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Pre-service Mathematics Teachers’ Noticing Skills and Scaffolding Practices

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International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

A 14-week course program was designed to investigate pre-service teachers’ noticing skills and scaffolding practices. Six pre-service teachers were matched with a pair of sixth grade students to observe and scaffold students’ mathematical understanding while they were working on the given tasks. Data was collected through pre-service teachers’ own recorded videos of implementation of tasks, their written reflections about the implementations, videos of group reflections before and after the implementations, and students’ written work. The analysis of data revealed that pre-service teachers mostly noticed students’ errors and strategies during their interactions with students, they attended important instances about students’ thinking and justified their reasoning for their comments in their written reflections. However, while interacting with students, they usually used low level scaffolding practices such as asking for clarification, explanation, and justification rather than attempting to elicit students’ thinking and improve their understanding.

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References

  • An, S., Kulm, G. & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145–172.

    Article  Google Scholar 

  • An, S. & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10, 717–753.

    Article  Google Scholar 

  • Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33–52.

    Article  Google Scholar 

  • Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

    Article  Google Scholar 

  • Barnhart, T. & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers’ ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83–93.

    Article  Google Scholar 

  • Baxter, J. A. & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13, 7–26.

    Article  Google Scholar 

  • Bliss, J., Askew, M. & Macrae, S. (1996). Effective teaching and learning: Scaffolding revisited. Oxford Review of Education, 22(1), 37–61.

    Article  Google Scholar 

  • Borko, H. & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673–708). New York, NY: Macmillan.

  • Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., … Choi, Y. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419–459.

  • Darling-Hammond, L. & Ducommun, C. E. (2010). Recognizing and developing effective teaching: What policy makers should know and do.  Retrieved from http://www.nea.org/assets/docs/HE/Effective_Teaching_-_Linda_Darling-Hammond.pdf.

  • Hiebert, J., Morris, A., Berk, D. & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47–61.

    Article  Google Scholar 

  • Hill, H. C., Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge. Journal for Research in Mathematics Education, 39, 372–400.

    Google Scholar 

  • Jacobs, V. R., Lamb, L. L. & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.

    Google Scholar 

  • Jacobs, V. R., Lamb, L. L. C., Philipp, R. A. & Schappelle, B. P. (2011). Deciding how to respond on the basis children’s understanding. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 97–116). New York, NY: Routledge.

  • Kellner, E., Gullberg, A., Attorps, I., Thoren, I. & Tarneberg, R. (2011). Prospective teachers’ initial conceptions about pupils’ difficulties in science and mathematics: A potential resource in teacher education. International Journal of Science and Mathematics Education, 9, 843–866.

    Article  Google Scholar 

  • Lannin, J. K., Webb, M., Chval, K., Arbaugh, F., Hicks, S., Taylor, C. & Bruton, R. (2013). The development of beginning mathematics teacher pedagogical content knowledge. Journal of Mathematics Teacher Education, 16, 403–426.

    Article  Google Scholar 

  • Leatham, K. R., Peterson, B. E., Stockero, S. L. & van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46(1), 88–124.

    Article  Google Scholar 

  • Mason, J. (2011). Noticing: Roots and branches. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35–50). New York, NY: Routledge.

  • McDuffie, A. R., Foote, M. Q., Bolson, C. Turner, E. E., Aguirre, J. M., Gau Bartell, T., … Land, T. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17, 245–270.

  • Morris, A. K., Hiebert, J. & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education, 40, 491–529.

    Google Scholar 

  • Moyer, P. S. & Milewich, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293–315.

    Article  Google Scholar 

  • Philipp, R. A., Ambrose, R., Lamb, L. L. C., Sowder, J. T., Schappelle, B. P., Sowder, L., … Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38, 438–476.

  • Pitts-Bannister, V. R. & Mariano, G. J. (2013). Snapshots of student thinking: An exploration of video cases for extending prospective teachers’ knowledge. Action in Teacher Education, 35, 430–444.

    Article  Google Scholar 

  • Roller, S. A. (2015). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education. doi:10.1007/s10857-015-9307-x.

    Google Scholar 

  • Rosaen, C. L., Lundeberg, M., Cooper, M., Fritzen, A. & Terpstra, M. (2008). Noticing noticing: How does investigation of video records change how teachers reflect on their experiences? Journal of Teacher Education, 59(4), 347–360.

    Article  Google Scholar 

  • Sanchez-Matamoros, G., Fernandez, C. & Llinares, S. (2014). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education. doi:10.1007/s10763-014-9544-y.

    Google Scholar 

  • Santagata, R., Zannoni, C. & Stigler, J. W. (2007). The role of lesson analysis in preservice 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 

  • Seidel, T., Sturmer, K., Blomberg, G., Kobarg, M. & Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27, 259–267.

    Article  Google Scholar 

  • Sherin, M. G., Jacobs, V. R. & Philipp, R. A. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–13). New York, NY: Routledge.

  • Sherin, B. & Star, J. R. (2011). Reflections on the study of teacher noticing. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 66–78). New York, NY: Routledge.

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

    Article  Google Scholar 

  • Sleep, L. & Boerst, T. A. (2012). Preparing beginning teachers to elicit and interpret students’ mathematical thinking. Teaching and Teacher Education, 28, 1038–1048.

    Article  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 

  • Sun, J. & van Es, E. A. (2015). An exploratory study of the influence that analyzing teaching has on preservice teachers’ classroom practice. Journal of Teacher Education, 66(3), 201–214.

    Article  Google Scholar 

  • van Es, E. (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, NY: Routledge.

  • 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, 244–276.

    Article  Google Scholar 

  • van de Pol, J., Volman, M. & Beishuizen, J. (2012). Promoting teacher scaffolding in small-group work: A contingency perspective. Teaching and Teacher Education, 28, 193–205.

    Article  Google Scholar 

  • Wood, D., Bruner, J. & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89–100.

    Article  Google Scholar 

Download references

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Correspondence to Hulya Kilic.

Appendix

Appendix

Table 4 Level of attending opportunities, students’ understanding, and own scaffolding in oral and written reflections in weekly basis

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Kilic, H. Pre-service Mathematics Teachers’ Noticing Skills and Scaffolding Practices. Int J of Sci and Math Educ 16, 377–400 (2018). https://doi.org/10.1007/s10763-016-9784-0

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