Exercises in mathematical imagining: setting out a teaching instrument that evokes imaginings and utilises visualisations in secondary school mathematics
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Authors
Weber, Christof
Author (Corporation)
Publication date
2014
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Type
04B - Conference paper
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Editor (Corporation)
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Parent work
Proceedings of the British Society for Research Into Learning Mathematics
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DOI of the original publication
Series
Series number
Volume
34
Issue / Number
1
Pages / Duration
125-130
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Abstract
This paper sets out a teaching instrument which could be referred to as ‘mental imagery exercises in mathematics’ or ‘exercises in mathematical visualisation’. Originally developed in the context of the teaching principles of the German-speaking countries, and then based on theories of the German mathematics education literature, the paper will reframe this task design and conclude that the term ‘exercises in mathemat- ical imagining’ is most appropriate. The fact that imagining—i.e. mentally forming and manipulating images—is personal means that this approach enables students to experience mathematics as commencing in their own minds. Teachers are also simultaneously able to gain insight into their students’ thought processes through this approach. In contrast with mental arithmetic, this task design does not focus on training a particular ability. Rather it promotes a specific heuristic strategy, within which students first conceive of and imagine a mathematical topic, and then construct and explore visualisations in order to understand their implications. This paper should be read as a case study of the researcher’s day-to-day teaching. It makes explicit a practice that has for many years produced positive results in terms of students developing mathematical understanding.
Keywords
Mental Imagery, Imagining, Secondary School Mathematics
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ISBN
ISSN
1463-6840
Language
English
Created during FHNW affiliation
Yes
Strategic action fields FHNW
Publication status
Published
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Expert editing/editorial review
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Citation
Weber, C. (2014). Exercises in mathematical imagining: setting out a teaching instrument that evokes imaginings and utilises visualisations in secondary school mathematics. Proceedings of the British Society for Research into Learning Mathematics, 34(1), 125–130. http://hdl.handle.net/11654/27724