Tag Archives: conceptual understanding

NCTM Process Standards vs CCSS Mathematical Practices

The NCTM process standards, Adding it Up mathematical proficiency strands, and Common Core State Standards for mathematical practices are all saying the same thing but why do I get the feeling that the Mathematical Practices Standards is out to get the math teachers. The NCTM’s process standards of problem solving, reasoning and proof, communication, representation, and connections describe for me… Read More »

Levels of math teachers expertise

Math teachers expertise can be characterized in three levels: The teachers at Level 1 can only tell students the important basic ideas of mathematics such as facts, concepts, and procedures. These teachers are more likely to teach by telling. For example in teaching students about the set of integers they start by defining what integers… Read More »

Why negative times a negative is positive

Among the ‘rules’ for working with negative numbers,  the most counter intuitive is “negative times a negative is a positive”. It is easily forgotten especially if it was learned by rote. It is also not an easy ‘rule’ to make sense of so it needs to be learned with conceptual understanding. Here’s my proposed lesson for… Read More »

Using cognitive conflict to teach solving inequalities

One way to teach and assess students understanding of math concepts and procedures is to create a cognitive conflict. Here is one way you can create cognitive conflict in solving inequalities: To solve the inequality x – 7 > 5, the process usually involve adding 7 to both sides of the inequality. This process uses… Read More »

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