# Growing mathematics teachers: Pre-service primary teachers’ relationships with mathematics

## Keywords:

pre-service teachers . affect . knowledge . growth mindset . longitudinal## Abstract

At the beginning of their programme in 2015, 40% of the 83 primary pre-service teachers at the University of Otago did not meet the required standard for content knowledge, and therefore their programme was adjusted. During their three-year programme, the pre-service teachers’ mathematical content knowledge was examined, as well as other affective aspects of their relationships with mathematics, including beliefs and feelings about mathematics and teaching, and associated identities. Pre-service teachers’ perceptions of the usefulness of the interventions were sought. Their relationships with mathematics generally became more positive as they grew towards becoming teachers and as they adopted a growth perspective. The pre-service teachers found the interventions useful although their confidence remained somewhat conditional on their knowledge and the age of the children. Many of the pre-service teachers moved from thinking about their own relationships with mathematics to thinking about the relationship of the children.

## References

Anakin, M., & Linsell, C. (2014). Foundation content knowledge: Pre-service teachers as half-empty or becoming fluent? In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice, Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 722-725). Sydney, Australia: MERGA.

Anderson, J. (2005). I didn't know what I didn't know: A case study of growth in teacher knowledge within the Intermediate Numeracy Project. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Research, theory and practice (Proceedings of the 28th Annual Conference of the Mathematics Education Group of Australasia, Melbourne, Vol. 1, pp. 97-104). Sydney: MERGA.

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics. Educational Series—19. Brussels: International Bureau of Education, Geneva.

Baxter, P., & Jack, S.(2008). Qualitaitive case study methodology: Study design and implementation for novice researchers, The Qualitative report, 13(4), 544-559.

Buerk, D. (1996). Our open ears can open minds: Listening to women's metaphors for mathematics. Focus on Learning Problems in Mathematics, 18(1,2 & 3), 26-31.

Delaney, S., Ball, D., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197.

Dweck, C. S. (1999). Self-theories: Their role in motivation, personality, and development. PA: Taylor and Francis.

Denzin, N. K., & Lincoln, Y., S. (2005). Introduction: The discipline and practice of qualitative research. In N. K. Denzin & Y. Lincoln, S. (Eds.), The SAGE handbook of qualitative research (Third ed.). Thousand Oaks, CA: SAGE Publications, Inc.

Gill, M. G., Ashton, P. T., & Algina, J. (2004). Changing pre-service teachers’ epistemological beliefs about teaching and learning in mathematics: An intervention study. Contemporary Educational Psychology, 29(2), 164-185.

Grootenboer, P., & Marshman, M. (2016). Mathematics, affect and learning: Middle school pre-service teachers' beliefs and attitudes about mathematics education. Singapore: Springer Science+Business Media.

Grootenboer, P., & Jorgensen, R. (2008). Identity as a lens to understand learning mathematics: Developing a model. Navigating currents and charting directions, 1, 243-250.

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65-97). New York, NY: MacMillan.

Homes, V.-L. (2012). Depth of teachers’ knowledge: Frameworks for teachers’ knowledge of mathematics. Journal of STEM Education, 13(1), 55-71.

Ingram, N. (2015). Students' relationships with mathematics: Affect and identity. In M. Marshman, V. Geiger & A. Bennison (Eds.), Proceedings of the 38th Mathematics Education Research Group of Australasia (MERGA): Mathematics in the Margins. (pp. 301-308). Sunshine Coast, Australia: MERGA.

Ingram, N., Asil, M., & Berg, D. (2017). The impact of mathematics teaching efficacy on teachers' pedagogical practices. Proceedings of the European Association for Research on Learning and Instruction (EARLI) Conference, Finland, August 2017. Retrieved from https://earli.org/earli-2017

Linsell, C., & Anakin, M. (2012). Diagnostic Assessment of Pre-Service Teachers’ Mathematical Content Knowledge. Mathematics Teacher Education and Development, 14(2), 4-27.

Linsell, C., & Anakin, M. (2013). Foundation Content Knowledge: What Do Pre-Service Teachers Need To Know? In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics Education: Yesterday, Today & Tomorrow, Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 442-449). Melbourne: MERGA.Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Erlbaum.

Malmivuori, M. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149-164.

Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10-32.

Miller-Reilly, B. (2006). Affective change in adult pre-service teachers in second chance mathematics courses: Three different teaching approaches. Unpublished doctoral dissertation, University of Auckland, New Zealand.

Moodley, T., Adendorff, S. A., & Pather, S. (2015). At-risk student teachers' attitudes and aspirations as learners and teachers of mathematics. South African Journal of Childhood Education, 5(3), 1-10.

Op 't Eynde, P., De Corte, E., & Verschaffel, L. (2006). "Accepting emotional complexity": A socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 63, 193-207.

New Zealand Teachers Council (2010). Approval, review and monitoring processes andr for initial teacher education programmes. Retrieved from http://www.teacherscouncil.govt.nz

Newton, K. J., Leonard, J., Evans, B. R., & Eastburn, J. A. (2012). Preservice elementary teachers' mathematics content knowledge and teacher efficacy. School Science and Mathematics, 112(5), 289-299.

Perkins, T. (2015). Mentoring to Alleviate Anxiety in Pre-Service Primary Mathematics Teachers: An Orientation towards Improvement Rather than Evaluation. Mathematics Education Research Group of Australasia.

Picker, S. H., & Berry, J. S. (2000). Investigating pupils' images of mathematicians. Educational Studies in Mathematics, 43(1), 65-94.

Ryan, J., & McCrae, B. (2005/6). Assessing pre-service teachers' mathematics subject knowledge. Mathematics Teacher Education and Development, 7, 72-89.

Ryan, J., & William, J. (2011). Teachers’ stories of mathematical subject knowledge: Accounting for the unexpected. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 251-271). Dordrecht, Netherlands: Springer.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teacher Education and Development, 77, 20-26.

Sloan, T. R. (2010, June). A quantitative and qualitative study of math anxiety among pre-service teachers. In The Educational Forum (Vol. 74, No. 3, pp. 242-256). Taylor & Francis Group.

Stake, R. E. (2005). Qualitative case studies. In N. K. Denzin & Y. Lincoln, S. (Eds.), The SAGE handbook of qualitative research (pp. 443-465). Thousand Oaks, California: Sage Publications.

Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage Publications.

Tertiary Education Commission. (2010). Literacy and numeracy for adults. Retrieved from http://literacyandnumeracyforadults.com/Wilkie, K. J. (2016). Learning to teach upper primary school algebra: changes to teachers’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28(2), 245-275.

Young-Loveridge, J., Bicknell, B., & Mills, J. (2012). The mathematical content knowledge and attitudes of New Zealand pre-service primary teachers.

Wilson, S. (2016). Quality of Life: Domains for Understanding Maths Anxiety in First Year Pre-Service Teachers through Identity Work. Mathematics Education Research Group of Australasia.

Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63(2), 113-121.