MÚLTIPLOS, DIVISORES Y FACTORES: EXPLORANDO LA RED DE CONEXIONES DE LOS ESTUDIANTES: .

Rina Zazkis

Artículos

Vol. 4 No 1 (2001): Marzo

MÚLTIPLOS, DIVISORES Y FACTORES: EXPLORANDO LA RED DE CONEXIONES DE LOS ESTUDIANTES: .

Rina Zazkis^▸^▾

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Soumis: mars 11, 2025
Publiée: mars 31, 2001

Résumé

L’étude ci-joint est une contribution à une recherche qui se déroule sur la compréhension et l’apprentissage de la théorie introductrice des nombres en futurs professeurs. L’intérêt central de cet article c’est les concepts fondamentaux de multiple, diviseur et facteur; les signifiés que les élèves construisent sur ces trois concepts, les liens entre les trois notions, du même avec les connexions avec d’autres concepts de la théorie élémentaire de nombres, telle que les nombres premiers, décomposition en nombres premiers et divisibilité. Envisageant les connexions faites entre les concepts, on a analysé dix neuf interviews cliniques d’étudiants dans un cours de futurs professeurs, on leur a demandé d’exemplifier et expliquer les concepts, en plus d’appliquer ses conceptions de diverses situations problème. Un contrôle des réponses des étudiants a montré que les signifiés qu’on assigne aux concepts très souvent diffère des signifiés que les mathématiciens assignent dans le contexte de la théorie de nombres, et les liens entre concepts sont assez souvent faibles et incomplets.

Références

Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1992). A framework for research and curriculum development in undergraduate mathematics education. En J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education (pp. 1-32). Providence, RI: American Mathematical Society.
Brown, A. (1999). Patterns of thought and prime factorization. Manuscrito enviado para su publicación.
Brown, A., Thomas, K. & Tolias, G. (1999). Conceptions of divisibility: Success and understanding. Manuscrito enviado para su publicación.
Campbell, S. & Zazkis, R. (1994). Distributive flaws: Latent conceptual gaps in preservice teachers' understanding of the property relating multiplication to addition. En D. Kirshner (Ed.), Proceedings of the Sixteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 268-274). Baton Rouge, Louisiana: Louisiana State University.
Davis, R., Maher, C. A. & Noddings, N. (Eds.). (1990). Constructivist views on the teaching and learning of mathematics. Journal for Research in Mathematics Education. Monograph Series Number 4. Reston, VA: National Council of teachers of Mathematics.
Ferrari, P. L. (1997). Action-based strategies in advanced algebraic problem solving. Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 257-264). Lahti, Finland. University of Helsinki.
Ginsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4-12.
Ginsburg, H. (1997). Entering the child's mind: The clinical interview in psychological research and practice. Cambridge, Cambridge University Press.
Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. En J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
Nicholson, A. R. (1977). Mathematics and language. Mathematics in School 6(5), 32-34. Noss, R. & Hoyles, C. (1996). Windows on mathematical meaning: Learning cultures and computers. Dordrecht: Kluwer Academic Publishers.
Simon, M. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Alathematics Education 24(3), 233-254.
Zazkis, R. (1998a). Odds and ends of odds and evens. An inquiry into students' understanding of even and odd numbers. Educational Studies in Mathematics 36(1), 73-89.
Zazkis, R. (1998b). Quotients and divisors.- Acknowledging polysemy. For the Learning of Mathematics, 18(3), 27-30.
Zazkis, R. & Campbell, S. (1996a). Divisibility and multiplicative structure of natural numbers: Preservice teachers' understanding. Journal for Research in Mathematics Education, 27(5), 540-563.
Zazkis, R. & Campbell, S. (1996b). Prime decomposition. Understanding uniqueness. Journal of Mathematical Behavior 15(2), 207-218.

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Mots-clés

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Merci de créditer les auteurs lors de toute citation : Revista Latinoamericana de Investigación en Matemática Educativa (2001)

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Comment citer

Zazkis, R. (2001). MÚLTIPLOS, DIVISORES Y FACTORES: EXPLORANDO LA RED DE CONEXIONES DE LOS ESTUDIANTES: . Revista Latinoamericana de Investigación en Matemática Educativa, 4(1), 63-92. https://www.relime.org/index.php/relime/article/view/608

[1] Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1992). A framework for research and curriculum development in undergraduate mathematics education. En J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education (pp. 1-32). Providence, RI: American Mathematical Society.

[2] Brown, A. (1999). Patterns of thought and prime factorization. Manuscrito enviado para su publicación.

[3] Brown, A., Thomas, K. & Tolias, G. (1999). Conceptions of divisibility: Success and understanding. Manuscrito enviado para su publicación.

[4] Campbell, S. & Zazkis, R. (1994). Distributive flaws: Latent conceptual gaps in preservice teachers' understanding of the property relating multiplication to addition. En D. Kirshner (Ed.), Proceedings of the Sixteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 268-274). Baton Rouge, Louisiana: Louisiana State University.

[5] Davis, R., Maher, C. A. & Noddings, N. (Eds.). (1990). Constructivist views on the teaching and learning of mathematics. Journal for Research in Mathematics Education. Monograph Series Number 4. Reston, VA: National Council of teachers of Mathematics.

[6] Ferrari, P. L. (1997). Action-based strategies in advanced algebraic problem solving. Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 257-264). Lahti, Finland. University of Helsinki.

[7] Ginsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4-12.

[8] Ginsburg, H. (1997). Entering the child's mind: The clinical interview in psychological research and practice. Cambridge, Cambridge University Press.

[9] Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. En J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.

[10] Nicholson, A. R. (1977). Mathematics and language. Mathematics in School 6(5), 32-34. Noss, R. & Hoyles, C. (1996). Windows on mathematical meaning: Learning cultures and computers. Dordrecht: Kluwer Academic Publishers.

[11] Simon, M. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Alathematics Education 24(3), 233-254.

[12] Zazkis, R. (1998a). Odds and ends of odds and evens. An inquiry into students' understanding of even and odd numbers. Educational Studies in Mathematics 36(1), 73-89.

[13] Zazkis, R. (1998b). Quotients and divisors.- Acknowledging polysemy. For the Learning of Mathematics, 18(3), 27-30.

[14] Zazkis, R. & Campbell, S. (1996a). Divisibility and multiplicative structure of natural numbers: Preservice teachers' understanding. Journal for Research in Mathematics Education, 27(5), 540-563.

[15] Zazkis, R. & Campbell, S. (1996b). Prime decomposition. Understanding uniqueness. Journal of Mathematical Behavior 15(2), 207-218.