Design of a mathematics learning environment: Contribution of metacognitive and argumentation practices on problem solving

Development of problem solving skills of students have been a topic on the agenda of teachers, researchers, and policymakers. The importance of students ability to articulate their thoughts, evaluate others' reasoning, and use metacognitive skills during problem solving activities is emphasized in the literature. The study aims to improve students' problem-solving abilities by incorporating argumentation and metacognition into classroom discussions. To achieve this, a learning environment is designed to foster the development of these critical skills, which are essential for effective problem solving. The design-based research was conducted over one school year in a public school in İstanbul, involving two fifth-grade classrooms and their mathematics teachers. The study included two iterative cycles using various tools and methods. Development in argumentation and metacognition is tracked through classroom talk analysis carried out at three different time periods, and presented with argumentation schemas and metacognitive talk analysis. Problem solving performance of students are examined with two mathematical tests that are applied at the beginning and end of the school year. Argumentation schemas and metacognitive talk analysis of classrooms indicate that there is an improvement in argumentation and metacognitive skills of students. Additionally, the results of mathematical tests show that students' problem solving performance improved in a statistically significant way. The findings of the study suggest that problem solving skill can be improved through designing a learning environment where argumentation and metacognitive skills are utilized and promoted in problem solving situations.