Parameterization-based instruction for symmetry transformations: A quasi-experimental study of students’ intra-mathematical modeling skills

Abstract

This article examines the potential of the proposed didactic framework for developing students’ intra-mathematical modeling skills. The aim of the study is to develop students’ model-building abilities, generalization competencies, and general logical thinking by teaching topics related to symmetry through a parametric approach. A mixed-methods study methodology was employed, including comparative analysis and pre- and post-test, combining quantitative data from student evaluations with qualitative data gathered from interviews. The experiment was conducted with 11th-grade students of the Academic Lyceum of Fergana State University. The results indicate that parameterization is a potent method for improving generalization and modelling skills in mathematics education. It showed that the percentage of high-level modelling students in the experimental group increased from 0% to 10.7%, exhibiting statistically significant differences (χ2 = 45.755, p < .001), while the indicators at the low level decreased. Statistical analyses confirmed the effectiveness of the didactic framework based on the parameterization method. As a result of the study, an original instructional development, a system of tasks designed for teaching symmetry transformations on the basis of parameterization—was created. It underscores the necessity for educators to implement varied strategies that promote improved mathematical modeling.