The concept of proof in the light of mathematical work

Richard, Philippe; Oller-Marcén, Antonio M.; Seguí, Vicente Meavilla

doi:10.1007/s11858-016-0805-9

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ZDM Mathematics Education

2016

DOI: 10.1007/s11858-016-0805-9

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The concept of proof in the light of mathematical work

Philippe Richard

Antonio M. Oller-Marcén

Vicente Meavilla Seguí

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Cited by 16 publications

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“…Like many other researchers in this field, we are inspired by Vérillon and Rabardel's (1995) approach of instrumental activity, using the notions of artefact, instrumental genesis and instrumented techniques. In parallel, we have drawn on the theory of MWS for specific research studies (Minh & Lagrange 2016, Richard & al., 2016. This theory also puts forward the notions of artefact and instrumental genesis, furthermore including two other geneses: semiotic and discursive.…”

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Instrumental Genesis in the Theory of MWS: Insight from Didactic Research on Digital Artifacts

Lagrange

Richard

2022

Mathematics Education in the Digital Era

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The central focus of this chapter is the relationship between the notions introduced by Vérillon and Rabardel (1995), 'artefact' and 'instrumental genesis', and the homonym notions in the theory of MWS. Following a brief overview of the Piagetian and Activity Theory perspectives which inspired Vérillon and Rabardel, we explore how didactic research on digital artefacts developed two viewpoints on the instrumental genesis: psychological and institutional. The idea of instrumental genesis in the theory of MWS is consistent with the concept of instrumented mediation by Vérillon and Rabardel, but is a more focused notion, since MWS include two additional geneses, semiotic and discursive. The theory of MWS moreover does not theorize about the mediation and as such, in a particular situation where a digital artefact is used, both viewpoints will be helpful. Regarding the poles of the instrumental genesis, we propose characterizing a digital artefact by the underlying data representations and algorithmic treatments, and constructions as data-result models of mathematical configurations, taking advantage of the representations and algorithms in the artefact. MotivationThe authors of this chapter are two researchers in mathematics education with a long experience in investigating the classroom use of digital artefacts and designing mathematical software environments. Like many other researchers in this field, we are inspired by Vérillon and Rabardel's (1995) approach of instrumental activity, using the notions of artefact, instrumental genesis and instrumented techniques. In parallel, we have drawn on the theory of MWS for specific research studies (Minh & Lagrange 2016, Richard & al., 2016. This theory also puts forward the notions of artefact and instrumental genesis, furthermore including two other geneses: semiotic and discursive.

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mentioning

confidence: 99%

Instrumental Genesis in the Theory of MWS: Insight from Didactic Research on Digital Artifacts

Lagrange

Richard

2022

Mathematics Education in the Digital Era

Self Cite

View full text Add to dashboard Cite

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Computer-Generated Geometry Proofs in a Learning Context

Quaresma

Santos

2019

Proof Technology in Mathematics Research and Teaching

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Issues and Challenges in Instrumental Proof

Richard

Venant

Gagnon

2019

Proof Technology in Mathematics Research and Teaching

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The concept of proof in the light of mathematical work

Cited by 16 publications

References 15 publications

Instrumental Genesis in the Theory of MWS: Insight from Didactic Research on Digital Artifacts

Instrumental Genesis in the Theory of MWS: Insight from Didactic Research on Digital Artifacts

Computer-Generated Geometry Proofs in a Learning Context

Issues and Challenges in Instrumental Proof

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