Comparative Efficacy of Heuristic, Discovery-Based, and Manipulative-Aided Instruction on Student Achievement in Middle School Geometry
Keywords:
Geometry Education, Instructional Methods, Heuristic MethodAbstract
Background: Effective geometry instruction is fundamental to mathematical proficiency, yet students often struggle with its abstract concepts. While various student-centered pedagogical approaches have been proposed, there is a need for direct empirical comparison of their effectiveness. This study investigates the relative impact of three prominent instructional strategies: the heuristic method, discovery-based learning, and manipulative-aided instruction.
Purpose: The primary purpose of this study was to compare the efficacy of these three teaching methods against a traditional, lecture-based approach on sixth-grade students' achievement in geometry.
Methods: A quasi-experimental, pre-test/post-test control group design was employed with 124 sixth-grade students from four intact classes in a public middle school. Each class was randomly assigned to one of four conditions for an eight-week instructional period: (1) Heuristic Method, focusing on structured problem-solving; (2) Discovery Learning, emphasizing student-led exploration; (3) Manipulative-Aided Instruction, utilizing concrete physical objects; and (4) a Control Group receiving traditional instruction. A validated Geometry Achievement Test was administered before and after the intervention. Data were analyzed using Analysis of Covariance (ANCOVA), with pre-test scores serving as the covariate.
Results: The ANCOVA revealed a statistically significant difference in post-test achievement scores among the four groups, F(3, 119) = 15.42, p < .001, partial η² = .28. Post-hoc comparisons using Tukey's HSD indicated that both the Manipulative-Aided (Adjusted M = 85.05) and Heuristic (Adjusted M = 81.85) groups were associated with significantly higher achievement than the Discovery Learning (Adjusted M = 74.58) and Traditional Control (Adjusted M = 73.90) groups. The manipulative group was associated with the highest mean score.
Conclusion: The findings suggest that instructional methods incorporating concrete experiences and structured problem-solving are associated with significantly more effective learning outcomes in geometry than either unguided discovery or traditional methods. The study provides strong evidence for integrating manipulatives and heuristic strategies into middle school mathematics curricula to enhance students' geometric understanding.
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