Abstract
This study examined the intersections of preservice elementary teachers’ (PSET) professional noticing (PN) of children’s mathematical thinking, two mathematical knowledge for teaching (MKT) domains: mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK), and two affective domains: attitudes and dispositions toward teaching mathematics. An instructional module focused on PN of children’s early algebraic thinking, as defined by Jacobs et al. (J Res Math Educ 41: 169–202, 2010) to include three components: attending, interpreting, and deciding, was implemented with 170 PSETs. The PSETs, who participated in the instructional module, the implementation group, showed significant positive growth in attending, interpreting, and attitudes toward mathematics. There was no significant change in dispositions toward teaching mathematics and a decrease was observed in PSET deciding and MKT. A comparison group of 126 PSETs enrolled in mathematics methods courses did not participate in the instructional module. PSETs in the comparison group showed a decrease across all measures including attending, interpreting, deciding, attitudes, dispositions, and MKT. Results showed statistically significant connections within and between some of the constructs; however, the limitations of the study call for further investigation.
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13 February 2021
A Correction to this paper has been published: https://doi.org/10.1007/s11858-021-01237-2
References
Aguirre, J., & Speer, N. M. (1999). Examining the relationship between beliefs and goals in teacher practice. The Journal of Mathematical Behavior, 18(3), 327–356.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554.
Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180. https://doi.org/10.3102/0002831209345157.
Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223(1), 3–13.
Brese, F., & Tatto, M. T. (2012). User guide for the TEDS-M international database. Amsterdam: International Association for the Evaluation of Educational Achievement (IEA).
Castro Superfine, A., Fisher, A., Bragelman, J., & Amador, J. M. (2017). Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 409–426). Cham: Springer.
Charalambous, C. Y. (2015). Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: A multiple-case study. Journal of Mathematics Teacher Education, 18, 427–445. https://doi.org/10.1007/s10857-015-9318-7.
Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: Exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23, 579–613. https://doi.org/10.1007/s10857-019-09443-2.
Cole, D. A., & Preacher, K. J. (2014). Manifest variable path analysis: Potentially serious and misleading consequences due to uncorrected measurement error. Psychological Methods, 19(2), 300–315.
Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–24.
Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339–358). Cham: Springer.
Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.
Fisher, M. H., Schack, E. O., Thomas, J., Jong, C., Eisenhardt, S., Tassell, J., & Yoder, M. (2014). Examining the relationship between preservice elementary teachers’ attitudes toward mathematics and professional noticing capacities. In J.-J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 219–237). Berlin: Springer International.
Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassel, J. (2018). Noticing numeracy now!: Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30(2), 209–232.
Fisher, M. H., Thomas, J., Jong, C., Schack, E. O., & Dueber, D. (2019). Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms. School Science and Mathematics, 119(3), 142–149.
Floro, B., & Bostic, J. (2017). A case study of middle school teachers’ noticing during modeling with mathematics tasks. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 73–89). Cham: Springer.
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.
Hanna, W. G. (2012). Examining what inservice elementary teachers notice when presented with instances of students mathematical thinking. Proceedings of the 34rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.
Harry, B., Sturges, K. M., & Klingner, J. K. (2005). Mapping the process: An exemplar of process and challenge in grounded theory analysis. Educational Researcher, 34(2), 3–13.
Hayduk, L. A. (1987). Structural equation modeling with LISREL: Essentials and advances. Baltimore: Johns Hopkins University Press.
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11–30.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235.
Ingram, N., Linsell, C., & Offen, B. (2018). Growing mathematics teachers: Pre-service primary teachers’ relationships with mathematics. Mathematics Teacher Education and Development, 20(3), 41–60.
Jacobs, V. R., & Spangler, D. A. (2017). Research on core practices in K-12 mathematics teaching. In J. Cai (Ed.) Compendium for research in mathematics education (pp. 766–792. National Council of Teachers of Mathematics.
Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.
Jacobs, V. R., Lamb, L. L. C., 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.
Jacobs, V. R., Sherin, M. G., & Philipp, R. A., (2013). Mathematics teacher noticing: A hidden skill of teaching. Work Group presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 723–729. Chicago, IL.
Jacobson, E., & Kilpatrick, J. (2015). Understanding teacher affect, knowledge, and instruction over time: An agenda for research on productive disposition for teaching mathematics. Journal of Mathematics Teacher Education, 18(5), 401–406.
Jong, C., & Hodges, T. E. (2015). Assessing attitudes toward mathematics across teacher education contexts. Journal of Mathematics Teacher Education, 18(5), 407–425.
Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13, 369–387.
Kanyongo, G. Y., Brook, G. P., Kyei-Blankson, L., & Gocmen, G. (2007). Reliability and statistical power: How measurement fallibility affects power and required sample sizes for several parametric and nonparametric statistics. Journal of Modern Applied Statistical Methods, 6(1), 81–90.
Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845–861.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington: National Academy Press.
Krupa, E. E., Huey, M., Lesseig, K., Casey, S., & Monson, D. (2017). Investigating secondary preservice teacher noticing of students’ mathematical thinking. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 49–72). Cham: Springer.
Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805.
Kutaka, T. S., Ren, L., Smith, W. M., Beattie, H. L., Edwards, C. P., Green, J. L., et al. (2018). Examining change in K-3 teachers’ mathematical knowledge, attitudes, and beliefs: The case of Primarily Math. Journal of Mathematics Teacher Education, 21(2), 147–177.
Larochelle, R., & Mammo, B. (2019). Correlations between professional noticing of students’ mathematical thinking and specialized content knowledge. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. St Louis: University of Missouri.
Linacre, J. M. (2018). Winsteps® (Version 4.3.1) [Computer Software]. Beaverton, Oregon: Winsteps.com.
Pehkonen, E., & Toerner, G. (1996). Introduction to the theme: Mathematical beliefs. Zentralblatt für Didaktik der Mathematik, 28, 99–100.
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester, Jr. (Ed.) Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 1, 257–315. Information Age.
Pourdavood, R. G., & Liu, X. (2017). Pre-service elementary teachers’ experiences, expectations, beliefs, and attitudes toward mathematics teaching and learning. International Journal of Learning, Teaching and Educational Research, 16(11), 1–27.
Roesken, B., Pepin, B., & Toerner, G. (2011). Beliefs and beyond: Affect and the teaching and learning of mathematics. ZDM, 43(4), 451.
Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’ competence. ZDM, 48(1), 153–165. https://doi.org/10.1007/s11858-015-0737-9.
Schack, E. O., Fisher, M. H., Thomas, J., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16, 379–397. https://doi.org/10.1007/s10857-013-9240-9.
Schack, E. O., Fisher, M. H., & Wilhelm, J. (Eds.). (2017). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks. New York: Springer.
Schack, E. O., Dueber, D., Jong, C., Thomas, J., & Fisher, M. H. (2019). Computer-programmed decision trees for assessing teacher noticing. Paper presented at the Annual Meeting of the American Educational Research Association. Toronto, Canada.
Schackow, J. B. (2005). Examining the attitudes toward mathematics of preservice elementary school teachers enrolled in an introductory mathematics methods course and the experiences that have influenced the development of these attitudes. Graduate Theses and Dissertations. Retrieved from http://scholarcommons.usf.edu/etd/853.
Schoenfeld, A. H. (2015). What counts, when? Reflection on beliefs, affect, attitude, orientations, habits of mind, grain size, time scale, context, theory, and method. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 395–404). Berlin: Springer International.
Sherin, M. G. (2017). Exploring the boundaries of teacher noticing: Commentary. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 401–408). Cham: Springer.
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.
Shulman, L. S. (1986). Those who understand?: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–23.
Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM, 48, 1–27.
Stockero, S. L. (2008). Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers. Journal of Mathematics Teacher Education, 11, 373. https://doi.org/10.1007/s10857-008-9079-7.
Swars, S. L., Smith, S. Z., Smith, M. E., Carothers, J., & Myers, K. (2018). The preparation experiences of elementary mathematics specialists: examining influences on beliefs, content knowledge, and teaching practices. Journal of Mathematics Teacher Education, 21(2), 123–145.
Tapia, M., & Marsh, G. E., II. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8, 16–21.
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3–25.
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. 97–116). New York: Routledge.
Wilkins, J. L. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139–164.
Wright, B. D., & Linacre, J. M. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370.
Acknowledgements
This research was supported by a collaborative grant from the National Science Foundation IUSE Awards: 1431098, 1431133, and 1431631. The opinions expressed herein are those of the authors and do not necessarily reflect views of the National Science Foundation.
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Jong, C., Schack, E.O., Fisher, M.H. et al. What role does professional noticing play? Examining connections with affect and mathematical knowledge for teaching among preservice teachers. ZDM Mathematics Education 53, 151–164 (2021). https://doi.org/10.1007/s11858-020-01210-5
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DOI: https://doi.org/10.1007/s11858-020-01210-5