Rigorous Mathematical Thinking: Conceptual Formation in the Mathematics Classroom

by James T. Kinard, Alex Kozulin

Overview

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students’ cognitive tools and operations. Though this approach can be applied in any classroom, it seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children’s cognitive functions cannot be viewed as following a natural maturational path: They should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches allowing such an active construction – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Product Details

ISBN-13:	9780521700269
Publisher:	Cambridge University Press
Publication date:	06/08/2008
Pages:	216
Product dimensions:	5.98(w) x 8.98(h) x 0.55(d)

About the Author

James T. Kinard Sr. earned his Ph.D. in electroanalytical chemistry from Howard University and is President of Innovations for Cognitive Literacy, Inc., Chicago, Illinois. He developed and implemented the Rigorous Mathematical Thinking program and is a certified trainer of the Feuerstein cognitive development program, Instrumental Enrichment. He lectures at the international cognitive enrichment workshops in the United States, Canada, the UK, France, The Netherlands, and India.

Alex Kozulin is Research Director of The International Center for the Enhancement of Learning Potential in Jerusalem, Israel, and teaches at Tel Aviv University and Hebrew University. He held academic appointment at Boston University, was Visiting Professor at the University of Exeter and at the University of Witwatersrand, and was Visiting Scholar at Harvard University.

Table of Contents

1. The culture of mathematics; 2. Goals and objectives of mathematics education; 3. Vygotsky's Sociocultural Theory and mathematics learning; 4. Mediated learning and cognitive functions; 5. Mathematical concept formation and cognitive tools; 6. Rigorous Mathematical Thinking – application, assessment and evaluation; 7. Conclusion.

Editorial Reviews

"Consultant Kinard, an expert in cognitive enrichment and Kosulin, research director of the International Center for the Enhancement of Learning Potential argue that children's fullest cognitive development does not follow a "natural" path but must be constructed during the educational process. Basing their model on Vygotsky's theory of psychological tools and Feuerstein concept of mediated learning experience, they demonstrate how developing a mathematically-based learning culture by applying the goals and objectives of mathematics education to all subjects can reach even those who have been marginalized intellectually and socially. They explain Vygotsky's socio-cultural theory and how it applies to mathematics learning, show how mediated learning develops cognitive function, describe the process of mathematical concept formation and give a set of cognitive tools for teachers and learners to use. They close with advice on applying, assessing and evaluating their methods."
—Book News


"...The book raises some interested ideas and should give rise to some productive reflections."
—Alan H. Schoenfeld, University of California, American Journal of Psychology

From the Publisher