2026 Theses Doctoral

Beyond the Notation: Strategy Use in Cross-Notation Magnitude Comparisons

Hahn, Yoojin

The integrated theory of numerical development posits that all real numbers can be represented on a unified mental number line. However, many adults possess only a weak integrated knowledge of rational number magnitudes—fractions, decimals, and percentages. I hypothesize that the persistent difficulty adults face when comparing across rational number notations stems from a failure to adaptively select strategies that coordinate magnitudes across these different symbolic formats.

Two experiments, a foundational investigation of spontaneous strategy use (n = 65 undergraduate students) and a larger study of strategic malleability (n = 100 adults), were conducted. These experiments utilized a process-oriented approach, grounded in the Adaptive Strategy Choice Model, to identify the mental procedures individuals use to solve cross-notation magnitude comparison problems. Experiment 1 integrated a magnitude comparison task with verbal self-reports to map the strategic landscape.

Results revealed that: (1) adults deploy a diverse repertoire of magnitude comparison strategies; (2) strategy efficacy varies significantly, with maladaptive heuristics (e.g., direct comparison) driving low accuracy and notation-based biases; (3) strategy selection is adaptive, shifting in response to problem features like notation type and benchmark saliency; and (4) distinct individual profiles of strategy use predict both cross-notation magnitude comparison accuracy and broader measures of rational number knowledge. Experiment 2 utilized a strategic instruction intervention to probe whether these strategic processes are malleable. Using a choice/no-choice paradigm, participants were explicitly taught to use translation-to-percentage and benchmarking-the-midpoint strategies. Targeted instruction significantly improved accuracy and reduced notation-based biases compared to baseline performance.

In sum, this dissertation seeks to make a scholarly contribution to the field by providing a process-level account of how individuals reason across rational number notations and by establishing that integrated rational number competence can be fostered through strategy-focused instruction.