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April 6, 2010

K-12 Math: The Separate Path and the Well Travelled Road

Barry Garelick:

It explores two different approaches to math; one is representative of the fuzzy math side of things, and the other is in the traditionalist camp. I make it clear what side I'm on. I talk about how the fuzzy side uses what I call a "separate path" in which students are given open ended and ill posed problems as a means to teach them how to apply prior knowledge in new situations. I present two different problems, one representing each camp.

The math may prove challenging for some readers, though high school math teachers should have no problems with it.

Much has been written about the debate on how best to teach math to students in K-12--a debate often referred to as the "math wars". I have written much about it myself, and since the debate shows no signs of easing, I continue to have reasons to keep writing about it. While the debate is complex, the following two math problems provide a glimpse of two opposing sides:

Problem 1: How many boxes would be needed to pack and ship one million books collected in a school-based book drive? In this problem the size of the books is unknown and varied, and the size of the boxes is not stated.

Problem 2: Two boys canoeing on a lake hit a rock where the lake joins a river. One boy is injured and it is critical to get a doctor to him as quickly as possible. Two doctors live nearby: one up-river and the other across the lake, both equidistant from the boys. The unhurt boy has to fetch a doctor and return to the spot. Is it quicker for him to row up the river and back, or go across the lake and back, assuming he rows at the same constant rate of speed in both cases?

The first problem is representative of a thought-world inhabited by education schools and much of the education establishment. The second problem is held in disdain by the same, but favored by a group of educators and math oriented people who for lack of a better term are called "traditionalists".

Posted by Jim Zellmer at April 6, 2010 5:45 AM
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