My sentiments exactly. We have teachers who teach challenging courses as
well as teachers who dumb down courses with or without technology. I think
we "dumbed dowm" mathematics years ago when we took out logic and
understanding of proof--leaving the Pre-calculus mathematics a hollow shell
of algorithms that students memorized but did not understand.
Back to the question I posed my College Algebra class last summer: If we
factor x^2 - x - 6, which of the following wrong answers are the "best"
answer?
a. (x + 3)(x - 2)
b. (x - 6)(x + 1)
c. (x - 2.9)(x + 2)
31 students chose (a) and 1 student chose (c). They were amazed when we
compared the answers graphically. From the traditional focus on the
algorithm of factoring, they had missed a very important mathematical
concept--that manipulation of an expression gives an equivalent expression.
Checking out what that means with a number of test points or by graphing
has been too tedious to incorporate into the classes as a method to check
the answer, so they seldom, if ever, discussed or worked with the overlying
concept.
By making the algorithms of algebra, and not the concepts, the primary
focus of pre-calculus mathematics, we have indeed dumbed down mathematics
long before technology hit the market. Unfortunately, if we continue to
make the algorithms of algebra (or calculus) the focus of the course, we
dumb down mathematics even more with technology because the algortihms are
not the challenge they used to be. When discussing technology and its
impact, truly we can, for the first time in 30 to 200 years, change the
focus of mathematics and discuss pure mathematical concepts at lower levels
than previously possible as well as do real-life mathematics.
Martha
Ed wrote:
>I want to add the following thoughts:
>Teaching mathematics well with hand-held technology requires learning on the
>part of the teacher. Beginners make mistakes in their craft. All that you teach
>must be re-thought in light of using hand-held technology as a teaching tool.
>Conference sessions and short courses help us take advantage of what others
>have learned. Some teachers don't or can't take advantage of this professional
>development and must learn on their own. The point is that we must "learn" how
>to teach mathematics. We must learn how to teach for understanding -- with or
>without the use of hand-held technology. But certainly, teaching with hand-held
>technology is not the reason that some students come to your class only knowing
>mindless button pushing. It was a teacher who didn't understand his/her craft.
>(Or maybe didn't care about the craft of teaching.)
>
>No matter how I look at teaching with hand-held technology it presents
>interesting challenges that some master and others don't. Kind of the same as
>teaching without technology. Some teachers may see challenges as obstacles and
>fail to learn good teaching. Some in our ranks may never teach well with
>technology, just like some will never teach well without technology.
>
>I wonder if the teacher who use to tell students to memorize algorithms is the
>same teacher telling students to memorize keystrokes and use programs blindly
>without understanding? I am reminded of another posting I made to this list
>when I overheard the TA telling a student who came in for help that the student
>would probably never understand the quadratic formula but that he should
>"learn" it for the next test. This kind of teaching takes place with or without
>the use of hand-held technology.
>
>Ed Laughbaum
>
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