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...
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learn...
As we enter into the 21"Century, the presence of technology, particularly techno-science, in everyday life is overwhelming. Institutions in the modem world are affected by this presence. Like Janus, the ancient Roman god whose double-faced head signified his knowledge of the present and the future, education has always been a two-faced enterprise. The past establishes goals and methods of Education, and the other face tries to capture the future and suggests and proposes new directions of thought and new styles of behavior for the generation which, in a few years, will take over both routines...
As we enter into the 21"Century, the presence of technology, particularly techno-science, in everyday life is overwhelming. Institutions in the modem ...
The Construction of New Mathematical Knowledge in Classroom Interaction deals with the very specific characteristics of mathematical communication in the classroom. The general research question of this book is: How can everyday mathematics teaching be described, understood and developed as a teaching and learning environment in which the students gain mathematical insights and increasing mathematical competence by means of the teacher's initiatives, offers and challenges? How can the 'quality' of mathematics teaching be realized and appropriately described? And the following more specific...
The Construction of New Mathematical Knowledge in Classroom Interaction deals with the very specific characteristics of mathematical communication ...
This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.
This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by ...
A significant driver of recent growth in the use of mathematics in the professions has been the support brought by new technologies. Not only has this facilitated the application of established methods of mathematical and statistical analysis but it has stimulated the development of innovative approaches. These changes have produced a marked evolution in the professional practice of mathematics, an evolution which has not yet provoked a corresponding adaptation in mathematical education, particularly at school level. In particular, although calculators -- first arithmetic and scientific, then...
A significant driver of recent growth in the use of mathematics in the professions has been the support brought by new technologies. Not only has this...
This book is a product of the BACOMET group, a group of educators-mainly educators of prospective teachers of mathematics-who first came together in 1980 to engage in study, discussion, and mutual reflection on issues in mathematics education. BACOMET is an acronym for BAsic Components of Mathematics Education for Teachers. The group was formed after a series of meetings in 1978-1979 between Geoffrey Howson, Michael Otte, and the late Bent Christiansen. In the ensuing years, BACOMET initiated several projects that resulted in published works. The present book is the main product of the...
This book is a product of the BACOMET group, a group of educators-mainly educators of prospective teachers of mathematics-who first came together in 1...
Mathematics education research as a discipline is situated at the confluence of an array of diffuse seemingly incommensurable and radically divergent discourses. Research claims that have grown out of mathematics education are wide-ranging and antagonistic rather than circumscribed by hidebound disciplinary frames. While there has never been a unified totalising discipline of knowledge labelled mathematics education research and while it has always been a contested terrain it is fair to say that the master paradigm out of which this field has been generated has been that of cognitive...
Mathematics education research as a discipline is situated at the confluence of an array of diffuse seemingly incommensurable and radically divergent ...
This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original manuscript was of course Freudenthal s, but his colleagues have carried the project through to its conclusion with love for the man, and his ideas, and with a respect developed over years of communal effort. Their invitation to me to write this Preface e- bles me to pay my respects to the great man, although I am probably incurring his wrath for writing a Preface for his book without his permission I just hope he understands the feelings of all...
This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original ma...
In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson and M. Otte, Perspectives on Mathematics Education, Reidel, Dordrecht, 1986). Underlying all of them was the fundamental problem area of the relationships between mathematical knowledge and the teaching and learning processes. The subsequent project BACOMET 2, whose outcomes are presented in this book, continued this work, especially by focusing on the genesis of mathematical knowledge in the classroom. The book developed over the period 1985-9...
In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson...
Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in social practices, including the market place and the home, have initiated a shift of focus. Culture has become identified as a key to understanding the basis on which the learner appropriates meaning. The chapters in this timely book attempt to engage...
Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus unde...
