Cognitive Development and Mathematical Performance of Elementary School Students

The current research has been designed and completed with the aim of assessing the relationship between levels of epistemological transformation of elementary school students with their mathematical performance. The research sample includes 240 female and male students in grade three to five of elementary school (80 students including 40 girls and 40 boys in each of the grade levels). The students in the research sample have been chosen by simple random sampling method among the students of 19 districts of city of Tehran. In this research the Piajetian concrete-operational testing (including the tests of seriation with model -and without model, classification, and number conservation) are used for determining the phase of cognitive transformation, teacher-made test for finding the performance of mathematics students in the way that is more popular in schools, and researcher-made educational advancement test in order to reach math students’ performance results and paying attention to understanding the taught math concepts. The statistical assessment of findings of this research, in the descriptive level, with quantitative statistics of percentage, median and standard deviation, and in the inferential level with measuring ÷2 (Khi square) coefficient and bi-variate, t test for the two dependent group, and oneway analysis of variance analysis and concurrent co-relational matrix has been performed. Statistical analysis of the data gathered in this research has been done in two levels of descriptive (frequencies, percentiles, means, and standard deviations) and inferential (÷2 –one and bivariate Khi squares–, t test for two related groups, one way analysis of variance, and correlation matrix) statistics. The results of the research show that there is positive correlation between cognitive transformation in Piajetian cognitive tests (seriation with model, without model, classification, and number conservation) with mathematical performance in the three desired grade levels. Therefore, the research findings confirm the need for reviewing mathematics teaching lessons in elementary grade levels, matching mathematics teaching with students’ cognitive transformation levels, teaching along with activity and work, and paying attention to hierarchical mathematical concepts and to the formation of qualitative concepts in mathematics