4 Uncovering Algebra Uncovering Algebra: Sense Making and Property Noticing

This paper articulates a perspective on learning to discuss ways in which students develop personal sense and negotiate meaning in a middle school algebra context. Building on a sociocultural perspective that incorporates mental objects, learning is described as a mutually dependent process involving personal sense making and the public negotiation of meaning. Analysis of student problem solving is focused on the development of taken-as-shared meaning through an individual and collaborative analysis of the properties of various conceptual entities. The results suggest that functional properties inherent in linear relationships were more supportive in eliciting meaning making exchanges than were algebraic properties associated with generalized arithmetic, although the contextual nature of the linear tasks may have also supported the meaning making activity. What is the difference between sense and meaning? Drawing on the philosophies of Vygotsky and Leont’ev, Wertsch (1991) distinguishes between sense and meaning by focusing on the personal and public aspects of activity. Lave, Murtaugh, and de la Rocha (1984) concur: “sense designates personal intent, as opposed to meaning, which is public