Skip to main navigation menu Skip to main content Skip to site footer

Special Article

Vol. 13 No. 4(II) (2010): Número Especial /Diciembre

HOW ARE LINEAR ALGEBRA CONCEPTS LEARNED?

Submitted
December 26, 2023
Published
2010-12-01

Abstract

This paper presents the results obtained so far in a long term project developed in Mexico with the purpose of studying in depth students' constructions when they study Linear Algebra at the university level. The goals of the project consist in developing theoretical analyses about the constructions involved in the learning of the different Linear Algebra concepts using APOS theory; validating those analysis by means of empirical research focusing on specific concepts and relationships between them; and making didactic suggestions that can contribute to the teaching of this subject. In particular we present in this study the results obtained for the following concepts: vector space, linear transformation, basis and systems of linear equations.

References

  1. Asiala, M., Brown, A., De Vries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A Framework for Research and Curriculum Development in Undergraduate Mathematics Education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1-32.
  2. Chargoy, R. M. (2006). Dificultades asociadas al concepto de base de un espacio vectorial. Tesis doctoral, Cinvestav-IPN.
  3. Cutz, B. (2005). Un estudio acerca de las concepciones de estudiantes de licenciatura sobre los sistemas de ecuaciones y su solución, Tesis de maestría, Cinvestav-IPN.
  4. Da Silva, A., & Lins, R. (2002), An Analysis of the production of meaning for the notion of Basis in Linear Algebra. Proceedings of the 2nd international conference on the teaching of mathematics at the undergraduate level. p. 106 (En CD-ROM).
  5. Dorier, J. L. (1995a). A general outline of the genesis of vector space theory. Historia Mathematica, 22 (3), 227-261.
  6. Dorier, J. L. (1995b), Meta level in the teaching of unifying and generalizing concepts in mathematics. Educational Studies in Mathematics, 29 (2), 175-197.
  7. Dorier J. L., Robert, A., Robinet, R., & Rogalski, M. (1997). L'Algèbre Linéaire: L'obstacle du Formalisme à travers diverses recherches de 1987 à 1995, En J.-L. Dorier (ed.). L'Enseignement de l'Algèbre Linéaire en Question, (pp.105-147), La Pensée Sauvage éditions, Grenoble.
  8. Dorier, L. & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. En Derek Holton (Ed.). The teaching and Learning of Mathematics at University Level: An ICMI Study, (pp. 255-273), Dordrecht: Kluwer Academic Publishers, Paises Bajos.
  9. Dubinsky, E. (1997). Some Thoughts on a First Linear Algebra Course. En D. Carlson, C.R. Johnson, D.C. Lay, R.D. Porter, A. Watkins, & W. Watkins (eds), Resources For Teaching Linear Algebra, (pp.85-106), MAA Notes, 42
  10. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. En D. Tall. (Ed.), Advanced Mathematical Thinking, (pp. 95-123). Dordrecht: Kluwer.
  11. Fischer, A. (2005). Mental models of the concept of vector space. Proceedings of the 4 CERME Conference, San Feliu de Guixols, España, 1830-1833.
  12. Ku, D., Trigueros, M. & Oktaç, A. (2008), Comprensión del concepto de base de un espacio vectorial desde el punto de vista de la teoria APOE. Educación Matemàtica, 20 (2), 65-89.
  13. Manzanero, L. (2007). Sistemas de Ecuaciones: una perspectiva desde la teoría APOE Maestria, Cinvestav-IPN.
  14. Maracci, M. (2005). On some difficulties in vector space theory, Proceedings of the 4* CERME Conference, San Feliu de Guixols, España, 1778-1787.
  15. Oktaç, A., Trigueros, M. & Vargas, X. N. (2006). Understanding of vector spaces - a viewpoint from APOS theory, Proceedings of the 3rd International Conference on the Teaching of Mathematics, (En CD-ROM) Istanbul, Turkey.
  16. Parraguez, M. & Oktaç, A. (2010), Construction of the vector space concept from the viewpoint of APOS theory, Linear Algebra and its Applications, 432, 2112-2124.
  17. Parraguer, M. (2009). Evolución cognitiva del concepto espacio vectorial. Tesis de doctorado, Cicata IPN
  18. Piaget J & Garcia R. (1983). Psicogénesis e historia de la ciencia. Editorial: Siglo XXI, México. Ramirez, C., Oktaç, A. & Garcia, C. (2005). Dificultades que presentan los estudiantes en los modos geométrico y analitico de sistemas de ecuaciones lineales. Acta Latinoamericana de Matemática Educativa, 19, 413-418.
  19. Roa-Fuentes, S. & Oktaç, A. (2010). Construcción de una descomposición genética: Análisis teórico del concepto transformación lineal. Revista Latinoamericana de Investigación en Matemática Educativa, 13 (1), 89-112.
  20. Roa, D. (2008). Construcciones y mecanismos mentales asociados al concepto transformación lineal, Tesis de Maestria, CINVESTAV-IPN, México.
  21. Sierpinska. A. (2000). On some aspects of students thinking in linear algebra. En J-L. Dorier (Ed), On the Teaching of Linear Algebra (pp. 209-246). Dordrecht: Kluwer Academic Publishers
  22. Sierpinska, A. Nnadozie, A. & Oktaç, A. (2002). A Study of Relationships between theoretical thinking and high achievement in Linear Algebra. Concordia University: Montreal. Disponible en: http://www.annasierpinska.wkrib.com/pdf/Sierpinska-TT-Report.pdf
  23. Trigueros, M. & Oktaç, A. (2005), La Théorie APOS et l'Enseignement de l'Algèbre Linéaire. Annales de Didactique et de Sciences Cognitives, vol. 10, 157-176.
  24. Trigueros, M., Oktaç, A. & Manzanero, L. (2007). Understanding of Systems of Equations in Linear Algebra, Proceedings of the 5th CERME (Congress of the European Society for Research in Mathematics Education), Larnaca, Chipre, 2359-2368.
  25. Vargas, X. N. (2007), El estudio de los espacios vectoriales desde el punto de vista de la teoria APOE Tesis de Maestria, Cinvestav-IPN.
  26. Weller, K., Montgomery, A., Clark, J., Cottrill, J., Trigueros, M., Arnon, 1. & Dubinsky, E. (2002) Learning Linear Algebra with ISETL. Disponible en: http://homepages.ohiodominican.edu/~cottrilj/datastore/linear-alg/LLAWI-P3.pdf

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 > >> 

You may also start an advanced similarity search for this article.