"The Role of Computers in Mathematics Teaching and Learning"
I appreciated the fact that this article categorized the various ways in which technology is changing the mathematics classroom, and differentiated between technology that is truly beneficial to students and technology that is simply another "gadget" for students to deal with. Often, a lot of focus goes toward the fact that technology has rendered some pencil-and-paper methods unnecessary. To some, this is seen as a benefit; to others, as the beginning of a trend toward a system of uninformed, uneducated students. Personally, I find the argument against technology based on the idea that calculators discourage students from learning basic math facts to miss the point of technology use. While I agree of course that there are students (and teachers) who misuse the calculator and other forms of technology--the article states that "using computers frequently and for lower level skills (e.g., drill and practice) may be detrimental to students"--there are many activities and problems which would be far too tedious to complete using only traditional methods. In this way, technology is truly changing the face of mathematics, as the article claims. Students who can use a calculator or a computer program to perform complex calculations almost instantly can use those calculations as part of much deeper, richer investigations than could students of yesteryear, who had to perform all calculations by hand.
I myself have experienced problem-solving situations where technology helped me understand the problem better than I could have otherwise, making technology more than just "a curricular add-on." For instance, with GSP I can generate and test conjectures extremely quickly--I usually find myself asking ten more questions about a problem situation while I'm searching for a solution to just one. As the article states, the immediate feedback of programs such as GSP lets students easily notice unusual phenomena in a dynamically changing environment, rather than trying to come up with conjectures about a set of tediously generated discrete cases. I can easily see on GSP that no matter what I can think of to do to a triangle, the interior angle sum remains 180°, whereas without such a program, I would have to create many different triangles and measure and add their interior angles before I could make such a conjecture. Of course, even with GSP, seeing a lot of examples doesn't constitute a proof, but the first part of writing a proof is deciding on something interesting to prove. GSP makes the process of investigation and exploration much easier and more enjoyable for students--certainly a major benefit of this technology.
I am curious about the author's opinion of technology other than computer programs, such as electronic remote response systems, graphing calculators, Smart Boards, etc. The article focuses entirely on computer and calculator use in the mathematics classroom, so I wonder what ideas might also apply to other forms of technology.
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