Cognitive, Affective and Learning Mechanism (CALM) Framework in Mathematics Enhancing Problem Solving-Skills among Students

Abstract

This study addressed the persistent challenge of mathematics problem-solving among Senior High School students who exhibited low performance, high math anxiety, and reliance on rote memorization. Recognizing the gap in existing research that often separated cognitive, affective, and learning processes, this study developed and validated the CALM Framework, an integrated instructional model combining Cognitive, Affective, and Learning Mechanisms to enhance students’ problem-solving skills in mathematics. Grounded in established theories such as Bloom’s Taxonomy, Polya’s problem-solving model, Krathwohl’s affective domain, and Flavell’s metacognitive theory, the framework targeted mental processes, emotional factors like motivation and confidence, and metacognitive strategies including reflection and self-regulation. Using a quasi-experimental design, the study compared an experimental group taught with the CALM Framework against a control group receiving traditional instruction. Findings revealed that the CALM Framework was highly accepted by experts and significantly improved students’ problem-solving abilities. The study recommended wider adoption of the CALM Framework, as the results of the Analysis of Covariance (ANCOVA) revealed a statistically significant effect of the intervention on students’ mathematical problem-solving skills, and the Pearson r correlation analysis showed a significant relationship between students’ problem-solving performance and their impressions of the framework. The integration of cognitive, affective, and learning mechanisms allowed the framework to effectively respond to the learning challenges faced by Filipino students.