Difference and Compensation: Emancipatory Research on Mathematics Learning Disability

• In Event: Cultural-Historical Approaches to Study the Teaching and Learning of Students With Dis/Abilities

Abstract

Disability studies scholars contend that there are systemic issues with traditional research paradigms used to study disability, in which the researcher rather than the “subjects” are the primary beneficiaries of the work (Oliver, 1992), and the individual with disabilities is understood through a deficit lens. In this paper we address these critiques by leveraging a Vygotskian (1993) notion of disability – which focuses on developmental difference and compensation – and engaging in emancipatory work. Emancipatory disability research attempts to disrupt the oppressive structures reproduced in traditional research on disabilities. It shifts research “on” individuals with disabilities to research “with” individuals with disabilities (Charlton, 2000; Rapp & Ginsburg, 2001). The traditional hierarchical relationship between researcher and researched is inverted (Mercer, 2004; Oliver, 1992) by placing decisions about the research agenda, methodology, interpretation, and final product into the hands of individuals with disabilities (Barnes, 2002; Stone & Priestley, 1996).

In this collaborative work, Dylan, an individual with a mathematics learning disability, and Katie, a researcher, worked to document Dylan’s unique experiences learning and doing mathematics. Dylan is particularly worthy of study because despite having a mathematics learning disability (MLD), she was incredibly successful in upper division mathematics classes and graduated from University of California, Berkeley with a degree in statistics. In this presentation we highlight the ways in which Dylan demonstrated characteristic patterns of reasoning, which have been documented in other students with MLD (Lewis, 2014). For example, students with MLD draw ½ in unconventional ways and often focus on the fractional complement rather than the fractional quantity when interpreting fraction representations (e.g., interpreting ¾ as ¼).

We analyzed 3 videotaped interview and problem solving sessions – taken from a larger project – in which we explored how Dylan represented, interpreted, and solved problems involving fractions. The analysis revealed that Dylan demonstrated the same patterns of reasoning as other students with MLD, which highlights the ways in which standard mediational tools (mathematical representations) were inaccessible for her. However, unlike other students with MLD, these issues of access were not similarly problematic for Dylan. We present a detailed analysis illustrating how Dylan had developed sophisticated ways of compensating. We frame compensation as an individual’s deliberate action to gain access to an otherwise inaccessible space (Lewis & Lynn, 2017).

Findings align with two key themes within a Vygotskian framing of disability. First, Dylan experienced issues of access because of the incompatibilities of standard mediational tools and her way of processing numerical information. Second, she was able to compensate for this issue of access in sophisticated ways in order to accurately solve problems. This work highlights how despite Dylan’s success in mathematics, she continued to rely upon characteristic patterns of reasoning identified in students with MLD. This suggests that standard notions about the need to extinguish (Munter, Stein, & Smith, 2015) these kinds of “misconceptions” are not appropriate. Instead, we need to honor and value the student’s understanding and reframe these patterns of reasoning as differences rather than deficits.

Author

• Katherine Lewis, University of Washington - Seattle