Academic Journal
Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm.
| Τίτλος: | Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm. |
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| Συγγραφείς: | Lagrange, Jean-Baptiste, Laval, Dominique |
| Πηγή: | Educational Studies in Mathematics; Feb2023, Vol. 112 Issue 2, p225-245, 21p |
| Θεματικοί όροι: | Algorithms, Mathematics, Mathematics theorems, Secondary education, Secondary school students |
| Περίληψη: | 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lagrange%2C+Jean-Baptiste%22">Lagrange, Jean-Baptiste</searchLink><br /><searchLink fieldCode="AR" term="%22Laval%2C+Dominique%22">Laval, Dominique</searchLink> – Name: TitleSource Label: Source Group: Src Data: Educational Studies in Mathematics; Feb2023, Vol. 112 Issue 2, p225-245, 21p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+theorems%22">Mathematics theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+education%22">Secondary education</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+school+students%22">Secondary school students</searchLink> – Name: Abstract Label: Abstract Group: Ab 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. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10649-022-10192-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 225 Subjects: – SubjectFull: Algorithms Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Mathematics theorems Type: general – SubjectFull: Secondary education Type: general – SubjectFull: Secondary school students Type: general Titles: – TitleFull: Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lagrange, Jean-Baptiste – PersonEntity: Name: NameFull: Laval, Dominique IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 00131954 Numbering: – Type: volume Value: 112 – Type: issue Value: 2 Titles: – TitleFull: Educational Studies in Mathematics Type: main |
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