The effect of mathematics teaching based on the Bianshi model of the theory of variation on elementary school students' academic achievement and inter-representational transition skills

In this study, the effect of the mathematics learning environment developed according to the Bianshi model based on the theory of variation on the academic achievement and interrepresentational transition skills of 3rd grade primary school students was examined. The study was designed in a quasi-experimental design with pretest-posttest experimental and control groups. The research was conducted in a public school in Zeytinburnu district of Istanbul province with the participation of 42 students in total, 21 experimental and 21 control groups. Before and after the experimental procedure, students were administered a two-stage academic achievement and transferability skills test. While the experimental group was taught in the learning environment developed based on the Bianshi model of the theory of variability, the control group was given addition and subtraction acquisitions from the Natural Numbers and Operations learning area in the mathematics textbook prepared by the Ministry of National Education. Independent samples t-test was used to examine the equivalence of the students' pre-test scores and repeated measures ANOVA test was used to examine the changes in the academic achievement and interrepresentational skills of the experimental and control groups between the pre-test and post-test measurements. Data analysis was carried out using SPSS 22 statistical package program. The findings of the study show that there is a significant difference in favor of the experimental group in terms of academic achievement and interrepresentational skills. Accordingly, it was determined that mathematics teaching based on the Bianshi model of variability theory was effective on academic achievement and interrepresentational skills. In the questions prepared according to the MATH taxonomy, the experimental group significantly increased the number of questions that they answered correctly and were effective in developing high-level skills. Although there was an increase in both the experimental and control groups in the ability to move between representations, it was observed that the increase in the experimental group was considerably higher than that in the control group. As a result of the research, it was observed that mathematics learning environments and materials developed with the Bianshi model were effective for primary school students.