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Abduction and the Emergence of Necessary Mathematical Knowledge

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Springer Handbook of Model-Based Science

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Abstract

The prevailing epistemological perspective on school mathematical knowledge values the central role of induction and deduction in the development of necessary mathematical knowledge with a rather taken-for-granted view of abduction. This chapter will present empirical evidence that illustrates the relationship between abductive action and the emergence of necessary mathematical knowledge.

Recent empirical studies on abduction and mathematical knowledge construction have begun to explore ways in which abduction could be implemented in more systematic terms. In this chapter four types of inferences that students develop in mathematical activity are presented and compared followed by a presentation of key findings from current research on abduction in mathematics and science education. The chapter closes with an exploration of ways in which students can effectively enact meaningful and purposeful abductive thinking processes through activities that enable them to focus on relational or orientation understandings. Four suggestions are provided, which convey the need for meaningful, structured, and productive abduction actions. Together the suggestions target central features in abductive cognition, that is, thinking, reasoning, processing, and disposition.

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Acknowledgements

The research that is reported in this chapter has been funded by the National Science Foundation under Grant Number DRL 0448649. All the views and opinions expressed in this report are solely the author’s responsibility and do not necessarily reflect the views of the foundation.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, San José University, 1 Washington Square, CA 95192, San Jose, USA

    Ferdinand Rivera

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  1. Ferdinand Rivera
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Correspondence to Ferdinand Rivera .

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  1. Department of Humanities, University of Pavia, Piazza Botta 6, 27100, Pavia, Italy

    Lorenzo Magnani  & Tommaso Bertolotti  & 

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Rivera, F. (2017). Abduction and the Emergence of Necessary Mathematical Knowledge. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_25

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  • DOI: https://doi.org/10.1007/978-3-319-30526-4_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30525-7

  • Online ISBN: 978-3-319-30526-4

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