Hybrid journal (It can contain Open Access articles) ISSN (Print) 0268-3679 - ISSN (Online) 1471-6976 Published by Oxford University Press[419 journals]

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Authors:Bos R; Kouropatov A, Swidan O. Pages: 87 - 91 PubDate: Tue, 07 Jun 2022 00:00:00 GMT DOI: 10.1093/teamat/hrac008 Issue No:Vol. 41, No. 2 (2022)

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Authors:Swidan O. Pages: 92 - 109 Abstract: AbstractThis study aims at exploring the role of argumentation in the process of shared meaning making that occurs between students as they use digital tools to explore the concept of the indefinite integral. The study followed 11 pairs of 17-year-old students as they worked together to solve the Indefinite Integral Task with the aid of a digital tool. The study was guided by the phenomenology perspective, which considers meaning making in mathematics as a progressive disclosure of the mathematical objects at stake. The data analysis tracked and categorized the components of students’ argumentation as they progress in the meaning-making process of the indefinite integral. Our research findings revealed that the digital tool allows the students to produce evidence with which to substantiate and justify their arguments, and we also found that their frequent use of statements that built upon one another’s arguments fostered the transition between one layer of disclosure and the next one. PubDate: Wed, 05 Jan 2022 00:00:00 GMT DOI: 10.1093/teamat/hrab034 Issue No:Vol. 41, No. 2 (2022)

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Authors:Kouropatov A; Ovodenko R. Pages: 142 - 166 Abstract: The learning of calculus concepts is considered challenging for students. This claim is actual for calculus in general and for specific concepts in particular. In this paper, we focus on the concept of the inflection point. We argue that one of the roots of this problem is the lack of a useful and productive meaning of the concept—the understanding of the inflection point as the point where the behaviour of a curve (graph of function) changes in relation to the tangent line. With the purpose of helping students to construct this meaning we developed a specific digital tool: a teaching unit based on the interactive diagrams framework. Does this tool help students to achieve this meaning (i.e., to construct and consolidate new knowledge)' To answer this question, we conducted an empirical feasibility experiment (in the form of a case study with two first-year students from the Industrial Engineering College) and analysed the gathered data using the framework of abstraction in context as the theoretical and methodological basis. Our findings show that the designed tool (the interactive digital teaching unit) has potential for helping students to make the above-mentioned meaning for this mathematical concept and can serve as a useful basis to continue the investigation of designing tools that support the meaning-making of advanced mathematical concepts. PubDate: Fri, 25 Mar 2022 00:00:00 GMT DOI: 10.1093/teamat/hrac007 Issue No:Vol. 41, No. 2 (2022)

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Authors:Elias D; Dreyfus T. Pages: 167 - 181 Abstract: We investigated how two didactical tools assist high school students in constructing knowledge about convergence and limits. The first tool is manual plotting of the terms of selected sequences, and the second, a technological applet. Student pairs worked in an interview setting on an activity designed for the purpose of this research. The interviews were transcribed and analysed using the RBC model of abstraction in context. The analysis of the interviews revealed that manual plotting supported students’ development of intuition about convergence and the technological tool supported students in constructing a notion of ‘as close as one pleases’, thus making a step in the direction of the formal definition of limit. As a result, a structure of the elements of knowledge of the concept of convergence of sequences has been developed, the support of the tools has been evaluated and possible obstacles of the process have been identified. PubDate: Wed, 05 Jan 2022 00:00:00 GMT DOI: 10.1093/teamat/hrab035 Issue No:Vol. 41, No. 2 (2022)

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Authors:Wangberg A; Gire E, Dray T. Pages: 110 - 124 Abstract: AbstractStudents need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In Raising Calculus to the Surface activities, multivariable calculus students collaboratively discover properties of derivatives by using tangible tools to solve context-rich problems. In this paper, we present examples of student reasoning about derivatives during the first of a sequence of three Raising Calculus activities. In this sequence, students work collaboratively on dry-erasable surfaces (tangible graphs of functions of two variables) using an inclinometer, a tool that can measure derivatives in any direction on the surfaces, to invent procedures to determine derivatives in any direction. Since students are not given algebraic expressions for the underlying functions, they must coordinate conceptual and geometric notions of derivatives, building on their understandings from introductory differential calculus. We discuss examples of student reasoning that demonstrate how the activity supports student realization of the need to define a path, attend to direction and the orientation of the coordinate axes and recognize covariation between related quantities. This first activity enables students to initially recognize the ratio of small changes approach to derivatives. We briefly describe how students utilize the ratio of small changes approach in subsequent activities as they measure partial derivatives on surfaces (using an inclinometer) and on contour maps. PubDate: Wed, 15 Dec 2021 00:00:00 GMT DOI: 10.1093/teamat/hrab030 Issue No:Vol. 41, No. 2 (2021)

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Authors:Bos R; Doorman M, Drijvers P, et al. Pages: 125 - 141 Abstract: AbstractWe study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks. Tiago’s work demonstrates the affordances of the ARSB, e.g. to trace a height line and to manipulate plastic planes either with or without feedback from projected height lines. Tiago’s reasoning about mathematical concepts, e.g. the parameters in a plane equation and the gradient vector, is supported by perceptual structures that he discovers during these embodied tasks. We distinguished two ways in which ARSB affordances were used in the learning sequence. In perception-based and action-based tasks, the affordances of the ARSB were immediately available and intensively involved in the interaction. In incorporation tasks, on the contrary, a critical affordance was deliberately removed and the student was able to reproduce its functionality without technology. PubDate: Mon, 04 Oct 2021 00:00:00 GMT DOI: 10.1093/teamat/hrab011 Issue No:Vol. 41, No. 2 (2021)