Mathematical knowledge is only powerful to the extent to which it is understood conceptually, not just procedurally. For example, students are taught the three ways of solving a system of linear equation: by graphing, by substitution and by elimination. Of these three methods, graphing is the one that would easily make sense to many students. Substitution, which…

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In my post Arithmetic and Algebra, I wrote that it’s how you solve a problem that tells whether you are doing algebra or arithmetic, not the problem itself. Here’s a description of algebraic thinking that I think teachers in elementary school mathematics might find useful especially when they are teaching about numbers and number operations:…

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There are at least three representational systems used to study function: graphs, tables and equations. But unlike graphs and tables that are used to visually show the relationships between two varying quantities, students first experience with equation is not as a representation of function but a statement which state the condition on a single unknown quantity. Also,…

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