Secondary Preservice Teachers’ Engagement in a Quadratic Functions Task: Reasoning and Content

Abstract

In this manuscript we present an exploratory case study investigating one group of four preservice secondary mathematics teachers as they used GeoGebra to explore and describe how varying a in y=ax²+bx+c affects the position of the vertex of the associated parabola. We examined their reasoning and identified four main reasoning sequences that helped them progress towards their final conjecture. Throughout these sequences they established (1) the path is linear, (2) the slope depends on b, (3), the slope is not dependent on a and not dependent on c, and (4) the path of the vertex is described by the equation y=(b/2)x+c. We further described and classified preservice teachers’ reasoning using Lithner’s (2008) creative mathematical reasoning framework. We identified which mathematical concepts anchored the preservice teachers’ arguments and were deepened through their reasoning process. Based on our results, we found that the preservice teachers were engaged in creative mathematical reasoning during each reasoning sequence. Finally, we determined that the preservice teachers deepened their knowledge of the concept of dependence, particularly in the context of linear functions.