Re-examining fractions from a measuring perspective: preservice teachers’ performance across fraction types and representations

Abstract Prospective teachers’ limited understanding of fractions, particularly improper fractions and continuous-quantity representations, poses persistent challenges for mathematics teacher education. This study examines pretest-to-posttest differences in prospective teachers’ performance on fraction-interpretation tasks across continuous and discrete models, including tasks involving improper fractions, following instruction organized from a measuring perspective. Drawing on theoretical work that defines fractions as multiplicative comparisons between commensurable quantities, the intervention engaged 96 prospective elementary teachers across five course sections in two semesters in a mathematics methods course. Using Cuisenaire rods as an exclusive linear model grounded in unitizing and measuring, they measured, compared, and operated on fractions. Pretest and posttest assessments used rectangular, circular, and discrete (set) representations not employed during instruction. Results showed a statistically significant improvement in overall task performance, with the strongest gains for continuous models and fractions greater than one. The score pattern is compatible with, but does not demonstrate, a change in participants’ fraction interpretations or conceptual repertoires because the assessments did not elicit explanations of their reasoning. Within this design, instruction organized from a measuring perspective was associated with improved performance on the assessed tasks, especially those involving fractions greater than one. Finally, implications are discussed for the design of mathematics methods courses.