# Conceptions About System of Linear Equations and Solution

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## 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.

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