The Role of Cognitive Conflicts in Teaching Second Order Equations

Abstract

This study focuses on pre-service elementary mathematics education students’ understanding of second-order equations and examines the effect of cognitive conflict on their comprehension and academic performance in solving these equations. The study aims to determine the role of cognitive conflict in learning second-order equations. Data were collected from pre-service mathematics teachers enrolled in their third year. A mixed-method design was used, and data gathering tools included algebra achievement tests on second-order equations (administered as pre-tests and post-tests), open-ended cognitive conflict questionnaires, and whole-class discussions. Common misconceptions among the participants included accepting a false root as a solution and failing to check for a zero solution. Additionally, pre-service mathematics teachers demonstrated misunderstandings in concepts such as variables, domain, solution set, and equation roots. To foster cognitive conflict, the researcher used an open-ended questionnaire presenting opposing student views. Results from a paired t-test indicated that implementing cognitive conflict significantly improved academic achievement. The study also found a significant reduction in the frequency of students’ misconceptions from pre- to post-testing.