CAS in teaching Linear Algebra: From Diagnosis, Connection, Deepening to Application
AbstractLinear algebra is a fundamental and important subject for students in science, engineering and management schools etc. Hence the study on the improvement of teaching and learning of linear algebra has been a crucial topic in undergraduate mathematics education. In this paper we present an experiment about integrate computer algebra system (CAS) in a Linear Algebra course carried out in the academic year 2013-14 at Tunghai University in Taiwan. The software is chosen to be MALAB and we divided the course into four stages: diagnosis, connection, deepening and application together with the use of CAS.
In the first stage “diagnosis”, we assess students’ prior knowledge (for examples, the notions about vector, inner product, matrix and determinant etc.) before processing the course. Secondly, we develop in the stage of “connection” the material for the bridging course according to the result of the diagnosis stage. Thirdly, we concern how to “deepen” the teaching of abstract theories. The final stage is to review whether students can “apply” learned knowledge to solve the practical problems designed by the characteristics of different fields. During the period of carrying out the four stages of the course, CAS will play the role to help instantaneous numerical and symbolical calculations: data collecting, analysis, exploration, and visualisation; modeling, simulation, and prototyping; presentation graphics and animation in 2D and 3D; and application development.