Professional Development for Mathematics Teachers: Examining the Impact on Knowledge and Instructional Practice

• In Event: Understanding the Development of High-Leverage Mathematical Teaching Practices

Abstract

Toward a Scalable Model of Mathematics Professional Development is a field study aimed at preparing facilitators to implement the Problem Solving Cycle (PSC). The PSC is an adaptive model of mathematics PD that can be shaped to meet local needs, with the goals of increasing mathematical knowledge for teaching and supporting high leverage instructional practices. Each iteration of the PSC involves three workshops based around a rich mathematics problem. In Workshop 1 teachers solve the problem, consider possible student solutions, and create individual lesson plans. They then teach the problem and are videotaped. Video clips from their “PSC lessons” anchor discussions in Workshops 2 and 3.

This presentation is based on data spanning a 2 ½ year period, in which 10 Instructional Leaders (ILs) participated in the field study. The ILs worked with 54 teachers in 8 middle schools in a large, urban school district. We address the following questions: What is the impact of the PSC on the participants’ mathematical knowledge for teaching? What is the impact on their instructional practices?

To measure impact on participants’ knowledge we conducted pre- and post-program administrations of the Mathematical Knowledge for Teaching assessment (Hill, Schilling, & Ball, 2004). We ran paired t-tests on the full sample and simple analyses of variance broken down by the two groups, ILs and teachers. There were significant gains for the participants as a whole, and for the teachers as a subgroup.

To measure impact on instructional practices we collected videotaped observations of the ILs and a subset of the teachers with whom they worked. During each year of the project, we videotaped their PSC lessons and several non-PSC lessons (“typical lessons”). The typical lessons were generally videotaped near the beginning and end of the academic year.

We are analyzing a set of 149 lessons using the Mathematics Quality in Instruction (MQI) instrument (Hill et al., 2008). The MQI measures five dimensions of instruction: (1) classroom work is connected to mathematics, (2) richness of the mathematics, (3) working with students and mathematics, (4) errors and imprecision, and (5) student participation in meaning-making and reasoning.

A team of four coders achieved interrater reliability for all codes in the MQI and is currently coding the lessons. Preliminary results suggest that there will be changes in instructional practices over time on most if not all of the dimensions. We hypothesize that there will be differences between the ILs and the teachers, with ILs experiencing more profound changes that reflect their dual roles as PSC facilitators and classroom teachers. We also anticipate that there will be differences in the participants’ PSC lessons compared to their typical lessons, suggesting that they are more frequently (and capably) using high leverage teaching practices in their PSC lessons. Overall, we hypothesize that the pattern of results will demonstrate the potential for growth among the participants taking part in the PSC.

Authors

• Karen A. Koellner, Hunter College - CUNY

• Jennifer K. Jacobs, University of Colorado - Boulder

• Hilda Borko, Stanford University