Problem-Solving Framework in Algebra Through Backward Error-Analysis
Keywords: Backward Error-Analysis, alternative assessment, BEA-Trick Framework
Abstract
This study aimed to propose Backward Error-Analysis (BEA) as an alternative assessment method in algebra by evaluating its relevance and effectiveness and developing a problem-solving framework for classroom use. Specifically, it compared the Conventional Assessment Method and BEA in evaluating learners’ algebra performance, tested BEA’s effectiveness, assessed learners’ perceptions including general perceptions and challenges and developed a BEA-based problem-solving framework. A Quantitative Research Design was used involving 60 Grade 9 learners from Pili National High School, divided into two groups: one using conventional assessment and the other BEA. Both groups took pre-tests and post-tests, with two interventions conducted for the BEA group, and a self-constructed survey assessed learners' perceptions. Findings showed no significant difference between the two groups’ test results, yet BEA proved effective as learners’ post-test scores significantly improved. Learner perceptions highlighted factors such as engagement, perceived usefulness, efficiency, learning outcomes, and commitment, with challenges including emotional resistance and cognitive struggles in error analysis. The study also introduced the “BEA-Trick Framework” as a foundation for classroom implementation. Overall, BEA was found effective and offered unique advantages over conventional methods. It is recommended for classroom adoption to foster 21st-century skills and higher-order thinking
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