Secondary Preservice Teachers’ Anticipated Objectives and Practices for Teaching Mathematics



preservice secondary mathematics teachers, teaching practices, learning objectives, positive disposition, interest, reasoning, problem solving, understanding


Australian students’ attitudes to mathematics are in decline relative to other countries. Their participation in senior secondary mathematics that provide pathways to further study is also falling. Pedagogical approaches that improve students’ attitudes to mathematics and knowledge of mathematics are required. This paper reports on preservice secondary mathematics teachers’ objectives for their students’ learning and their anticipated teaching and learning activities. The study was conducted over one year using quantitative analysis of paired responses to items in pre and post questionnaires. At the end of the year, the preservice teachers emphasised objectives for understanding and positive disposition but anticipated using fluency activities almost daily. Investigations involving problem solving and reasoning were anticipated to occur at least weekly. However, a significant decline in their anticipated use of activities that link mathematics to other disciplines or applying mathematics to real world problems occurred. Other data suggest a lowering of emphasis on developing students’ disposition and interest in mathematics. The findings suggest that more attention needs to be given to raising preservice teachers’ awareness of the importance of students’ disposition. Further research on the impact of teaching experience and opportunities to develop all proficiencies and to link mathematics to other disciplines and real-world problems during preservice teacher education is recommended.

Author Biographies

Colleen Vale, Monash University

Prof. Mathematics Education, Faculty of Education

Sandra Herbert, Deakin University

Senior Lecturer, School of Education


Adler, J., Ball, D., Krainer, K., Lin, F-L., & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational Studies in Mathematics, 60, 359–381.

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

Australian Curriculum, Assessment and Reporting Authority (2017a). Australian Curriculum: Mathematics. Retrieved from

Australian Curriculum, Assessment and Reporting Authority (2017b). Australian Curriculum: General Capabilities, Numeracy.

Attard, C. (2013). “If I had to pick any subject, it wouldn't be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25, 569–587.

Barkatsas, A. T., & Malone, J. (2005). A typology of mathematics teachers’ beliefs about teaching and learning mathematics and instructional practices. Mathematics Education Research Journal, 17(2), 69–90.

Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17, 39–68.

Beswick, K, (2007). Teachers’ beliefs that matter in secondary classrooms. Educational Studies in Mathematics, 65, 95–120.

Beswick, K, (2012). Teachers’ beliefs about school mathematics and mathematician’s mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127–147.

Bieg, M., Goetz, T., Sticca, F., Brunner, E., Becker, E., Morger, V., & Hubbard, K. (2017). Teaching methods and their impact on students’ emotions in mathematics: An experience-sampling approach, ZDM Mathematics Education, 49, 411–422.

Brown, M., Brown, P., & Bibby, T. (2008). “I would rather die”: Reasons given by 16-year-olds for not continuing their study of mathematics. Research in Mathematics Education, 10(1), 3-18.

Bryman, A. (2016). Social research methods (5th edition). Oxford University Press.

Cady, J., Meier, S. L., & Lubinski, C. A. (2006). The mathematical tale of two teachers: A longitudinal study relating mathematics instructional practices to level of intellectual development. Mathematics Education Research Journal, 18(1), 3–26.

Carmichael, C., Callingham, R., & Watt, H. M. G. (2017). Classroom motivational environment influence on emotional and cognitive dimensions of student interest in mathematics. ZDM Mathematics Education, 49, 449–460.

Charalambous, C. U., Philoppou, G. N., & Kyriakides, L. (2008). Tracing the development of preservice teachers’ efficacy beliefs in teaching mathematics during field work. Educational Studies in Mathematics, 67, 125–142.

Chubb, I. (2013). Mathematics, Engineering & Science in the national interest: A strategic approach: A position paper. Canberra: Commonwealth of Australia.

Commonwealth of Australia. (2011). Skill shortages Australia.

Conner, A. M., Edenfield, K. W., Gleason, B. W., & Ersoz, F. A. (2011). Impact of a content and methods course sequence on prospective secondary mathematics teachers’ beliefs. Journal of Mathematics Teacher Education, 14, 483–504.

Cross, D. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 29, 325– 346.

Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Dede, Y., & Karakus, F. (2014). The effect of teacher training programs on pre-service mathematics teachers' beliefs towards mathematics. Educational Sciences: Theory and Practice, 14(2), 804–809.

Department for Employment and Education. (2014). Primary National Curriculum: Mathematics. curriculum/primary/

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–253). Fahner.

Ensor, P. (2001). From preservice mathematics teacher education to beginning teaching: A study in recontextualizing. Journal for Research in Mathematics Education, 32(3), 296-320.

