The opaque nature of generic examples: The structure of student teachers’ arguments in multiplicative reasoning

The study aims to explore the structural aspects of generic examples, to get better insight into what makes them potentially opaque for learners. We have analyzed 27 written arguments, for which student teachers (grades 1–10) were asked to use a generic example to prove a given statement in multipli...

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Vydané v:The Journal of mathematical behavior Ročník 58; s. 100755
Hlavní autori: Rø, Kirsti, Arnesen, Kristin Krogh
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.06.2020
Predmet:
Generic examples
Mathematical arguments
Proof and proving
Structural analysis
Student teachers
Mathematical arguments
Proof and proving
Generic examples
Student teachers
Structural analysis
ISSN:0732-3123, 1873-8028
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Shrnutí:The study aims to explore the structural aspects of generic examples, to get better insight into what makes them potentially opaque for learners. We have analyzed 27 written arguments, for which student teachers (grades 1–10) were asked to use a generic example to prove a given statement in multiplication. Using Toulmin’s framework, we developed five categories of arguments based on their structure: examples, empirical arguments, leap arguments, embedded arguments, and other arguments. Also, we conclude that none of the student teachers provided arguments that we recognize as complete generic examples. The results bring us to a discussion about features of generic examples making them difficult to come to grips with, having implications for how teacher educators can support student teachers’ learning to prove. From this, we propose a definition of generic examples that attends to the criteria suggested in previous research, yet, emphasizing their structural nature.
ISSN:0732-3123
1873-8028
DOI:10.1016/j.jmathb.2019.100755