Using an Iceberg Intervention Model to Understand Equivalent Fraction Learning when Students with Mathematical Learning Difficulties use Different Manipulatives

Abstract

This study examined variations in 43 fifth-grade Tier II students’ learning of equivalent fractions using physical and virtual manipulatives during intervention instruction. The overarching research question focused on how different manipulatives types support learning fraction sub-concepts during mathematics intervention instruction for students with mathematical learning difficulties. Over a three-week period, students participated in ten small group sessions using different manipulatives during instruction (physical, virtual, and combination). Data were collected from pre/post testing and daily monitoring assessments. An Iceberg Intervention Model was used to document student learning for five equivalent fraction sub-concepts and nine general fraction sub-concepts. Results showed that physical manipulatives were favoured for 5 sub-concepts, virtual manipulatives for 4 sub-concepts and combined manipulatives for two sub-concepts. The results demonstrate that an understanding of relationships between manipulative type and equivalent fraction subtopics can be used to guide the use of manipulatives during intervention instruction.