What mathematics is entailed in knowing to act in a moment? Is  tacit, rhetorical knowledge significant in mathematics education? What  is the role of intuitive models in understanding, learning and  teaching mathematics? Are there differences between elementary and  advanced mathematical thinking? Why can't students prove? What are the  characteristics of teachers' ways of knowing?   This book focuses on various types of knowledge that are significant  for learning and teaching mathematics. The first part defines,  discusses and contrasts psychological, philosophical and didactical  issues related to various types of knowledge involved in the learning  of mathematics. The second part describes ideas about forms of  mathematical knowledge that are important for teachers to know and  ways of implementing such ideas in preservice and in-service  education.   The chapters provide a wide overview of current thinking about  mathematics learning and teaching which is of interest for researchers  in mathematics education and mathematics educators.   Topics covered include the role of intuition in mathematics learning  and teaching, the growth from elementary to advanced mathematical  thinking, the significance of genres and rhetoric for the learning of  mathematics and the characterization of teachers' ways of knowing.

Forms of Mathematical Knowledge - Learning and Teaching with Understanding PDF

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