Algebra is the consequence of precisely formulatable cognitive mechanisms

Year: 2004

Author: Menzel, Brenda

Type of paper: Abstract refereed

Abstract:
Deliberation about teaching algebra must include some analysis of early algebraic thinking and the kinds of activity that might prepare young students to think and operate algebraically. The Victorian Board of Studies (BOS) has emphasised that students’ thinking needs to be the centre of mathematics instruction and that appropriate pedagogy and curriculum content needs to stress reasoning and strategies. This emphasis is evident from the CSF Strand “Reasoning and Strategies Levels 1-6” (BOS, 2002), and the “Annotated Work Samples” (BOS, 2001). Examples from these documents and tasks used for this study will be used to illustrate how we can utilize students’ thinking to develop arithmetic and algebraic understanding as a natural extension of students’ analysis of their sensory-motor experiences.

Analysis of the data for this paper are drawn from the work of Lakoff and Nunez (2000) who believe that, from a cognitive perspective, “mathematics is deep, fundamental, and essential to the human experience” (p. XI). The reason for their belief stems from the premise that the “brain and body co-evolved so that the brain could make the body function optimally” (p.1). Mathematics has arisen from our inclination to communicate generalizations arising from body-based experiences with space and quantities. Generalizations from such body-based activities have become metaphors we utilize for thinking about quantities and space. They are the mechanism for creating and understanding mathematical concepts because they utilize natural language and ways of thinking about our natural world. They also provide the neural link between abstract and real experiences because they employ modes of reasoning from sensory-motor experience. A pedagogical implication is that, students need to be encouraged and given adequate resources with which to make connections between their everyday experiences and the abstract even if the links seem obscure to others.

Back