Developing problem solving heuristics, self-regulated learning, and mathematics self-efficacy beliefs through cognitive modeling: A case analysis

• Main Author: Oryan, Serano Lippad
• Format: text
• Language: English
• Published: Animo Repository 2005
• Subjects: Problem solving; Learning strategies; Mathematics; Self-efficacy; Motivation in education; Academic achievement.; Science and Mathematics Education
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/89; https://animorepository.dlsu.edu.ph/context/etd_doctoral/article/1088/viewcontent/CDTG003927_P.pdf
• Institution: De La Salle University

This study aims to describe and analyze the following: the nature of problem solving processes employed by the students, their self-regulatory learning processes, and their general efficacy perceptions in mathematics. The respondents of this study include a section of freshman engineering students and a subgroup of six students from this section who enrolled in College Algebra at Benguet State University in Benguet during the school year 2004 2005. The tools used to gather data include problem solving tests (pretest & posttest), problem sets, journal writing, mathematics self-efficacy scale, and informal interviews. The intervention used during the conduct of the study is cognitive modeling which has enabled the teacher to verbalize the cognitive and metacognitive processes involved in problem solving. The results show substantial improvement in the students problem solving processes toward the end of the intervention. They are more successful in solving structured problems than in solving less structured ones; also, their problem solving competences have progressed better in structured problems. The more persistent weaknesses of their solutions include mathematically modeling a problem situation, making logical steps, and checking results with given solutions. In terms of problem solving processes, the major weaknesses of their activities are planning and reflection because majority of them fail to do such activities properly. Their general mathematical efficacy beliefs are more positive after the intervention than before it. The major contributors to their efficacy beliefs are extrinsic motivation and intrinsic motivation, whereas the lesser contributors are subjective competence and locus of control. The important bases of their extrinsic motivation include those that relate to their careers, vi success in life and prestige in society, whereas that of their intrinsic motivation include those that relate to their intellectual development and sense of achievement and gratification from problem solving success. The more important bases of their sense of control over their performance outcomes include those that relate to the perceived do ability of mathematical tasks through effortful learning engagement and to their perceived ability to do mathematics in general, while that of their sense of mathematical competence include those that relate to their perceived ability to do mathematical tasks, persistence, and readiness to solve mathematical problems. In the case of their self regulatory processes, the middle performers show more skillful self-regulatory learning behavior toward the end of the intervention than at the beginning. The top performers have manifested skillful self-regulatory learning behavior throughout the duration of the intervention; also, they are either the most successful problem solvers throughout the duration of the intervention or the most improved problem solvers at the end of the intervention. The bottom performers fail to improve their self-regulatory learning skills as well as their problem solving skills. The major weaknesses of the students self regulatory processes across the groups lie in strategic planning and intentional monitoring. Based on the foregoing results, it is theorized that by modeling an appropriate thinking schema and exposing students to appropriate learning situations in which they can experience and reflect on how the schema works, they can develop a thinking schema as desirable as the modeled one.