The Dynamics of Students' Heuristic Failure and Mathematical Perseverance in Solving Contextual Problems Across Cognitive Demand Levels

Abstract

This study aimed  the dynamics of heuristic failure and mathematical perseverance among students in solving contextual problems across different cognitive demand levels. A descriptive qualitative approach was employed involving three purposively selected tenth-grade students representing high, medium, and low mathematical ability. The research instruments consisted of a mathematics ability test, a contextual problem-solving test on Systems of Linear Equations in Three Variables comprising Procedures with Connections (PWC) and Doing Mathematics (DM) tasks, and retrospective interviews. Data were analyzed using the heuristic failure framework adapted from Schoenfeld and the Three-Phase Perseverance Process (3PP) proposed by DiNapoli and Miller. The findings revealed that the high-ability student experienced heuristic failure at the execution and reflection stages and discontinued effort after reaching an impasse on the DM task. The medium-ability student revised errors and sustained productive effort until obtaining a correct solution, whereas the low-ability student experienced more dominant heuristic failures and did not continue solving the problem after encountering an impasse. The findings indicate that mathematical ability alone did not determine perseverance patterns, particularly when students encountered an impasse in the more cognitively demanding DM task.