Initial Understandings of Fraction Concepts Evidenced by Students With Mathematics Learning Disabilities and Difficulties: A Framework

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students may face understanding fraction concepts. One way to characterize such conceptions is through the creation of a framework that depicts key understandings evidenced as students work with problematic situations. The present study extends current literature by presenting key understandings of fractions, documented through problem-solving activity, language, representations, and operations, evidenced by students with LD and mathematics difficulties as they engaged with equal sharing problems. Clinical interviews were conducted with 43 students across the second, third, fourth, and fifth grades. Results of the study suggest that students with LD hold similar informal notions of key understandings of fractions as students with mathematics difficulties and that many of the students evidenced rudimentary understandings of fractional quantities. Researchers discuss implications of the findings in relation to considerations for designing interventions to support and extend students' initial conceptions of fractional quantity.