The ideas presented in this article came about as a response to a perfectly awful third grade text book lesson which my wife was forced to present when she was student teaching. The lesson was intended (I suppose) as an introduction to algebraic concepts.Without any motivation or other rationale, the text introduced a problem:
If 3 × X = 12 what is X?This was followed by a description of the standard algebraic procedure for solving the problem:
Divide both sides of the equation by three;
"Cancel" the "3"s on the left hand side;
Divide 12 by 3;
Conclude that X = 4.
This procedure was described by a sequence of diagrams, each showing the next step in the transformation. The authors of the text were clearly under no ill
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