Understanding and Organizing Mathematics Education as a Design Science–Origins and New Developments

Wittmann, Erich Ch.

doi:10.1007/978-3-030-61570-3_14

Cited by 1 publication

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“…To clarify this, we refer to pre-formalist categorisations of proofs (e.g. Blum & Kirsch, 1991;Brunner & Reusser, 2019;Semadeni, 1984;Wittmann, 1996Wittmann, , 2009Wittmann, , 2019Wittmann & Müller, 1990) which allow us to legitimate proofs at different levels and are useful for designing a suitable proving task. Per Reid and Knipping (2010), '[f]or the preformalists the nature of the premises (concrete objects, etc.)…”

Section: A Way To Characterize Proof and Proving: An Analytical Frameworkmentioning

confidence: 99%

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

Shinno

Fujita

2021

International Journal of Mathematical Education in Science and

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In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between 'construction' and 'substantiation' based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.

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Section: A Way To Characterize Proof and Proving: An Analytical Frameworkmentioning

confidence: 99%

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

Shinno

Fujita

2021

International Journal of Mathematical Education in Science and

View full text Add to dashboard Cite

show abstract

Understanding and Organizing Mathematics Education as a Design Science–Origins and New Developments

Cited by 1 publication

References 13 publications

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

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