Mathematics Teaching 183 - June 2003
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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MT183 Contents
Mathematics is like football - Paul Andrews
I was prompted to write this article after reading Geoff Faux's article on the inscribed circle of the 3, 4, 5 Pythagorean triangle. Geoff began in typically tentative style but led the reader quickly to the assertion that the radius of the circle was of unit length, a 'surprising and beautiful result' before offering a couple of proofs. The proofs themselves were elegant, independent of high level mathematics, and clearly a product of a mind used to working creatively.
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Numero - a numerate game - Jenny Murray
A basic set of 'Numero' consists of sixty number cards made up of 1 to 15 in four different colours. As well as these there are 'wild cards' which put other operations besides addition into the game, taking it beyond the first level. The first four of these 'wild cards' introduce subtraction, then come four multiplication and four division cards. For the more advanced player there are thirteen fraction decimal, or percentage cards and for those looking for a real challenge there are also square root, cube root, squared and cubed ones.
Learning about my learning - Becky Silvester
I find it incredibly to pin down my general approach to teaching and learning. However, there are a few points that I do feel strongly about, and in order to illustrate these, here are three examples of learning that I have recently had. None are set in a classroom situation, but I believe that the 'morals' to be learnt from the stories are strongly linked to my classroom ethos.
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You haven't seen it all before! - Jennifer Bush
I began the lesson by writing the title 'equations' on the whiteboard. There were a few groans and murmurs of 'we've done this!' as I expected there to be. I ignored these comments and proceeded to write up five equations. I then asked the pupils to write down the equations and solve them. I made some comment about knowing that they had done equations before in order to acknowledge the remarks that had been made. I had deliberately chosen the five equations to provoke discussion and show the pupils that the topic of equations is larger than the material that they had covered before.
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Power to the people - Jonny Griffiths
Power. That which must be obeyed, the scheme of work, allows me just one lesson for my A2 Mechanics group on this. I scratch my head. "How was I taught about power at school?" I wonder. Twenty-five years after leaving the place, I am sometimes shocked as to how my teaching is still subliminally affected by what happens there. "What would my old teachers have done?"
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Discover units with the eyes of a mathematician - Judit Kerekes
The following three activities can be incorporated into the curriculum for children from the ages of six to ten, either individually or as a sequence of extended projects. At least ninety minutes should be allocated for each activity. The activities are structured generally in three stages: pose the problem, investigate, and share findings. The commentary for each activity describes the classroom setting, lists materials needed, and suggests strategies for teaching.
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Casual conversations - Graham Beeden
The danger with having casual conversations is that they can return to haunt one! Attending a training session at BEAM I casually made a remark to the tutor about some work I was doing in my role as a numeracy consultant in Slough. The phone call duly followed: 'Can you write...' The numeracy strategy 'lunch box' training materials for primary schools contained a wealth of valuable material.
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Primary CAME in the classroom - Nicki Landau
It is a series of twenty-four specially devised thinking maths lessons that can help children to maximise their learning potential through active engagement in carefully planned sequential challenges. The lessons are taught approximately every two weeks, the first twelve to Y5 and the second twelve in the following academic year to Y6. Most of the lessons are structured as a cycle of two distinct episodes, ending with a short period of reflection.
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An Avon local branch meeting - Alf Coles
A quick way I found of finding the sum of the squared numbers in any line of Pascal's triangle is to follow the lines from the 'ones' down diagonally until they meet at a number. That number will be the sum...
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Mystery cookie recipes - Audrey C. Rule
True problem-solving activities challenge students by allowing them to creatively use their background knowledge to solve a complex problem that has multiple correct answers. Finding fraction problems that meet these qualifications can be difficult for teachers. Here is an engaging activity that challenges students to create their own mystery cookie recipes, and in doing so, satisfying the criteria for true problem solving.
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DIY fraction pack - Alan Graham and Louise Graham
Traditionally, children have tended to find fractions difficult. One reason may be that fractions is a multi-faceted topic requiring an understanding of different but related ideas. For example, a child needs to grasp: that a fraction is a number; the notion of the equivalence of fractions; and, a strong mental model of what a fraction represents and how the parts relate to the whole.
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Desert Island Games
Games are often an enjoyable way of practising and applying some mathematics. The best games are those that involve some strategic thinking and prediction. Favourite games, like favourite books, can be enjoyed many times, on different levels. If a game is played frequently, we have the opportunity to look beyond the rules to make predictions to sniff patterns, to experiment, to conjecture - all valuable components of mathematical thinking.
The editors invited people to describe a favourite game - interestingly nearly all the games received were invented or handed down from others rather than commercially produced. This feature provides everything you need to use the games yourself.
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Conference 2003
The ATM Easter Conference was held this year in Bath and from the wide range of workshops on offer we bring you a selection of pictures, accompanied by some comments from delegates. The photographs were taken by Pauline Neild.
Transcript of the opening session: Barbara and Derek Ball
Reflections - Malcolm Swan
During my early years as a teacher, I remember being told that I was working too hard and my students weren't working hard enough. The criticism stung because it was true. My classroom was an orderly place (well, most of the time) and students were compliant, but many were mentally passive and disinterested. I was the active participant, doing all the creative thinking , while my students followed instructions and completed exercises with the least possible effort.
Professional Officer's Update - Barbara Ball
My enduring memory of this year's annual conference at Bath University will be the weather. We enjoyed an unusually warm and sunny few days, which made the walks between the different buildings a pleasure rather than a chore.
Letter: Counting by tens - a first grader's explanation
You have all been working for some time now on the question, ‘What happens when you count by ten?’ Who would like to give us an explanation?
A note from the Web Editor
There followed some interesting debates such as: when is a course a conference and when is a conference a course?
Reviews
Key Stage 3 Mathematics: A Guide For Teachers; Primary Mathematics Teaching Theory and Practice; Hinged Dissections: Swinging and Twisting; Dave Benson Phillips’s Maths Machine; Aspects of Teaching Secondary Mathematics: Perspectives on Practice; Teaching Mathematics in Secondary Schools: A Reader; Becoming a Successful Teacher of Mathematics; Issues in Mathematics Teaching; Listening Skills – Maths Early Years; 101 Red Hot Starters; Fractal Geometry: Mathematical Methods, Algorithms and Applications; Primary Mathematics Knowledge and Understanding.
