The goal of this project is to study and support the development of conceptual understanding of fractions by students with learning disabilities (LD). The researcher proposes that rather than focusing on whether LD students can or cannot develop conceptual understanding of fractions, research should attempt to uncover the understanding LD students have and examine how growth of conceptual knowledge occurs in these students. This approach suggests a reconceptualization of research and instructional practice in mathematics that focus on the conceptual knowledge students with LD can in fact develop.
Through a series of teaching experiments that involve cycles of theorizing, design, implementation, and refinement, the project develops instructional trajectories for LD students in the area of fractions. The research question addressed are: What initial and developing key developmental understandings of fractions do students with learning disabilities evidence through employed strategies, language, and representations? How do students with learning disabilities progress in developing and solidifying conceptual understandings of fractions through their mathematical activity? And, to what extent does an intervention reflective of a research based instructional trajectory facilitate strategic development and increased fraction conceptual knowledge in students with learning disabilities?
The main outcomes of the project include (a) a research-based instructional trajectory for students with LD specific to conceptual understandings of fractions as numeric quantities, (b) a set of 90 fraction tasks to be used for instruction and/or formative assessment in fraction concepts, (c) scoring/coding frameworks and checklists for use with key tasks as formative assessments, (d) decision-making frameworks, task sequencing guides, and suggestions to aid teachers in designing individualized, student-centered instruction, all available via the Internet. Most important, the project has the potential to offer a transformative approach to mathematics instruction for students with LD, bringing together expertise on learning disabilities and mathematics education to address a area in which there is very little research.
The PI will incorporate finding from the study into methods courses for both mathematics education and special education students. She will also develop a graduate course entitled Diagnosis and Remediation.
