Janet Duffin

A Search for Understanding

Abstract We discuss an important breakthrough for us in our search for a technical meaning of “understanding” in mathematics education. In this article, we describe the background to this discovery, the catalyst for the breakthrough, and a concise explanation of our new definition. In discussing the consequences of this definition, both in terms of the theoretical implications for the internal characteristics and external manifestations of understanding with some initial practical consequences for a teachers attempts to model a learners understanding, we begin to describe our ongoing search for a more comprehensive theory.

When does a way of working become a methodology

We discuss the question of how to determine what are valid methodologies in mathematics education and the problems associated with developing new ways of working into acceptable research methods. We develop the idea of a two-stage validation process and look at the consequences for communicating between what we term methodological neighbours, an alternative diffusion model that explores the relationship between teachers and researchers, and the role of the PhD within the validation process. We then describe our own way of working and suggest how it is beginning to evolve into a methodology.

Mathematics Across the University: Facing the Problem

Abstract We explore the development of a Mathematics Advisory and Co‐ordinating Service (MACS) at Hull University. We discuss a theory of learning which supports our distinction between two types of mathematics support required in universities today. These two aspects of the problem lead to two distinct teaching models which relate back to the learning theory.

Is it a times, Miss?

This lucid article takes what was for many teachers of young children one of the most significant aspects of the Cockcroft Report as its starting point: the role of language in mathematics. The author draws upon her own classroom-based investigations into ‘the differing ways in which people perceive the same thing’ and explores the implications of that and of some of the forms of words which, she claims, often obfuscate children.