Do Problems with Fractions Start Early? : Home Math Environment and Children's (Mis)Understandings of Half

Abstract

Although fractions are challenging for many students, children as young as four demonstrate informal fraction understanding (Hurst, et al., 2020). Everyday experiences, like sharing food, expose children to fraction concepts. First graders’ fraction knowledge predicts later math achievement (Viegut et al., 2023). Children demonstrate conceptualization of “half” earlier than other fraction words (Brizuela, 2006), but also hold misconceptions, like believing half means “a little bit” or is equivalent to any divided object (Björklund, 2018). This study examined children’s understandings and misunderstandings of half from preschool to second grade as well as the role of children’s Home Math Environment (HME) (Lefevre et al., 2009). This study included 55 children and their guardians. Children completed three fraction tasks: Matching (identifying correct depictions of half), Equal Sharing (dividing items fairly), and Endorsement of Misconceptions (judging the “cleverness” of fictional definitions of half). Guardians completed a survey on background characteristics and HME. As hypothesized, an ANOVA showed statistically significant differences in performance on all tasks between the two younger grades (preschool/4K, kindergarten) and the two older grades (1st, 2nd). Unexpectedly, regression analyses showed no significant correlation between task performance and HME. We discuss how our findings may inform early instruction to support fraction learning