Everyone is immersed in algebra because algebra is the expression and manipulation of generality. Whenever a generality is present, algebra is present too; wherever a generality is manipulated or varied, algebra is taking place. Whenever you purchase something, you are immersed in algebra. As a customer, you are interested in the final price, whereas the […]

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‘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. […]

Read moreA 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 […]

Read moreDo 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 […]

Read moreWhat do learners think mathematics is actually about? Their opinion is likely to be developed from the sorts of tasks they are given to do in lessons: getting well known answers to collections of tasks assigned by teachers. Do they ever see someone thinking mathematically – and realise that that is what is happening? Are […]

Read moreWhen this question arises, I have a habit of immediately replying “because it is absolutely essential in the oil industry.” Then I watch their face fall. I am convinced that rarely are learners actually asking where the topic of the ideas or the procedures are going to be useful, even when it comes out that […]

Read moreHave 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 […]

Read moreMathematical 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 […]

Read moreJohn Mason grew up in Canada where he received his BSc and MSc in mathematics. He then went to Madison Wisconsin for a PhD, and it was there that he encountered the film Let Us Teach Guessing featuring George Pólya. Inspired, John changed his teaching overnight, developing an interactive style in alignment with the film […]

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