Exploring Attention to Numerical Features in Proportional Reasoning

Abstract

Human infants show relatively sophisticated abilities to track and use proportional information. However, by the age of 6, children tend to make predictable errors in their proportional reasoning and later encounter significant challenges in many aspects of formal fraction learning. Thus, one of the central questions motivating this research is to identify the factors leading to these difficulties, in light of evidence of early intuitions about these concepts. In the current dissertation, I address this question by investigating the tradeoff between attending to proportional magnitude information and discrete numerical information about the components (termed “numerical interference”) across both spatial (i.e., area models, number lines) and symbolic (fractions, decimals) representations of proportion information. These explorations focus on young children (5-7 year olds) who have yet to receive formal fraction instruction, older children (9-12 year olds) who are in the process of learning these concepts, and adults who have already learned formal fractions. In Project 1, I investigated how older children and adults map between symbolic and spatial representations, particularly focusing on their strategies in highlighting componential information versus magnitude information when solving these mapping tasks. In Projects 2 and 3, I explore the malleability of individual differences in this numerical interference in 4- to 7-year-old children. Across the three projects, I suggest that although numerical interference does impact proportional reasoning, this over-attention to number can be reduced through modifying early experiences with proportional information. These findings have implications for education and the way we conceptualize numerical interference more generally.