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“Whiteboxing” the Content of a Formal Mathematical Text in a Dynamic Geometry Environment

Jankvist, UT; Geraniou, E; (2021) “Whiteboxing” the Content of a Formal Mathematical Text in a Dynamic Geometry Environment. Digital Experiences in Mathematics Education , 7 pp. 222-246. 10.1007/s40751-021-00088-6. Green open access

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Abstract

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering—or whiteboxing—the content of a mathematical proof, in this case that of Proposition 41 from Euclid’s Elements. In the discussion of the example, we look into the impact of GeoGebra’s “dragging” functionality on students’ interactions and the possession and development of students’ proof schemes. The study and accompanying analysis illustrate that, despite the positive whiteboxing effects in relation to the mathematical content of the proposition, whiteboxing through dragging calls for caution in relation to students’ work with proof and proving—in particular, in relation to students seeing the necessity for formal proof. Moreover, caution must be paid, e.g., by teachers, so that students do not jump to conclusions and in the process develop inexpedient mathematical proof schemes upon which they may stumble in their future mathematical work.

Type: Article
Title: “Whiteboxing” the Content of a Formal Mathematical Text in a Dynamic Geometry Environment
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s40751-021-00088-6
Publisher version: https://doi.org/10.1007/s40751-021-00088-6
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Euclid’s Elements, Whiteboxing, GeoGebra, Dragging, Formal proof schemes, History and pedagogy of mathematics (HPM), Dépaysement
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education > IOE - Curriculum, Pedagogy and Assessment
URI: https://discovery.ucl.ac.uk/id/eprint/10128552
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