We evaluate how learners construct internal representationsof fraction values. Symbolic numbers written using fractionnotation are difficult for both children and adults to use.Errors made by learners suggest that even experienced adultscan lack fluency with fractions. One such error is the NaturalNumber bias phenomenon: when the relative size of fractionsvalues to be compared is incongruent with the relative size ofthe fraction components learners show a reaction time delayor decreased accuracy. For example, noting that 1/7 is smallerthan 1/5 may take longer that noting that 3/10 is smaller than5/10. We adjust the temporal dynamics of the fractioncomparison task to characterize how learners constructfraction values from the constituent parts. We also create amathematical model of the fraction value construction.

In this study we attempted to predict individual participants single trial behavior (response and reaction time) on anon-symbolic number comparison task. Experimental sessions included the completion of the number comparison task alongwith concurrent EEG measures. We then used a dynamic systems model with evolutionary algorithm updating to predict be-havior for each participant independently. The computational model approximated neural coding of number by calculatingtuning curves implemented through multilayered dynamic systems architecture. Typically dynamical systems models of cogni-tion have fixed parameters tailored to the particular task being modeled and selected by the researcher. The models used weredesigned to adapt such that each participant’s model is individually customized to their particular data. Average ERP amplitudeacross occipitoparietal areas were used as model input in addition to participant’s prior responses and reaction time.

This study assessed whether a sample of two hundred seven 3- to 7-year-olds could interpret multidigit numerals using simple identification and comparison tasks. Contrary to the view that young children do not understand place value, even 3-year-olds demonstrated some competence on these tasks. Ceiling was reached by first grade. When training was provided, there were significant gains, suggesting that children can improve their partial understandings with input. Findings add to what is known about the processes of symbolic development and the incidental learning that occurs prior to schooling, as well as specifying more precisely what place value misconceptions remain as children enter the educational system.