Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra

Luiz G. X. de Barros; Marc Rogalski

doi:doi:10.11648/j.sjedu.20130105.15

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Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra

Luiz G. X. de Barros, Marc Rogalski

Published in Science Journal of Education (Volume 1, Issue 5)

Received: 11 November 2013 Published: 30 November 2013

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Abstract

We study knowledge and competencies of Brazilian university students after an one year course in linear algebra, concerning various aspects: the global landscape of linear algebra as seen by students, how they do cope with modelization problems through linear algebra, what are their knowledge and competencies about the duality of representation equations/parametrization of subspaces of Rn, their ability in calculations for solving linear equations and their understanding of the symbolic algebra used in linear algebra. The results are coherent with such previous studies, which underlined that the learning of linear algebra by students is generally poor after a one year course.

Published in	Science Journal of Education (Volume 1, Issue 5)
DOI	10.11648/j.sjedu.20130105.15
Page(s)	77-89
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Mathematics Education, Linear Algebra, Teaching and Learning at University Level, Diagnostic of Knowledge

References

[1]	Alves Dias, M. (1998). Les problèmes d’articulation entre points de vue « cartésien » et para¬métrique » dans l’enseignement de l’algèbre linéaire, Thèse de doctorat de l’Université de Paris 7.
[2]	Alves Dias, M. and Artigue, M. (1995). Articulation problems between different systems of symbolic representations in linear algebra, in The Proceedings of the 19th Annual Meeting of International Group for Psychology of Mathematics Education (PME), Universidade Federal de Pernambuco, Recife, Brazil, vol 2, 34-41.
[3]	Alves Dias, M. et Rogalski, M. (2011). Articulation of cartesian and parametric viewpoints in linear algebra: didactic problems, to appear.
[4]	Dorier, J. L. (1990). Contribution à l'étude de l'enseignement à l'université des premiers concepts d'algèbre linéaire:Approches historique et didactique, Thèse de doctorat de l'Université Joseph Fourier –Grenoble
[5]	Dorier, J. L. (1991). Sur l'enseignement des concepts élémentaires d'algèbre linéaire à l'université, Recherches en Didactique des Mathématiques 11-2/3, 325-364.
[6]	Dorier, J. L., Robert A., Robinet J., Rogalski M. (1994). L'enseignement de l'algèbre linéaire en DEUG première année, essai d'évaluation d'une ingénierie longue et questions, in Artigue M. et al. (eds) Vingt ans de Didactique des Mathématiques en France, pp. 328-342, Grenoble : La Pensée Sauvage éditions.
[7]	Dorier, J. L. (1995). Meta level in the teaching of unifying and generalizing concepts in mathematics, Educational Studies in Mathematics 29-2, 175-197.
[8]	Dorier J. L. (éd.) (1997). L'enseignement de l'algèbre linéaire en question, Grenoble: La Pensée Sauvage.
[9]	Dorier J. L. (2006). La recherche en didactique à propos de l’enseignement de l’algèbre linéaire, RADISMA, 2006, n. 1.
[10]	Harel, G. (1987). Variations in Linear Algebra Content Presentations, For the Learning of Mathematics, 7, 29-32.
[11]	Harel, G. (1989). Learning and teaching linear algebra: Difficulties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11, 139-148.
[12]	Harel, G. (2000). Three principles of learning and teaching mathematics: Particular reference to linear algebra—Old and new observations. In Jean-Luc Dorier (Ed.), On the Teaching of Linear Algebra, Kluwer Academic Publishers, 177-190.
[13]	Hillel, J. (2000). Modes of description and the problem of representation in linear algebra, in J.-L. Dorier (ed.), On the Teaching of Linear Algebra, Kluwer Academic Publishers, Dortrecht/Boston/London, pp. 191-208.
[14]	Hillel, J. and Sierspinska, A. (1994). On one persistent mistake in linear algebra, In Proceedings of the XVIII International Conference of PME, Portugal, Vol. II, 65-72.
[15]	Ousman, R. (1996). Contribution à l'enseignement de l'algèbre linéaire en première année d'université, Thèse de doctorat de l'Université de Rennes.
