Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 15 No. 2 (2012): Julio

VALIDATION OF A GENETIC DECOMPOSITION OF LINEAR TRANSFORMATION: AN ANALYSIS REFINED BY THE IMPLEMENTATION OF THE RESEARCH CYCLE RELATED TO APOS THEORY

Submitted
July 14, 2023
Published
2012-07-01

Abstract

Based on the theoretical analysis in Roa-Fuentes and Oktaç (2010), we present the third component of the research cycle related to APOS theory: data analysis and verification. Using the design and application of a diagnostic test and an interview, we propose a refined genetic decomposition of the linear transformation concept. Based on the data analysis we suggest the development of lesson models that would take into account the research results, and some methodological ideas to build this concept.

References

  1. Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D. & Thomas, K. (1996), A Framework for Research and Curriculum Development in Undergraduate Mathematics Education In 1. Kapat, A. H. Schoenfeld & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education II (Vol. 6, pp.1-32). Rhode Island, U.S.A.: American Mathematical Society.
  2. Chargoy, R. (2006). Dificultades asociadas al concepto de base de un espacio vectorial. Tesis de doctorado no publicada, Centro de Investigaciones y de Estudios Avanzados del IPN, D.F., México.
  3. Clark, J., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D., St. John, D., Tolias, G. & Vidakovic, D. (1997), Constructing a schema: The case of the chain rule. The Journal of MathematicalBehavior 16 (4), 345-364.
  4. Dubinsky, E., Weller, K., Stenger, K. & Vidakovic, D. (2008) . Infinite iterative processes: TheTennis Ball Problem. European Journal of Pure and Applied Mathematics 1 (1), 99 - 121.
  5. Dubinsky, E. & McDonald, M. (2002). APOS; A constructivist theory of learning in undergraduate mathematics education research, InD.Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study, (Vol. 7, pp. 275-282), Kluwer, Netherlands: Springer. DOI: 10.1007/0-306-47231-7 25
  6. Kú,D., Trigueros, M. y Oktaç, A. (2008). Comprensión del concepto de base de un espacio vectorial desde el punto de vista de la teoría APOE. Educación Matemática 20 (2), 65-89.
  7. Maher, P. (1987). What makes an operator linear? International Journal of Mathematics Education in Science and Technology 18 (2), 177-179.
  8. McDonald, M., Mathews, D. & Strobel, K. (2000). Understanding sequences: A tale of two objects. In E. Dubinsky, A. Schoenfeld, & J. Kaput. (Eds.), Research in Collegiate Mathematics Education (Vol. IV, pp. 77-102). Providence, EE.UU: American Mathematical Society.
  9. Parraguez, M. & Oktaç, A. (2010). Construction of the vector space concept from the viewpoint APOS theory. Linear Algebra and its Applications 432 (8), 2112-2124.
  10. Roa-Fuentes, S. y 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.
  11. Roa-Fuentes, S. (2008). Construcciones y Mecanismos mentales asociados al concepto transformación lineal. Tesis de Maestría no publicada, Centro de Investigaciones y de Estudios Avanzados del IPN, D.F., México.
  12. Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M. & Merkovsky, R. (2003). Studen performance and attitudes in courses based on APOS theory and the ACE teaching cycle CBMS Issues in Mathematics Education 12, 97-117.
  13. Weller, K., Montgomery, A., Clark, J., Cottrill, J., Trigueros, M., Arnon, I. & Dubinsky, E (2002). Learning Linear Algebra with ISETL. Recuperado el 21 de junio de 2007 & http://homepages.ohiodominican.edu/-cottrilj/datastore/linear-alg/LLAWI-P3.pdf.
  14. Zazkis, R., Dubinsky. E. & Dautermann, J. (1996). Coordinating Visual and Analytic Strategies A Study of Students' Understanding of the Group D. Journal for Research it Mathematics Education 27 (4), 435-457.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

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

Most read articles by the same author(s)