Attributes of Professional Learning Communities that Support Meaningful Discourse About Learning and Teaching
The four PLC facilitators who are the focus of this study were each from a different school within the same school district in a large metropolitan school district in the southwest United States. Two of the facilitators, Dan and Sharon, are math teachers. The other two, Jason and Karen, are science teachers. The project leaders relied on the District Math and Science Curriculum Coordinator to select the facilitators based on his judgment of who he believed had the greatest potential to emerge as a leader among the teachers enrolled in the course. The facilitators had all been teaching for at least five years.
The subjects were concurrently enrolled in a three-hour graduate mathematics education course and an accompanying one-hour, school-based PLC for secondary mathematics and science teachers. The goal of the course was to deepen teachers' understanding of rate-of-change and function through a covariational approach to teaching function (Carlson, Jacobs, Coe, Larsen, Hsu, 2002; Thompson, 1994). A primary purpose of the PLC sessions was to engage the PLC members in meaningful discourse (as defined above) about issues of knowing, learning and teaching secondary mathematics and science content that is related to what the PLC members were learning in the course.
PLC sessions and PLC agendas were designed to improve teachers' ability to i) engage in conceptual conversations about knowing and learning central ideas of the course; ii) discuss and assess student thinking; iii) develop inquiry based, conceptually focused lessons; and iv) engage in meaningful reflection on the effectiveness of their instruction.
The PLC facilitators were expected to follow a general agenda that was developed by project faculty, although they were encouraged to deviate from the agenda as needed in order to allow the continuation of meaningful discussions. The facilitator received 18 hours of summer training and met weekly with a PLC coach who provided general tips for improving her/his effectiveness in facilitating meaningful discourse among PLCs. In addition, they attended three 3-hour training workshops spaced about one month apart each semester. A project leader who reviewed video recordings of recent PLC meetings between each coaching session led the training sessions and coaching. The viewing of the videos by the coach was key to assuring that the coach had current information on how the PLC facilitators were implementing the agenda and interacting with other members of the PLC. The coach met for 30 minutes with all four facilitators once per week to support PLC facilitators in promoting high quality discourse in their PLCs. The PLC agendas included tasks that supported reflection and discussion among the PLC members about knowing, learning and teaching concepts that were central to the course. As one example, early in the semester the PLC members were asked to conduct an interview with a student for the purpose of gaining insights about what the student understood about that idea. The PLC agenda then prompted the facilitator to ask specific questions to the PLC members to promote discussions about the central issues of learning that concept. Later in the semester the PLC members were supported in developing, teaching, studying, and refining a lesson.
The coach's strategies for promoting reflection about PLC interactions progressed from general discussions to making specific prompts to each PLC facilitator. During the first few coaching sessions the PLC coach discussed mostly positive moves that she and the research team were noticing in hopes that the PLC facilitators who were less effective would begin adopting some of the more effective strategies. As the PLC coach sensed that the facilitators were becoming more comfortable in their role as a facilitator she became more direct with each of the PLC facilitators about behaviors that were less effective. As one example, she asked Jason, one facilitator, if he felt uncomfortable in probing his peers when they were providing weak explanations. As another example, she asked another facilitator, Sharon, why she never allowed Anne to answer a question. These specific questions were gleaned from viewing the videos that were reviewed the previous week.
Each course and PLC meeting was videotaped. Each PLC group was assigned two researchers who videotaped each session. These videos were then digitized and analyzed by the two researchers who taped the meetings. The same researchers then coded the videos using Studiocode (2007) for both occurrences of and lack of decentering. Videos selected by the researchers who coded the videos were then discussed among the research team each week, with video excerpts related to decentering also shared with the PLC coach. The research team was composed of both researchers and course instructors. Episodes believed to reveal instances of decentering were then transcribed for further analysis.
We examined the mathematical constructions and conversations that occurred between the facilitator and the teachers in an attempt to understand their mathematical thinking occurring during these interactions. Our analysis began by our identifying video clips that revealed insights about the facilitator's thinking and/or meanings. When analyzing an instance of a discussion about a mathematical idea, say proportional reasoning, we first needed a model of what was involved in reasoning proportionally. We also needed terms for referencing the mathematical thinking associated with the idea. For instance, in the case of proportional reasoning we needed to be explicit about what it means for two quantities to be related proportionally. We agreed that two quantities are proportionally related if, as their measures vary, one quantity is always the same multiple of the measure of the other, or the two quantities are always in the same ratio. We then analyzed the utterances and products displayed in the video clip in an effort to characterize the mental actions and meanings of the individual. In doing so, we drew from our model of what was involved in reasoning proportionally to describe what we were observing (e.g., he noticed that as the two quantities varied they continued to be related by a common ratio). Our goal was to describe the quality of the mathematical discourse, and in particular, the meaning(s) of an individual that were being constructed and communicated between the facilitator and other members of the PLC. Once the meanings were deciphered, specific labels emerged for characterizing the common interaction patterns and/or meanings. The assigned codes were validated by having 8 different researchers examine, discuss and negotiate the meanings until a consensus was achieved.
