Rigorous mathematical thinking

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 that allow such an active construction of cognitive functions: 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 students with a history of educational failure who were considered hopeless underachievers. James T. Kinard, Sr., earned his Ph.D. in electroanalytical chemistry from Howard University and is president of Innovations for the Development of 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 international cognitive enrichment workshops in the United States, Canada, the United Kingdom, 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 an academic appointment at Boston University, was a visiting professor at the University of Exeter and at the University of Witwatersrand, and was a visiting scholar at Harvard University. Dr.Kozulin is author of Vygotsky’s Psychology: A Biography of Ideas (1990) and Psychological Tools: A Sociocultural Approach to Education (1998).