A joke on precision? Revisiting “precision” in the school mathematics discourse

Ryan, Ulrika; Chronaki, Anna

doi:10.1007/s10649-020-09963-2

Educ Stud Math

2020

DOI: 10.1007/s10649-020-09963-2

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A joke on precision? Revisiting “precision” in the school mathematics discourse

Ulrika Ryan

Anna Chronaki

Abstract: This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning. The paper uses theories on humour and inferentialism to revisit the normative place of "precision" in mathematics classroom discourse.

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Cited by 4 publications

References 25 publications

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Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

Uegatani,

Otani,

Fujita

2024

Educ Stud Math

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This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton’s distinction between reasoning and argument, and Ernest’s concept of intrapersonal dialogue, we propose two theoretical perspectives for understanding the roles of informal reasoning in argumentation: the semi-formal, and the negotiation perspectives. From the latter perspective, we can say that informal reasoning involves creating alternatives, eschewing the relatively unpromising ones, and choosing the most promising one. To illustrate the advantage of the negotiation perspective over the semi-formal perspective, we present two examples of students’ statistical written reports from a previous study. These examples illustrate that spontaneous concepts influenced the students’ creation of multiple alternatives, and choice of the most promising one, in informal reasoning. Therefore, to better understand the development of mathematical concepts, we need to recognise the role of spontaneous concepts through decentralising mathematics. Finally, we introduce inferentialism as an additional theoretical perspective for investigating both the mathematical development of spontaneous concepts, and the spontaneous development of mathematical concepts. The inferentialist idea of the game of giving and asking for reasons indicates how to empirically investigate the mutual development of spontaneous and mathematical concepts.

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Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

Uegatani,

Otani,

Fujita

2024

Educ Stud Math

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Real and illusionary difficulties in conceptual learning in mathematics: comparison between constructivist and inferentialist perspectives

Uegatani,

Otani,

Shirakawa

et al. 2023

Math Ed Res J

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Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term difficulty in mathematics education research. We start this paper by arguing that a constructivist perspective, which has often been adopted in researches on mathematical task design, can deal with difficulties in solving a mathematical problem, but it cannot theoretically deal with those in understanding a mathematical concept. Therefore, we need the alternative philosophy of Robert Brandom’s inferentialism to capture students’ real difficulties in conceptual learning. From an inferentialist perspective, we introduce the idea of illusionary and real difficulties. The former is defined as what students cannot do, but they are not conscious of what they should do, while the latter is defined as what students cannot do despite their consciousness of what they should do. Through an eighth grade classroom episode, we argue that it is important in mathematics education research to focus not only on illusionary difficulties but also on the transition from illusionary to real difficulties. Researchers are encouraged to design a learning environment in which students become conscious of what they cannot do and to observe their mathematics learning in such an environment.

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Solidarity acts in the context of language diversity: Students’ encounters with epistemological difference

Ryan

2022

The Journal of Mathematical Behavior

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A joke on precision? Revisiting “precision” in the school mathematics discourse

Cited by 4 publications

References 25 publications

Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

Real and illusionary difficulties in conceptual learning in mathematics: comparison between constructivist and inferentialist perspectives

Solidarity acts in the context of language diversity: Students’ encounters with epistemological difference

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