Seeing beyond the explicit: Orienting learners to perceive underlying mathematical structure

Georgia Maria Garay, Fordham University

Abstract

Research has shown that experts are able to see beyond explicitly presented content and identify relevant structural information that determines correct problem solutions. Two experiments were conducted to investigate whether a triad judgment task could be used to orient learners to detect deep structural features within two mathematical content areas: factoring polynomial expressions and solving percent word problems. Three triad types were designed to manipulate surface and deep feature similarity between source and target problems. One triad type contrasted a problem that was similar to the target in terms of surface features with a problem that was similar in terms of structural features (SS-SD). A second triad type contrasted a problem that possessed similar deep features with an unrelated problem (SD-U). The third contrasted a problem with similar surface features and an unrelated problem (SS-U). Learners were presented with six triads of each type and asked to identify which of two source problems went best with the target. Triad types were presented in different blocked sequences to determine whether order of presentation of triads can be used to orient learners towards deep structure. Additionally it was investigated whether the triad judgment task would influence subsequent problem solving performance. Results of both experiments suggested that learners can be oriented toward deep mathematical structure and away from distracting surface features by completing SD-U triads first in a blocked sequence of triads. Learners’ ability to perceive underlying structure had no significant impact on problem solving ability.^

Subject Area

Mathematics education|Educational psychology|Cognitive psychology

Recommended Citation

Garay, Georgia Maria, "Seeing beyond the explicit: Orienting learners to perceive underlying mathematical structure" (2016). ETD Collection for Fordham University. AAI10248992.
https://fordham.bepress.com/dissertations/AAI10248992

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