Mathematics Teaching 191 - Jun 2005

Functional Mathematics - Barbara Ball

The Association of Teachers of Mathematics is very disappointed that the government has rejected so much of the Tomlinson report. Those of us involved in mathematics education awaited the government's response to Tomlinson with particular interest because, after all, in their response to Adrian Smith's report Making mathematics count they had said that 'we will...secure the engagement of all learners through increased pathways, better vocational options and stretching curricula for the most able. This will be integrated with our approach to broader curriculum reform to ensure consistency and portability of skills across the whole 14 - 19 curriculum.'

Transformation Geometry - Maria Wesslén and Saínza Fernandez

During our initial teacher training we were both asked to teach a class of Y8 students a sequence of lessons on transformation geometry. Soon the inevitable questions came. Students began to ask us what the purpose of it all was. To our surprise we both found ourselves struggling to find an answer and even afterwards we could not think of a good reply in terms of some utilitarian purpose. This led us to think about the mathematics.

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A Problem with the Letter M (on its side) - John Hancock

This article has been written to give a flavour of the work being done by a group of ATM members who meet each term to discuss ideas about how to work with students who have not been grouped according to some notion of mathematical ability. The article reflects the simple format of the meetings: some one shares a classroom idea and members of the group work on it with the intention of exploring its depth and richness.

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Friday Reflections 2 - Emily Lipman

This article describes Emily's weekly notes made during her second half-term of secondary teacher training - a dairy of thoughts and observations about the course and her time in school. In the last issue of MT (MT 190, March, 2005), we published her first half-term of notes.

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Another Look at Revision - Colin Foster

The first time I taught a revision lesson, it was a disaster - one of those lessons you wish you could forget! I had cut and pasted together a sheet of miscellaneous problems and handed them out. The pupils worked quietly for about five minutes. Then a hand went up, then another and another. I hurried from person to person dealing with completely different enquiries. Within a few more minutes almost every hand in the room was in the air, all with different difficulties. Everyone had found something they were stuck on and it was my job to sort it out. In the meantime the noise went up and the behaviour went down.

Maths Talk - Paula Ross

The 2003 primary national strategy's speaking, listening and learning document emphasises the need for children to learn to:

• Use exploratory language to try out ideas
• Stretch their language as they talk constructively and critically
• Support and build on each other's contributions as well as using talk in different ways, such as discussing, hypothesising, agreeing and disagreeing, questioning and reflecting.

Download a copy of the 'Discussing our maths...' sheet

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Starters at KS3 - Ceri Fiddes

It appears that the original intention of the starter is to set out the learning objectives for the lesson, however there are other recommendations in the DfEE: The National Strategy; Framework for teaching mathematics: years 7, 8 and 9, which hint at different intentions. It is suggested that starters are more effective if they start the lesson at a good pace, include strategies to absorb stragglers, involve the whole class and include opportunities for informal assessment.

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Effective Use of the Plenary - Rachel Jennings

I was particularly interested in using the plenary for formative assessment purposes and wanted to use some of the ideas I had come across during my study, especially those that related to the way in which teachers used questioning. These included:

• Asking open questions so that all students felt they had something to say;
• Giving pupils sufficient 'think time' - asking pupils to work in pairs on the question;
• Asking pupils to make up their own questions and answers.

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Joining Luke's Wires - Susan Saunders

Luke is a Y5 boy in a Brighton and Hove school. This article provides the background to Luke's story and gives the detail of a project that was devised to help children like Luke who are unable to 'move on' in mathematics - the child who continually has the target 'number bonds to 10' on his/her IEP.

This article mentions the Numicon maths system: The Numicon maths system is a multi-sensory approach to arithmetic teaching for pupils aged 3-8 years and pupils of all ages with special needs. Numicon uses structured patterns to represent numerals encouraging an understanding of number and number relationships which is important for successful mental and written arithmetic.

Find out more about maths shapes and resources at Numicon

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Freedom and Constraint - Colin Foster, Linda Galligan, Kate Mackrell, John Mason, Ali Melville, Jennifer Piggot, Anne Watson

Every year for the last five years a small conference has been held at which some 20 people discuss a theme in mathematics education over four days. We call this the Institute of Mathematics Pedagogy. It is a little like a very long intense ATM conference session: an intellectual, emotional and social workshop during which we do maths, talk, eat, play, dream and write, with the sole aim of understanding more. In 2004 the theme was 'freedom and constraint'.

At the end of this article Malcolm Swann adds his thoughts, which are interesting, as usual.

Story as a Tool for Learning - Alison Davies

Alison is a writer and storyteller who works in schools running storytelling activities. She is interested in how storytelling can be used to teach a range of subjects, including mathematics. In the March issue of MT (MT 190) we published Alison's story: 'Playing by numbers'. In this issue she outlines her ideas for how teachers may use this story in a KS3 mathematics classroom.

Download a PDF copy of the storyboard template shown in this article...

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More Sliceforms and Cylinders - John Sharp

This is the second part of John's article on Sliceforms. Part one: 'Slicing Cylinders using Sliceforms' appeared in MT188, September 2004. For those of you who thoroughly enjoyed that piece and there were many of you, this one will be equally compelling.

A PDF copy of the Slice Forms template in this article can be downloaded here...

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Hands on Subtraction - Audrey C. Rule

Many young students have difficulty with word problems involving subtraction because they only know subtraction as a 'take away' operation: "How many are left when some are removed?" There are, however, many different simple situations that require subtraction including completion, comparison and whole-part-part analysis. Students need to experience these less familiar subtraction settings many times so that they internalise the language of subtraction:

"How many more are needed?"
"How much larger?"
"What is the difference between these?"
"How many more of these are not like the subgroup just identified?"

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Reflections - Len Sparrow

Teachers thinking and teachers resolving dilemmas are somewhat interlinked but when they are used carefully they make teaching a professional and personal occupation rather than an uncritical, conforming reiteration of someone else’s commands.

Professional Officer's Update - Barbara Ball

Classroom-based research – whereby teachers are given the support and space to try out new ideas and develop their own models for teaching – is so vital.

Letters - Paul Stephenson and Derek Ball

Paul Stephenson: I found a duality which is much shallower mathematically but at least illustrates the concept of duality.

Derek Ball: What particularly impressed me was the students’ engagement with geometry.