Books by Paul Ernest

This book treats all the key issues concerning the teaching and learning of mathematics for students with special needs. It analyses the range of meanings given to the term special needs in mathematics. It analyses the concepts of intelligence and mathematical ability and the underlying concepts and theories. It devotes an extensive chapter to the diagnosis and remediation of specific learning difficulties in mathematics. An important issue is that of attitudes to mathematics, because low attainment is often associated with poor attitudes, and this is treated in depth. Another chapter focuses on the role of language, which is especially prominent in problems of dyslexia and dyscalculia and mathematics. High attainers and gifted and talented students in mathematics have their own special needs so that their unique talents can flourish, and there is an extensive treatment of students of these types. Lastly, the implications for the teaching of mathematics for students with special needs is considered. The penultimate chapter presents the most effective forms of mathematical pedagogy and curriculum modifications required to ensure success for all students.

This book overviews concepts, theories and research in the psychology of learning mathematics, including research methodologies. The organising framework is the classification of the central learning outcomes of school mathematics into facts, skills, conceptual structures, general strategies and appreciation. Each component is treated in one or two dedicated chapters. There is a chapter on theoretical and practical aspects of constructivist learning theory, and another on the mathematical processes, strategies, and thinking involved in mathematical problem solving, including meta-cognition. A further chapter treats attitudes to and the appreciation of mathematics. The last two chapters explore a theme that has emerged as important in the psychology of mathematics education in recent years, the impact of context, both task and social context. This concerns the cognitive and psychological significance of both the external representations and situated embodiments of mathematical ideas and tasks, and also their internal, mental representations. It also concerns the links between these two domains including theories of transfer of learning.

Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education. Building on the work of Lakatos and Wittgenstein, it challenges the notion that mathematical knowledge is absolute.

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics.

Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.