Moments of Emergence: A Networked Collaborative Inquiry to Enhance Mathematics Teaching and Learning in a Canadian Context

Author(s):

Martha Koch(presenting / submitting)Christine Suurtamm(presenting)

Conference:

ECER 2017

Network:

24. Mathematics Education Research

Format:

Paper (Copy for Joint Session)

Session Information

24 SES 06 JS, Cultural Approach in Mathematics Education

Joint Paper Session NW 24 and NW 27

Time:

2017-08-23

15:30-17:00

Room:

K6.04

Chair:

Florence Ligozat

Contribution

This paper examines a two-year initiative by policymakers, practitioners and researchers to enhance mathematics teaching and learning in Ontario, Canada. The initiative focused on the province’s Grade 9 Applied Mathematics course. In Ontario, students completing “Applied” courses are eligible for workplace or college programs while those completing “Academic” courses can apply for university admission. School data and provincial test results (EQAO, 2016) suggest that students in the Applied Mathematics course are not meeting course expectations as well as students in the Academic course. The magnitude of this achievement gap has drawn the attention of the Ontario Ministry of Education (OME), the mathematics education community and the public for more than a decade (Koch & Watters, 2013; OSSTF, 2009; People for Education, 2013; Reith, 2003). Accordingly, the OME provided funding to a provincial mathematics education association to work with researchers to plan and implement a professional learning initiative to help address this concern. As university-based researchers, we worked with a steering committee from the participating organizations to design and facilitate this initiative and we conducted research as the initiative unfolded.

The initiative began with selecting ten school teams in nine school divisions across the province. Each team included a school administrator, a school or district mathematics leader, two or three Grade 9 mathematics teachers, and a special education teacher. Each team determined the focus and process of their inquiry. Teams were given funds to meet for one day per month for two years. A member of the research team attended the team meetings and provided resources and other forms of support. Funds were also provided for the school teams and the researchers to come together at a central location to share their learning at several multi-team events. The initiative culminated with two conferences where the school teams and researchers shared their learning with teams from more than 100 other schools across the province. Many elements of the initiative were planned from the outset, while other aspects emerged as the project unfolded. Throughout the initiative, the research team documented the experiences of each school team, thereby creating ten case studies. The researchers also documented the events where teams came together to share their learning. Analysis of this data provides a rich description of each team’s goals, inquiry process, and learning and reveals how participants enhanced their understanding of mathematics teaching through collaborative inquiry.

In light of the Network 24 Special Call at ECER 2017, we will focus our presentation on what our research reveals about collaborative partnerships among researchers, practitioners and policymakers when this initiative is considered from the perspective of complexity thinking. Complexity thinking can inform educational change in many ways (Lemke & Sabelli, 2008; Mason, 2008; St. Julien, 2005). A key feature of complex systems is their capacity to continually adapt to changing circumstances (Davis & Sumara, 2006). This capacity stems from the way individual elements of the system interact and generate new phenomena. Complex systems become more generative as the number of interactions between elements increases, thus creating momentum and the potential for change. Our objective in this paper is to contribute to understandings of collaborative partnerships in mathematics education by modeling the professional learning and research components of the Grade 9 Applied Mathematics initiative as a complex network. We identify the conditions for emergence (Davis & Sumara, 2006) that were present, the interactions that took place and the unanticipated moments of emergence that occurred. This approach enables us to understand the momentum that can be created by moments of emergence and to consider the impact this momentum can have within and beyond Ontario’s Grade 9 Applied Mathematics course.

Method

The research team included professors at three universities and eight graduate student research assistants (RAs). The team gathered many forms of data including: contextual information about schools and school team members; observation notes, artifacts, and audio-recordings of monthly school team meetings and from the multi-team events; and individual and focus group interviews with school team members. The research team met monthly to share preliminary observations, discuss strategies for supporting school teams, and plan multi-team events. Analysis of the data began with transcribing audio-recorded team meetings, interviews and focus groups. This was done incrementally with updated case study reports written for each school team after each monthly meeting. In addition, at the end of each year a summary report was written by each RA drawing on the transcripts and other data. These reports describe the areas of inquiry each team focused on, the activities they engaged in to further their learning, the ways the team worked collaboratively, resources they used, challenges encountered and progress made. At the end of the project, a cross case analysis was conducted to better understand the experiences that were shared by more than one team (Stake, 2006; Yin, 2009). The case studies and cross case analysis were also the basis for a project report for the funding organizations. For the paper we propose to present at ECER 2017, our methodology began with creating a model of this initiative as a complex network. We created this model by delineating a series of connected elements within the two intersecting realms of the initiative; the professional learning dimension and the research dimension. Elements in the resulting network include: individuals and groups (research team members, school teams, organizations, steering committee etc.) at various levels of the education system as well as the many interactions (school team meetings, research team meetings, steering committee meetings, multi-team events etc.) that were part of the initial structure of the initiative. We then examined this network, the case studies and the cross case analysis to identify the “conditions for emergence” (Davis & Sumara, 2006, p. 129) that existed and to pinpoint examples of emergent phenomena that occurred. In the final stage of analysis, ongoing at the time of this submission, we focus on identifying the broader impacts of the momentum this initiative has generated to contribute to more effective mathematics teaching and learning in Ontario.

