The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students' responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of…

In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in Mexico was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model…

The purpose of this paper is to describe the process by which a pair of undergraduate students, participating in a teaching experiment, reinvented (with guidance) the concepts of group and isomorphism beginning with an exploration of the symmetries of an equilateral triangle. The intent of this description is to highlight some important insights…

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

Presents a summary report of a discussion subgroup of the Algebra Working Group at the Seventh International Conference on Mathematics Education held in Quebec City, Canada in August 1992. Argues that pre-algebra should be viewed as a continuation of arithmetic that asks different questions about numbers. (12 references) (Author/MKR)

Presents a summary report of the Algebra Working Group's discussion subgroup on secondary algebra at the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Three appendixes include the reactions to the keynote addresses in this issue. (MKR)

This article is the last keynote address of the Algebra Working Group of the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Attempts to integrate, and react to, the broad range of issues raised by the Algebra Working Group. (35 references) (MKR)

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers.…

Examples of relatively novel computer software environments from the representation perspective are described. Even more novel approaches to curriculum reform to cultivate higher-order thinking skills are then discussed. (MNS)

Examines the potential role for Computer Algebra Systems (CAS) when teaching courses as functions, calculus, and linear algebra to students with low prerequisite algebra skills. A study reports the rationale, planning, and implementation of a functions course integrating Maple CAS into instruction. (MDH)

This longitudinal study investigated the ways in which two groups of eight students used spreadsheets to represent and solve algebra problems and related this to their previous arithmetical experiences and evolving use of symbolic language. The spreadsheet environment supported students to move from specific to general thinking. Includes story…