This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

In this work, a bibliometric analysis of the investigations of the last 54 years focused on the teaching of topology and its applications in the learning of other areas of knowledge was carried out. The articles that appear in the SCOPUS database were taken into account under the search criteria of the words topology and teaching, connected with…

Factors and multiples are important aspects of mathematical structure that support the understanding of a range of other ideas including multiplication and division, and later on, factorization. At primary school level, it is important that factors and multiples are taught as a connected enterprise and as vital parts of the multiplicative…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

Background: Knowledge of quantum computing is arguably inaccessible to many, with knowledge of the complex mathematics involving a particular barrier to entry, creating difficulty in terms of teaching and inclusive learning for those without a high level of mathematics. Meanwhile, it is increasingly important that the knowledge of quantum…

This book provides an introduction to what it means to be numerate, and how numeracy can best be developed and nurtured in children and in adults. It also presents a cohesive coverage of numeracy development from early childhood to adulthood. This book draws on international research and practice to provide a comprehensive overview on the topic.…

The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial…

This paper describes the development of a concept inventory, a test designed to investigate undergraduate students' understanding of the concept of function. A central purpose was to address "conceptual" understanding. We outline a set of elements of the understanding of function, based on key properties of the function concept, which…

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts.…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

This study investigates students' ways of attending to linear sequential data in two tasks, and conjectures possible relationships between those ways and elements of the task design. Drawing on the substantial literature about such situations, we focus for this paper on linear rate of change, and on covariation and correspondence approaches to…

Science and mathematics share a common purpose: to explore, understand and explain the pure beauty of our universe and how it works. Using mathematics in science enquiry can enhance children's understanding of science and also provide opportunities for children to apply their mathematical knowledge to "real" contexts. The authors…

Universities are increasingly engaging with non-academic professionals in facilitating performance outcomes, reaffirming themselves as purposive organisations, i.e. institutions with the ability to organise strategically in the pursuit of goals and standards. However, there is little empirical evidence for the impact of professional staff on…

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In…

In this paper, we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a theorem, emphasizing that a definition was just an arbitrary assumption, a student rejected the…