Toward a Framework for Using Student Mathematical Representations as Formative Assessments

This article explores how students' mathematical representations can be used as formative assessments. We introduce a framework for teaching and learning that integrates representations as instructional and assessment tools, and illustrate these uses of student representations with reference to a study conducted with 250 5th-grade students. This study focused on students' ability to recognize and use a variety of representations of the fraction concept. Finally, we discuss the implications of the framework for teacher knowledge and classroom practice.