Association Between Symbolic and Nonsymbolic Representations of Number Across Development

• In Event: Poster Session 01
  In Poster Session: PS 01 Topic - Cognitive Processes

Abstract

Whether Arabic numerals and sets of dots are represented by the approximate number system (ANS) across development is a subject of long-standing interest in the field of numerical cognition, with seemingly contradictory results reported in studies of educated adults, school-aged children, and children too young to enter school. Here we tested a developmental framework that can reconcile these discrepancies in 186 4-year-olds to 12-year-olds and 66 adults. The framework posits that numerical understanding progresses through three phases of associative learning. Phase 1 is when approximate sense of discrete number is present, but symbols are meaningless. In phase 2, symbols are associated with the ANS from single-digit to multi-digit numerals, leading symbolic numerals being processed by the ANS. Phase 3 is when overlearning of symbols cause symbolic numerals to be processed more automatically than nonsymbolic numerosities. Even though numerical symbols seem to be estranged from the ANS in phase 3, symbols are continued to be represented approximately and treated like continuous quantity (e.g., length of lines). Based on this three-phase theory, we investigated whether (1) difference between symbolic and nonsymbolic representations would decrease from phase 1 to phase 2 and would increase from phase 2 to phase 3, and (2) multiple phases would overlap in a given age range. In Experiment 1, participants were asked to compare quantities ranged between 1-9, 10-99, and 100-999 which were presented in dot-dot and numeral-numeral formats. Consistent with the framework, we found evidence for all three phases, depending on age and numerical magnitude. Comparing numerals were slower than comparing dot arrays in the youngest age group (phase 1), but became similar (phase 2) or faster (phase 3), b = .36, SE = .05, p < .001, in the order of quantities 1-9, followed by quantities 10-99 and quantities 100-999, b = -.31, SE = .02, p < .001. This gradual change from small to large quantities yielded coexistence of multiple phases during childhood. We further provided support for the three-phase theory using dot-numeral comparison task in Experiment 2. Comparing different formats of magnitudes was affected by the ratio, b = .35, SE = .02, p < .001, suggesting that symbolic and nonsymbolic numbers were represented by a common system. In addition, the effect of ratio increased with age, b = .45, SE = .04, p < .001, and decreased in larger numeric range, b = -.38, SE = .03, p < .001. The results from Experiment 1 and Experiment 2 illustrated that meanings of symbolic numerals are acquired by mapping symbols to the ANS gradually from small to large numbers and that the different formats of magnitudes are processed by the ANS even after symbols acquire automaticity.

Authors

• Hyekyung Park, Ohio State University
  Presenting Author

• John E Opfer, The Ohio State University
  Non-Presenting Author