Learning the work of ambitious mathematics teaching

Project Description

This project sought to improve the mathematical experiences and educational outcomes for all students by looking to advance current practices for the preparation of mathematics teachers.  In looking for new ways to support prospective teachers to not only ‘think’ like teachers, but also to put what they know into action, this project looked to introduce practice-based pedagogies within our university-based mathematics methods courses.

Aims

This project investigated how changes in our initial mathematics teacher education curriculum and pedagogies could better support prospective teachers develop a vision of practice, knowledge of students and content, dispositions for using this knowledge, and a repertoire of practices and tools that align with current reforms in mathematics education. Specifically, we aimed to strengthen our knowledge of the kinds of intellectual and practical resources that support prospective and beginning teachers to engage in the practices of ambitious mathematics teaching. Teaching mathematics ambitiously involves teachers structuring complex interactions to focus on mathematical goal all while managing varied levels of student competence and interest and supporting students to develop productive dispositions towards mathematics.   Developing  ‘pedagogies of practice’, we looked closely at the design, enactment, and practice phases of instructional activities associated with professional noticing of students’ mathematical thinking and orchestrating inquiry learning/discussions in the mathematics classroom. In doing this, our aim was to support prospective teachers to learn how to engage in authentic interactions with learners in ways that avoided them being overwhelmed with the unpredictability and complexity of teaching in-the-moment.

Why is this research important?

Preparing teachers for ambitious mathematics teaching requires new forms of teacher education. We know that equipping pre-service teachers with knowledge of core or high-leverage practices or making them aware of a range of routines is not enough. Knowing how to act interactively in a way that is both responsive to the content and the learner is essential if teachers are to provide equitable learning opportunities that support diverse students to make sense of and become powerful learners of mathematics. Creating a pedagogical structure that explicitly links coursework with fieldwork and instructional investigation and inquiry with enactment will help counter the commonly cited theory practice divide of teacher education.

What did we do?

Using ‘pedagogies of practice’ we designed and trialled and evaluated a range of instructional interventions that focus on high-leverage or core practices associated with ambitious mathematics teaching. Instructional Activities (IA), each with particular mathematical learning goals, enabled opportunities for modelling in class, engagement in guided rehearsal with feedback, teaching in school settings, and reflective debriefing using video records and other evidence of student learning.  In the second and third years of the project, the mathematics methods courses, and a classroom inquiry course, were adapted to include opportunities for prospective teachers to teach IA within the school setting.  For each school visit, prospective teachers collaboratively planned the teaching sessions and one or two prospective teachers taught a group of children (between 2 and 8 times dependent on the course). Peers observed each of the teaching episodes (videoed) and contributed towards group- and whole-class reflective activities. Additionally, in the third year of the project we worked with a group of our beginning teachers focusing on their development of adaptive expertise and experiences in using ambitious teaching practices.

Data

During the initial teacher education phase we collected video records of rehearsal and school-based practice-focused learning opportunities across different programme sites alongside prospective teacher interviews and surveys. In school-based phase we collected videos of sample lessons of Year 1 teachers and discussions from cluster group professional meetings.

Analysis

We used video records of practice across program sites as data to analyse the suitability of the designed IAs for opportunities for learning— in terms of representation, decomposition, and approximation of core practices. In particular, we focused on how coaches modelled and used coach moves to highlight professional noticing and culturally responsive practices. In addition to the analysis of opportunities to learn, we examined the development of expertise, be it routine or adaptive, for a group of prospective teachers who had participated in an extended practice-based classroom inquiry. Further analysis focused on our own learning and mathematics teacher educators, and the potential generative learning of beginning teachers.

Project Outputs

Publications

Anthony, G., & Hunter, R. (2012). (Re)thinking and (re)forming  initial mathematics teacher education New Zealand Journal of Educational Studies, 47(1), 145-151.

Anthony, G., & Hunter, R. (2013). Learning the work of ambitious mathematics teaching. In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia, pp. 699-702). Melbourne, VIC: MERGA.

Anthony, G., Hunter, J., & Hunter, R. (2015). Learning to professionally notice students' mathematical thinking through rehearsal activities. Mathematics Teacher Education & Development, 17(2), 7-24.

