In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge...
In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - ...
This book is centrally concerned with how mathematics education is represented and how we understand mathematical teaching and learning with view to changing them. It considers teachers, students and researchers. It explores their mathematical thinking and the concepts that this thought produces. But also how these concepts acquire cultural layers that mediate our apprehension. The book examines some of the linguistic and socio-cultural filters that influence mathematical understanding. But above all it introduces some contemporary theories of human subjectivity, in which subjectivity is...
This book is centrally concerned with how mathematics education is represented and how we understand mathematical teaching and learning with view t...
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.This volume underscores the power of attending to basic ideas...
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from fir...
Exploring Probability in School provides a new perspective into research on the teaching and learning of probability. It creates this perspective by recognizing and analysing the special challenges faced by teachers and learners in contemporary classrooms where probability has recently become a mainstream part of the curriculum from early childhood through high school. The authors of the book discuss the nature of probability, look at the meaning of probabilistic literacy, and examine student access to powerful ideas in probability during the elementary, middle, and high...
Exploring Probability in School provides a new perspective into research on the teaching and learning of probability. It creates t...
This book focuses on how major curriculum reform shapes mathematics in schools and the practice of mathematics teachers. It details in real time the complete life span of the implementation of a major government numeracy programme and its effect on teachers.
This book focuses on how major curriculum reform shapes mathematics in schools and the practice of mathematics teachers. It details in real time th...
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.
It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning." These approaches and others of similar nature lead to a focus on competence rather than a user's activity with mathematical language.
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allo...
This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.
This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathemat...
New Directions for Situated Cognition in Mathematics Education represents the maturation and expansion of the situated cognition theories applied to mathematics education. All of the situations on which the chapters of this book are based exemplify activity which would be described as mathematical, whether they are classrooms, workplaces, homes or the street. In identifying mathematical activity, this book examines the ways people talk, what they talk about, what they focus on, how they classify experience, what levels and kinds of generality occur to them, what is varied and what is...
New Directions for Situated Cognition in Mathematics Education represents the maturation and expansion of the situated cognition theories applied t...
In this chapter we interrogate the debate between mathematicians and mathematics educators. This debate is widely recognized in the United States, for instance, where the term math wars is often used in reference to the heated disagreements between mathematicians and mathematics edu- tors. Such recognition might suggest that this topic itself has relevance both for the academy and for educational policy pertaining to mathematics edu- tion. We propose to locate this debate, unavoidably, whenever and wherever mathematics education is written. Our aim is to show how the debate itself gives rise...
In this chapter we interrogate the debate between mathematicians and mathematics educators. This debate is widely recognized in the United States, for...
