Bar Model Thinking for Visual Reasoning in Elementary Word Problems

Abstract

This study investigated how bar model thinking contributed to visual reasoning in elementary word-problem solving among 190 Grade 5 and Grade 6 learners in Alabang, Muntinlupa City. Using a task-based explanatory predictive design, the study assessed representation accuracy, relational mapping, solution transfer, and visual reasoning through a 24-item performance-based instrument. Descriptive statistics and Generalized Structured Component Analysis were used to determine performance patterns and predictive relationships among the constructs. Results showed that learners performed strongest in representation accuracy, while solution transfer emerged as the weakest area. Performance was also higher in part-whole and comparison problems than in multiplicative comparison and multi-step tasks. The structural model demonstrated satisfactory explanatory power, with bar model thinking accounting for 63.0% of the variance in visual reasoning. Among the dimensions, relational mapping produced the strongest predictive effect, followed by representation accuracy and solution transfer. These findings indicate that the effectiveness of bar models extends beyond producing correct diagrams and depends greatly on learners’ ability to recognize, organize, and interpret quantitative relationships. The study concludes that bar model instruction should emphasize relational reasoning and progressive exposure to varied problem structures to strengthen the transfer of visual reasoning across increasingly complex mathematical tasks.