Investigation of students' cognitive processes towards the concepts of equality and variables within the theoretical framework of mathematical workspace

In this research, it is aimed to examine the interaction of students' cognitive processes between epistemological-cognitive planes in the mathematical study designed for the concepts of equality and variable by making use of the theoretical framework of MWS (mathematical working space) in the context of genesis and planes formed by the pairwise combination of genesis. In this qualitative research, the teaching experiment design was adopted. The participants of the study were selected through criterion sampling, one of the purposeful sampling methods, among fifth grade students at a public school. In the research, MWS became a theoretical framework adopted both in the design of the teaching process and in the analysis process. In order to reveal the change and development in the cognitive schemas and techniques used by the research participants during the teaching process, prepared data collection tools were applied, and the data obtained through individual and group interviews were analyzed. The results of the research show that the students showed improvement in using different interpretations of the equal sign, the scale model, and different representations of the variable as an effective instrument. The techniques they used and their images of the concept were enriched; It has been shown that the concepts of equality and variable differ in the planes in which they are used in their studies.