Mathematics Teaching 205 - November 2007
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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Special Edition: Visualisation
This edition and the next (MT206) are special issues on visualisation.
In this issue, the paper version has a ‘flicker book’ image in the margin of each page. It is reproduced here as an animated image. Hold down ‘SHIFT’ and click ‘Reload’ or ‘Refresh’ to re-start it.
View this as a video clip here...
MT205 Contents
Visualising geometry - Barbara Ball and Derek Ball
As a result of attending the weekend on moving images, Barbara and Derek Ball consider the balance between visualising and verbalising.
The Trevor Fletcher Cardioid film referred to in this article
Canonical images - Dave Hewitt
Dave Hewitt offers two well-known mathematical images and considers their power for developing mathematical thinking.
Making animations - James Robinson
James Robinson describes as simply as possible how to make an animation using PowerPoint.
Powerpoint file [.ppt] and FAQ document [PDF] to accompany this article
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Steiner's amazing porism - Trevor Fletcher
Trevor Fletcher played with an animation of circles and found some surprises.
View a Cinderella version of the Steiner Porism
Download a Cabri file [.fig] of the Steiner Porism
Not a member? Join or click to buy ‘Steiner's amazing porism’ for £3
Using moving images with Year 2 - Geoff Faux
Geoff Faux uses James Robinson’s PowerPoint film Slideshapes1 to generate some mathematical thinking with 7-year-olds.
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Yes, but can they solve right-angled triangles? - John Hancock
John Hancock works with all-ability Y8 students using a well-known moving image. He accepts it is hard work for the teacher but thinks it might be worth the effort!
Not a member? Join or click to buy ‘Yes, but can they solve right-angled triangles?’ for £3
The method of Jean Louis Nicolet - Caleb Gattegno
J L Nicolet is a Swiss teacher of mathematics who found his subject so fascinating that he was puzzled as to why so many pupils could not share this enjoyment in their studies.
The Nicolet film referred to in this article
Not a member? Join or click to buy ‘The method of Jean Louis Nicolet’ for £3
Images: static, dynamic and mental - John Mason
John Mason discusses some pedagogical issues to do with working on images with learners.
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Truncation
The ideas on this page were stimulated by working with a Geometer's Sketchpad file designed by Kate Mackrell.
Geometer's Sketchpad files [.gsp] for the Octa-, Hexa-, Icosa- and Dodecahedron
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Geoff Giles and Geometry - David Fielker
Geoff Giles died suddenly in 2005. Thanks to a donation from his widow, Bet Sampson, Geoff Faux and David Fielker were asked to run seminars at the 2007 Easter conference in his memory. David Fielker describes his here.
Not a member? Join or click to buy ‘Geoff Giles and Geometry’ for £3
Linkages to op-art - John Sharp
John Sharp explores the mathematics of mechanical linkages and turns the results into art.
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The Cuisenaire product finder - Paul Stephenson
Readers delighted by the simplicity of the method of multiplication shown in MT203 (Foster, 2007) may be interested in a Gattegno-inspired variant.
Misunderstanding of fractions! - Caroline Rickard
Having just spent an hour with a Y5 class investigating their understanding of various aspects of fractions, I wanted to share some of my observations.
Line multiplication: a response to Colin Foster (MT203) - Marion Walter
I really liked the piece, but I think it is not quite as simple as described.
A cautionary tale - Wendy Brady
The need to move on can sometimes make it easier to accept the right answer and explain for them.
Reflections - Geoff Faux
Some of us, Derek Ball counted 40, spent a weekend over the early May bank holiday this year [2007] working on visualisation in mathematics.
13 Correlation Street - Jonny Griffiths
I want my students to be able to improvise on a mathematical theme, to enjoy their mathematical uniqueness, and not to fear mistakes but to be thankful for them.
News from ATM
It would be good to hear from members who might have done similar work in the classroom and wish to contribute ideas via email that we can incorporate.
Hod-Lines
Interestingly, we have only one male English teacher and five out seven of the maths team are male. I think in the next learning area meeting we will explore the issue of gender.
Puzzle page
The flicker-book in the corners of the pages of this copy of MT shows that it is possible to find an infinity of lines that divide a long L in half.
Film of the dissection of a polyomino
