Re: [MATHEDCC] Graph paper

Lillie Crowley (lillie@POP.UKY.EDU)
Tue, 03 Mar 1998 08:45:51 -0500

Yes, I think you should allow graphing calculators in high school. I
recently was trying to help my nephew with his high school algebra II
homework -- he goes to one of the better high schools in San Antonio,
Texas. He was finding roots and finding f(x) for, say, x = 3, 4, etc.
using synthetic division (!). He'd gotten confused and was finding f(3),
etc. the old fashioned way, by evaluating the function. They were using
synthetic division to factor equations (fourth and fifth degree
polynomials) and stuff. I asked him if he knew what the zeros were on a
graph. He didn't, of course, so I dragged out my graphing calculator and
got it to sketch the graphs of a couple of them. Best I could tell, all he
is seeing in that course is a series of disjoint algorithms. Lots of
routine manipulations. No connections.

Lillie

At 07:38 PM 2/27/98 -0800, The Old Pro (Jim C. Gajniak) wrote:
>>Date: Wed, 25 Feb 1998 19:39:58 -0800
>>To: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
>>From: "The Old Pro (Jim C. Gajniak)" <jgajniak@ix.netcom.com>
>>Subject: Re: [MATHEDCC] Graph paper--use it (or not)
>>
>To RWW Taylor and to others on this list:
>
>At the high school where I teach
>Algebra and Geometry, our schools provide
>graphic calculators only for the "higher level" classes.
>
>For Algebra and Pre-Algebra classes, Scientific calculators
>are provided to calculate square roots, trig ratios,
>to add or subtract, multiply or divide fractions,
>to change from standard number notation to "scientific
>notation", etc.
>
>
>I guess I'm old fashioned and slow to change; in Algebra-I and also in
>Pre-Algebra, I require the students to:
>
>(1) start with some equation which I provide
>(2) develop an x-y data table of "values"
>(3) choose 8-10 "x-values" with 4 or 5 negative x's.
>(4) manually plot the 8 or 10 points from the data table
>(5) connect the points to get a straight line or
> a parabola
>(6) then, make some conjectures about the equation
>and try to see if or how the equation gives any hints
>about what the shape and/or the location of the function
>will be.
>
>I believe that it's still
>OK for today's students to begin to "feel" and to "see"
>how certain equations give certain plots, and to
>be able to construct/draw the graphs independent of the
>graphic calculator.
>
>>From time to time, when I've allowed students to draw the
>graphs on lined paper, most of the time, what
>they "draw" is fairly removed from what the actual
>graph looks like; so I keep returning to graph
>paper.
>
>In California, our State Math Framework, recommends the use of graph paper
>for high school Algebra (now called "Integrated Math"); I'm not sure what
>percent of our teachers
>use graph paper, but I think that I will poll our
>15 teachers and report back on what they are doing.
>
>The question I have for readers of this list; do you
>think it's OK for students to use Graphic Calculators
>while they are in high school???
>
>Regards,
>
>The Old Pro
>
>
>
>
>>
>>At 10:02 AM 2/25/1998 -0500, you wrote:
>>>
>>> I would like to ask a question concerning current instructional
>>>practices among the individuals contributing to this list. Specifically,
>>>to what extent and in what ways do you use _graph paper_ in conjunction
with
>>>teaching of graphing?
>>>
>>> While some of my colleagues here at NTID believe strongly in having
>>>students "develop a feel" for plotting points by actually setting up axes
>>>on a sheet of graph paper and marking down points with given (or
determined)
>>>coefficients, and some still have students carry out the plotting of (say)
>>>a parabola point by point, I myself have not touched graph paper (nor
>asked my
>>>students to) for some years now. The explorations that can be carried
>out with
>>>a graphing calculator (which we require of all our students), combined
>with the
>>>experience and insight to be gained from producing an acceptable _sketch_
>(on
>>>plain paper) of what one sees in the calculator window -- a report of what
>>>_ought_ to be showing if the calculator could produce a perfect graph --
>>>together allow me to get at all the areas of understanding that I used to
>>>depend on the use of graph paper to develop in students.
>>>
>>> In fact I now find the use of graph paper (or the use of lined
>>>notebook paper functioning as "half-graph" paper) to be _limiting_. I
>find it
>>>much more satisfactory to have students practice setting up approximate
>(but
>>>fairly accurate) scales of their own, and estimate positions of points and
>>>shapes of curves "by eye", rather than having them automatically follow
the
>>>blue lines.
>>>
>>> But I've always been the radical in this department! Every department
>>>needs one, but also needs a degree of control. I've had to retreat in
>the past
>>>from positions I've taken and experiments I've tried, and in general am
>happy
>>>to bow to wisdom from my colleagues. Perhaps I have gone off the deep
>end here
>>>again. What is your take?
>>>
>>>RWW Taylor
>>>National Technical Institute for the Deaf
>>>Rochester Institute of Technology
>>>Rochester NY 14623
>>>
>>>>>>> The plural of mongoose begins with p. <<<<
>>>
>>>P.S. I have no financial stake in this issue, having long ago sold off
>>> all my stock in graph-paper-printing comapnies. :-)}
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>
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Lillie R.F. Crowley
Professor, Mathematics
138 Moloney Building
Lexington Community College
Cooper Drive
Lexington, KY 40506-0235

(606) 257-2797 Phone
(606) 257-4988 Fax
lillie@pop.uky.edu e-mail
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