[16]	Robert, A. et Robinet, J. (1989). Quelques résultats sur l'apprentissage de l'algèbre linéaire en première année de DEUG, Cahier de Didactique des Mathématiques 53, IREM de Paris VII.
[17]	Robert, A. et Robinet, J. (1996). Prise en compte du méta en didactique des mathématiques, Recherches en Didactique des Mathématiques 16-2, 145,176.
[18]	Robinet, J. (1986). Esquisse d'une genèse des concepts d'algèbre linéaire, Cahier de Didactique des Mathématiques 29, IREM de Paris VII.
[19]	Rogalski, M. (1990). Pourquoi un tel échec de l'enseignement de l'algèbre linéaire?, in Enseigner autrement les mathématiques en DEUG Première Année, Commission inter-IREM Université, IREM de Lyon, France, pp. 279-291.
[20]	Rogalski, M. (1991). Un enseignement de l'algèbre linéaire en DEUG A première année, Cahier de Didactique des Mathématiques 53, IREM de Paris VII.
[21]	Rogalski, M. (1994). L'enseignement de l'algèbre linéaire en première année de DEUG A, La Gazette des Mathématiciens 60 (Société Mathématique de France), 39-62.
[22]	Rogalski, M. (1995). Que faire quand on veut enseigner un type de connaissances tel, que la dialectique outil/objet ne semble pas marcher, et qu'il n'y ait apparemment pas de situation fondamentale ? L'exemple de l'algèbre linéaire, Séminaires DidaTech 1994-1995 - n°169, Grenoble, France, 127-162.
[23]	Rogalski, M. (1996). Teaching linear algebra: role and nature of knowledge in logic and set theory which deal with some linear problems, Proceedings of the XX° International Conference for the Psychology of Mathematics Education (PME XX), Valence 1996.
[24]	Rogalski, M. (2011). Une expérience d’enseignement de l’algèbre linéaire s’appuyant sur les analyses épistémologiques et didactiques des difficultés de cet enseignement, Séminaire de formation de l’Université Fédérale de Sergipe, Brazil.
[25]	Sierpinska, A. (2000). On some aspects of students’ thinking in linear algebra, in J.-L. Dorier (ed.), On the Teaching of Linear Algebra, Kluwer Academic Publishers, Dortrecht / Boston / London, pp. 209-246.
[26]	Sierpinska, A., Dreyfus, T., Hillel, J. (1999). Evaluation of a teaching design in linear algebra: the case of linear transformations, Recherches en Didactique des Mathématiques 19.1, 7- 41.
[27]	Sierpinska, A., Nnadozie, A. & Oktac, A. (2002). A study of relationships between theorical thinking and high achievement in Linear Algebra. Concordia University. Unpublished manuscript.

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Luiz G. X. de Barros, Marc Rogalski. (2013). Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Science Journal of Education, 1(5), 77-89. https://doi.org/10.11648/j.sjedu.20130105.15

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Luiz G. X. de Barros; Marc Rogalski. Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Sci. J. Educ. 2013, 1(5), 77-89. doi: 10.11648/j.sjedu.20130105.15

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AMA Style

Luiz G. X. de Barros, Marc Rogalski. Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Sci J Educ. 2013;1(5):77-89. doi: 10.11648/j.sjedu.20130105.15

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@article{10.11648/j.sjedu.20130105.15,
  author = {Luiz G. X. de Barros and Marc Rogalski},
  title = {Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra},
  journal = {Science Journal of Education},
  volume = {1},
  number = {5},
  pages = {77-89},
  doi = {10.11648/j.sjedu.20130105.15},
  url = {https://doi.org/10.11648/j.sjedu.20130105.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjedu.20130105.15},
  abstract = {We study knowledge and competencies of Brazilian university students after an one year course in linear algebra, concerning various aspects: the global landscape of linear algebra as seen by students, how they do cope with modelization problems through linear algebra, what are their knowledge and competencies about the duality of representation equations/parametrization of subspaces of Rn, their ability in calculations for solving linear equations and their understanding of the symbolic algebra used in linear algebra. The results are coherent with such previous studies, which underlined that the learning of linear algebra by students is generally poor after a one year course.},
 year = {2013}
}

