Mathematics Teaching 215 - Sep 2009

Editorial - Margaret Jones

We want to hear what you think. We would like your ideas for further developments and, of course, we would like you to feel motivated to respond and contribute.

Retrospective - The Editors

It was a policeman that broke my reverie. “It’s all clear now – let’s get moving!” A switch, back in the webmaster’s office had, as agreed, been flicked...

Place value - Ian Thompson

Mental calculation strategies and informal written procedures are based on the quantity aspect of place value, whereas standard (or compact) algorithms are based on the column aspect.

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Trigonometry with Year 8: part 3 - Jessica Steer, Maria Antonieta de Vila and James Eaton

Introducing students to a complete picture of trigonometry – ratio and function. They are able to get used to modelling trigonometry using a dynamic geometry package.

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Pascal pictures - Paul Stephenson

Most students of Pascal’s Triangle know the ‘Christmas stocking’ theorem: but do you know the ‘tick’ theorem?

Download Paul Stephenson’s solution

Centres and circles of a triangle - Sue Forsythe

Using paper folding and ruler and compasses students have seen, through the many examples generated, that perpendicular bisectors intersect at the centre of a circle which passes through the vertices of a triangle.

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Playing games - Carol Kohlfeld

These game playing behaviours are needed not only in the classroom but in many different social situations. Student behaviour is friendlier, more cooperative, and respectful.

Further workshop jottings - Colin Jackson

Someone will bring a problem that a class has explored which is a seemingly straightforward problem, but which either turns out to be much more problematic than it seemed at first glance, or presents several different avenues to explore.

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Puzzle page - Paul Stephenson

Fibonomino Spirals: The problem you’ll find there is called ‘Building Gnomons’. The term gnomon usually refers to the piece needed to complete a similar shape

Dutch principles - Pamela Moffett

The students were treated as active participants in the learning process, rather than receivers of ready-made mathematics: a purposeful, interactive and relevant mathematics lesson.

Jumping to conclusions - Derek Ball

Andreas Stylianides’ article in MT213 raises interesting issues concerning students’ thinking about mathematical proof, but I am not entirely convinced by his reasoning...

The geometry of the universe: part 2 - Stephanie Francis

I am none-the-wiser as to the shape of the universe I now know that if I had a space ship and was able to fly extremely long distances I may be able to work out the intrinsic curvature of the universe.

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Isosceles triangle problem - Derek Ball

Enclose an isosceles triangle in the smallest possible square. Construct the required square. When is the triangle half or one third the area of the square?

Download the Geometer’s Sketchpad file to accompany this article

News from ATM - George Knights

Government policy is pointing teachers and schools toward closer cooperation. This is thus a key time for local and branch activity in the association.

RISP 12 - Jonny Griffiths

Students are all able to appreciate a tasty conundrum, and indeed, what better way to invite them into participating in mathematical conversations?

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Proof without words - Sanjay Khattri

Sanjay Khattri provides us with a response to Andreas Stylianides’s article in MT213.

Inverse of a 2x2 matrix - John Suffolk

When we define a word we can, like the Red Queen, make it mean whatever we like. The definition of matrix multiplication that Cayley adopted in 1858 is rather odd.

Sacred cows - Mike Ollerton

I am sceptical and highly critical of some of the systems and accepted orthodoxies which appear to dominate what happens in mathematics lessons.

Active assessment - Stuart Naylor and Brenda Keogh

Feedback from many of the teachers who now use the Active Assessment approach in their teaching has been highly positive.

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Provocation 5 - Two Old Men

Just when I had conveniently pushed an ex-colleague to the darker corners of my memory – you catapult him straight back with your mention of ‘real mathematics’.

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Trigonometry from first principles - Andy Kemp

They are now doing it from the understanding of where these functions come from, and why basic trigonometry only works for right-angled triangles.

Download worksheets that accompany this article

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Professor points: part 1 - Mary Karacalik

If I want the children in my class them to co-operate genuinely I have to make it my task to teach them explicitly how to talk to each other constructively.

Oral and mental mathematics - Sue Davis

A small amount of input for initial teacher training students can have a large impact on their understanding, knowledge and ability to focus on these key strategies in school.

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