Mathematical inquiry has been long promoted in mathematics education, but little traction has been made into schools. Research has documented challenges of implementing inquiry pedagogies in mathematics, and pockets of innovation have documented progress. Few research projects have engaged the participating teachers directly in seeking ways to address these challenges and scale progress. A longitudinal study over 7 years worked collectively with a small number of teachers to wrestle with ways to identify and address challenges they faced in learning to teach mathematics with inquiry, and then to support additional teachers to come on board. Follow up studies included these same teachers to develop strategies for teachers new to inquiry to develop students’ classroom talk and build a positive culture to enable intellectual risk.

Although teachers’ voices and experiences were always meant to be a substantial focus of the research, their knowledge contributions to the research were vital in ensuring findings were practical, progressive, responsive, beneficial for students and increasingly, scaleable. Initially, the teachers did not recognise the importance of their contributions (Makar & O’Brien, 2013), but as they attended and presented at research conferences, they were more able to see the novelty of their ideas in practice and how these ideas could be considered knowledge contributions to the field. Furthermore, the direction and impact of the research increasingly shifted in unanticipated ways in response to the teachers’ contributions. In effect, the teachers changed the nature of the research and role of being researched as knowledge emerged out of their practice. That is, the teachers’ insights enabled the research to not only accumulate, but also adapt to emerging ideas and epistemological shifts.

The theoretical perspective of knowledge-building (Scardamalia & Bereiter, 2006) was embraced by the teachers and researcher to capture both the interactions between the teachers and their students in the context of mathematical inquiry, but also the ways of working and learning involving the teachers and research team. Knowledge-building is considered to be “deliberate, conscious action, which produces knowledge that has a public life” (Bereiter & Scardamalia, 2014, p. 35). Knowledge-building is more than just generation of ideas, but a process of operationalising, improving and extending them. A knowledge-building perspective of learning in particular embraces idea improvement, collectivism and learning in discourse. This perspective encouraged the teachers and researcher to see the work as ongoing, collaborative and aimed at improving the greater teaching profession. For the teachers, these elements were equally beneficial for them to help students see learning as progressive and aiming to improve learners in the classroom, rather than understanding as a destination for each individual.

The presentation will focus on the ways that a knowledge-building perspective enabled the collaboration between the teachers and researchers to deliberately reflect on, respond to and progress emerging findings.

The research question is How did the researcher and researched co-construct the outcomes and direction of the research? The methodology recognises that this is a study retrospectively using data from a larger program of research led by the author (2006-2017). The program of research used a design research methodology to allow the research team to concurrently study and seek to improve the study context, as well as respond to contingencies as they arose (Cobb et al., 2003). The research program consisted of a 7-year three-phase longitudinal study, and two smaller, intensive follow-up projects each with their own (related) aims and outcomes. Later phases included the teachers in the previous phases, allowing a foundation of knowledge to be built upon. At any one time, the program of research involved 4-40 teachers (varying with each aspect of the program) from 1-5 primary schools in a mixture of low and middle class suburban and rural schools. The aim of the longitudinal study was to understand teachers’ changing experiences and pedagogies in learning to adopt mathematical inquiry over time; the followup studies intensively examined the strategies that teachers used to develop students’ classroom talk and create a positive classroom culture that allowed students to take intellectual risks. The study reported in this proposal examines the reflexivity of the researcher, the larger cohort of teachers in the research, and a particular core group of 5 teachers who significantly contributed to the direction and impact of the overall program of research. The study draws on interviews from the cohort of teachers at the beginning and end of the longitudinal study, with the core teachers on subsequent follow-up projects, and interviews conducted with the core teachers about their contributions to the research. Interviews were transcribed and then analysed in two ways. Interviews of the larger cohort of teachers underwent coding of key themes (beginning and end of longitudinal study) during the research program and the themes were then traced to the research activities. Next, the interviews of the core teachers were subjected to a process adapted from Powell et al (2003) that involved describing content, selecting and annotating critical events (based on the links between teachers’ ideas and research activities), developing storylines and constructing narrative in a non-linear, back-and-forth process. Both analyses were then examined in relation to knowledge-building (Scardamalia & Bereiter, 2006) to respond to the research question.

1. The teachers’ ideas had a substantial impact on the direction, impact and quality of the research program. 2. The roles of the teachers and researcher morphed through the research program as each came to appreciate the value of the teachers’ contributions of knowledge. 3. Knowledge-building perspective provided an important lens for re-thinking the epistemological basis for how knowledge was reflexively co-constructed.

Bereiter, C., & Scardamalia, M. (2014). Knowledge building and knowledge creation: One concept, two hills to climb. In S.C. Tan et al. (Eds.), Knowledge creation in education (pp. 35-52). Springer, Singapore. DOI 10.1007/978-981-287-047-6_3 Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13. Makar, K., & O’Brien, M. (2013). Blurring the boundaries: The transformative nature of research participation. In W. Midgley, P. A. Danaher, and M. Baguley (Eds.), The role of participants in education research: Ethics, epistemologies, and methods (pp. 110-125). New York: Routledge. Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435. Scardamalia, M., & Bereiter, C. (2006). Knowledge building: Theory, pedagogy, and technology. In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 97-116). Cambridge, UK: Cambridge University Press.