From quantity-based to operation-based errors: Developmental shifts in one-step additive word problem solving

This study investigates developmental changes in the patterns of errors produced by primary school students when solving one-step additive arithmetic word problems. A sample of 3,111 students from Grades 1 to 6 completed a battery of Change, Combine, and Compare problems presented in a multiple-choice format with theoretically motivated distractors. These distractors captured three recurrent error types: selection of the higher quantity, selection of the lower quantity, and application of the inverse operation. Results show clear grade-related shifts in the distribution of error types. In the early grades, students’ incorrect responses are dominated by quantity-based choices, indicating a strong reliance on salient numerical values in the problem statement. From approximately Grade 3 onward, quantity-based errors decrease substantially, while inverse-operation errors account for an increasing proportion of remaining errors, particularly in Change and Compare problems. Importantly, these developmental trajectories are not uniform across semantic families: Combine problems exhibit comparatively stable error profiles, whereas Change and Compare problems show pronounced reorganization in the nature of errors across grades. Rather than focusing exclusively on accuracy, the findings highlight how developmental progress in additive word problem solving is reflected in systematic changes in error profiles that are sensitive to semantic structure. By treating errors as diagnostically meaningful outcomes, this study provides a fine-grained account of how students’ interpretations of additive situations evolve across primary education and offers insights relevant for both research and instructional design in mathematics education.