Algebra Teachers’ Interpretation and Responses to Student Errors in Solving Quadratic Equations

To improve students’ mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers’ analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers’ responses were analyzed quantitatively and qualitatively. Analyses results revealed a gap between identified errors and addressed ones, as well as a gap between interpreting a knowledge weakness and explaining a knowledge focus. While the errors came from conceptual aspects of the factoring method, most of the participants offered conceptual explanations addressed in a teacher-centered way. The results also revealed that student errors and mathematical knowledge were two foci of the teachers’ responses to students. The broader implications of the study for the international community are discussed in accordance with the findings.