Building fraction magnitude knowledge with number lines: Partitioning versus analogy.

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use partitioning: Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on area models. However, partitioning may not take full advantage of children's prior knowledge or the structure of the number line. We tested an alternative fraction number line lesson that leveraged children's preexisting whole number knowledge using a domain-general learning tool: analogy. In a preregistered online experiment, second and third graders (N = 84, M = 8.83 years) were randomly assigned to an analogy lesson (e.g., if I know how big 3 is on a 0-4 line, I know how big ¾ is on a 0-1 line), a partitioning lesson on number lines, or a control lesson using square area models. Results showed that the analogy lesson was more effective for promoting fraction magnitude understanding than the control lesson, and it was at least as effective as the partitioning lesson. The analogy group, but not the partitioning group, significantly outperformed the control group with large-denominator fractions at retention (i.e., 1-week delayed posttest) and on transfer tests (i.e., fraction comparison). We also replicated past findings that fraction partitioning lessons are more effective on number lines than on area models, and this advantage was partially sustained after a 1-week delay. Overall, these findings highlight the power of domain-general analogy to support mathematical development. (PsycInfo Database Record (c) 2023 APA, all rights reserved).