Author Archives: chapelhillmathcircle

When (Not) to Give a Hint

The other night my 10-year old son came to me for help with a word problem involving volume. It was late at night and I was tired. I could’ve given him a hint about how to solve it, or even … Continue reading

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The Three Stages of the Problem-Solving Cycle

Essentially every problem-solving heuristic in mathematics goes back to George Polya’s How to Solve It; my approach is no exception. However, this cyclic description might help to keep the process cognitively present. A few months ago, I produced a video … Continue reading


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Making “Maths” Make Sense

When I was in the process of publishing Math Makes Sense!: A Constructivist Approach to the Teaching and Learning of Mathematics!, my oldest daughter saw the cover the publisher had sent for my approval. “Dad”, she shrieked in disbelief, “that title … Continue reading

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Problem-Solving Pedagogy

As a math circle leader or math teacher, there are some basic pedagogical principles that must be observed. First, watch this 4-min video about my heuristic to problem-solving: The 3-Step Problem-Solving Cycle. The three steps are understanding, strategizing, and implementing. These … Continue reading

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