Multiplicative thinking is a critical component of mathematics which largely determines the extent to which people develop mathematical understanding beyond middle primary years. We contend that there are several major issues, one being that much teaching about multiplicative ideas is focussed on algorithms and procedures. An associated issue is…

This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that…

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…

339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998)…

In this article, the author looks at some of the aspects of the equals sign. He shares several insights from his colleagues on the meaning of the equals sign. He also discusses how children view "=" as a sign which is written before "the answer," and, in the recording of the many practical activities that form the basis for the…

Investigates English students' strategies for addition and subtraction problems. Suggests some teaching methods for the results. (YP)

Describes the PrIME working group experience. Provides three problems on combination and typical answers from primary school students. Discusses some findings. (YP)

Describes methods for teaching able students mathematical problems. Provides four problems and discusses the students' responses to them. (YP)

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…