Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks

Morten Misfeldt; Uffe Thomas Jankvist

doi:10.1007/978-3-319-76575-4

Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks

Morten Misfeldt, Uffe Thomas Jankvist

The Center for Applied Game Research

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

Abstract

In this chapter we investigate the role of Computer Algebra Systems (CAS) in textbook proofs. We describe two cases of CAS use in textbook proofs and use the instrumental approach, and in particular the distinction between epistemic and pragmatic mediations, to understand the consequences of the so-called CAS-assisted proofs. We end with a discussion of the experienced shortcomings of the instrumental approach in relation to CAS use in justification of mathematical results, and suggest the inclusion of alternative frameworks for filling the gap.

Original language	English
Title of host publication	Uses of Technology in Primary and Secondary Mathematics Education : Tools, Topics and Trends
Editors	Lynda Ball, Paul Drijvers, Silke Ladel, Hans-Stefan Siller, Michal Tabach, Colleen Vale
Number of pages	11
Place of Publication	Cham, Switzerland
Publisher	Springer
Publication date	2018
Pages	375-385
Chapter	22
ISBN (Print)	978-3-319-76574-7
ISBN (Electronic)	978-3-319-76575-4
DOIs	https://doi.org/10.1007/978-3-319-76575-4
Publication status	Published - 2018
Event	ICME, 13 International Congress on Mathematics Education - University of Hamburg, Hamburg, Germany Duration: 24 Jul 2016 → 31 Jul 2016 Conference number: 13

Conference

Conference	ICME, 13 International Congress on Mathematics Education
Number	13
Location	University of Hamburg
Country/Territory	Germany
City	Hamburg
Period	24/07/2016 → 31/07/2016

Series	ICME-13 Monographs
ISSN	2520-8322

Keywords

proof
computer algebra system
instrumental genesis

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Misfeldt, M., & Thomas Jankvist, U. (2018). Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks. In L. Ball, P. Drijvers, S. Ladel, H-S. Siller, M. Tabach, & C. Vale (Eds.), Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends (pp. 375-385). Springer. https://doi.org/10.1007/978-3-319-76575-4

Misfeldt, Morten ; Thomas Jankvist, Uffe. / Instrumental genesis and proof : Understanding the use of computer algebra systems in proofs in textbooks. Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends. editor / Lynda Ball ; Paul Drijvers ; Silke Ladel ; Hans-Stefan Siller ; Michal Tabach ; Colleen Vale. Cham, Switzerland : Springer, 2018. pp. 375-385 (ICME-13 Monographs).

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abstract = "In this chapter we investigate the role of Computer Algebra Systems (CAS) in textbook proofs. We describe two cases of CAS use in textbook proofs and use the instrumental approach, and in particular the distinction between epistemic and pragmatic mediations, to understand the consequences of the so-called CAS-assisted proofs. We end with a discussion of the experienced shortcomings of the instrumental approach in relation to CAS use in justification of mathematical results, and suggest the inclusion of alternative frameworks for filling the gap.",

keywords = "proof, computer algebra system, instrumental genesis",

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Misfeldt, M & Thomas Jankvist, U 2018, Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks. in L Ball, P Drijvers, S Ladel, H-S Siller, M Tabach & C Vale (eds), Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends. Springer, Cham, Switzerland, ICME-13 Monographs, pp. 375-385, ICME, 13 International Congress on Mathematics Education, Hamburg, Germany, 24/07/2016. https://doi.org/10.1007/978-3-319-76575-4

Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks. / Misfeldt, Morten; Thomas Jankvist, Uffe.
Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends. ed. / Lynda Ball; Paul Drijvers; Silke Ladel; Hans-Stefan Siller; Michal Tabach; Colleen Vale. Cham, Switzerland: Springer, 2018. p. 375-385 (ICME-13 Monographs).

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

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AB - In this chapter we investigate the role of Computer Algebra Systems (CAS) in textbook proofs. We describe two cases of CAS use in textbook proofs and use the instrumental approach, and in particular the distinction between epistemic and pragmatic mediations, to understand the consequences of the so-called CAS-assisted proofs. We end with a discussion of the experienced shortcomings of the instrumental approach in relation to CAS use in justification of mathematical results, and suggest the inclusion of alternative frameworks for filling the gap.

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Misfeldt M, Thomas Jankvist U. Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks. In Ball L, Drijvers P, Ladel S, Siller H-S, Tabach M, Vale C, editors, Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends. Cham, Switzerland: Springer. 2018. p. 375-385. (ICME-13 Monographs). doi: 10.1007/978-3-319-76575-4

Instrumental genesis and proof: Understanding the use of computer algebra systems in proofs in textbooks

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