This open access book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem solving with the treatment of the curricular contents. It has gained international recognition since the 1990s and thanks to it mathematics...

Covering thinkers from Aristotle to Saussure and Chomsky, "Introducing Linguistics" reveals the rules and beauty that underlie language, our most human skill.

In its first two decades, much of cognitive science focused on such mental functions as memory, learning, symbolic thought, and language acquisition -- the functions in which the human mind most closely resembles a computer. But humans are more than computers, and the cutting-edge research in cognitive science is increasingly focused on the more mysterious, creative aspects of the mind. The Way We Think is a landmark synthesis that exemplifies this new direction. The theory of con...

How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for t...

Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the stre...

This book is addressed to students and teachers in design degrees and researchers interested in logical thinking of design. Just like any other discipline, design must accredit its rational fundamentals to refer the conditions of knowledge that determine it as a specific object of study. Methodology is a bridge between the general principles of doing and knowing. The analysis of the design theoretic fundamentals involves an approach to its models as well as the conceptual assumptions. Like...

While the theories of Matte Blanco about the structure of the unconscious and the way in which it operates are generally recognised to be the most original since those of Freud, for many people the ways in which his ideas are expressed, including the use of terminology from mathematics and logic, make them difficult of access.Eric Rayner has written the first clear introduction to Matte Blanco's key concepts for psychotherapists and psychoanalysts and all those concerned with movin...

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research.Areas covered include:• Algebra:...

Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the ...

This book addresses the linguistic challenges faced by diverse populations of students at the secondary and post-secondary levels as they engage in academic tasks requiring advanced levels of reading and writing. Learning to use language in ways that meet academic expectations is a challenge for students who have had little exposure and opportunity to use such language outside of school. Although much is known about emergent literacy in the early years of schooling, much less has been writ...

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach fo...

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientati...