The Missing Middle? General and Special Educators' Views of Effective Mathematics Instruction

• In Event: Preparing General Education Teachers to Promote Justice and Equity for Students With Disabilities

Abstract

Objective & Framework

General education teachers typically lack preparation to work with students with disabilities (SWDs) (Brownell, Sindelar, Kiely, & Danielson, 2010). This concern is especially relevant in elementary mathematics where SWDs lag behind their peers in mathematics achievement as early as in Kindergarten, and these gaps only grow over time (Schulte & Stevens, 2015). Addressing this issue necessitates coordinated supports from general and special educators, but the fields of mathematics education and special education have historically worked from district, often contradictory epistemological and pedagogical approaches. Part of the tension stems from the fact that general mathematics education privileges student-centered approaches that foreground student sense-making and inductive approaches to learning (Boaler, 2002). In contrast, special education methods are often characterized as teacher-centered, with demonstration of step-by-step routines and consistent teacher feedback (Jones & Brownell, 2014).

The goal of this study was to identify the challenges that exist in designing instruction that is responsive to the instructional goals of both general and special educators, in service of determining ways to address these challenges.

Data & Methods
We conducted hour-long interviews with 25 mathematics general educators and mathematics special educators focused on their views about the goals of mathematics education, teacher and student roles in achieving those goals, and challenges involved in addressing the needs of students with disabilities in general education mathematics classrooms.

All interviews were transcribed and structurally coded by question (Saldaña, 2014). We iteratively developed memos synthesizing themes within and across special and general education. At all stages, we searched for confirming and disconfirming evidence (Dyson & Genishi, 2005).

Results
Special educators, in general, foregrounded proximal instructional goals, including developing students’ mathematics knowledge, helping students’ complete tasks successfully, and performing well on standardized assessments. General mathematics educators prioritized more distal goals such as developing students’ identities as mathematical sense makers, who use mathematics to engage with the world. Mathematics educators described using instruction to re-envision school-based mathematics, and special educators privileged instructional supports to maximize student success in the current landscape of K-12 mathematics teaching. Special educators talked more often about “efficiency” and the “tyranny of time” in elementary mathematics classrooms, while general educators spoke in more aspirational terms about the potential for “an entirely different” model of mathematics teaching.

Both general and special educators emphasized that effective instruction is predicated on deep understanding of students and the fostering of flexible, conceptual understanding, rather than rule-bound, procedural understandings. This suggests possible areas of convergence that could be leveraged in building bridges across these discourse communities.

Significance
By engaging leaders in both fields in a focused conversation around a shared problem, students with disabilities struggling in general education mathematics classrooms, we hope to better understand barriers and ultimately to improve the connection between two fields, which have often operated in isolation from one another. Our longer-term aim is to develop an instructional framework that reflects the epistemological beliefs of both fields and articulate conceptions of teaching and learning that serve to connect these two communities.

Authors

• Julie Jackson Cohen, University of Virginia
  Presenting Author

• Nathan Jones, Boston University
  Non-Presenting Author

• Lynsey K. Gibbons, University of Delaware
  Non-Presenting Author