Students\' Heuristics in Solving Mathematics Problems

This study aimed to investigate students' heuristics in solving mathematics problems on topic domains such as division of polynomials, solving problems involving polynomial equations and functions, and plane coordinate geometry. The study employed mixed methods of investigation. It used quasi-experimental research with a one-group pretest-posttest design. The participants were the intact group of forty (40) Grade 10 students in As-Salihein Integrated School. The findings of this study showed that 1) StudentsÂ’ problem-solving solutions in selected problems in the problem-solving performance test were analyzed to identify heuristics. The following are the studentsÂ’ emerging heuristics as categorized according to the sequence of the studentsÂ’ solutions as to what generalized heuristics used after the intervention: 1. Citing the given information in the problem (CIP), applying mathematics general principle (AMGP), evaluating and simplifying the equation (ESEQ), and arriving at the correct answer (ACA); 2. Setting the mathematical working principles (SMWP), evaluating and simplifying the equation (ESEQ), and arriving at the correct answer (ACA); 3. Applying the mathematical general principle (AMGP), evaluating and simplifying the equation (ESEQ), and arriving at the correct answer (ACA); and 4. Applying the mathematical general principle (AMGP), simplifying the problem (SP), and arriving at the correct answer (ACA); and 2) The changes of studentsÂ’ heuristics on the topic domains of the study were categorized thematically based on the studentsÂ’ constructed solutions after intervention: 1) CIP-AMGP-ESEQ-ACA heuristic; 2)SMWP-ESEQ-ACA heuristic; 3) AMGP-ESEQ-ACA Heuristic; and 4) AMGP-SP-ACA heuristic. Students employed a variety of heuristics because they were free to demonstrate their approaches or methods for solving problems and improvements in their solutions were documented. Some students demonstrated their heuristics, while others followed their teachers' heuristics when solving problems. Furthermore, the heuristic-guided problem-solving approach used to teach mathematical topic domains was proven to be effective in assisting students in solving mathematical problems. Furthermore, students who were exposed to the instructional intervention in which they were exposed to solving problems improved their problem-solving skills.