Re: meeting the needs of today's students
Gary Helmer (helmerg@OPERATNS.MOHAWKC.ON.CA)
Mon, 3 Feb 1997 18:40:41 -0500
Well thank you Wayne Mackay! You happened along with your posting just
in time tosave me from expressing my frustration with the ongoing
discussion of quadratics. While the discussion of 19th and 20th century
algorithms and proofs is interesting, I agree with Wayne that none of
that is what we should be "pushing" in math education, with the possible
exception of courses for students whose future will be mathematics.
Not only with respect to quadratics and factoring, but with most topics
in college mathematics, the availability of tools like graphing
calculators and the various computer algebra software packages makes it
possible for us to significantly update the mathematics curriculum. The
new curriculum (call it reformed if you wish) must change the emphasis
of what we do. The trend must be away from teaching algorithmic
techniques and towards more understanding and problem solving. My
experience (and perhaps a bit of a guess) is that typically, about 70%
of course time is devoted to teaching and practicing mathematical
technique - such as factoring quadratic trinomials, leaving only 30% of
course time for understanding mathematical concepts and their
application to real world problem solving. My feeling is that with
readily accessible computers and modern software like Derive for Windows
and Scientific Notebook (I'm not advertising, and recognize there are
other good CAS packages), we can reverse those numbers. Not only does
the technology take care of the "grunge" work of manual solution
techniques, but it also provides a means to explore and better
understand the concepts involved.
The question is, what should we change and how should we change it?
Gary Helmer
Wayne Mackey wrote:
>
>SNIP
... what I mean by teaching factoring is teaching the PROCESS of
> finding factors. So what would be meant by teaching factors? Clearly
> teaching factors would mean teaching what factors ARE rather than some
> algorithm for finding factors. SNIP
> As long as the overwhelming majority of American mathematics education
> consists of teaching "how to" instead of understanding, it is not goin to
> matter at all whether we teach students how to factor trinomials on paper
> or on a calculator or computer. It also won't matter whether we teach them
> how to factor trinomials or how to gather data and put it into a graphing
> calculator or how to approximate the real roots of a polynomial by looking
> at the graph.
>
> In an attempt to end(hooray) on a slightly more positive note, it has been
> my experience that students are, in general, perfectly willing and able to
> learn to understand, communicate, and apply the concepts of mathematics if
> it is made clear to them that in order to pass the course they must do
> those things. This does of course imply that the teacher can no longer get
> by with just working examples and homework problems in class. It is my
> fervent hope that that won't bother many of the math teachers. Sorry this
> was so long.
>
> Wayne F. Mackey
> SCEN #301
> University of Arkansas
> (501) 575-7661
> wmackey@comp.uark.edu
--
Gary Helmer helmerg@operatns.mohawkc.on.ca