# Task dynamics reveal how fraction values are constructed

- Richard Prather, University of Maryland, College Park, Maryland, United States

**Abstract**We evaluate how learners construct internal representations of fraction values. Symbolic numbers written using fraction notation are difficult for both children and adults to use. Errors made by learners suggest that even experienced adults can lack fluency with fractions. One such error is the Natural Number bias phenomenon: when the relative size of fractions values to be compared is incongruent with the relative size of the fraction components learners show a reaction time delay or decreased accuracy. For example, noting that 1/7 is smaller than 1/5 may take longer that noting that 3/10 is smaller than 5/10. We adjust the temporal dynamics of the fraction comparison task to characterize how learners construct fraction values from the constituent parts.
We also create a mathematical model of the fraction value construction.