Supporting and Evaluating Professional Collaboration Among Secondary Mathematics and Science Teachers
We collected data in a teacher professional development project operating in six large urban school districts in the Southwestern U.S. Teams of science, technology, engineering, math (STEM) faculty partnered with education faculty and teachers to develop four interdisciplinary graduate courses and PLCs focused on connections among key STEM ideas and processes. The design of all aspects of the project was informed by discipline-specific frameworks for the processes of engaging in mathematical problem-solving (Polya, 1957; Schoenfeld 1985, 1989, 1992; Carlson & Bloom, 2005), scientific inquiry (Wallas, 1926; Koestler, 1989; Lawson 2001), and engineering design (Fogler & LeBlanc, 1995; Voland, 1999; Atman et al., 1989, 1999, 2001, 2003). We collected and reviewed video data from every course and PLC session and selected over 100 hours of video from the courses and over 100 hours of video from the PLCs for in-depth analysis. Two research teams engaged in multiple rounds of open, axial, and selective coding (Strauss and Corbin, 1990) relative to issues defined by our initial frameworks.
Initial open coding of course and PLC involved at least two researchers independently reviewing each video to identify elements from the discipline-specific frameworks. For example, from the Problem-Solving Framework in Carlson and Bloom (2005) we coded group and individual activity according to the following four basic categories.
i) observation of a problem and orienting oneself to its nature, elements, and structure,
ii) conjecturing solution paths (involving a sub-cycle of considering several possible plans of attack without actually carrying them out, evaluating the potential effectiveness and requirements of each, then making a decision on how to proceed),
iii) execution of a plan and monitoring progress, and
iv) checking and evaluation of whether the result makes sense and whether a viable solution has been achieved occurs near the end of a problem solving cycle.
The scientific inquiry and engineering design frameworks contained similar categories of activity for which we coded the video. Additionally, the problem-solving framework outlines attributes of the individual for which we also coded including
i) affective qualities such as curiosity, intimacy, frustration, and defense mechanisms as well as ethical concerns related to ones reasoning and adherence to intellectual integrity,
ii) metacognitive skills such as monitoring for quality and effectiveness of thought processes and motivation as well as attention to efficiency and aesthetics, and
iii) available resources such as knowledge and experience and heuristics for solving various problems.
At semiweekly research team meetings we compared and discussed coding and constructed timelines indicating the flow of coded activity through each episode. We added major events to these timelines where the teachers made breakthroughs, gave up on their work, argued, etc, then reviewed the timelines for patterns. We generated initial hypotheses about these patterns and interviewed teachers from the project for their feedback our characterizations of their work. We then developed fixed coding categories, criteria and numerical scales and engaged teachers, personnel, and researchers from the project in scoring selected video using these rubrics. We obtained feedback on aspects of the coding scheme that did not adequately apply to the data and on confusing categorization or wording. Based on this data, we revised the codes and criteria to produce the following framework outlining the most crucial factors in a PLC operating productively and the observed relationships among these categories.
