Web-based Multimedia Activities as Pedagogical Models

Abstract

Some research indicates that "our thinking is deeply molded by material devices and socio-technical collectives" (Levy, 1993, p. 10). In fact, a powerful trend in psychology and cognitive science argues that mind and environment may be best treated as a unity (Rosch, 1996). It may be possible that well designed and easily accessible web-based multimedia activities, activities that allow students to use and explore algebraic relationships, may affect what Levy refers to as the "cognitive ecology" of learning environments, thus changing how and what algebra is taught and learned. Confrey (1996) suggests that "new forms of representation change the mathematics being taught." (p. 335) Likewise, diSessa (2000) states "We don't always have ideas and then express them in the medium. We have ideas with the medium. Making progress is an episode of materially mediated thinking - reasoning or coming up with a new idea - happens jointly in the mind and in the medium at every stage." (p. 116) And perhaps more importantly, some research indicates that there may be a spillover effect, where learning to think with material devices affects our thinking even when the devices are not present (Borba & Villarreal, 1998).

The study centred on three grades 5-6 teachers' pedagogical conceptions of algebra and their teaching practice while using a web-based multimedia activity whose focus is on exploring area and perimeter relationships. It appears that the conceptions of algebra held by the teachers in this study correspond to the typical view of algebra that emerges from research, which sees the teaching of algebra being instrumental rather than relational, with a dominance of symbolic algebra over other representations (Kieran, 1992; Borba & Confrey, 1996; Kieran & Sfard, 1999). It also appears that their conceptions do not include algebra as a study of relationships. The WM activities may have acted as pedagogical models for teachers' classroom practice, shifting the teaching focus from the learning of isolated concepts to algebraic relationships among concepts.