Research about Definitions in Mathematics Teaching and Learning

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The article referenced at the end of this essay is excellent.  Please read it.  Most of the comments in this essay are rooted in that article. In the opening paragraph the authors point out that throughout an individual’s mathematics education teaching the language of mathematics is an essential aspect of learning mathematics. Mathematical vocabulary affords

Explaining the Roles of Definitions in Mathematics VI

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Role #6: They facilitate applications.    See 21 Feb blog. If the model for a “word” problem is the equation it should be recognized as a linear equation in one variable (because it matches the definition of a linear equation in one variable) then any one of the general properties known about linear equation is one