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On explanatory proofs in school mathematics
10.2.2022, 16:15 - 17:15
Speaker:Taro Fujita, Exeter University, UK
Location:Mathematisches Institut, Bunsenstr 3-5-Zoom: oder -Live stream:
Organizer:Mathematisches Institut
Proving is an essential but challenging activity in mathematical learning. Recent curricula in various countries require proof and proving to be taught at all levels (e.g. the National Curriculum for Mathematics from the Department for Education in England). Among many functions of proof and reasoning, an explanation is seen as important as it plays a role in enriching students’ mathematical understanding. However, mathematicians, philosophers, and mathematics educators are still debating what explanations and explanatory proofs are and their educational values. In this talk, I will provide an overview of research related to exploratory proving and reasoning in school mathematics, and discuss what activities and tasks can be designed to foster students’ mathematical understanding through explanatory proofs. My tentative suggestion is that an explanation in mathematics is a social attempt to describe why something happens, and it might have all, or some of the following three properties: EX1. An explanation can make explicit which mathematical properties are used, and make it evident/salient that the result depends on the properties; EX2. An explanation can unify a set of statements which initially appeared to be different; EX3. An explanation can generate a representation about mathematical concepts, procedures, etc. for understanding. I will refer to examples from primary and secondary schools (UK and Japan in particular).
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