Coordinating representation registers: linear algebra students' understanding of orthogonal Legendre polynomials in the inner product space ℙn in a technology-assisted learning environment
The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of the orthogonal Legendre polynomials as vectors of the inner product space ℙn in a DGS (Dynamic Geometry Software)-MATLAB facilitated learning environment. Math majors c...
Gardado en:
| Publicado en: | URI:https://journals.openedition.org/adsc, |
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| Autor Principal: | |
| Formato: | Article ou chapitre numérique |
| Idioma: | Anglais |
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Annales de Didactique et de Sciences Cognitives
2022
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| Acceso en liña: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Résumé: | The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of the orthogonal Legendre polynomials as vectors of the inner product space ℙn in a DGS (Dynamic Geometry Software)-MATLAB facilitated learning environment. Math majors came up with a diversity of innovative and creative ways in which they coordinated semiotic registers (Duval, 1993, 2006) for understanding inner products of Legendre polynomials along with other notions inherent in the inner product space, such as Triangle Inequality, Pythagorean Theorem, Parallelogram Law, Orthogonality and Orthonormality, Coordinates Relative to an Orthonormal Basis. Research participants not only produced such creative inner product space visualizations of the Legendre polynomials with the associated integral inner product 〈f,g〉 = ∫1-1 f(x)g(x)dx on the DGS, but they also verified their findings both analytically and visually in coordination. The paper concludes by offering pedagogical implications along with implications for mathematics teaching profession and recommendations for future research. |
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