Demonstrating Conceptual Understanding of Fraction Arithmetic: An Analysis of Pre-Service Special and General Educators’ Visual Representations

To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The present study examines the performance of 55 pre-service teachers (PSTs) on tasks assessing their procedural and conceptual knowledge of fractions, including a test of their ability to generate visual representations and story problems to model fraction multiplication and division. PSTs demonstrated high levels of procedural and conceptual knowledge of fraction addition and subtraction, moderate procedural knowledge for fraction multiplication and division, and relatively weak conceptual knowledge of fraction multiplication and division. Weak conceptual knowledge was related to inability to accurately model fraction multiplication and division using visual representations and story problems. Implications for research and practice are presented.