Advertisement

Conceptions About System of Linear Equations and Solution

  • Asuman OktaçEmail author
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

Understanding of systems of linear equations permeates in the study of several topics of importance in linear algebra, such as rank, range, linear independence/dependence, linear transformations, characteristic values and vectors. After giving an overview of the literature on the teaching and learning of systems of linear equations, research results on student difficulties at different school and university levels are presented, establishing relationships with the way this topic is taught. The conceptions that students develop about ‘system’ and ‘solution’ are discussed in synthetic-geometric and analytic contexts in two and three dimensional spaces. Based on these observations, some pedagogical suggestions about planning instruction on this topic are offered. Although the findings reported in this chapter correspond to research undertaken in Mexico and Uruguay, they might be reflecting a more general phenomenon related to conceptions that students develop in relation with systems of linear equations and their solutions.

Keywords

System Linear equations Modes of thinking 

Notes

Acknowledgements

I would like to thank Bonifacio Mora, Blanca Cutz, Cristina Ochoviet, Irving Alcocer, Carina Ramírez and Juan Guadarrama for their collaboration on parts of the project and data collection as well as the insights they brought to the project meetings.

References

  1. Borja-Tecuatl, I., Trigueros, M. & Oktaç, A. (2013). Difficulties in Using Variables—A Tertiary Transition Study. In S. Brown, G. Karakok, K. Hah Roh & M. Oehrtman (eds.), Proceedings of the 16th Annual Conference on Research in Undergraduate Mathematics Education, vol. 1, (pp. 80–94). Denver, Colorado.Google Scholar
  2. Cutz Kantún, B. M. (2005). Un estudio acerca de las concepciones de estudiantes de licenciatura sobre los sistemas de ecuaciones y su solución. Unpublished masters’ thesis. Cinvestav-IPN, Mexico.Google Scholar
  3. DeVries, D. & Arnon, I. (2004). Solution-What does it mean? Helping linear algebra students develop the concept while improving research tools. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 55–62.Google Scholar
  4. Duval, D. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.Google Scholar
  5. Eslava, M. & Villegas, M. (1998). Análisis de los modos de pensar sintético y analítico en la representación de las categorías de tres rectas en el plano. Unpublished certification course thesis, Universidad Autónoma del Estado de Hidalgo, Mexico.Google Scholar
  6. Kieran, C. (1981). Concepts Associated with the Equality Symbol. Educational Studies in Mathematics, 12, 317–326.Google Scholar
  7. Mora Rodríguez, B. (2001). Modos de pensamiento en la interpretación de la solución de sistemas de ecuaciones lineales. Unpublished masters’ thesis. Cinvestav-IPN, Mexico.Google Scholar
  8. Ochoviet Filgueiras, T. C. (2009). Sobre el concepto de solución de un sistema de ecuaciones lineales con dos incógnitas. Unpublished doctoral thesis. Cicata-IPN, Mexico.Google Scholar
  9. Panizza, M., Sadovsky, P. & Sessa, C. (1999). La ecuación lineal con dos variables: Entre la unicidad y el infinito. Enseñanza de las Ciencias, 17(3), 453–461.Google Scholar
  10. Sfard, A. & Linchevski, L. (1994a). Between arithmetic and algebra: In the search of a missing link. The case of equations and inequalities. Rend. Sem. Mat. Univ. Pol. Torino, 52(3), 279–307.Google Scholar
  11. Sfard, A. & Linchevski, L. (1994b). The gains and pitfalls of reification—The case of algebra. Educational Studies of Mathematics, 26, 191–228.Google Scholar
  12. Sierpinska, A. (2000). On some aspects of students’ thinking in linear algebra. In J.-L. Dorier (ed.), On the teaching of linear algebra (pp. 209–246). Dordrecht: Kluwer Academic Publishers.Google Scholar
  13. Stadler, E. (2011). The same but different—Novice university students solve a textbook exercise. In M. Pytlak, T. Rowland & E. Swoboda (eds.), Proceedings of the 7th Conference of European Researchers in Mathematics Education (pp. 2083–2092). Rzeszow, Poland.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Cinvestav-IPNMexico CityMexico

Personalised recommendations