Cambridge: Cambridge University Press, 2013. — 484 p.
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child’s experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra and the introduction of definitions and proof. Tail’s explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick and Visiting Professor at the Mathematics Education Centre, Loughborough University. He is internationally known for his research into long-term mathematical development at all levels, from preschool to the frontiers of research, including in-depth studies explaining mathematical success and failure.