Recursive Exploration Space for Concepts in Linear Algebra

Abstract

The complexity of the role of digital media in facilitation of learning mathematics can be approached by utilizing multiple theoretical frameworks. In this chapter, three theoretical frameworks have been applied with an aim to analyze the contribution of a created Dynamic GeometryDynamic geometryEnvironment in developing deep understanding of conceptsConceptsin linear algebraAlgebra. The first one, which is in the main focus, refers to the integration of different description and thinking modes in linear algebraAlgebra, such as synthetic-geometric, arithmetic and analytic-structural (Hillel in On the teaching of linear algebra. Springer, Netherlands, pp. 191--207, 2000; Sierpinska in On the teaching of linear algebra. Springer, Netherlands, pp. 209--246, 2000). The second one is related to the attributes of Dynamic Technological Environments, such as Recursive Exploration Space (Hegedus et al. in Proceedings of CERME5, WG 9. Tools and technologies in mathematical didactics 1331, pp. 1419--1428, 2007); and the third one is semiotic mediationMediation(Bussi and Mariotti in Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective handbook of international research in mathematics education. New York, pp. 746--783, 2008) of the draggingDraggingtool. A landscape of networking strategies for connecting theories (Prediger et al. in ZDM Math Educ 40(2):165--178, 2008) has been exploited as an attempt to ensure quality of the analysis.