Exercise is good for you

‘Practice makes perfect’ is a commonplace phrase, but like most commonplace phrases, it is an over simplification. Certainly an expert has to put in lots and lots of practice, but the psychology of successful exercising involves a particular flow of energy. The mathematics has, in some way, to inspire the learner to want to practice. […]

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Square Removal

A select few of us gathered for a double session at the latest Mathematical Association conference. Attention was drawn to two actions involving squares. Action 1 Start with two or more squares drawn side by side in a line (on the left below).     Now use the long edge to form a square adjacent […]

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Doing & Undoing

Do you have any learners who finish their work quickly and then make a nuisance of themselves disturbing others who have not completed the work? Do you have disaffected or disengaged learners in your classes? Do you have learners who are unmotivated mathematically? One way to address both of these situations is to challenge learners […]

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Rolling fog

Have you ever said something to a class and felt something like a fog of non-understanding rolling towards you from the class? It has happened to me many times. Sometimes, especially if I am near the end of the session, I acknowledge the fog-of-non-comprehension but keep going; other times I pause and ask people to […]

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Conjecturing Atmosphere

Mathematical thinking can only take place in what I call a conjecturing atmosphere. This means that everything that is said is treated as a conjecture that may require modifying. If you disagree with someone you “invite them to modify their conjecture” or you ask how their conjecture applies to some example (which perhaps you think […]

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