Early Understanding of Fractions via Early Understanding of Proportion and Division

This chapter reviews the literature examining children’s early understanding of proportional reasoning and division, and how these early conceptions contribute to children’s later understanding of fractions. Although the earliest literature on proportional reasoning suggested that only adolescents have a true understanding of proportional reasoning, more recent research suggests that very young children, if asked properly, do demonstrate a basic or intuitive understanding of proportion. Similarly, young children also have an intuitive understanding of division concepts, stemming from the concept of sharing, in particular, through a sharing action schema. Children’s understanding of both proportion and division concepts does vary depending on whether the stimuli used are continuous or discrete, with continuous stimuli being favorable for proportional reasoning and discrete stimuli being favorable for division. Children also demonstrate an intuitive understanding of how the changes to the numerator and denominator affect the proportion, division, or fraction, and they also demonstrate an intuitive understanding of half. Taken as a whole, the research on the early learning of proportion and division suggests that the factors that help children with these tasks can also help them with their understanding of fractions, and we offer some recommendations about how to do so.