Nancy
At 04:53 PM 4/30/97 -0400, you wrote:
>Here we go again on the big debate--which is important enough to resurface
>many times. When we arbitrarily say students have to "learn the stuff"
>before using the graphing calculators, etc., we continue to focus
>mathematics instruction on the procedures surrounding the nice, factorable
>functions. Since most of our students do not take classes beyond an
>algebra class, we teach them the misconception that mathematics is a study
>of procedures. The procedures that we mostly focus on have little to no
>use--I have tried for 5+ years to find non-contrived real-life uses of a
>factorable function or the rational function with nice coefficients and
>have failed miserably.
>
>Solving systems of equations are very important, but why do the 2x2 systems
>always fit in a standard window? Why do the 3x3 systems always have nice
>coefficients and the answers generally come out just as nice? The problems
>need to change to make good use of calculators.
>
>If we teach factoring, why not teach a simplified verstion of the rational
>root theorem at the intermediate algebra/beginning algebra levels so that
>students can estimate roots of the graph and use the roots to help them
>make factoring choices? At very least, students can use the graph and
>concept of identity to check whether factoring, simplification,
>multiplication, etc. is correct. When comparing the graph of the factored
>vs. non-factored forms of the expression, there is no partially correct
>answer--either the original expression and the answer graph out to be the
>same, or the answer is wrong. If the expression has more than one
>variable, the students can use the straight-up calculations feature to test
>points a few values to see whether the question expression and answer
>expression seem to be identities. We can use the calculator to train the
>student to build in checks and balances--let's ween them off of the back of
>the book.
>
>We do a disservice to the few students who do go on to higher levels of
>mathematics. At the lower levels, they also are allowed to think that
>mathemtics is the study of manipulation skills and 10 minute applications.
>The graphing calculator allows us and them to focus on mathematical
>concepts. A graphing calculator can help broaden the concepts that we
>already teach as well as bring higher level concepts to lower level
>classes. However, overlaying a graphing calculator over a very traditional
>"focus on the procedures" course can have the effect of dummying down the
>class.
>
>Where does data collection and curve fitting or real-life problem solving
>that involves REAL-life numbers and functions fit into the curriculum or
>these courses? To point to a recent discussion, why should Johnny factor
>at the expense of understanding percent change, looking at raw data and
>producing a function that approximates the data? Why would anyone in their
>right mind study curve fitting and real-life problems and real-life very
>large and very small real numbers without using technology? Why would
>anyone in their right mind study behaviour of polynomial and rational
>functions and limit their study to the nice functions that can be analyzed
>easily with pencil and paper techniques?
>
>Even students who are struggling with basic arithmetic skills can study
>mathematical concepts of the real world along with adding, subtracting,
>multiplying and dividing. We too many times assume that a student cannot
>think mathematically or apply mathematics before they become skilled at a
>myriad of procedures. The truth is, when students learn mathematics from
>in-context use which often requires the use of technology, students can
>then learn to think mathematically and make sense of the procedures.
>
>By refusing to "let" students use technology, we short change them by
>focusing mathematics so much on abstract procedures and contrived
>substitutes for applications that they miss out on a lot of usefull as well
>as theoretical mathematics.
>
>Martha
>
>>In a message dated 97-04-30 00:49:16 EDT, you write:
>>
>><< The WAMATYC conference was also this last weekend, 212 participants seems
>> to ring a bell. One of the topics discussed was the extent to which
>> graphing technology should be integrated into intermediate algebra. The
>> panel that discussed the issue seemed comfortable with graphing
>> calculators in calculus and pre-calculus but questionable in
>> intermediate. What do you all think? >>
>>
>>I think that they should be used in Intermediate Algebra for *demonstrations
>>and simulation* purposes only. Actually letting the students use them at
>>this point in their young math careers will cause them to become too
>>dependent. They students really need to learn to do stuff by hand first.
>>
>>I think the calculators should be first introduced to the students (for use
>>on exams and homework) in some of the freshman level courses: Pre-calc,
>>business calc, stats, etc.
>>
>>I teach a pre-calc course using the TI-85....... but I test my students with
>>and WITHOUT their calculators! My students have told me that if I hadn't
>>done this (ie tested them without), they would have become addicted to the
>>calculator and wouldn't have learned to do the stuff themselves.
>>
>>Karen
>>Orange Coast College
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>
>Martha Haehl
>Maple Woods Community College
>2601 N. E. Barry Rd.
>Kansas City, Missouri 64156
>
>(816)437-3147
>
>
>
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Nancy J. Sattler
Curriculum Chair
Terra Community College
2830 Napoleon Road
Fremont, OH 43420
phone:419-334-8400, ext. 179
fax: 419-334-9414
email: nsattler@terra.cc.oh.us
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