Metacognitive Problem Solving: Effects on Students’ Metacognition and Mathematical Academic Performance, Self-Efficacy, and Lifelong Learning Skills

Abstract

Problem solving ability is an important skill for 21st century learners. This study examined the effects of the intervention, Metacognitive Mathematical Problem Solving, on students’ metacognition, mathematical academic performance, self- efficacy, and lifelong learning skills. An interrelationship among these variables was further studied and explored. A total of 277 students were involved in the study. Mathematics academic performance was measured using a researcher-made instrument named, Mathematical Achievement Test Questionnaire. Students’ metacognition, self-efficacy, and lifelong learning skills were assessed using adopted and modified instruments namely the Metacognitive Awareness Inventory, General Self-Efficacy Scale, and Lifelong Learning Inventory – all using a 5-point Likert scale. Using t-test, metacognitive components under knowledge of cognition such as declarative, procedural, and conditional all have significant results at p < 0.05. In addition, planning and evaluation under regulation of cognition had similar statistically significant outcomes. However, no significant improvement was shown among the sub-components, comprehension monitoring, information management strategies, and debugging strategies. In addition, the intervention resulted to an increase in students’ mean gain in terms of academic performance and self-efficacy. The analysis of variance was used to confirm mean differences between groups. Analysis of covariance was employed to adjust for baseline differences between groups using the pretest scores as covariates. Structural Equation Modelling (SEM) was utilized to determine the interrelationships of metacognition, mathematical academic performance, self-efficacy, and lifelong learning. Results showed significant negative direct effect of planning to students’ academic performance. On the other hand, both declarative knowledge and evaluation did not have direct significant effect to academic performance. However, both had a negative indirect effect to academic performance through lifelong learning skills. This means that while declarative knowledge and evaluation contributed to the development of lifelong learning, the mediating pathway resulted in lower academic performance. Furthermore, metacognition and general self-efficacy suggest a strong positive covariance. Students who demonstrated higher levels of metacognition exhibit stronger self-efficacy, suggesting a meaningful and positive relationship between the two latent constructs. Metacognitive learning approach in problem solving needs to be incorporated in the everyday teaching-learning activities of the students. Allowing students to create own reflection in their own thinking processes can help them become good problem solvers. This is one objective of the K to 12 2012 Mathematics Curriculum Guide in the Philippines. This interplay between metacognition and problem solving can lead to an innovative or an enhanced educational framework or model that will help redesign a curriculum that focuses not only in the improvement of students’ academic performance, but as well as the enhancement of self-efficacy and lifelong learning skills.