Navigating geometric thought: A classroom-based intervention using discovery-contextual strategies aligned with van Hiele’s cognitive framework

Purpose: This study aims to investigate the enhancement of students’ geometric thinking through the integration of Discovery–Contextual learning strategies with van Hiele’s levels of reasoning. In addition, it examines the contribution of logical–mathematical intelligence to mathematics learning outcomes by synthesizing findings from prior research. Method: The research employed a classroom action research design implemented in three iterative cycles involving 13 fifth-semester mathematics education students. Data were collected through geometry thinking tests, observation notes, and the van Hiele-based assessment tool, then analyzed descriptively to track cognitive development across cycles. Complementing this, a meta-analysis of 41 empirical studies was conducted using a random-effects model to evaluate the consistency of logical–mathematical intelligence on students’ mathematics achievement. Findings: The results indicate steady improvement in students’ geometric reasoning, particularly at the deduction and rigor levels, with mean performance rising from 78.4% in the first cycle to 92.8% in the third. Reflection across cycles also revealed stronger engagement, reflective thinking, and collaborative learning. The meta-analysis further confirmed that logical–mathematical intelligence consistently exerts a strong and stable influence on mathematical performance across different educational stages and contexts. Significance: Findings highlight the pedagogical value of combining Discovery–Contextual learning with van Hiele’s framework to cultivate higher-order geometric thinking. At the same time, the evidence underscores the necessity of integrating logical reasoning into curriculum design and instructional strategies. Together, these contributions provide both theoretical insights and practical guidance for advancing mathematics education, especially in preparing prospective teachers to meet diverse cognitive needs.