Concomitant Analysis in Considering Teacher Development and Professional Development Materials Over Time

• In Event: Understanding Change Within Discussions of Mathematics Teacher Professional Learning Communities: Methodological Frameworks

Abstract

This study was based on analyses of a year-long professional development designed to support teachers in drawing on students’ out-of-school mathematics practices to support the design of lessons building on this knowledge and considering the affordances of representations in problem solving tasks that may or may not be linked to children’s everyday practices. We were interested in how teachers initially conceptualized school/home mathematics connections and how that might change over the year. Would teachers begin with particular conceptualizations of appropriate in school/ out-of-school connections? How might these change over time?
The PD design draws from socio-cultural approaches to learning, particularly from research describing how students develop mathematical understandings as they encounter mathematical problems that emerge in everyday activities. New mathematical understandings emerge as they try to solve these problems (Saxe, 1991) but students don’t necessarily see connections between these understandings and mathematics they encounter in classrooms. Thus, teachers and curriculum become important supports for making these connections and creating opportunities for students to build on that knowledge (Gonzalez, Andrade, Civil & Moll, 2001; Lipka, 1994).
The PD design was built on Putnam & Borko (2000) and resulted in the Reflection Connection Cycle (Author, 2009). The design included various opportunities to reflect on issues related to designing connecting lessons, including discussion of video, written reflections, and small group discussion. From a research perspective these multiple sources provided a wealth of data to analyze in regards to change over time.
Whole group and small group discussions were transcribed along with teachers’ monthly reflections. A small team of researchers used methods derived from grounded theory (Glaser, 1992, Strauss, 1987). Open codes were refined and reduced to focused codes. This resulted in a coding with a final coding scheme with all the data sources. Our first approach to examine patterns that emerged was not necessarily novel. We were able to examine the ways particular orientations and codes related to making connections to out of school practices change from month to month in the PD. To investigate unexpected patterns that emerged from this initial analysis we included what we called concomitant analysis, that is, looking into the ways teachers’ changing discourse and conceptualizations might be related to changes in the types of readings we provided, lessons we presented, and provided frameworks. Thus, we not only included coding of teachers’ reflections and talk, we also included line-by-line analysis of every reading and handout provided to teachers. One of the findings related to this latter analysis was related to the ways teacher reflections and talk were less related to changes in the session topic, or even the topic of the reading, but the number of opportunities teachers were provided to consider a particular conceptualization of connections in readings, particularly where these conceptions were actual specific examples.
Concomitant analysis becomes a particularly useful way not only to consider changing teachers conceptions, but also supports closer reflection and analysis of materials provided as resources to teachers, or as supports for particular ways to consider student thinking.

Author

• Edd V. Taylor, University of Colorado - Boulder