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Mathematics Teaching 187 - Jun 2004
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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MT187 Contents
Did I tell you my Pythagoras horror story? - Paola Iannone
The idea to write this article came from a talk I gave at the Mathematical Association annual conference held in Norwich in April 2003. This was a challenging task for me as I have no experience in school teaching and as the Mathematical Association is primarily aimed at creating 'improvements in the teaching of mathematics and its applications, and to provide a means of communication among students and teachers of mathematics'. My background is in pure mathematics and I have taught in a mathematics department in the UK for a few years before getting involved with mathematics education. Therefore I decided to present in my talk how university lecturers experience the difficulties that their first year students have with proof.
Crazybones - Richard Foster
Everybody knows that the best way to get children involved in activities is to make links to their own worlds. A great opportunity for generating addition and multiplication practice is to use CrazyBones. In case you don't know these are little plastic objects that are currently much sought after by children. There are various games that can be played with them, but a good one is the so-called traditional game where players take turns to throw five CrazyBones into the air and then score points depending on how they land.
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Inclusion through mathematics education - Tony Cotton
As part of a research project I had to revisit a school very close to the area where I started my career. This school is now held up as a 'beacon' of success. It is successful in terms of examination results and is bursting at the seams with parental choice turning this once 'failing' school into a new improved institution and popular place for children to learn. I remembered the estate on which the school is situated as fairly run down but with a positive community feel and was expecting to see the area around the school equally rejuvenated. I was stunned as I drove towards the school to see how obviously deprived the area had become, most of the shops and many houses were boarded up, groups of children stood chatting and smoking on the street corners. These were the children not fortunate enough to gain a place at the new school who could reject local children, as it was 'full'.
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Hold on to your hat - Thomas O'Brien and Judy Barnett
For several months a veteran teacher and a university professor have been conducting occasional problem solving sessions with three of the teacher's sixth grade mathematics classes in the teacher's elementary school. The results have been surprising and the activities have given rise to several articles over the past year. The latest problem session took place after a dozen sessions or so involving similar activities. The issue was inference, the notion that one can derive new information from old information with logical certainty. Put a coin in one hand, make fists, show the fists to a child at age five or so, and ask the child to find the coin. The child will find the coin with certainty. She may see the coin with her eyes or if she is shown an open hand she can see the penny with her mind. The deriving of information with logical certainty is at the heart of mathematical thinking.
An additional article by Thomas O'Brien with Ann Moss: 'Real Math?' not in the printed MT
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Challenging education - Iain Macdonald
I should state at the outset that I am not a maths teacher! Indeed I was a high school English teacher. I now work for the Great Yarmouth Achievement Education Action Zone and over the last three years, across its 33 schools, we have been training and supporting the Zone's teachers to address both learning and behavioural standards through a model, 'Challenging Education', which essentially employs:
- Collaborative working
- Critical thinking
- Clear quality criteria for how they work together (behaviour and attitudes) and for their final outcome and group presentation.
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Young children exploring early calculation - Elizabeth Carruthers and Maulfry Worthington
Counting has been identified by many as being one of the significant ways in which young children develop mathematical understanding. This has been well documented. Gelman and Gallistell found that many young children under the age of three had already developed useful knowledge of counting. Gelman went on to claim that children are born with an innate learning devise, a non-verbal counting mechanism, called an accumulator. From this basic understanding of counting children go on to use this knowledge for more complex number operations.
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Instilling thinking - Eis De Geest and Anne Watson
The improvement Attainment in Mathematics Project aims were to improve attainment of students in KS3 who are underachieving in mathematics according to national expectations. The project's purpose was to identify and develop ways of working that stimulate mathematical thinking and help the understanding of key ideas. We knew from research that students in the lowest achieving groups are often given repetitive, simplified mathematics that focuses on arithmetic in imaginary 'everyday contexts. They are expected to memorise unconnected topics and methods and re-do, again and again, work they have already done.
Download 'Deep Progress in Mathematics: The Improving Attainment in Mathematics Project'
Reflections on a problem - Dave Hewitt
This article is written in response to reading a geometry problem in John Sharp's article printed in MT 184. Something happened when I read the problem; I was excited and had a strong desire to work on the problem myself. This does not happen with every problem I read. What was it about this particular problem that energised me? I am aware that there do seem to be some problems which engage many people; however, I am not convinced that problems are engaging per se. The engagement with a problem is about a dynamic between a person and the problem and involves both.
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The plane-sphere project - Istvan Lenart
Euclid said: 'There is no royal route to geometry.' True, but let me add something. There is no slavish route either. In fear and trembling no science can be approached or even liked. There is but one way to any science: The route of equal ranks. When reading Newton, Euler or Bolyai I am an equal partner of the author. Not because I think I am as great as they were, but because they did expect me to be an equal partner. Not a rote learner, but a thinking head to whom they relate their ideas.
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'Maths is not a spectator sport' - Peter Lacey and Johnston Anderson
Although I was reasonably competent and passed some examinations I was not inspired.
The text of Peter Lacey's address [Text File 22kb]
Accompanying PowerPoint File [Warning: 8MB Zipped]
Reflections - Helen Williams
I learnt late in life that mathematics offers many opportunities to be inventive and creative – to make all our brains grow.
Professional Officer's Update - Barbara Ball
Mathematics is not only taught because it is useful. It should be a source of delight and wonder, offering students intellectual excitement and an appreciation of its essential creativity.
Reviews
How Long is a Piece of String; Primary Maths Problem Solving Ages 6-11; Main Activity: Problem Solved!; Key Stage 3 Developing Numeracy: Algebra; Probability Pack: Mathematical Activities for Primary to VI Form; Forty Problems for the Classroom.
