Paula Castagna
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>From: "Martha Haehl" <haehl@KCMETRO.CC.MO.US>
>To: "AMATYC list serve" <mathedcc@archives.math.utk.edu>
>Subject: Re: [MATHEDCC] Re: calculation skills (fwd)
>Date: Sat, 2 Jan 1999 10:41:24 -0500
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>Reply-To: "Martha Haehl" <haehl@KCMETRO.CC.MO.US>
>
>Hi all,
>
>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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