Epistemological beliefs on mathematics, achievement goal orientation, and non-routine problem-solving skills among Filipino seventh graders - Sumagit, Katrina Grace Q. (College of Education, University of the Philippines Diliman, 2020)
This study, examined the relationships among epistemological beliefs on mathematics, mathematical beliefs on problem-solving, achievement goal orientation on mathematics, and non-routine problem-solving skills of Filipino students, using mixed-methods research design. Researcher-made self-report surveys and problem set were administered to 464 seventh graders enrolled in public high schools in an urban area. Descriptive statistics, exploratory factor analysis (EFA), confirmatory factor analysis (CFA), structural equation modeling (SEM), correlation analysis, and multiple regression analysis (i.e. stepwise) were used to analyze the data collected. A researcher-made interview to 60 selected students to substantive findings. The results obtained indicate that the structure of epistemological beliefs on mathematics is multidimensional. Five dimensions of epistemological beliefs emerged in this study: learning effort perseverance, speed and source, innate/fixed ability, learning process, and learning effort-diligence. The means and standard deviations of the composite scores indicate that while students hold naive epistemological beliefs on mathematics in speed and source aside from innate/fixed ability, they hold sophisticated epistemological beliefs on mathematics in learning effort and process. Moreover, three classifications of mathematical beliefs on problem-solving were derived in this study: motivation, algorithm, and correct answer. The means and standard deviation of the composite scores reveal that students hold non-availing mathematical beliefs in algorithm and correct answer while holding availing mathematical beliefs in motivation. Further, the results show that students hold multiple achievement goal orientation on mathematics, namely performance-approach, mastery-approach, and mastery-avoidance. In terms of non-routine problem-solving skills, the results indicate that students lack (or at least insufficiency master) the secondary skills to solve mathematical problems (in non-routine problems). The result of the CFA conducted on the hypothized measurement model of relationships among epistemological beliefs on mathematics, mathematical beliefs on problem-solving, achievement goal orientation on mathematics, and non-routine problem-solving skills reveal that significant correlations only existed among epistemological beliefs on mathematics, mathematical beliefs on problem-solving, and achievement goal orientation on mathematics but not in non-routine problem-solving skills. The results of the SEM conducted in the structural model indicate that epistemological beliefs on mathematics and mathematical beliefs on problem-solving are significantly related. The results of the SEM also reveal that epistemological beliefs on mathematics and mathematical beliefs on problem-solving takes simply, product achievement goal orientation on mathematics.