How are fraction values constructed? [post]

Richard Prather
2018 unpublished
Fractions are a difficult symbolic number format to master for children and adults alike. Errors made with symbolic fraction numbers suggest that even experienced adults can lack fluency with fractions. The importance of the fraction format in formal education has motivated a great deal of research in focused on why fractions are so difficult for peoples to use. In the current study, we investigate the question of how people construct an internal representation of fraction values from the
more » ... s. We present data across two behavioral experiments and mathematical modeling to demonstrate how people construct fraction values from the constituent parts. In the behavioral experiments we manipulate the temporal dynamics of stimulus presentation in the canonical number comparison task. We demonstrate that a small delay in the presentation of specific fraction components affects the relative response time. We find that participants are significantly faster to complete numerator delayed trials, suggesting that participants can use the denominator to begin construction of the fraction value. We further characterize the cognitive processes and strategies that account for the behavioral data using a dynamic systems neural network mathematical model. We conclude that participants begin the construction of fraction values with the denominator and can initiate such construction before the numerator is known.
doi:10.31234/ fatcat:tiltydjxubczddwz6ao4yyfrbi