Anthony, G., Hunter, J., & Hunter, R. (2015). Prospective teachers’ development of adaptive expertise. Teaching and Teacher Education, 49, 108-117.

Anthony, G., Hunter, R., Hunter, J., & Duncan, S. (2015). How ambitious is "ambitious mathematics teaching"?  Set: Research Information for Teachers, 2.

Averill, R., Anderson, D., & Drake, M. (2015). Developing culturally responsive teaching through professional noticing within teacher educator modelling. Mathematics Teacher Education and Development, 17(2), 64-83.

Averill, R., Drake, M., & Harvey, R. (2013). Coaching pre-service teacher for teaching mathematics: The views of students. In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia, pp. 707-710). Melbourne, VIC: MERGA.

Averill, R., Drake, M., Anderson, D., & Anthony, G. (2016). The use of questions within in-the-moment coaching in initial mathematics teacher education: enhancing participation, reflection, and co-construction in rehearsals of practice. Asia-Pacific Journal of Teacher Education, 1-18.

Drake, M. (2016). Learning to coach in practice-based teacher education: A self-study Studying Teacher Education.

Hunter, J., Anthony, G., & Hunter, R. (2015). Exploring and critiquing practice-based approaches in teacher education Mathematics Teacher Education & Development, 17(2), 1-6.

Hunter, R., Hunter, J., & Anthony, G. (2013). Using instructional activities to learn the work of ambitious mathematics in pre-service teacher educator settings. In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia, (pp. 703-706). Melbourne, VIC: MERGA.

Presentations, conferences and workshops

Anthony, G. (2013, June). Learning, in, from, and for practice. Paper presented at the Institute of Education Research Seminar Series, Massey University, Palmerston North.

Anthony, G., & Averill, R. (2014, 10 July). Learning the work of ambitious mathematics teaching. Paper presented at the Ako Aotearoa/Teaching & Learning Research Initiative Research in Progress Colloquium IV, Wellington.

Anthony, G., Hunter, J., & Hunter, R. (2014, July). Prospective mathematics teachers’ adaptive expertise. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the joint meeting of Psychology of Mathematics Education 38 and PME-NA 36 (Vol. 6, p. 9). Vancouver: PME.

Averill, R., Drake, M., Anderson, D., & Anthony, G. (2014). Promoting ambitious teaching: Using questions within in-the-moment coaching in initial teacher education. Paper presented at the Faculty of Education Seminar Series Victoria University of Wellington.

Averill, R., Drake, M., Anderson, D., & Anthony, G. (2014, Dec). Promoting ambitious teaching: Using questions within in-the-moment coaching in initial teacher education. Paper presented at the Speaking back through Research AARE-NZARE 2014 Conference, Brisbane, Australia.

Drake, M., Anderson, D., & Averill, R. (2015, April). Exploring productive pedagogies for teacher education: Developing wānanga and ako in rehearsals with coaching. Paper presented at the Faculty of Education Seminar Series. Victoria University of Wellington.

Hunter, J. (2012). Learning the work of ambitious mathematics teaching. Paper presented at the Collaborative Action Research Network Palmerston North.

Hunter, R. (2013). Instructional activities as a way to support diverse learnings access to classroom talk. Invited workshop, Canterbury University, Christchurch.

Hunter, R., Hunter, J., Anthony, G., Averill, R., Drake, M., Harvey, R., & Rawlins, P. (2012, Dec). Learning the work of ambitious mathematics teaching. Paper presented at the annual conference New Zealand Association of Educational Research, Waikato.

Rawlins, P., Anthony, G., Hunter, R., Averill, R., Drake, M., & Hunter, J. (2013, Dec). Pedagogies of practice in initial teacher education settings: Strengthening links between coursework and fieldwork. Paper presented at the NZARE conference and annual meeting, Dunedin.

Rawlins, P., Averill, R., Anthony, G., Hunter, R., Drake, M., & Hunter, J. (2014, Dec). Pedagogies of practice: Strengthening links between coursework and fieldwork in initial teacher education. Paper presented at the Speaking back through Research, the AARE-NZARE 2014 Conference, Brisbane, Australia.