Connecting Algorithmics to Mathematics Learning: A Design Study of the Intermediate Value Theorem and the Bisection Algorithm
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| Title: | Connecting Algorithmics to Mathematics Learning: A Design Study of the Intermediate Value Theorem and the Bisection Algorithm |
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| Language: | English |
| Authors: | Lagrange, Jean-Baptiste (ORCID |
| Source: | Educational Studies in Mathematics. Feb 2023 112(2):225-245. |
| Availability: | Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/ |
| Peer Reviewed: | Y |
| Page Count: | 21 |
| Publication Date: | 2023 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Secondary Education |
| Descriptors: | Algorithms, Mathematics Education, Mathematical Concepts, Design, Secondary School Students, Foreign Countries, Mathematics Skills, Programming |
| Geographic Terms: | France |
| DOI: | 10.1007/s10649-022-10192-y |
| ISSN: | 0013-1954 1573-0816 |
| 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. |
| Abstractor: | As Provided |
| Entry Date: | 2023 |
| Accession Number: | EJ1364086 |
| Database: | ERIC |
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| 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. |
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| ISSN: | 0013-1954 1573-0816 |
| DOI: | 10.1007/s10649-022-10192-y |
