Connecting Algorithmics to Mathematics Learning: A Design Study of the Intermediate Value Theorem and the Bisection Algorithm

Autor/inn/en	Lagrange, Jean-Baptiste; Laval, Dominique
Titel	Connecting Algorithmics to Mathematics Learning: A Design Study of the Intermediate Value Theorem and the Bisection Algorithm
Quelle	In: Educational Studies in Mathematics, 112 (2023) 2, S.225-245 (21 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Lagrange, Jean-Baptiste)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-022-10192-y
Schlagwörter	Algorithms; Mathematics Education; Mathematical Concepts; Design; Secondary School Students; Foreign Countries; Mathematics Skills; Programming; France + Suchen Sie Ihr Suchwort? Algorithm; Algorithmus; Mathematische Bildung; Sekundarschüler; Ausland; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Programmierung; Frankreich
Abstract	Programming-based activities are becoming more widespread in curricula. Our theoretical and empirical investigation seeks to identify appropriate ways to connect computer programming and algorithmics to mathematical learning. We take the intermediate value theorem as our starting point, as it is covered by the French school curriculum, and because of its links with the bisection algorithm. We build upon the theory of mathematical working spaces, distinguishing between algorithmic and mathematical working spaces. Both working spaces are explored from the semiotic, instrumental, and discursive dimensions that support learning. Our two research questions focus on the suitable algorithmic and mathematical working spaces in which students develop an understanding of the intermediate value theorem, and the bisection algorithm. Our method starts at the reference level, with an epistemological and curricular analysis. Then, a series of tasks is designed for students working in adidacticity, and suitable working spaces are determined a priori. The tasks have been implemented in French classrooms with students aged 16-19. An analysis of their work supports an a posteriori examination of the working spaces. Our findings demonstrate that the students were able to make connections between algorithmics and mathematics in each of the three dimensions, semiotic, instrumental, and discursive, and point out the interplay between these dimensions. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01