Mathematical Understanding and Multiple Representations
Representation is a strong tool to help understand mathematical concepts. Representation comes in a lot of different forms. For example, drawing a rough sketch to solve a word problem, or plotting points on a graph to see how a function looks. One of the author's main convincing point in his argument is the experiment Tchoshanov performed in Russia. To be honest, I do not find the results of this experiment surprising. I believe that a student who is able to put his thoughts(sketches) on paper combined with strong analytic skills will excel greatly compared to students who are only strong in one suit. An example of a mathematical representation would be the blocks used for teaching kids how to count. Kids are able to count quickly if they learn to represent 10 blocks as the 1 long stick, or to represent 100 blocks as the big flat piece. Another example they use is the different ways of presenting a set of 20 dots. On the left, the 20 dots are scattered and in no particular pat...
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