Linear Algebra—A Companion of Advancement in Mathematical Comprehension

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.