Representational Coordination in Deaf and Hard-of-Hearing Mathematical Problem Solving

Abstract

Historically, mathematics education research regarding deaf and hard-of-hearing (D/HH) students has often relied on ‘modality-comparison’ designs, which treat formats such as printed English, annotated diagrams, and signed explanations as simple, interchangeable containers for mathematical content. This exploratory qualitative case study shifts the analytic focus from modality-based performance outcomes to a ‘representational coordination’ framework, investigating how two D/HH eighth-grade students construct meaning as they solve algebraic word problems. Using a hybrid deductive-inductive approach to analyze video-recorded sessions and ‘word-for-sign’ transcripts, this study examines four core analytic processes: representational entry, transformation, coordination, and externalization. Findings indicate that students do not simply receive information in a given modality; rather, they engage in ongoing, dynamic representational conversion and ‘representational repair’ (i.e., moments where errors become visible sites of semiotic negotiation and self-monitoring). The study highlights that D/HH students utilize diverse, interconnected strategies, ranging from silent written inscription to active signed explanation, gesture, and embodied action, to construct mathematical relationships. These results suggest that equitable instruction must move beyond ‘access’ defined as the provision of modalities, and instead foster representational competence through explicit instruction, multimodally attentive assessment, and collaborative interpretation practices. The findings underscore that ASL, visual-spatial reasoning, embodied action, and formal notation should be valued as a single, interconnected system essential for long-term mathematical success.