Exploring Preservice Teachers’ Conceptual Understanding of Algebraic Ideas:
Abstract
This study investigated preservice teachers’ conceptual understanding of algebraic ideas focused on two specific mathematical concepts: slope and linear function. A Diagnostic Content Knowledge Assessment (DCKA) instrument was purposefully designed to assess participating preservice teachers’ relevant knowledge levels through both quantitative and qualitative data collection and analyses. It was found that participating preservice teachers possessed poor understanding on these two concepts: only 26% percent of participants were able to reach a benchmark of 80% correctness, paralleling the standard of the state’s content knowledge requirement for teacher certification. Special attention was given to the qualitative results of follow-up interviews with eight low-performing preservice teachers. Their responses supported the quantitative finding and also shed light on many common misconceptions in linear function and slope: lack of solid understanding of basic mathematical concepts and failure in using varied approaches. In addition, directions for further research are discussed.