Understanding mathematical learning disabilities as developmental difference: a fine-grained analysis of one student’s partitioning strategies for fractions / Las discapacidades para el aprendizaje de las matemáticas como diferencia en el desarrollo: un análisis detallado de las estrategias de una estudiante al partir enteros para obtener fracciones

Abstract

Research has documented that children’s informal partitioning activity (i.e., splitting a whole into equal parts) serves as the foundation for the development of rational number understanding. Although developmental studies have suggested that partitioning skills are mastered by late childhood, it is unknown if this holds true for students with disabilities. Research has yet to document when and how students with disabilities develop these foundational skills. This study examined the partitioning activity of one adult student with a mathematical learning disability during one-on-one videotaped tutoring sessions. A fine-grained analysis revealed that although the student shifted from a less sophisticated strategy to a more sophisticated strategy over the course of the sessions, both strategies led to difficulties. Furthermore, the student’s partitioning strategies directly contributed to her difficulties understanding and representing fractions. This case study supports the notion that students’ partitioning activities are intimately linked to their ability to conceptualize fractional quantities, but suggests that typical developmental progressions are an inappropriate model for students with mathematical learning disabilities, who may develop in qualitatively different ways.