I hope everyone had a great holiday season. I did.
This email hit one of my soap boxes. It seems to me that we still need to
determine how to teach a number sense to students who use calculators. The
problem with "the good old days" where the student worked the problem out by
hand first, implies that the problem had nice numbers in it. Don't get me
wrong. I think students should know their multiplication tables and be able
to estimate answers to messy arithmetic problems and understand the
magnitude of numbers, but I do not see us doing a good job of teaching such
thinking abilities even if we teach Basic Math without calculators--because
the primary focus in most courses is to teach pencil and paper skills using
nice numbers.
I just talked to a parent of a third grader whose teacher was having her
students add 7 and 9 using a calculator. Outrageous!!!! However, third
graders SHOULD use calculators to help them determine each U. S. citizen's
share of the national debt and discuss how that compares to each taxpayer's
share and each family's share--and how long it would take their family to
pay off their share at an additional x-amount per year. Unfortunately, we
still define much of mathematics as the algorithmic skills themselves and
live by the myth that if students get the skills, and can work
overly-simplified word problems closely related to a particular skill, that
they can use mathematics in life and on the job. If you think that is true,
check out your colleagues with Masters degrees or higher in non-mathematical
fields (most of whom passed college algebra with a C or higher) and see if
they can tackle mathematical reasoning. Most of them were at least above
average in math classes.
Learning arithmetic skills without a calculator no doubt teaches reasoning
better than learning to use a calculator for arithmetic. However, taking
calculators away from students and focusing as we have traditionally almost
entirely on the arithmetic itself does not generally build reasoning
abilities in students.
For 20 years we have had the wrong debate about calculators in arithmetic
class--whether to allow them or not to allow them. We need to change the
debate to "How can we teach mathematical reasoning and number sense to
students who use calculators?" We had an easy solution on the number sense
question for students who used slide rules. We have a tougher challenge for
students who use calculators--but I think those of us who learned by the old
school should have enough reasoning abilities to come up with new and good
solutions.
Martha
-----Original Message-----
From: Rob Kimball <rlkimbal@WTCC-GW.WAKE.TEC.NC.US>
To: AMATYC list serve <mathedcc@archives.math.utk.edu>
Date: Friday, January 01, 1999 11:33 PM
Subject: [MATHEDCC] Re: calculation skills (fwd)
>
>The eng tech list serve has a discussion on going
>much like the discussion that the amatyc list sere
>had a couple of weeks ago--studetn abilit or the lack
>theirof.
>
>Here is a message that should be of interest to us
>especially those who teach two-year tech degree students.
>...
>Robert L Kimball 919-662-3602 (Office)
>Chair, Mathematics and Physics Dept 919-266-0850 (Home)
>Wake Technical Community College Raleigh, NC 27603-5696
>
>---------- Forwarded message ----------
>Date: Tue, 22 Dec 1998 22:10:06 +0000
>From: Mark E. Furber <mfurber@computer.org>
>To: ET List <etd-l@OIT.EDU>
>Subject: Re: calculation skills
>
>> Date: Mon, 21 Dec 1998 16:07:05 -0500
>> From: steve ryan <s_ryan@tec.nh.us>
>> Organization: NH Technical Institute
>> To: ET List <etd-l@OIT.EDU>
>> Subject: calculation skills
>> Reply-to: s_ryan@tec.nh.us
>>
>> Maybe it's just that I've got end-of-the-semester grading on the brain,
>> but it seems to
>> me that some (many?) of my students would either not be in a technical
>> program or
>> might be doing much better if not for the calculator. For so long, the
>> slide rule provided
>> a real litmus test: if it was not mastered, then goodbye, don't let the
>> door hit you on the
>> way out. It also encouraged one to understand and set up a problem
>> thoroughly, to avoid
>> having to recalculate. It forced assessment of order of magnitude, and
>> it limited significant
>> figures. I am not advocating a return to the slide (I used mine to work
>> through an exam
>> a few months ago and it almost killed me), but I am planning to assign
>> some "naked"
>> problems in class next semester. No books, no notes, no calculator.
>> Just make some
>> estimates, dredge the brain, work it out on paper. Skip the
>> forest-for-the-trees obstacles
>> and get them to really think about the question and solution. I'd
>> appreciate hearing other
>> thoughts on this issue.
>>
>
>
>
>
>As one of Professor Ryan's former colleagues, having taught in the EET/CPET
>department at NHTI during 1996-1997, I agree with his observation. I am not
>suffering from any end of the semester grading fatigue, since I now work,
once
>again, for a defense contractor.
>
>My observations were that the traditional college-age students I
encountered at
>NHTI:
>
>1. Could not estimate orders of magnitude and did not pay attention to the
>nature of the answers they calculated. They therefore could not find gross
>errors (such as using 10^6 instead of 10^-6) in their work.
>
>2. Were resistant to the concept of memorization, even for basic values or
>relationships. In the electronics field, you should not have to look up
Ohm's
>law. Period. You also should know what "a factor of 3 dB" means without
>having to calculate anything.
>
>3. Did not use calculators to assist them in their calculations, but rather
to
>do their calculations for them. This is the way they are taught in their
math
>courses, at least as the NHTI math faculty explained it to me, and it is
not
>the way one would do things with a slide rule.
>
>A simple example: A phase locked loop problem requires solving an equation
>something like f = k/RC for C, given a target for f and values for R and k.
>
>The old way: Solve the equation by hand in your lab notebook for C = k/fR,
>put in the numbers and turn the crank, writing down some intermediate
results.
>The only thing computational aids do for you here is make turning the crank
>more efficient, and the approach with a simple calculator is the same as
with a
>slide rule. You still see how the calculation is performed, and if nothing
else
>you can see how the exponents work out and get an idea of whether C is
>nanofarads or picofarads. Anyone who gets megafarads (and I have seen that)
>will have a problem finding the component he wants in even a well-equipped
lab.
>
>Today's way: Get a calculator that solves equations, type in the equation,
>press the "Solve" key and write down the number that appears on the
display.
>You don't see the process, you just get an answer. If you do get an answer
in
>megafarads and suspect that something is wrong, it is hard to back up and
see
>what happened and where, since there is no paper trail.
>
>As a attempt to counter this problem, and just to be odd, I used to give
>electronics tests with "essay questions." No calculations required at all.
An
>example in an introductory electronics course: "You have a dual trace
>oscilloscope, an ohmmeter and a roll of duct tape. Explain how to measure
the
>AC collector current in the transistor amplifier shown." This can be
answered
>easily with a few sentences and a sketch or two.
>
>I also gave oral exams, where students had to convince me they understood
>something by talking it through with me on the board, with chalk, for 10
>minutes or so. No calculators, notes, books or computers allowed, or
needed.
>
>This approach does produce tests that are more time consuming to administer
or
>grade, but I found it quite effective at identifying students who did not
know
>what was going on, and that was my real goal. A "pass or fail" test to
identify
>students in trouble.
>
>A better solution, of course, would be to have the engineering technology
>faculty closely involved with the prerequisite math courses, so they can
make
>sure that students receive appropriate preparation. The subjects and
techniques
>that some mathematicians, or mathematics education faculty, want to teach
may
>not be what we need ET students to know. I suspect, however, that manpower
>considerations and academic turf issues would work against such an approach
in
>most institutions.
>
>Mark E. Furber
>
>
>
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