Development of Mathematics Learning Management Models to Promote Problem Solving Abilities and Analytical Thinking for Mathayom 1 Students
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Abstract
This study aimed to develop a mathematics learning management model and examine its effectiveness in promoting problem-solving ability and analytical thinking among Mathayomsuksa 1 students, employing a Research and Development methodology. The sample consisted of 39 students from Mathayomsuksa 1/2 at Buayai School, Nakhon Ratchasima Province, selected through cluster random sampling. The research yielded the IPADE Model, distinguished by three innovative features. First, the model systematically integrates multiple theoretical frameworks with clearly identifiable mechanisms underpinning each instructional stage: Stages 1–3 (Introduction, Planning, and Analyzing) are grounded in Piaget's Assimilation and Accommodation; Stage 4 (Demonstration) draws upon Vygotsky's Zone of Proximal Development and Mathematical Discourse; and Stage 5 (Elaboration) corresponds to the attainment of Equilibration, ensuring high theoretical validity. Second, the model incorporates a three-directional feedback component encompassing teachers, peers, and students themselves. Third, the development process began with a contextual needs analysis, ensuring strong alignment with real classroom challenges. The implementation trial revealed an efficiency ratio of 80.98/82.13, surpassing the 80/80 benchmark, and an effectiveness index of 0.7503, reflecting a 75.03 percent learning gain. Students' problem-solving ability and analytical thinking scores were significantly higher post-instruction than pre-instruction at the .05 significance level. Student satisfaction and expert validation were both rated at the highest level of appropriateness. The IPADE Model provides a theoretically grounded and empirically validated instructional framework suitable for fostering higher-order thinking skills in lower secondary mathematics education.
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