Teaching symmetry through mathematical thought experiments: A quasi-experimental study

Source abstract

Abstract This study examined the impact of educating axial and central symmetry, as key concepts in geometric transformations, through mathematical thought experiments on fifth-grade students’ academic achievement and APOS-based learning levels. This study employed an explanatory sequential mixed-methods design. The quantitative phase used a quasi-experimental pretest–posttest design with experimental and control groups, while the qualitative phase involved thematic analysis of task-based interviews and classroom observations to explain and enrich the quantitative findings. The population consisted of all male fifth-grade students in Tehran, Iran, during the 2023–2024 academic year. A convenience sample of 34 students took part in the research. A researcher-made test grounded in the APOS theory (Cronbach’s alpha = 0.72) assessed academic achievement and learning levels. Over twelve 45-minute sessions, the experimental group learned symmetry through mathematical thought experiments, whereas the control group received conventional instruction. Descriptive results included means and standard deviations for all variables. The Kolmogorov–Smirnov test verified that the data followed a normal distribution. Hypotheses were tested with ANCOVA and Quade’s ANCOVA. Findings showed that instruction based on mathematical thought experiments produced significant gains in both learning levels and academic achievement. Thematic analysis further identified key patterns in students' reasoning that supported these outcomes. The approach supported the development of solid knowledge structures and deeper conceptual understanding of symmetry.