Advantages of discussion and cognitive conflict as an instructional method in contemporary teaching of mathematics

Contemporary theories of teaching and learning mathematics emphasise the importance of learner’s active participation in the teaching process, in which discovery and logical reasoning lead to the construction of student’s knowledge. In this form of teaching, it is important to detect students’ misunderstandings and errors that can occur during learning. Uncovered tacit and false conceptions of students’ knowledge can greatly contribute to the opposite effect in the construction of knowledge. In teaching mathematics, there are many situations which leave students with ambiguities and misunderstandings, and create an impression in children that teaching of mathematics and mathematical knowledge itself is something that is not possible. Discussion and cognitive conflict are methods which have their starting point in the theory of constructivism. The aim of our study has been to determine whether application of the method of discussion and cognitive conflict in learning to divide decimal numbers leads to the enhancement of student’s procedural knowledge and conceptual knowledge about the division of decimal numbers. Longitudinally, we monitored two groups of 117 pupils of the fifth grade. In the first group, which was taught according to the guidelines of contemporary mathematics education, students engaged in discussion, discovering their misunderstandings and errors, and the cognitive conflict resulted in correct concepts. The second group of students were taught traditionally, learning the procedure and then practicing it. The paper presents a descriptive analysis of the process of teaching and quantitative analysis of the performance based on the comparison of conceptual and procedural knowledge of both groups. Results of our work show that the application of contemporary methods of discussion and cognitive conflict affects the increase of procedural and conceptual knowledge of the division of decimal numbers