title: Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later.
abstract: The classic bat-and-ball problem is used widely to measure biased and correct reasoning in decision-making. University students overwhelmingly tend to provide the biased answer to this problem. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective? One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. Most of this cueing effect was confined to a condition that required participants to solve isomorphic algebra equations corresponding to the structure of bat-and-ball question types. On a subsequent critical question with differing item and dollar amounts presented without a cue, participants were able to generalize the learned information to significantly reduce overall bias. Math anxiety was also found to be significantly related to bat-and-ball problem accuracy. These results suggest that, under specific conditions, algebraic reasoning is an effective debiasing strategy on bat-and-ball problem variants, and provide the first documented evidence for the influence of math anxiety on Cognitive Reflection Test performance.
authors.affiliation: Department of Psychology and Neuroscience, University of Colorado Boulder, Boulder, CO, 80309-0345, USA.
authors.forename: Jerome D
authors.initials: JD
authors.lastname: Hoover
authors.affiliation: Department of Psychology and Neuroscience, University of Colorado Boulder, Boulder, CO, 80309-0345, USA. Alice.Healy@Colorado.EDU.
authors.forename: Alice F
authors.initials: AF
authors.lastname: Healy
mesh_terms: D000293:Adolescent; D000328:Adult; D000818:Animals; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D008433:Mathematics; D008875:Middle Aged; D013850:Thinking / Q000502:physiology*; D055815:Young Adult
keywords: Algebraic reasoning; Cognitive Reflection Test; Debiasing; Decision-making; Judgment; Math anxiety; Reasoning