Mathematics Teaching 190 - March 2005
Mathematics Teaching is the journal of the Association of Teachers of Mathematics. It is a professional journal sent to all members of the Association. It is not a refereed journal. Submissions are reviewed by the editorial team. Many articles have additional information or associated files placed on the journal website. To make your views known go to the ATM forum add your views, ideas and comments.
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MT190 Contents
Friday reflections - Emily Lipman
Emily allows us to read her weekly notes made during her first half-term of secondary teacher training, a diary of thoughts and observations about the course and her time in school. Next issue will include her second half-term notes. They make a very interesting read.
Proof and insight - Alf Coles
Every proof must contain an insight and I see it as part of my job as a teacher to work until I find it before I offer anything to students. I now see that if I want to work with students on the irrationality of root two I need to start by working with prime factors. Students could explore the challenge: 'Find a number that has two different factorisations' (the first task being to sort out what the words mean).
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Negative information - Paul Stephenson
Can you swing a heavy armchair about its corners by one quarter turns, so as to bring it to a position adjacent to the original and facing in the same direction? Teachers love this problem because, as the authors realised, it exercises the student's resourcefulness in modelling the situation and choosing a notation that can deal with it. However, and there's the rub, the answer is no.
Paul Stephenson's chart from this article
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Whose lesson am I teaching? - Margaret Sangster
Mathematics, like no other subject, has a long tradition of using detailed texts for students to work from. Using published lessons is something I am not comfortable with and when the discussion arises with my students we get as far as saying, 'They need to be adapted' and 'The writer doesn't know our children 'which are both fair comments. Even with these sensible practical statements my unease remains, particularly in my role as teacher trainer.
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Responding to Geoff Faux's challenge - Derek Ball and Julian Gilbey
In MT189, Geoff Faux challenges us to find a different proof of Cross's Theorem...
Caterpillar collection - Jill Russell
In 1994 I wrote about my 'Catalogue of caterpillars'. This army of creatures have marched from one century to the next, supplying me with a wealth of opportunities in my new role of primary supply teacher. As only befits caterpillars the have metamorphosed during the last ten years. I am now sure there is a clan of caterpillars suitable for every age range and every mathematical ability. Interestingly, I was in a classroom the other day and found a set of marked caterpillar work so their fame continues to spread.
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Too much teaching? - Christine Barnes
Do we spend too much time teaching our children and not enough time watching them learn? At a recent conference in Cornwall many teachers and other professionals listened to Iram Siraj-Blatchford talking about her large-scale research project, Researching effective pedagogy in the early years. She spoke particularly about the balance between adult-directed and child-initiated play in the foundation stage. For many teachers this is a particularly difficult problem, especially in mathematics, as they feel that they need to follow the basic structure of the daily mathematics lesson as used in key stages 1 and 2.
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Golden opportunities for creativity! - Colin Foster
Is mathematics a creative subject? I certainly believe so, yet it can be difficult to find mathematical tasks which give pupils the opportunity to work in genuinely creative and imaginative ways. To be creative, pupils need more than to be presented with several options to choose from - they need the space to develop and pursue original work and see their ideas take form. I tried to provide some scope for this while working on volume with my Y9 class.
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Questioning their mathematics - Vicky Inman
The idea for this article came from observing a Y9 SAT's revision class. On test day they would be on their own, relying on their own mathematics. The teacher posed questions that brought out the pupils' knowledge, their thinking and their conceptions and guided them into using their own mathematics to answer the questions. Observing the class I began to understand more about the phrase questioning skills.
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The MultiGrid Stencil - Paul Richards
I believe the Gelosia method of multiplication is the most effective way to teach children of all ages long multiplication. When the Gelosia method is used to perform decimal multiplication it really come into its own. It was decided, three years ago, as a mathematics department we would all teach the Gelosia method. This decision has proved successful for many of our pupils and is backed up by their continual progress in examinations.
The Gelosia software referred to in the foot of this article
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Before teaching calculus - Sidney Schuman
In most teaching of calculus to sixth-form students, there is an assumption that they understand the concept of gradient. I want to suggest that perhaps this is not best practice. Most sixth-formers will, after all, have had only limited experience of gradient (performing friction experiments, drawing linear graphs, cycling up a hill) and the concept of gradient may not have been internalised securely from their experience. It is no surprise then that, after happily calculating the point at which a secant becomes a tangent, their attempt to understand the underlying theory quickly becomes almost theological in character...
Sidney Schuman has a website at powermaths.org.uk
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Word meanings - Daria Shields, Cinda Findlan and Cyndy Portman
This article will present three effective methods of mathematics vocabulary instruction using best practices from literacy instruction. First, graphic organisers, such as word webs or semantic maps, will be discussed and their use in the classroom will be described. Next, vocabulary games will be recommended as learning tools and not just extras when time permits. Then, morphology as the root of mathematics language will be examined and morpheme activities will be explained.
The booklist to accompany this article
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Cyclic and tangential polygons revisited - Francis Lopez-Real and Allen Leung
In MT179 and MT180, two related articles looked at the concept of cyclic and tangential polygons and established a number of properties or 'theorems' associated with them. Of particular interest was the difference between even-sided and odd-sided polygons for both cases. However, one case was left unresolved in those articles. This concerned odd-sided cyclic polygons for which it was intuitively felt that a relationship should exist between the interior angles of the polygon (given that a clear relationship was established for even-sided cyclic polygons).
Geometer Sketchpad files to accompany this article
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Playing by numbers - Alison Davies
Alison is a writer and storyteller. Her work has been published in the TES, Teaching Statistics and the Royal Statistical Society journals, and she has her first novel due for publication this year. She works in schools running storytelling activities and is interested how storytelling can be used in a range of subjects, including mathematics. In the June issue of MT (MT 191) Alison will outline her ideas for how teachers may use the following piece in the classroom. Sophie hated hockey...
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Two successful mathematical days in 2004: Maths is special in the North West - Joe Murray
The first North West conference for mathematics at KS3 in SEN took place in June 2004 at the Woodlands Conference Centre in Chorley, Lancashire. Over 100 co-ordinators from special schools in every type of setting across the North West region attended this one-day conference, which was arranged and presented by KS3 mathematics consultants from the region. This is an account of the day.
Primary puzzles day - Keith Windsor
Activities included ‘home made’ tasks, commercial puzzles, electronic challenges and computer software.
Reflections - Sam Ladner
We need to encourage pupils to be able to use internal dialogue to think around a problem.
Professional Officer's Update - Barbara Ball
Well, I suppose I quite like that, but I don’t see why you can’t be ‘seeking out ways to engage the power of the learner’ while dressed in a tie or a smart skirt.
Letter - Trevor Fletcher
I was not myself a signatory of the Report, but I was an adviser to the committee, and I am sure the current MT would give great pleasure to all associated with the report’s production.
