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Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm

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Τίτλος: Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm
Συγγραφείς: Lagrange, Jean-Baptiste, Laval, Dominique
Συνεισφορές: lagrange, jean-baptiste, Laboratoire de Didactique André Revuz (LDAR (URP_4434)), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Université de Lille-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris Cité (UPCité)-CY Cergy Paris Université (CY), Institut national supérieur du professorat et de l'éducation - Académie de Versailles (INSPÉ Versailles), CY Cergy Paris Université (CY)
Πηγή: Educational Studies in Mathematics. 112:225-245
Στοιχεία εκδότη: Springer Science and Business Media LLC, 2022.
Έτος έκδοσης: 2022
Θεματικοί όροι: Algorithmic and mathematical working spaces Mathematics-computer science connections Bisection algorithm Intermediate value theorem Programming tasks Algorithmic thinking Adidacticity, 4. Education, 05 social sciences, [INFO]Computer Science [cs], [MATH] Mathematics [math], [MATH]Mathematics [math], [INFO] Computer Science [cs], 0101 mathematics, 0503 education, 01 natural sciences
Περιγραφή: 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.
Τύπος εγγράφου: Article
Γλώσσα: English
ISSN: 1573-0816
0013-1954
DOI: 10.1007/s10649-022-10192-y
Σύνδεσμος πρόσβασης: https://hal.science/hal-04238840v1
https://doi.org/10.1007/s10649-022-10192-y
Rights: Springer Nature TDM
Αριθμός Καταχώρησης: edsair.doi.dedup.....86c41e6dc86e5d31438cd03d6e21ef49
Βάση Δεδομένων: OpenAIRE
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  Data: 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.
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