Source: http://www.ejmste.com/Further-Investigation-into-the-Quality-of-Teachers-Noticing-Expertise-A-Proposed,92019,0,2.html
Timestamp: 2019-04-25 00:01:54+00:00

Document:
Because teachers cannot directly access the processes by which students construct their mathematical knowledge, Teacher Noticing, an activity that involves observing students’ work, interpreting students’ mathematical thinking about a task based on their remarks or actions, and responding to their thinking, is important to grasp students’ mathematical understanding. A possible way for teachers to develop noticing expertise is to engage in a situation focused on student thinking such as clinical interviews. However, noticing students’ thinking productively through clinical interviews remains a challenge, especially for pre-service teachers, not only because it requires a broad range of knowledge but also because of the absence of a framework to inform and evaluate the process. This paper addresses the development of such a framework for evaluating the quality of pre-service teachers’ noticing expertise in a context where students’ thinking is emphasized by removing normal classroom interruptions. It then demonstrates how the framework can be used for this purpose through three empirical examples of pre-service teachers who engaged in an intervention that involved conducting clinical interviews and analyzing students’ mathematical thinking by watching video-recordings of their clinical interviews.
Ball, D. L. (1991). Teaching mathematics for understanding: What do teachers need to know about subject matter? In M. Kennedy (Ed.) Teaching academic subjects to diverse learners (pp. 63-83). New York: Teachers College Press.
Boaler, J., & Humphries, C. (2005). Connecting mathematical ideas: Middle school video cases to support teaching and learning. Portsmouth, NH: Macmillan.
Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teachers’ pedagogical content knowledge of students’ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19(5), 385-401. https://doi.org/10.2307/749173.
Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94. https://doi.org/10.2307/748576.
Colestock. A., & Sherin, M. G. (2009). Teachers' sense making strategies while watching video of mathematics instruction. Journal of Technology and Teacher Education, 17, 7-29.
Confrey, J. (1990). What constructivism implies for teaching. Journal for Research in Mathematics Education. Monograph, 4, 107-122. https://doi.org/10.2307/749916.
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403-434. https://doi.org/10.2307/749875.
Ginsburg, H. P. (1989). Children’s arithmetic: How they learn it and how you teach it (2nd ed.). Austin, TX: ProEd.
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Hackenberg, A. (2005). A model of mathematical learning and caring relations. For the Learning of Mathematics, 25(1), 45-51.
Iterative Model Building Project [IMB]. (2010). M201 Elementary Field Experience Manual (Fall 2010 edition). Indiana University. Funding Agency: NSF Program Discovery Research K-12 (Grant #073214).
Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal of Research in Mathematics Education, 41(2), 169-202.
Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In M. G. Sherin, V. R., Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 97–116). New York: Routledge.
Lampert, M. & Ball, D. L. (1998). Teaching, multimedia and mathematics: Investigations of real practice. New York: Teachers College, Columbia University.
Lee, M. Y. (2013). Pre-service teachers’ ability to understand students’ mathematical thinking: The iterative model building field experience (Unpublished doctoral dissertation). Indiana University, Bloomington.
Mason, J. (2002). Researching your own practice: The discipline of noticing. New York: Routledge.
Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 51-65). New York: Routledge.
Olive, J. (2001). Children’s number sequences: An explanation of Steffe’s constructs and an extrapolation to rational numbers of arithmetic. The Mathematics Educator, 11(1), 4-9.
Philipp, R. A., Ambrose, R., Lamb, 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(5), 438-476.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. NY: Routledge.
Schoenfeld, A. H. (2010). How we think. New York: Routledge.
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 (pp. 223–238). New York: Routledge.
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. 1-13). New York: Routledge.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Hillsdale, NJ: Erlbaum.
Steffe, L. P., & Wiegel, H. G. (1996). On the nature of a model of mathematical learning. In L. Steffe, P. Nesher, P. Cobb, G. Goldin & B. Greer (Eds.), Theories of mathematical learning (pp. 477-498). Mahwah, NJ: Lawrence Erlbaum Associates.
Steffe, L. P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. New York: Praeger.
van Es, E. A. (2011). A framework for learning to notice student thinking. In M.G. Sherin, V. Jacobs, & R. Philipp (Eds.) Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134-151). Routledge: New York.
von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. P. Steffe & J. Gale (Eds.), Constructivism in Education (pp. 3-15). Hillsdale, NJ: Erlbaum.

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.