{"product_id":"how-humans-learn-to-think-mathematically-exploring-the-three-worlds-of-mathematics-hardback-9781107035706","title":"How Humans Learn to Think Mathematically; Exploring the Three Worlds of Mathematics (Hardback) 9781107035706","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHow Humans Learn to Think Mathematically\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eExploring the Three Worlds of Mathematics\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eHow Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDavid Tall (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107035706, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 2 September 2013\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e484 pages, 175 b\/w illus.  4 tables\u003cbr\u003e23.1 x 16 x 3 cm, 0.77 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eHow 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Prelude: 1. About this book\u003cbr\u003e Part II. School Mathematics and its Consequences: 2. The foundations of mathematical thinking\u003cbr\u003e 3. Compression, connection and blending of mathematical ideas\u003cbr\u003e 4. Set-befores, met-befores and long-term learning\u003cbr\u003e 5. Mathematics and the emotions\u003cbr\u003e 6. The three worlds of mathematics\u003cbr\u003e 7. Journeys through embodiment and symbolism\u003cbr\u003e 8. Problem-solving and proof\u003cbr\u003e Part III. Interlude: 9. The historical evolution of mathematics\u003cbr\u003e Part IV. University Mathematics and Beyond: 10. The transition to formal knowledge\u003cbr\u003e 11. Blending knowledge structures in calculus\u003cbr\u003e 12. Expert thinking and structure theorems\u003cbr\u003e 13. Contemplating the infinitely large and the infinitely small\u003cbr\u003e 14. Expanding frontiers through mathematical research\u003cbr\u003e 15. Reflections\u003cbr\u003e Appendix: where the ideas came from.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e], Educational psychology [\u003ca title=\"See our other books on Educational psychology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Educational%20psychology%20%5BJNC%5D%22\"\u003eJNC\u003c\/a\u003e], Psychology [\u003ca title=\"See our other books on Psychology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Psychology%20%5BJM%5D%22\"\u003eJM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265529336088,"sku":"9781107035706","price":95.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107035706i.jpg?v=1692023933","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/how-humans-learn-to-think-mathematically-exploring-the-three-worlds-of-mathematics-hardback-9781107035706","provider":"Freshly Printed Books","version":"1.0","type":"link"}