Ertl, H., & Kremer, H. (2010). Educational change and innovative teaching practice: A study of the impact of reforms on the work of lecturers in vocational education and training in England and Germany. Orbis Scholae, 4 (2), 133–147.

Forgasz, H. & Leder, L. (2008). Beliefs about mathematics and mathematics teaching. In P. Sullivan & T. Wood (Eds.), Knowledge and beliefs in mathematics teaching and teaching development (pp. 173– 194). Sense Publishers.

Frykholm, J. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.

Goos, M., Geiger, V. & Dole, S. (2014). Transforming professional practice in numeracy teaching. In Y. Li, E. Silver & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 81–102). Springer.

Goos, M., Smith, T., & Thornton, S. (2008). Research on the pre-service education of teachers of mathematics. In H. Forgasz, A. Barkatsas, A. Bishop, B. Clarke, S. Keast, W-T., Seah & P. Sullivan (Eds.), Research in Mathematics Education in Australasia 2004-2007 (pp. 291–311). Brill Sense.

Grootenboer, P. (2008). Mathematical belief change in prospective primary teachers. Journal of Mathematics Teacher Education, 11, 479–497.

Horizon Research. (2000). 2000 National survey of science and mathematics education: School mathematics program questionnaire.

Jao, L. (2017). Shifting pre-service teachers’ beliefs about mathematics teaching: the contextual situation of a mathematics methods course. International Journal of Science and Mathematics Education, 15, 895–914.

Kaur, B., Lee, N. H., Ng, K. T. D., Yeo, J. B. W., Yeo, K. K. J., & Safii, L. (2019). Instructional strategies adopted by experienced secondary teachers when enacting the Singapore school mathematics curriculum. In G. Hine, S. Blackley, & A. Cooke (Eds.). Mathematics education research: Impacting practice (Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia) pp. 81–98. MERGA.

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academy Press.

Langford, K., & Huntley, M. A. (1999). Internships as commencement: Mathematics and science research experiences as catalysts for preservice teacher professional development. Journal of Mathematics Teacher Education, 2, 277–299.

Little, J., & Anderson, J. (2015). What factors support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience? Asia-Pacific Journal of Teacher Education, 44(5), 504–521.

MacFarland T.W., & Yates J.M. (2016). Wilcoxon Matched-Pairs Signed-Ranks Test. In Introduction to Nonparametric Statistics for the Biological Sciences Using R (pp. 133–175). Springer

Maxwell, K. (2001). Positive learning dispositions in mathematics. Retrieved from

Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International Results in Mathematics. Retrieved from:

Ng, W., Nicholas, H., & Williams, A. (2010). School experience influences on pre-service teachers’ evolving beliefs about effective teaching. Teaching and Teacher Education, 26(2), 27–289.

Pampaka, M., Williams, J., Hutcheson, G., Wake, G., Black, L., Davis, P., & Hernandez‐Martinez, P. (2012). The association between mathematics pedagogy and learners’ dispositions for university study. British Educational Research Journal, 38(3), 473–496.

Pawson, R., & Tilley, N. (1997). Realistic evaluation. SAGE Publications.

Peressini, D., Borko, H., Romagnano, L., Knuth, E., & Willis, C. (2004). A conceptual framework for learning to teach secondary mathematics: A situative perspective. Educational Studies in Mathematics, 56(1), 67–96.

Prescott, A., & Cavanagh, M. (2006). An investigation of pre-service secondary mathematics teachers’ beliefs as they begin their teacher training. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 424–431). MERGA.

Prescott, A., & Cavanagh, M. (2008). A situated perspective on learning to teach secondary mathematics. In M. Goos, R. Brown & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, pp. 407– 413). MERGA.

Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

Tatto, M., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in mathematics (TEDS-M): Conceptual framework. Teacher Education and Development International Study Center, College of Education.

Teacher Policy Research. (2006). Examining teacher preparation: Does the pathway make a difference (Survey of second year teachers). University of Albany and Stanford University.

Thomson, S., de Bortoli, L. & Buckley, S., (2013). The PISA 2012 Assessment of students’ mathematics, scientific and reading literacy. ACER. 2016 TIMSS report.

Van Zoest, L. R., Jones, G. A., & Thornton, C. A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first-grade mentorship program. Mathematics Education Research Journal, 6(1), 37–55.

White-Clark, R., DiCarlo, M., & Gilchriest, S. N. (2008). "Guide on the side": An instructional approach to meet mathematics standards. The High School Journal, 91(4), 40–44.

Weisstein, E. W. (n.d.). Bonferroni correction.

Wienke, M. (2017). Discipline profile of mathematical sciences 2017. Australian Mathematical Sciences Institute.