Three Modes of Description and Thinking of Linear Algebra Concepts at Upper Secondary Education

Many researchers point out that appropriate combinations of concept's representations lead to improved students' learning outcomes and translations between different representations support conceptional understanding (Ainsworth et al., 1997; Panasuk & Beyranevand, 2010). Multiple representations are important for acquiring deeper knowledge about a domain (van der Meij & de Jong, 2006). It is well known that quick and correct calculations or apparently fluent procedural skills are not necessarily proceeded by conceptual understanding. Previous research reports that one of the indicators of conceptual understanding is “the capability for recognizing structurally the same connections posed via multiple representations” (Panasuk & Beyranevand, 2010, p. 2). How can translations across more representations of linear algebra concepts be supported to maximize students' learning outcomes and effectiveness of multiple-representational learning environments? The phenomenon of dynamic multiple representations in computer based learning environments in comparison with single static representations, single dynamic representations and multiple static representations offers the most opportunities and challenges (van der Meij & de Jong, 2006). Let us first explain multiple modes of descriptions, representations and thinking in linear algebra more in details.