Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. In the context of China, normal university (colleges) severed as mono-purpose institutions, mainly responsible for cultivating future teachers at different levels.

  2. Rank refers to the particular position one individual has among 101 PSTs in the performance of PCK or CK items. The top 30 students in the programs are rated as High; those ranking between 31 and 70 are rated as Intermediate, and those after 71 are rated as Low.

  3. All names used are pseudonyms.

  4. The PCK questionnaire consisted of content items from three aspects: knowledge of students (KOS), knowledge of teaching (KOT), and content knowledge (CK).

References

  • 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 

  • 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.

  • 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.

  • 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.

    Article  Google Scholar 

  • Davis, B. (1996). Teaching mathematics: Towards a sound alternative. New York: Garland Publishing.

  • 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.

    Article  Google Scholar 

  • Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Jenkins, O. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13(2), 141–154.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.

    Article  Google Scholar 

  • Li, S. (1999). Does practice make perfect? For the Learning of Mathematics, 19(3), 33–35.

    Google Scholar 

  • Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: L. Erlbaum Associates.

    Google Scholar 

  • 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.

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183.

    Article  Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.

    Article  Google Scholar 

  • Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the Learning of Mathematics, 10(3), 24–41.

    Google Scholar 

  • Sierpinska, A. (1994a). Understanding in mathematics. London, Washington, DC: Falmer Press.

    Google Scholar 

  • 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 

  • Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9–15.

    Google Scholar 

  • Star, J. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Resource Centre for Interdisciplinary and Liberal Studies (RCILS), The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong

    Lin Ding

  2. Department of Teacher Education, Michigan State University, 116K Erickson Hall, East Lansing, MI, 48824-103, USA

    Higinio Domínguez

Authors
  1. Lin Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Higinio Domínguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lin Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, L., Domínguez, H. Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. J Math Teacher Educ 19, 325–347 (2016). https://doi.org/10.1007/s10857-015-9301-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-015-9301-3

Keywords

Search

Navigation