Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

In this article, the author discusses the creativity of origami and discusses a model she designed in May 2008 in Freiburg at the 20th International Origami Convention of Origami Deutschland. The model resulted from her investigation of a geometric model that exposes the centre part of a square paper sheet. The base model of the series called…

This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…

Effective teaching includes enabling learners to make connections within mathematics. It is easy to accord with this statement, but how often is it a reality in the mathematics classroom? This article describes an approach in "connecting equivalent" fractions and whole number operations. The authors illustrate how a teacher can combine a common…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

The ability of interlocking polygonal tiles, like those in the "Polydron Frameworks kit," to flex can give rise to polyhedra whose faces don't quite fit. In this article, the author discusses what happens with polyhedra whose faces don't quite fit. (Contains 2 notes.)

Presents an activity for weaving polyhedron shapes out of paper strips. (MVL)

Discusses children's concept of number and number operations and describes activities which help to develop number concepts and skills. (JP)

Discusses a tally device using discs on a paper diagram. Instructions given for number representation, negative values, games, addition and subtraction. (RS)

Uses Stern patterns and Cuisenaire manipulatives to help Down's Syndrome children learn arithmetic. Concludes that the opportunity to discover an arithmetic based upon an algebra of patterns and lengths, and not upon an elaborate counting apprenticeship, might prove of particular further benefit to children with Down's Syndrome. (ASK)

This article was written as a result of the author reading "MT177," a special issue dedicated to the teaching of "proof" in mathematics. He used the ideas in this special issue for planning his session "mathematical reasoning and proof," which was part of a weekend course for primary trainees. It consisted of three activities: (1) How many…

Counting and dividing activities for 5- and 6-year-old children, using base ten multibase arithmetic blocks, are described. (DT)