Development and Evolution of Instrumented Schemes: A Case Study of Learning Programming for Mathematical Investigations

Autor/inn/en	Gueudet, Ghislaine; Buteau, Chantal; Muller, Eric; Mgombelo, Joyce; Sacristán, Ana Isabel; Rodriguez, Marisol Santacruz
Titel	Development and Evolution of Instrumented Schemes: A Case Study of Learning Programming for Mathematical Investigations
Quelle	In: Educational Studies in Mathematics, 110 (2022) 2, S.353-377 (25 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Gueudet, Ghislaine)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-021-10133-1
Schlagwörter	College Students; College Mathematics; Models; Concept Formation; Learning Processes; Mathematical Logic; Programming + Suchen Sie Ihr Suchwort? Collegestudent; Analogiemodell; Concept learning; Begriffsbildung; Learning process; Lernprozess; Mathematical logics; Mathematische Logik; Programmierung
Abstract	We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of development of schemes by students; these development processes are called instrumental geneses. Nevertheless, how these schemes evolve has not been fully explained. In this paper, we propose to enrich the theoretical frame of the instrumental approach by a model of scheme evolution and to use this new approach to investigate learning to use programming for pure and applied mathematics investigation projects at the university level. We examine the case of one student completing four investigation projects as part of a course workload. We analyze the productive and constructive aspects of the student's activity and the dynamic aspect of the instrumental geneses by identifying the mobilization and evolution of schemes. We argue that our approach constitutes a new theoretical and methodological contribution deepening the understanding of students' instrumented learning processes. Identifying instrumented schemes illuminates in particular how mathematical knowledge and programming knowledge are combined. The analysis in terms of scheme evolutions reveals which characteristics of the situations lead to such evolutions and can thus inform the design of teaching. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01