Perimeter, Area, Volume, and All That: A Study of Measurement

Introduction and Rationale

At Albert Hill Middle School of Richmond Public Schools, the pattern where black-male children are over represented as students with special needs is all too plain. In my self-contained mathematics classroom of 2018-2019, the portion of black boys fluctuated between two thirds and three quarters of the classroom population while the overall percentage of black-students in the school was just under one half.¹ Students within such special-educational settings are often offered lessons that have been modified substantially and that contain activities incorporating the use of what are customarily called “manipulatives,” or hand-held objects connected in some way to the lesson. In observing the use of these manipulatives in the self-contained setting, I have concluded that teachers do not always introduce manipulatives in effective ways for these students. While Van de Walle states, “hands-on, reflective, and interactive experiences are at the heart of good geometry activities at the elementary and middle school levels,” I have seen manipulative-based pedagogy that leads students away from mastering concepts of geometry.¹ Indeed, in their review of research, Laski et al. find that negative results stem from improper use of manipulatives.² In view of this issue, I argue that improper manipulative use makes the fact that geometry is under-emphasized within our curriculum framework more problematic for students with special needs. As Karp and Wasserman state, while geometry is emphasized less in middle-school curricula, it is a substantially vital field of study because it serves as a bridge between visual geometry learned in elementary school and abstract geometry taught at the high-school level.³ Again, this is especially important for those students who are over-represented in special education settings. The use of effective, evidence-based methods such as manipulatives in the mathematics classroom is critical if we hope to meet the educational needs of students who have substantial learning disabilities. Further, to ensure that such students can access mathematics in visual ways, ways which geometry facilitates, is to take a step toward equity. Considering the above conditions, this curriculum unit is built as an intervention for such students who are learning geometry and measurement.