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How humans learn to think mathematically: Exploring the three worlds of mathematics, by David Tall. (2013)

Cambridge University Press. 484 pages. Paperback: ISBN: 9781107668546 [$39.99 US], eBook Reader: ISBN: 9781107496835 [$32 US]. Hardback: ISBN: 9781107035706 [$99 US]

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Abstract

This is a fascinating and important book that should be read by anyone who is interested in mathematics and mathematics education.

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References

  • Byers, W. (2007). How mathematicians think: Using ambiguity, contradiction, and paradox to create mathematics. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Byers, W. (2014). Deep thinking: What mathematics can tell us about the mind. Singapore: World Scientific.

  • Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A ‘proceptual’ view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.

    Article  Google Scholar 

  • Sfard, A. (1994). Reification as a birth of a metaphor. For the Learning of Mathematics, 14(1), 44–55.

    Google Scholar 

  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169.

    Article  Google Scholar 

  • Thurston, W. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30(2), 161–177.

    Article  Google Scholar 

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Correspondence to William Byers.

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Byers, W. How humans learn to think mathematically: Exploring the three worlds of mathematics, by David Tall. (2013). Educ Stud Math 88, 159–162 (2015). https://doi.org/10.1007/s10649-014-9579-6

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  • DOI: https://doi.org/10.1007/s10649-014-9579-6

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