The problems of problem-solving

In my last blog I set a task, which was to find out and explain what happens in this situation: Given a set of consecutive natural numbers from 1 to 2n, choose any n of them. Arrange these n numbers in ascending order. Next to them, in one-to-one correspondence, arrange the remaining numbers in descending […]

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Now you see it; now you don’t

I presented some visual approaches in an earlier blog called ‘Finding Nemo’ and I am now going to elaborate one of the ideas to show the value of looking at a mathematical structure in different ways.  Each of these needs learners to ‘see’ the diagram or expression in one way, and then in another way. […]

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Eliminate the Negative

I have been thinking about negative integers and wondering how anyone I taught ever managed to understand them. Many did, but when I am asked, by KS2 and KS3 teachers, ‘Is there a good task for discovering the rules of negative numbers?’, I find it impossible to answer. There seem to be a few popular […]

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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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Short Summary Sheets

One of my Y13 students intends to resit Statistics 1 and Core 2 in summer this year, alongside Core 3, Core 4, and Mechanics 1.  I devised a 5 week plan to cover the entire course in an hour per week.  This centred on 5 one-page summary sheets for five broad areas.  For some reason […]

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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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Being Mathematical in Public

What 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 […]

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Character Counting

A little while ago one of my students told me an interesting fact: he claimed that four is the only number where the number of letters in its name is equal to the number itself.  This then clearly sparked something in one of my other students as the following lesson she disputed this fact, and […]

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Finding Nemo and Dissection

I attended both conferences over Easter, ATM and MA.  As OUP was sponsoring the MA conference it was well attended by authors and publishing people. A major theme among secondary teachers in informal discussions at both conferences is whether and how the requirements for problem-solving at GCSE will affect teaching throughout secondary. Another major theme […]

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