Solution--What Does It Mean? Helping Linear Algebra Students Develop the Concept While Improving Research Tools.

Abstract

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed shortcomings of the questionnaire that was used in the interviews: It did not permit making a distinction between lack of knowledge and partial knowledge. Research tools were improved (questionnaire, GD, and suggestions for teaching materials) and prepared for the next cycle of research. THEORETIC PERSPECTIVE The research reported here is part of a broader research effort conducted by the RUMEC (Research in Undergraduate Mathematics Education) group, which is dedicated to research within the scope of the theory named APOS. APOS is an acronym for the ideas of Action, Process, Object and Schema. This theory is an elaboration of Piaget’s cognitive theory (Piaget, 1975) for learning mathematics. Detailed description of this theory can be found, for example, in Asiala et al., (1996).