Raising the Floor and Lifting The Ceiling: Math For All

Perhaps more than any other discipline, the teaching of mathematics lends itself to procedural recipes where students memorize and duplicate procedures by rote: if it looks like this, do that to it. “If one believes that mathematics is mostly a set of procedures—rules and truths—and the goal is to help students become proficient executors of the procedures, then it is understandable that mathematics would be learned best by mastering the material incrementally, piece by piece” (Stigler and Hiebert, 1999, p.90). Teaching practices that commonly flow from this view are demonstration, repetition and individual practice. In addition to being a misunderstanding of the discipline of mathematics itself, this belief also colors people’s views about who can learn mathematics. Curricula and teaching practices are often based on what Mighton calls a destructive ignorance “that leads us, even in this affluent age, to neglect the majority of children by educating them in schools in which only a small minority are expected to naturally love or excel at learning” (2007, p.2) particularly mathematics. He insists that too many students lose faith in their own intelligence, and too much effort is directed at creating artificial differences between fast and slow, gifted and “special”, advanced and delayed.

And worse yet, procedural approaches to the teaching of mathematics that create problems of understanding and engagement are applied with even more vigor in remedial programs designed to help those very students for whom such practices did not work in the first place.

A growing number of researchers argue that other approaches are needed to help students learn mathematics. “Today, mathematics education faces two major challenges: raising the floor by expanding achievement for all, and lifting the ceiling of achievement to better prepare future leaders in mathematics, as well as in science, engineering, and technology. At first glance, these appear to be mutually exclusive” (Research Points, 2006, p.1). But are they? Is it possible to design learning that engages the vast majority of students in higher mathematics learning?

To answer these questions, I designed a research study to determine whether the principles of Universal Design for Learning (UDL) resulted in increased student mathematical proficiency and achievement for all students in a typical Grade 7 classroom. Was it possible, in a regular classroom to lift the ceiling and raise the floor?