You have probably been puzzled at various times in your teaching career by the thinking strategies that students appear to use to solve problems. It is difficult for most of us to understand that many students do not use reasoning patterns that seem obvious to us. Many students substitute numbers into a formula they remember even though the formulas may not be applicable to the problem at hand. This situation quite naturally leads us to wonder about the reasoning that students utilize when we would employ mental operations such as separating variables, excluding an irrelevant factor, or applying a mathematical relationship such as ratios.

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Module 1 - How People Reason - Overview

The Mr. Short / Mr. Tall Puzzle