Using Tools of Improvement Science to Advance Instructional Practice in Community College Developmental Mathematics Classes

• In Event: Problem-Disciplined Practice-Based Inquiry for Improving Mathematics Teaching and Learning: Plan-Do-Study-Act Cycles as Tools for Improvement

Abstract

Although interest in improving the outcomes of developmental math students is high, efforts to make such improvements have rarely focused on instructional practice in students’ regular classroom settings. We report here on our effort, part of the Community College Pathways initiative, to take what is known about effective K-12 mathematics instruction and apply it to community college developmental mathematics classroom instruction.

With improving students’ conceptual understanding as our goal, and the review by Hiebert and Grouws (2007) as our guide, we worked to (1) help instructors and students attend explicitly to concepts, and (2) help students struggle with important mathematics. These learning opportunities were a central element of the instructional design principles for the Statway® curriculum, which was used by all of the instructors who participated in our study. One other element was central to the design: the problem cycle. Regarded as the mechanism by which the learning opportunities would largely be achieved, the problem cycle was modeled after the typical organization of mathematics lessons in Japan (Shimizu, 1999).

A team of mathematics educators identified specific instructional moves for faculty to incorporate at particular points in the problem cycle, with the goal of improving students’ learning opportunities. In particular, we focused on how problems were worked on and discussed. Our process for testing change ideas was heavily influenced by the traditions of improvement science. Our primary tool was the PDSA (plan-do-study-act) cycle. Over the course of two academic years, we met regularly with faculty to conduct iterative cycles. In this paper, we describe three series of PDSA cycles, as illustrations of that work. The first two describe efforts to change instruction. The third example is of a series of PDSA cycles focused on enhancing lesson materials so that they would better support the kinds of instructional changes we sought.

The study revealed lessons related both to the process of improvement and to the instructional improvements themselves. Regarding the process of improvement, the iterative nature of the work proved critical. Never did we reach our desired outcome in the first cycle. Each successive attempt at a change pointed to a new, unforeseen challenge. It was only through repeated cycles that barriers were identified and worked through. The doing phase of our PDSA cycles was a key element of the experience. Not only did it bring to light challenges, it served to win instructors over to the ideas behind the changes we were trying to encourage. With regard to the instructional improvements themselves, our work suggested that the problem cycle phases are a helpful way to break down work on a problem and to break down improvement efforts into practical chunks. Further, the instructional moves we targeted were, over time, a productive way to initiate desired changes in classrooms. They were manageable as starting points, and had leverage sufficient to support meaningful change. Finally, the lesson materials saw significant advances in format. By testing the design principles behind them, we’ll be well-positioned to apply them to other Pathways lessons.

Authors

• Karen B. Givvin, University of California - Los Angeles

• William M. Saunders, University of California - Los Angeles