Expected Outcomes

Our analysis revealed many conditions of emergence (Davis & Sumara, 2006) were present such as: "diversity of roles" within school teams, "redundancy of roles" across school teams, opportunities for "interactions among neighboring elements" in the network, "decentralization of control" as teams chose their focus and process, effective ways of "preserving and sharing information", and a "sufficient scale" to constitute a complex system. We found that the researchers, steering committee, and funding organizations were highly responsive to participant needs throughout the initiative and there were lots of examples of emergence at multiple levels of the initiative. For instance, we observed new classroom practices and new ways of thinking about both mathematics and mathematics teaching and learning. Moreover, several teams chose to involve other teachers at their school and/or from neighboring schools thereby spreading the initiative beyond Grade 9 Applied Mathematics and beyond the original schools. Along similar lines, some teams formed ongoing collaborative connections with other teams to continue to share their learning thereby extending the initiative beyond its two-year time frame. Emergent phenomena at a larger scale include the decision to hold a multi-team event at the end of year one and the decision to expand the final conferences to include teams from over 100 Ontario schools; events that were not part of the original project plan. Moments of emergence were also identified within the research team. Our analysis using complexity thinking reveals that the many interactions that took place over time and among practitioners, researchers and policymakers in this initiative facilitated emergence and built momentum toward enhanced mathematics teaching and learning in Ontario. We anticipate that learning about the initiative and the ways complexity thinking can inform educational change will be valuable for those interested in working collaboratively to improve mathematics teaching and learning in their own context.

References

Davis, B., & Sumara, D. (2006). Complexity and education: Inquiries into learning, teaching and research. Mahwah, NJ: Lawrence Erlbaum. Education Quality & Accountability Office [EQAO]. (2016). Provincial Secondary School Report 2016. Retrieved from: http://www.eqao.com/en/assessments/results/assessment-docs-secondary/provincial-report-secondary-school-board-results-2016.pdf Koch, M.J. & Watters, B. (2013). Teachers’ interpretations of province-wide assessment results in the context of a streamed high school mathematics course. Paper presented at the Canadian Society for the Study of Education Annual Meeting, Victoria, BC, Canada. Lemke, J. L., & Sabelli, N. H. (2008). Complex systems and educational change: Towards a new research agenda. Educational Philosophy and Theory, 40(1), 118-129. Mason, M. (2008). What is complexity theory and what are its implications for educational change? Educational Philosophy and Theory, 40(1), 35-49. doi:10.1111/j.1469-5812.2007.00413.x Ontario Secondary School Teachers Federation. (2009, Sept. 21). EQAO Grade 9 Assessment of Math test results show worrisome achievement gaps. Marketwire. People for Education. (2013). Mind the gap: Inequality in Ontario’s schools. Retrieved from http://www.peopleforeducation.ca/wp-content/uploads/2013/05/annual-report-2013-WEB.pdf Reith, B. (2003). What's wrong with these figures? Provincial results of the Grade 9 Assessment of Mathematics 2003-2003. Update, 31. St. Julien, J. (2005). Complexity: Developing a more useful analytic for education. In W. E. Doll Jr., M. J. Fleener, D. Trueit & J. St. Julien (Eds.), Chaos, complexity, curriculum, and culture (pp. 101-116). New York, NY: Peter Lang. Stake, R. E. (2006). Multiple case study analysis. NY: The Guilford Press. Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.

Author Information

Martha Koch (presenting / submitting)

University of Manitoba, Canada

Christine Suurtamm (presenting)

University of Ottawa, Canada

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