Mathematics is an activity—something we do—not just something inert that we study. This rich collection begins from that premise to explore the various social influences, institutional forces and lived realities that shape and mould the study and practice of mathematics, and are moulded by it in turn.These twenty-one essays explore questions of mathematics as a topic of philosophy, but also the nature and purpose of mathematics education and the role of mathematics in moulding citi...

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical t...

The word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics in society and the ...

Providing a solid foundation in second language acquisition, this book has become the leading introduction to the subject for students of linguistics, psychology and education, and trainee language teachers. Now in its third edition, the textbook offers comprehensive coverage of fundamental concepts, including second language acquisition (SLA) in adults and children, in formal and informal learning contexts, and in diverse socio-cultural settings, and takes an interdisciplinary approach, e...

Whether we grow up with one, two, or several languages during our early years of life, many of us will learn a second, foreign, or heritage language in later years. The field of Second language acquisition (SLA, for short) investigates the human capacity to learn additional languages in late childhood, adolescence, or adulthood, after the first language --in the case of monolinguals-- or languages --in the case of bilinguals-- have already been acquired. Understanding Second Language A...

An investigation into the conceptual foundations of a new way of thinking about the mind that does not locate all cognition "in the head."There is a new way of thinking about the mind that does not locate mental processes exclusively "in the head." Some think that this expanded conception of the mind will be the basis of a new science of the mind. In this book, leading philosopher Mark Rowlands investigates the conceptual foundations of this new science of the mind...

The first full-scale history of cognitive science, this work addresses a central issue: What is the nature of knowledge?

In recent decades cognitive science has revolutionised our understanding of the workings of the human mind. Philosophy has made a major contribution to cognitive science and has itself been hugely influenced by its development. This dynamic book explores the philosophical significance of cognitive science and examines the central debates that have enlivened its history.In a wide-ranging and comprehensive account of the topic, philosopher M.J. Cain discusses the historical origins o...

What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and off...

Vygotsky Philosophy and Education reassesses the works of Russian psychologist Lev Vygotsky work by arguing that his central ideas about the nature of rationality and knowledge were informed by the philosophic tradition of Spinoza and Hegel.Presents a reassessment of the works of Lev Vygotsky in light of the tradition of Spinoza and Hegel informing his workReveals Vygotsky’s connection with the work of contemporary philosophers such as Brandom and McDowell

This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing...

Unique in offering a multidisciplinary perspective on key issues of alternative epistemologies in education, this collection includes contributions from scholars in family therapy, epistemology, and mathematics, science, and language education. These respected researchers were brought together to develop the theme of constructivism as it applies to many diversified fields.This book examines key distinctions of various constructivist epistemologies, comparing and contrasting the var...