Student-Generated Representations by Middle-Schoolers with MLD: An Exploration of Accessibility within an Equal Sharing Fractions Intervention

Abstract

An exploratory qualitative case study of three middle-school students with MLD was conducted to explore the accessibility of a Cognitively Guided Instruction Equal-Sharing intervention. Here I employ a difference perspective to extend Vygotsky’s sociocultural theory of mediational tools in relation to the theoretical constructs of student-generated representations (SGRs) to consider issues of accessibility. SGRs are appropriate for this inquiry as they are both evidence of students’ conceptualizations and of patterns of reasoning during mathematical problem-solving. Student-generated representations have not been typically used to think about issues of accessibility, however they are well-suited to. Through 3 case studies with 5-8 hour long session each, I explored the ways in which students, who exemplify unique patterns of reasoning around fraction content, engaged with the Equal-Sharing intervention, isolating their use and creation of SGRs. In a detailed retrospective analysis of conceptualizations in conjunction with tool use and problem-solving, it was revealed that some aspects of SGRs and the action-oriented environment of the intervention enhanced accessibility, but that some issues of inaccessibility remained. Differentiated and scaffolded content was still necessary to alleviate tensions created between inaccessible SGRs and the students’ conceptualizations. Implications for research and practice are provided.