Evaluating the Impact of Active-Learning Strategies on Students' Understanding of Mathematics in a Public Secondary School of Chitral Lower

Abstract

This study examined the impact of active-learning strategies on the geometry and measurement performance of Grade X female students in a public secondary school in district Chitral Lower. A pre-experimental one-group pre-test/post-test design was employed with a purposive sample of 25 students. A self-developed, curriculum-aligned Geometry Achievement Test (GAT) comprising 25 items (10 MCQs and 15 constructed-response questions) totalling 50 marks was administered before and after a four-week active-learning intervention. The GAT assessed four cognitive domains: understanding, application, analysis, and problem-solving. Expert review yielded a Content Validity Index of 0.86, and Cronbach's Alpha reliability was 0.88. Descriptive statistics revealed a mean gain of 9.44 marks (pre-test M = 28.12, SD = 3.98; post-test M = 37.56, SD = 4.22). Domain-wise analysis showed the greatest gain in the analysis domain (MG = 3.04), followed by application (MG = 2.74), understanding (MG = 2.02), and problem-solving (MG = 1.64). A one-sample paired t-test confirmed a statistically significant improvement, t(24) = 15.45, p < 0.001, with a large effect size (Cohen's d = 1.25). These findings affirm that structured, active-learning interventions can meaningfully enhance geometry achievement at the secondary level in resource-constrained rural settings.