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Erschienen in:
The Ontology of Models Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

25. Abduction and the Emergence of Necessary Mathematical Knowledge

verfasst von : Ferdinand Rivera

Erschienen in: Springer Handbook of Model-Based Science

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Model-Based Reasoning in Mathematical Practice
Nächstes Kapitel Vision, Thinking, and Model-Based Inferences
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Metadaten
Titel
Abduction and the Emergence of Necessary Mathematical Knowledge
verfasst von
Ferdinand Rivera
Copyright-Jahr
2017
Verlag
Springer International Publishing
Buch
Springer Handbook of Model-Based Science

Print ISBN: 978-3-319-30525-7

Electronic ISBN: 978-3-319-30526-4

Copyright-Jahr: 2017

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