Connecting Research to Teaching: Quadratic Functons: Students Graphic and Analytic Representations

Abstract

When designing and implementing a lesson, a teacher must draw upon knowledge of the difficulties his or her students are experiencing in order to help them understand the mathematics being taught. We have examined student work in an attempt to identify the difficulties— which we have called cognitive obstacles (Herscovics 1989)—encountered by tenth-grade honors algebra students learning about quadratic functions. We think that calling attention to these results will help classroom teachers in the process of planning instruction. If teachers know about potential obstacles to understanding before a lesson is taught, they can devise well-developed lesson plans and use modified teaching strategies to help students overcome or at least minimize these obstacles.