Abstract
This chapter focuses on an inferential view on elaborating concepts in mathematics classrooms. A framework is going to be presented and used, which helps to analyse and to reflect on the processes of teaching and learning mathematical concepts. The framework is based on Wittgenstein’s theory of language-games and especially its core, the primacy of the use of words. Concerning the theory of inferentialism by Robert Brandom, the inferential use of words in language-games can be regarded as an indicator of the understanding of a concept. Together, the theoretical framework combines the role of judgements and their connections via rules in inferences in order to describe processes of concept formation.
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Appendix
Appendix
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Transcription
1. Paralinguistic signs
- ,:
-
a short stop while speaking, max. one second
- ..:
-
a short break, max. two seconds
- sure-:
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the voice lingers on at the end of a word or a comment
- sure :
-
emphasis has been placed on this word
- sure:
-
word spoken with a drawl
2. Other characterizations
- (..):
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vague, but assumed words
- (shows):
-
characterization of body language and facial expressions
A row starts at the end of the last word of the previous statement: Noticeable quick follow-up, e.g.:
- M::
-
why that
- F::
-
therefore
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Meyer, M. (2018). Using Rules for Elaborating Mathematical Concepts. In: Ernest, P. (eds) The Philosophy of Mathematics Education Today. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-77760-3_18
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DOI: https://doi.org/10.1007/978-3-319-77760-3_18
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