# Linear Algebra—A Companion of Advancement in Mathematical Comprehension

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## Abstract

Linear algebra is considered a core subject with its specific cognitive and teaching challenges at the very start of university mathematics teaching. By views and experience of many students and teachers linear algebra ‘defines the change of culture between secondary and university teaching’. Lots of educational research has explored productive transitions to ‘higher levels of conceptualization’ symbolized by linear algebra. We propose a rather different and simple perspective: linear algebra might be motivated and its basics successfully taught if presented as a tool for mastering diverse mathematical problems. Basic linear algebra concepts can be used for a smooth transitions from intuitive to abstract cognition and to deepen student’s understanding. ‘Scholar-teacher’ can use rich linear algebra contents for guided learning through exploration and discovery. We will present a few samples of challenging mathematical problems where ‘linear algebra reasoning intuitively comes to rescue’ and gradually develops into a powerful and beautiful subject of its own value.

## Keywords

Intuitive Abstract Visualization Linear Geometric Challenge## References

- Castelnuovo, E. (1969). Différentes Représentations Utilisant la Notion de Barycentre. In T. E. B. of Educational Studies in Mathematics (Ed.), Proceedings of the First International Congress on Mathematical Education, Lyon, 24–30 August 1969 (pp. 175–200).Google Scholar
- Claudi, A. (2002). Why the Professor Must be a Stimulating Teacher: Towards a New Paradigm of Teaching Mathematics at University Level. In H. Derek (Ed.), The Teaching and Learning of Mathematics at University Level (pp. 3–12). Springer, Netherlands.Google Scholar
- Dorier, J., Robert, A., & Sierpinska, A. (2000). Conclusion. In J. Dorier (Ed.), On the Teaching of Linear Algebra (pp. 273–276). Springer, Netherlands.Google Scholar
- Fung, C., & Siu, M. (2005). Mathematics in Teaching and Teaching of Mathematics [Private correspondence]. Fourth Asian Mathematical Conference, Singapore.Google Scholar
- Klein, F. (1923). Retrieved 24 October 2017, from http://www.icmihistory.unito.it/
- Kobal, D. (2016). Basic Linear Algebra Samples—Visualisations; GeoGebra book. Retrieved 24 October 2017, from https://www.geogebra.org/m/CTXPCC5x