Journal of Mathematics Teacher Education

, Volume 19, Issue 4, pp 325–347 | Cite as

Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson

  • Lin Ding
  • Higinio Domínguez


This paper investigates the noticing of six Chinese mathematics prospective teachers (PSTs) when looking at a procedural error and responding to three specific tasks related to that error. Using video clips of one student’s procedural error consisting of exchanging the order of coordinates when applying the distance formula, some variation was found in how PSTs attended to, interpreted, and responded to this error. A more important finding is represented by the inconsistent responses that individual PSTs provided to the three related tasks. This finding suggests that, to some extent, prior learning experience, beliefs, and orientations inform what PSTs notice. But the finding also suggests the centrality of selecting tasks that provide accurate representations of PSTs’ emerging professional noticing. Implications for teacher educators are discussed.


Prospective teacher education Professional noticing Students’ mathematical thinking Lower secondary, K-8 


  1. Ball, D. L. (2011). Foreword. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. xx–xxiv). New York: Routledge.Google Scholar
  2. Biggs, J. B., & Watkins, D. A. (2001). Insights into teaching the Chinese learner. In D. A.Watkins & J. B. Biggs (Eds.), Teaching the Chinese learner: Psychological and pedagogical perspectives (pp. 277–300). Hong Kong; Melbourne, Australia: Comparative Education Research Centre; Australian Council for Educational Research. Educational Research.Google Scholar
  3. Charalambous, C., Hill, H., & Ball, D. (2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441–463.Google Scholar
  4. Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.CrossRefGoogle Scholar
  5. Davis, B. (1996). Teaching mathematics: Towards a sound alternative. New York: Garland Publishing.Google Scholar
  6. Goulding, M., Rowland, T., & Barber, P. (2002). Does it matter? Primary teacher trainees’ subject knowledge in mathematics. British Educational Research Journal, 28(5), 689–704.CrossRefGoogle Scholar
  7. Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.CrossRefGoogle Scholar
  8. Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics (pp. 309–347). Singapore: World Scientific.CrossRefGoogle Scholar
  9. Hand, V. (2012). Seeing culture and power in mathematical learning: Toward a model of equitable instruction. Educational Studies in Mathematics, 80(1–2), 233–247.CrossRefGoogle Scholar
  10. Huang, R., & Leung, K. S. F. (2004). Cracking the paradox of Chinese learners: Looking into the mathematics classrooms in Hong Kong and Shanghai. In F. Lianghuo, W. N. Ying, C. Jinfa, & L. Shiqi (Eds.), How Chinese learn mathematics: Perspectives from insiders (Vol. 1, pp. 348–381). Singapore: World Scientific.CrossRefGoogle Scholar
  11. Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of students’ mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.Google Scholar
  12. Jenkins, O. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13(2), 141–154.CrossRefGoogle Scholar
  13. Kahan, J. A., Cooper, D. A., & Bethea, K. A. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6(3), 223–252.CrossRefGoogle Scholar
  14. Kinach, B. M. (2002a). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51–71.CrossRefGoogle Scholar
  15. Kinach, B. M. (2002b). Understanding and learning-to-explain by representing mathematics: Epistemological dilemmas facing teacher educators in the secondary mathematics “methods” course. Journal of Mathematics Teacher Education, 5(2), 153–186.CrossRefGoogle Scholar
  16. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  17. Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.CrossRefGoogle Scholar
  18. Li, S. (1999). Does practice make perfect? For the Learning of Mathematics, 19(3), 33–35.Google Scholar
  19. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: L. Erlbaum Associates.Google Scholar
  20. McDuffie, A. R., Foote, M. Q., Bolson, C., Drake, C., Turner, E. E., Aguirre, J. M., et al. (2013). Prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases using video case analysis. Paper presented at the 2013 annual meeting of the American Educational Research Association.Google Scholar
  21. Miller, K., & Zhou, X. (2007). Learning from classroom video: What makes it compelling and what makes it harder. In R. Goldman-Segal & R. Pea (Eds.), Video research in the learning sciences. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
  22. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2), 165–190.CrossRefGoogle Scholar
  23. Santagata, R., Zannoni, C., & Stigler, J. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123–140.CrossRefGoogle Scholar
  24. Schoenfeld, A. H. (2011). Noticing matters. A lot. Now what? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.Google Scholar
  25. Seawright, J., & Gerring, J. (2008). Case selection techniques in case study research: A menu of qualitative and quantitative options. Political Research Quarterly, 61(2), 294–308.CrossRefGoogle Scholar
  26. Sherin, M. G., Buss, R. S., & Colestock, A. A. (2011). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79–94). New York: Routledge.Google Scholar
  27. Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183.CrossRefGoogle Scholar
  28. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.CrossRefGoogle Scholar
  29. Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the Learning of Mathematics, 10(3), 24–41.Google Scholar
  30. Sierpinska, A. (1994a). Understanding in mathematics. London, Washington, DC: Falmer Press.Google Scholar
  31. Sierpinska, A. (1994b). The cultural roots of epistemological obstacles. In A. Sierpinska (Ed.), Understanding in mathematics (pp. 159–169). London, Washington, DC: Falmer Press.Google Scholar
  32. Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9–15.Google Scholar
  33. Star, J. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.Google Scholar
  34. Star, J., & Strickland, S. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107–125.CrossRefGoogle Scholar
  35. Turner, E., Drake, C., McDuffie, A., Aguirre, J., Bartell, T., & Foote, M. (2012). Promoting equity in mathematics teacher preparation: A framework for advancing teacher learning of students’ multiple mathematics knowledge bases. Journal of Mathematics Teacher Education, 15(1), 67–82.CrossRefGoogle Scholar
  36. van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). New York: Routledge.Google Scholar
  37. van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571–596.Google Scholar
  38. van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244–276.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Resource Centre for Interdisciplinary and Liberal Studies (RCILS)The Hong Kong Institute of EducationTai PoHong Kong
  2. 2.Department of Teacher EducationMichigan State UniversityEast LansingUSA

Personalised recommendations