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Drake, Michael – Mathematics Teaching, 2012
The author tells the story of an exploration he undertook, what he learned, and the questions he was able to answer as a result. Thinking, on the part of the learner, is complex, far from explicit, and some might say intangible. But, by recognising certain "clues" it might be possible to begin to understand how different types of thinking…
Descriptors: Mathematics Instruction, Mathematical Logic, Mathematical Concepts, Thinking Skills
Handa, Yuichi – Mathematics Teaching, 2009
Many high-school mathematics teachers have likely been asked by a student, "Why does the cross-multiplication algorithm work?" It is a commonly used algorithm when dealing with proportion problems, conversion of units, or fractional linear equations. For most teachers, the explanation usually involves the idea of finding a common denominator--one…
Descriptors: Geometric Concepts, Equations (Mathematics), Algebra, Mathematics Instruction