How Humans Learn To Think Mathematically Exploring The Three Worlds Of Mathematics

the long version

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. Tall'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. Traces mathematical development from child to adult ; Encourages a common framework useful for researchers across different fields ; Looks at teaching, curriculum, and cognitive development in elementary school through postgraduate research.--Publisher website.