Equations with Parameters: A Locus Approach

摘要

This article introduces technology-based teaching ideas that facilitate the development of qualitative reasoning techniques in the context of quadratic equations with parameters. It reflects on activities designed for and used with prospective secondary mathematics teachers in accord with standards for teaching and recommendations for teachers in North America. The main educational implications of the proposed didactics include an emphasis on using geometric constructions in the context of algebra, emergence of residual mental power that can be used in the absence of technology, and development of skills in problem posing.