The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

This article outlines an extension exercise that is based on the elementary geometrical constructions in the National Curriculum. The challenge for students is to organise and execute an extended construction. The hidden, parallel agenda is proof, for the teacher's role is to convince students that they "must" succeed and that doing so is a…

In this article, the author describes what his students are doing following the ATM Easter conference in Telford, where he was inspired by a workshop entitled "Vitamin D Maths," conducted by Jocelyn D'Arcy. He describes an activity that allows his Year 11 students to walk through angles drawn on the floors. This topic will now literally…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

The author discusses how she made up some dice problems for a child's birthday. She presents some activities that can be used with younger and older children based on dice. (Contains 4 figures.)

Emergency shelters for disaster relief are an ever present necessity. Anyone who has ever camped in a tent will understand that finding the perfect design, that will be simple and quick to erect, be stable in a variety of weather conditions, and will accommodate a number of people sleeping, sitting or even standing is not straightforward and…

The authors explore the teaching of trigonometry using a method developed by Jeremy Burke of Kings College. A series of lessons was planned using an approach which looks at moving from a mathematical description of the topic, to a sequence plan, to a set of activities, which students can use to help them come to understand the topic. This is…

This final article focuses in particular on the engagement of year 8 students who were taught trigonometry using dynamic geometry software ("Geometer's SketchPad"), as outlined in "MT214" and with resources from the ATM website. The project was implemented in three different classrooms in two different, multiracial,…

Young children evolve their own rules for "playing" together. This author believes that people have to learn, and teach, the techniques for "working well" together, and the sooner this begins, the better. In this article, the author provides an account of a task she has sometimes given to groups of five-year-olds in year one, with the intention…

One of the major characteristics of mathematics is that one can derive new information from old information with logical certainty. The fancy word for deriving information is inference. The elementary school and secondary school years are the time for the construction of logical operations and the development of tactics and skills which are at…

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)

Each of the primary problems described in this article encourage children to "get into" the process of problem solving, and all can be introduced without written instructions. A demonstration by the teacher with large hands-on materials can involve all the children effectively and give him/her the opportunity to highlight key points and deal with…

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)

Exercises designed to aid students to practice or apply particular mathematical concepts and/or relationships using calculators are promoted, with four specific reasons for allowing this kind of activity. Specific cases dealing with number relationships and estimation are covered as examples. (MP)