Mathematics Teaching 177 - December 2001

Reflections - Kath Cross

Thinking about polyominoes reminds me not only of rich opportunites that I have seen used in primary and secondary schools, but also of opportunities lost.

Proof: Setting the scene

In September 2000 a long weekend was organised by ATM members to raise the profile of proof in mathematics teaching at all levels.

Proof: Opening session - Geoff Faux and John Mason

We both believed that proof was very central to mathematics and that we believed that proof was an important way of knowing.

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Proof - Alf Coles

I see my main task in teaching mathematics as creating a classroom environment in which students are asking and working on their own questions.

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An invitation to prove

What is the least number of questions with only yes or no answers needed to identify my number.

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Working with a Nicolet film - Alf Coles and Geoff Faux

I find the three part framework: convincing myself, convincing a friend, convincing an enemy helps me in making decisions.

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Understanding then doing: doing then understanding - Aidan Harrington

What is clear is that many of my students are end gaining and as a consequence are developing approaches to their learning which are very ineffective – a heavy reliance on memorising rules or scripts for solving types of problems.

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Noticeboard

News and other bits.

How many snow people? - Penny Latham

I said I wasn’t really convinced by that argument, that just because they couldn’t think of any more that there weren’t any other possibilities.

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Handshakes and number bonds in Y1 - Kath Halfpenny

When asking children if they remember the bonds to ten, the children who tend to be less confident in maths usually offer 5+5 first. Is this because they remember doubles more easily? Or are they remembering it for its unique nature as a palindrome?

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The matchstick array - Charlie Wall

This voyage is into a mathematical space of infinite dimension and scale as well as of infinite variety, intricacy, complexity and beauty.

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How do you know you have them all? - David Fielker

Naturally, the problem of proof – proof that you have all the possibilities – is a more difficult one than just finding ‘as many as you can’. In most cases it involves some systematic way of counting, and for younger children one can choose situations where this is easier, but still challenging.

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Proof from the classroom

Real accounts of the use of proof in the Key Stage 2 and Key Stage 3 classroom.

A pre-conference paper - Dick Tahta

I see two strands in any pedagogic discussion of proof. First, in terms of collecting and illustrating ways in which mathematical deduction can be grasped and applied by children of any age. Second, in terms of clarifying why it might be useful and/or important to have this aim in the classroom, yet at the same time to explore just what the alternatives might be.

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Some elements of proof in KS1 shape and space - Marjorie Gorman

Proof in the Early Years: Teachers encouraged the discussion, naturally and informally, by providing the relevant vocabulary, sometimes modelling a statement but always by giving the children an opportunity to think about what they had been doing and reflecting on what they had learned. The sort of questions they posed were the how, what, why type of questions that encourage higher levels of thinking.

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Convincing myself and others - John Mason

Some people expect students to learn to justify their conjectures, but assessors currently seem content to get children to make conjectures in their coursework.

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Seeing, convincing and proving - Anne Watson

There are lovely moments in mathematics when algebraic and geometric representations coincide; where an algebraic proof exactly mirrors a spatial argument that can be seen, or a geometric representation generates a sequence of algebraic statements.

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There's proof and there's proof - Morgan Sweeney

I would peer beyond proof, which hung like an obfuscating net-curtain, and sometimes see perfectly obvious, common-sense ideas, which you were forbidden to believe until you had passed through the veil. Vertically opposite angles: I mean, really, have you ever met anyone who needed proof that they were equal?

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Generic proofs: setting a good example - Tim Rowland

There’s been some talk recently about mathematics as a ‘creative’ discipline, and of ‘creative moments’ in mathematical activity. Jill reminds us that such moments rarely, if ever, just happen: they have to be striven for, and they are all the more wonderful for that when - and if - they come.

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Reviews

Geometry with Trigonometry; The Story of Mathematics.

Letter - David Fielker

Royal Society enquiry into Geometry teaching.

Words with... - Jill Faux

I would contend that, at both home and school, most children are told what to do most of the time. When they are not being told what to do they are being told what to learn or memorise.