of my talk, "What has Technology Added?". An example
of topic C (generalized to things that will probably
be irrelevant several decades from now as technology
becomes "smarter" and more user-friendly) is all the
calculator-dependent graphing menu knowledge a student
needs to be familiar with ("trace", turn off STAT-PLOTS
when graphing y = f(x), various ZOOM options, etc.).
Dave L. Renfro
Gary Schnabl
>
> Without getting into the other things you said,
> I disagree with the part about calculus. In the
> last 10 or 20 years many, many more U.S. high school
> students (as a percentage of the population, even)
> have taken calculus than in the decades before this.
> My high school didn't even offer calculus (well into
> the early 1980's, I think), but they do now. I think
> you'll find the number of high school students taking
> AP-calculus is far higher in recent years than it
> was 30 or more years ago, before calculators were
> in general use. Now, the question of whether this is
> a good thing or not is another issue, one that is
> often brought up by college faculty who have to
> deal with students that took calculus in high school
> and then wind up not_even_placing_into_precalculus.
>
AP calculus need not be axiomatically based and usually isn't. The bloom
is off the AP craze so much so that better colleges like Harvard now do
not accept any AP scores lower than 5. Still, many colleges today accept
AP scores of 3, 4, or 5. There's a huge difference between a 3 and a 5.
An honors curriculum usually teaches more depth and retention than the
"mile-wide, nanometer-deep" AP curricula.
Those HS students taking the lower quality AP calculus (especially when
not axiomatic based) do not receive the mathematical education you seem
to think they do. And because of AP, they do not take the higher quality
courses they would have otherwise taken. Therefore, they're worse off
academically. But what the hell--getting a good education doesn't matter
to many of today's crowd...
Lehigh doesn't seem to have high regard for HS AP courses: "Placement
and Advanced Placement Credit & Calculus Readiness Test"
"There is a big difference between calculus study at Lehigh and calculus
at most high schools. A solid high-school precalculus course is
necessary background for calculus at Lehigh. Students need a strong
foundation in functions (forms, graphs, roots) and trigonometry to
really thrive in calculus. Most students who take calculus in high
school are accustomed to using a graphing calculator. Calculators are
not permitted in Lehigh calculus classes. Lehigh has very high
standards, and calculus students are expected to learn calculus without
relying on calculators. Many students find a summer course in calculus
at a local community college to be helpful in bridging from high school
mathematics to Lehigh calculus."
"We recommend that students consider beginning Lehigh calculus a
semester below their advanced placement. If you have credit for Math 21
and are eligible for Math 22, consider taking Math 21; if you have
credit for Math 21 and Math 22 and are eligible for Math 23, consider
taking Math 22. You will relinquish some or all of your AP credit, but
experience has shown that many AP courses do not provide adequate
preparation for calculus at Lehigh."
BTW, Lehigh accepts AP grades 4 or 5.
Herman Rubin
Bob LeChevalier <loj...@lojban.org> wrote:
>"Mark" <mshapiro2@nospam -adelphia.net> wrote:
>>Some schools introduce calculators as early as the third grade, well before
>>students have mastered the basics of arithmetic.
>They also introduce dictionaries, and spell-checking on the computer,
>before students have mastered the basics of spelling. That does not
>mean that they are telling kids that learning spelling is unnecessary.
>Students may come up with the idea that it is unnecessary, but the
>teachers aren't telling them so.
Computers and calculators, properly used, can help
understand what arithmetic means; this is far more
important than being able to do it. Mastery of
base 10 arithmetic does not add to understanding
of the integers.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
laraine
I don't think it's really the calculator that
is the only problem here--I don't think people
always gain the skill of estimating until
they have more experience, or unless
it is emphasized to them.
Even without the calculator, someone
in high school might, instead of thinking
about the problem, just draw the graphs
first, and look at them, rather than make
up a table.
Yet it also sounds like the student in
this particular case would feel a bit
lost if he ever misplaced his calculator
because it does all the calculations for him.
You would think that one could figure out
the square of a small number without a
calculator.
BTW, these graphing calculators seem
to average at least $100! Thought I saw
some when they first came out that
were only ~$50.
C.
laraine
But, you know, if the calculator had a
grid on the screen, and one could overlay
one plot over another, the student might be
right that it is easier to solve the problem
that way. One could even overlay y=x**2
on it as well.
I see Casio makes some less expensive
models.
C.