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TY  - JOUR
T1  - Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra
AU  - Luiz G. X. de Barros
AU  - Marc Rogalski
Y1  - 2013/11/30
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AB  - We study knowledge and competencies of Brazilian university students after an one year course in linear algebra, concerning various aspects: the global landscape of linear algebra as seen by students, how they do cope with modelization problems through linear algebra, what are their knowledge and competencies about the duality of representation equations/parametrization of subspaces of Rn, their ability in calculations for solving linear equations and their understanding of the symbolic algebra used in linear algebra. The results are coherent with such previous studies, which underlined that the learning of linear algebra by students is generally poor after a one year course.
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Author Information

Luiz G. X. de Barros

Universidade Bandeirante Anhanguera (Uniban), S?o Paulo, Brasil
Marc Rogalski

Université de Lille 1, Université Pierre et Marie Curie and Université Paris-Diderot, France

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APA Style

Luiz G. X. de Barros, Marc Rogalski. (2013). Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Science Journal of Education, 1(5), 77-89. https://doi.org/10.11648/j.sjedu.20130105.15

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ACS Style

Luiz G. X. de Barros; Marc Rogalski. Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Sci. J. Educ. 2013, 1(5), 77-89. doi: 10.11648/j.sjedu.20130105.15

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AMA Style

Luiz G. X. de Barros, Marc Rogalski. Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra. Sci J Educ. 2013;1(5):77-89. doi: 10.11648/j.sjedu.20130105.15

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@article{10.11648/j.sjedu.20130105.15,
  author = {Luiz G. X. de Barros and Marc Rogalski},
  title = {Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra},
  journal = {Science Journal of Education},
  volume = {1},
  number = {5},
  pages = {77-89},
  doi = {10.11648/j.sjedu.20130105.15},
  url = {https://doi.org/10.11648/j.sjedu.20130105.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjedu.20130105.15},
  abstract = {We study knowledge and competencies of Brazilian university students after an one year course in linear algebra, concerning various aspects: the global landscape of linear algebra as seen by students, how they do cope with modelization problems through linear algebra, what are their knowledge and competencies about the duality of representation equations/parametrization of subspaces of Rn, their ability in calculations for solving linear equations and their understanding of the symbolic algebra used in linear algebra. The results are coherent with such previous studies, which underlined that the learning of linear algebra by students is generally poor after a one year course.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Contribution to the Diagnostics of University Students’ Knowledge and Competencies in Linear Algebra
AU  - Luiz G. X. de Barros
AU  - Marc Rogalski
Y1  - 2013/11/30
PY  - 2013
N1  - https://doi.org/10.11648/j.sjedu.20130105.15
DO  - 10.11648/j.sjedu.20130105.15
T2  - Science Journal of Education
JF  - Science Journal of Education
JO  - Science Journal of Education
SP  - 77
EP  - 89
PB  - Science Publishing Group
SN  - 2329-0897
UR  - https://doi.org/10.11648/j.sjedu.20130105.15
AB  - We study knowledge and competencies of Brazilian university students after an one year course in linear algebra, concerning various aspects: the global landscape of linear algebra as seen by students, how they do cope with modelization problems through linear algebra, what are their knowledge and competencies about the duality of representation equations/parametrization of subspaces of Rn, their ability in calculations for solving linear equations and their understanding of the symbolic algebra used in linear algebra. The results are coherent with such previous studies, which underlined that the learning of linear algebra by students is generally poor after a one year course.
VL  - 1
IS  - 5
ER  -

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