The Use of Heuristics in Solving Non- routine Problems

Despite curricular reforms in the Philippines that emphasize critical thinking and problem-solving, Filipino students remain accustomed to routine procedures and traditional textbook problems that do not develop these skills. Exposing students to nonroutine problems provides an opportunity for students to use varied or multiple solution strategies that encourage and develop these skills. This study aimed to explore the use of heuristics in solving non-routine problems. Using qualitative content analysis with data triangulation, 42 top-performing Grade 10 students in Mathematics completed a problem-solving test consisting of 4 non-routine problems, a reflective journal, and participated in oneon-one interviews afterwards. Findings revealed that multiple heuristics were generated in solving four non-routine problems. This includes pattern recognition, drawing a diagram, making a systematic list or table, using simpler cases, deriving a formula, using equations, arithmetic calculation, using analogies, guess-check-revise, eliminating possibilities, and working backwards. However, errors emerged in the students’ use of heuristics as mapped in Newman’s Error Analysis Stages. Across the data, participants displayed a lack of conceptual understanding, mapped as a comprehension error; inappropriate mathematical modeling was classified as a transformation error; inconsistencies in procedural execution were identified as an error in Process Skills; and incorrect or incomplete final answers were classified as an encoding error. Based on the findings, a teacher-supplementary resource material was developed. Results highlight that while heuristics can support non-routine problemsolving, successful outcomes depend on conceptual understanding, appropriate modeling, procedural precision, and clear communication of final answers.