P-K Theory Through Their Eyes: New Teachers’ Conceptualisations of Connection Making

Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397. https://doi.org/10.1086/461730

Article  Google Scholar 

Bleiler, S., Ko, Y. Y., Yee, S. P., & Boyle, J. D. (2015). Communal development and evolution of a course rubric for proof writing. Annual perspectives in mathematics education: Assessment to enhance teaching and learning, 97–108.

Chapman, O. (1999). Inservice teacher development in mathematical problem solving. Journal of Mathematics Teacher Education, 2, 121-142. https://doi.org/10.1023/A:1009980911674

Article  Google Scholar 

Clark, C. M., & Lampert, M. (1986). The study of teacher thinking: Implications for teacher education. Journal of Teacher Education, 37(5), 27-31. https://doi.org/10.1177/002248718603700506

Article  Google Scholar 

Clark, C., & Peterson, P. (1984). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching 3rd ed. pp. 255-296. Macmillan.

Google Scholar 

Collier-Reed, B. I., & Ingerman, Å. (2013). Phenomenography: From critical aspects to knowledge claim. In Doing qualitative research: The craft of naturalistic inquiry pp. 129–140. Routledge.

Cramer, K., Post, T., & del Mas, R. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144. https://doi.org/10.2307/749646

Article  Google Scholar 

Entwistle, N. (1997). Introduction: Phenomenography in higher education. Higher Education Research & Development, 16(2), 127-134. https://doi.org/10.1080/072943697016020

Article  Google Scholar 

Evans, R. (1989). Teacher conceptions of student problem-solving. Journal of Mathematics Education, 20(3), 225-232. https://doi.org/10.1007/BF00312806

Article  Google Scholar 

Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38(1), 47-65. https://doi.org/10.1080/0013188960380104

Article  Google Scholar 

Gonzalez Thompson, D. (1984). Teacher understanding and use of mathematical problem solving. Journal for Research in Mathematics Education, 15(2), 95-107. https://doi.org/10.2307/748987

Article  Google Scholar 

Herbel-Eisenmann, B., Drake, C., & Cirillo, M. (2009). “Muddying the clear waters”: Teachers’ take-up of the linguistic idea of revoicing. Teaching and Teacher Education, 25(2), 268–277. https://doi.org/10.1016/j.tate.2008.07.004

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. Macmillan.

Holincheck, N., & Galanti, T. (2022). Teachers’ beliefs about mathematical problem solving: Implications for professional development. Journal of Mathematics Teacher Education, 25, 189-206. https://doi.org/10.1007/s10857-021-09482-3

Article  Google Scholar 

Kane, R., Sandretto, S., & Heath, C. (2002). Telling Half the Story: A Critical Review of Research on the Teaching Beliefs and Practices of University Academics. Review of Educational Research, 72(2), 177–228. https://doi.org/10.3102/00346543072002177

Kasmer, L., & Kim, O. (2012). The nature of predictions made by middle school students in mathematical tasks. Educational Studies in Mathematics, 79(1), 133-147. https://doi.org/10.1007/s10649-011-9336-5

Article  Google Scholar 

Kinnunen, P., & Simon, B. (2012). Phenomenography and grounded theory as research methods in computing education research field. Computer Science Education, 22(2), 199-218. https://doi.org/10.1080/08993408.2012.692928

Article  Google Scholar 

Ko, Y. (2010). Mathematics teachers’ conceptions of proof: Implications for educational practice. Journal of Education and Practice, 1(1), 19-29. https://doi.org/10.1007/s10763-010-9235-2

Article  Google Scholar 

Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55(2), 178–194. https://doi.org/10.17763/haer.55.2.56142234616x4352

Lampert, M. (1991). Teaching problems and the problems of teaching. Yale University Press.

Google Scholar 

Lepak, J. (2014). Enhancing Students’ Written Mathematical Arguments. Mathematics Teaching in the Middle School, 20(4), 212-219.

Article  Google Scholar 

Martin, L., & Towers, J. (2016). The practice of theorizing in teacher education. Educational Studies in Mathematics, 93(1), 87-102. https://doi.org/10.1007/s10649-016-9718-8

Article  Google Scholar 

Nisbet, S., & Warren, E. (2000). Primary school teachers’ beliefs relating to mathematics teaching and assessing. Mathematics Education Research Journal, 12(1), 34-47. https://doi.org/10.1007/BF03217073

Article  Google Scholar 

Orrill, C. H., & Kittleson, J. (2015). Conceptualizing connection making as the construction of a coherent understanding. Journal of Mathematics Teacher Education, 18(1), 1-20. https://doi.org/10.1007/s10857-013-9261-8

Article  Google Scholar 

Pirie, S. E. B., & Kieren, T. E. (1988). A recursive theory of mathematical understanding. For the Learning of Mathematics, 8(1), 7-11.

Google Scholar 

Pirie, S. E. B., & Kieren, T. E. (1992). Watching Sandy’s understanding grow. Journal of Mathematical Behavior, 11(3), 243-257.

Google Scholar 

Pirie, S. E. B., & Kieren, T. E. (1994a). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26(2-3), 165-190. https://doi.org/10.1007/BF01273662

Pirie, S. E. B., & Kieren, T. E. (1994b). Beyond metaphor: Formalizing in mathematical understanding within constructivist environments. For the Learning of Mathematics, 14(1), 39-43.

Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574. https://doi.org/10.1037/0022-0663.99.3.561

Article  Google Scholar 

Russo, J., Bobis, J., & Downton, A. (2020). Exploring the mathematical problem-solving beliefs of Australian pre-service elementary teachers. Journal of Mathematics Teacher Education, 23, 531-552. https://doi.org/10.1007/s10857-019-09447-y

Article  Google Scholar 

Sato, M., & Takahashi, A. (2004). Establishing learning community through lesson study. In Proceedings of the NCTM research pre-session (pp. 126–139). National Council of Teachers of Mathematics.

Sawada, T. (1996). Developing mathematical thinking in the classroom: A Japanese perspective. National Center for Improving Science Education. https://doi.org/10.1007/s11858-007-0052-1

Article  Google Scholar 

Schoenfeld, A. H. (2014). Mathematical problem solving. Academic Press.

Google Scholar 

Smith, M. S., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematics discussions. NCTM.

Star, J. R., Newton, K. J., Pollack, C., Kokka, K., Rittle-Johnson, B., & Durkin, K. (2015). The development of flexibility in equation solving. Contemporary Educational Psychology, 41, 45-59. https://doi.org/10.1016/j.cedpsych.2014.10.003

Article  Google Scholar 

Takahashi, A. (2011). Japanese lesson study: Teacher professional development through communities of inquiry. Mathematics Teacher Education and Development, 13(1), 3-18.

Google Scholar 

The National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. NCTM.

Tsui, A. B. M. (2003). Understanding expertise in teaching: Case studies of second language teachers. Cambridge University Press. https://doi.org/10.1017/CBO9781139524698

Article  Google Scholar 

Wright, P. (2014). Supporting mathematical thinking through anticipatory strategies. Mathematics Teacher Education and Development, 16(1), 54-70.

Google Scholar 

Comments (0)

No login
gif