Are content effects out of sight? An eye-tracking study of arithmetic problem solving

General, non-mathematical knowledge about the entities described in an arithmetic word problem may interfere with its encoding. We used behavioral and eye-tracking measures to investigate how the use of specific quantities may foster a cardinal representation of the numbers mentioned in a problem, whereas other quantities may favor an ordinal representation instead. We asked 50 pre-service teachers to complete a solution validity assessment task. We compared participants’ gaze patterns on isomorphic problems to gather insights into their encoded representations. On problems featuring cardinal quantities, we found that specific sentences describing elements relevant in a cardinal understanding of the problems but irrelevant otherwise were looked at longer and were the focus of a higher number of backward eye movements. Additionally, an increase in pupil dilation on correctly solved cardinal problems supported the idea that participants need to engage in a recoding process when facing semantic incongruence.

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Eye gaze patterns reflect how young fraction learners approach numerical comparisons

Journal of Numerical Cognition ◽

10.5964/jnc.v6i1.119 ◽

2020 ◽

Vol 6 (1) ◽

pp. 83-107

Author(s):

Alison T. Miller Singley ◽

Jeffrey Lynn Crawford ◽

Silvia A. Bunge

Keyword(s):

Academic Achievement ◽

Eye Movements ◽

Problem Solving ◽

Eye Tracking ◽

Conceptual Development ◽

Eye Gaze ◽

Proficiency Levels ◽

Gaze Patterns ◽

Different Levels ◽

Fraction Comparison

Learning fractions is notoriously difficult, yet critically important to mathematical and general academic achievement. Eye-tracking studies are beginning to characterize the strategies that adults use when comparing fractions, but we know relatively little about the strategies used by children. We used eye-tracking to analyze how novice children and mathematically-proficient adults approached a well-studied fraction comparison paradigm. Specifically, eye-tracking can provide insights into the nature of differences: whether they are quantitative—reflecting differences in efficiency—or qualitative—reflecting a fundamentally different approach. We found that children who had acquired the basic fraction rules made more eye movements than did either adults or less proficient children, suggesting a thorough but inefficient problem solving approach. Additionally, correct responses were associated with normative gaze patterns, regardless of age or proficiency levels. However, children paid more attention to irrelevant numerical relationships on conditions that were conceptually difficult. An exploratory analysis points to the possibility that children on the verge of making a conceptual leap attend to the relevant relationships even when they respond incorrectly. These findings indicate the potential of eye-tracking methodology to better characterize the behavior associated with different levels of fraction proficiency, as well as to provide insights for educators regarding how to best support novices at different levels of conceptual development.

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