Online context are becoming more frequently used in mathematics teacher professional development. Mathematics teacher educators’ creation of such contexts and engagement with teachers in them provokes research questions about teaching and learning within the spaces.  In particular, the reports in the proposed session will focus on findings from explorations of mathematical knowledge for teaching conducted in online environments and will address the question: How do online learning environments provide opportunities for mathematics teacher learning? Three facets of mathematics teacher learning will be addressed.  The first report will share the teacher-researcher’s questions about teacher-researcher learning, roles, and potential actions in asynchronous online (AO) contexts.  The second report will explore norms and collective practices that emerged and developed in an AO professional development context.  The third report will share instructional design decisions that are linked to teacher learning in online professional development contexts.  The session will consist of a brief overview of a proposed research program, followed by presentations of the research studies.  A discussant/reactor with expertise in mathematics teacher professional development research will share insights on the reports and proposed research program followed by audience questions and discussion.

Part 1:  (10 minutes) Brief Introduction to the Proposed Research Program

Part 2:  (45 minutes) Reports on the design and interactions of mathematics teachers in online professional development environments

The first report shares questions that emerged from the pilot of an AO learning environment created to build understanding of proportional reasoning for teaching will be shared.  While we elected to use an AO learning environment because it provided opportunities for our collaboration and learning, in reading and interacting with the participants, questions relevant to our work as constructivist teachers (Author1, 2005) emerged.  First, what is evidence of learning in online contexts? Typically, inferences about learning are drawn from a teacher’s effort to “listen” (Author1, 2004; Davis, 1997; Hackenberg, 2005; Weissglass, 1990) to the utterances, movements, gestures, and emotional responses of leaners. These inferences are then used to build productive instructional activities that challenge the models teachers make of learners’ systems of understandings.  Are teacher’s written posts sufficient evidence? What does it mean to “listen” in an online context? Second, what are the roles of the teacher/researcher in an online context?  Typically, press for understanding is a component of professional learning communities.  When and how does one press when the press will be experienced at some distance from the original contribution?  Data in the form of teacher-research reflections and participant feedback will be shared.

The second report extends an existing research and development project focusing on developing Mathematical Knowledge for Teaching (MKT) through online collaboration. We have had success documenting individual teachers’ development of MKT for teaching algebra and geometry (Author2, 2010; Author2, 2011; Author2, in press). While this individual development is important, we also recognize that thinking and learning are social phenomena and that the development of MKT can also be described as appropriating the knowledge and skills that define a particular community of mathematics educators. As such, we have begun to widen our focus to include studying the emergence of norms and collective mathematical practices and how these norms and practices support or constrain individual development. In this session, we will present a brief overview of traditional methods for documenting norms and collective mathematical practices, including Rasmussen and Stephan’s (2008) methodology that served as the basis for our work, highlight a number of norms and collective practices that emerged in our AO mathematics class for teachers, and discuss the ways in which traditional methods, needed to be augmented and adapted for use with data from online professional development.

The third report shares a model for online synchronous instruction used in a graduate course about proportional reasoning. The course was taught to 25 middle school mathematics and science teachers in fall 2010 as part of an online master’s program about integrating science and mathematics in the middle grades (Author3, 2011). The same course will be taught to a new group of 24 middle school mathematics and science teachers in fall 2011. Historically, mathematics educators model face-to-face instruction in face-to-face environments as a way to teach about learner-centered instruction. Technological advancements have pushed us to broaden our views of best practices when teaching teachers. The research emerging from this project is driven by the paradox of teaching teachers about face-to-face learner-centered instruction with children in an online environment with teachers. Archived video of synchronous whole-group instruction and small-group discussions and the corresponding analysis regarding interactions and teacher learning will illustrate instructional design decisions that have been made in the spirit of design-based research (Barab & Squire, 2004; Collins, Bielaczyc, & Joseph, 2004). Questions that have emerged in light of this work are: What does learner-centered instruction look like and what are affordances and constraints of online environments when teaching teachers about learner-centered instruction.

Part 3:  (15 minutes) Reaction/discussion by discussant: with comments on the studies discussed and potential questions/facets to be included in the research program focused on building understanding of design, interaction, mathematics learning for teaching as it emerges from online professional development for mathematics teachers. 

Part 4:  (20 minutes) Audience question/contributions/insights

Focus Questions for discussion

1. What are critical elements of a research program that explores mathematics teacher learning in online contexts?
2. How might Author4 (2011) standards for reporting mathematics professional development apply to online professional development?
3. What constitutes “listening” in online mathematics education professional development?

References

Barab, S., & Squire, K. (2004). Design-based research: Putting a stake in the ground. Journal of the Learning Sciences, 13(1), 1-14.

Collins, A., Bielaczyc, K., & Joseph, D. (2004). Design experiments: Theoretical and methodological issues. Journal of the Learning Sciences, 13(1), 15−42.

Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education, 1997, 355-376.

Hackenberg, A. J. (2005). A model of mathematical learning and caring relations. For the Learning of Mathematics, 25(1), 45-51.

Rasmussen, C. L., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh & J. Y. Baek (Eds.), Handbook for innovative design research in science, technology, engineering, and mathematics (STEM) education (pp. 195-215). New York, NY: Taylor & Francis.

Weissglass, J. (1990). Constructivist listening for empowerment and change. The Educational Forum, 54, 351-370.