Category Archives: Math investigations

What is cognitive conflict approach to teaching?

According to Piaget, knowledge is constructed when a learner encounters input from the environment and incorporates the new experiences to his/her existing schemes and mental structures (assimilation). When this new assimilated information conflicts with previously formed mental structures, the result is called disequilibrium – a cognitive conflict. This state of disequilibrium motivates the learner to… Read More »

Teaching combining algebraic expressions with conceptual understanding

In Math investigation about polygons and algebraic expressions I presented possible problems that students can explore. In this post, I will share some ideas on how the simple investigation of drawing polygons with the same area can be used as an introductory lesson to teach operations with algebraic expressions with meaning and understanding. Like the rest of… Read More »

Math investigation lesson on polygons and algebraic expressions

Understanding is about making connection. The extent to which a concept is understood is a function of the strength of its connection with other concepts. An isolated piece of knowledge is not powerful. To understand mathematics is to make connections among concepts, procedures, contexts. A lesson that has a very good potential for learning a well-connected… Read More »

Solving systems of equations by elimination – why it works

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… Read More »

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