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Disclosure of mathematical relationships with a digital tool: a three layer-model of meaning

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Abstract

This paper examines mathematical meaning-making from a phenomenological perspective and considers how a specific dynamic digital tool can prompt students to disclose the relationships between a function and its antiderivatives. Drawing on case study methodology, we focus on a pair of grade 11 students and analyze how the tool’s affordances and the students’ engagement in the interrogative processes of sequential questioning and answering allow them to make sense of the mathematical objects and their relationships and, lastly, of the mathematical activity in which they are engaged. A three-layer model of meaning of the students’ disclosure process emerges, namely, (a) disclosing objects, (b) disclosing relationships, and (c) disclosing functional relationships. The model sheds light on how the students’ interrogative processes help them make sense of mathematical concepts as they work on tasks with a digital tool, an issue that has rarely been explored. The study’s implications and limitations are discussed.

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Notes

  1. They had already encountered the integral symbol and its computational uses in their physics and electronics lessons, however. The integral in such cases had the meaning of an area (definite integral). Nonetheless, they had not been exposed to the fundamental theorem of calculus, which links the two meanings.

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Authors and Affiliations

  1. Department of Science & Technology Education, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Osama Swidan

  2. Department of Philosophy & Science of Education, University of Turin, Turin, Italy

    Cristina Sabena

  3. Department of Mathematics, University of Turin, Turin, Italy

    Ferdinando Arzarello

Authors
  1. Osama Swidan
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  2. Cristina Sabena
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  3. Ferdinando Arzarello
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Correspondence to Osama Swidan.

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Swidan, O., Sabena, C. & Arzarello, F. Disclosure of mathematical relationships with a digital tool: a three layer-model of meaning. Educ Stud Math 103, 83–101 (2020). https://doi.org/10.1007/s10649-019-09926-2

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  • DOI: https://doi.org/10.1007/s10649-019-09926-2

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