Abstract:

Spatial ability has been shown to predict achievement in mathematics and science, particularly in geometry. This study examines whether a short instructional intervention focused on four-dimensional (4D) geometry, supported by GeoGebra, can enhance secondary students’ spatial ability.

A quasi-experimental pre-test/post-test design was implemented to examine changes across three groups of upper secondary students: a group exploring 4D geometric configurations using GeoGebra, a group receiving 4D instruction without dynamic software support, and a control group that did not receive the 4D geometry intervention.

Data were analysed using analysis of covariance (ANCOVA), with post-test scores as the dependent variable, instructional condition as the factor, and pre-test scores as the covariate. The analysis revealed a statistically significant effect of instructional condition on post-test performance (F(2, 166) = 3.452, p = .034, η²ₚ = .040). Post hoc comparisons showed that students who engaged with 4D geometry using GeoGebra achieved significantly greater gains than students in the control group (p = .027), while no statistically significant differences were found between the 4D instruction without software group and either the GeoGebra group (p = .289) or the control group (p = .630).

Overall, the findings suggest that engagement with 4D geometric concepts can lead to measurable improvements in students’ spatial ability, with the strongest gains observed when instruction is supported by GeoGebra. The observed effect size indicates a small but meaningful impact within a relatively short instructional period.

Keywords:

Spatial ability, 4D geometry, GeoGebra, Dynamic visualization, Mathematics education, Quasi-experimental design, Secondary education.