Synthesizing Big Ideas in the Understanding of Fractions: A Learning Progression

• In Event: Student Mathematics Learning Pre-K–12

Abstract

Fractions are a foundational concept in mathematics, and there are five ways that they can be interpreted: as a part-whole relationship, as a quotient, as a measurement, as a ratio or a rate, or as an operator. We argue that these five interpretations, in this order, form a coherent learning progression through the construct of fractions. We provide both theoretical and empirical support for this claim using the curricular ordering and the vertical scale of the i-Ready Diagnostic assessment to demonstrate that items associated with more sophisticated interpretations are more difficult than are those at the earlier stages of our progression.

Authors

• Sarah Wellberg, University of Colorado - Boulder

• Derek C. Briggs, University of Colorado - Boulder

• Sanford Reid Student, University of Colorado - Boulder