ACTIONS, PROCESSES, OBJECTS, SCHEMAS (APOS) IN MATHEMATICS EDUCATION: A CASE STUDY FOR MATRIX OPERATIONS

Matrix algebra forms a core part of the first year mathematics curriculum at the Vietnam universities and colleges and is applicable to many other areas besides pure mathematics. Besides, the transfer of knowledge from a primarily procedural or algorithmic school approach to formal presentation of concepts is a priority for conceptualization of matrix algebra concepts. The mastery of matrix operations was a necessary step for graduate students in higher education. On the other hand, they lack adequate knowledge of advanced linear algebra, such as matrix operations, which are fundamentals in quantitative research method learning and students often find the course difficult. However, the difficulty may not be solely because of the content but also because of the transition from elementary to advanced mathematics itself. This paper presents an application of APOS (Actions, Process, Object and Schema) theory to teach matrix operations at universities. APOS theory focuses on models of what might be going on in the mind of an individual when he or she is trying to learn a mathematical concept and uses these models to design instructional materials and/or to evaluate student successes and failures in dealing with mathematical problem situations.