11/2018 vol. 14
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RESEARCH PAPER
Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study
Vecihi S. Zambak 1
,
 
Marta T. Magiera 1
 
 
 
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1
Marquette University, Department of Mathematics, Statistics and Computer Science, Milwaukee, WI, USA
 
 
Publication date: 2018-06-06
 
 
Corresponding author
Marta T. Magiera   

Marquette University, Department of Mathematics, Statistics and Computer Science, Milwaukee, WI, USA
 
 
EURASIA J. Math., Sci Tech. Ed 2018;14(11):em1572
DOI: https://doi.org/10.29333/ejmste/92021
 
 
Article (PDF)
References (52)
 
KEYWORDS
pre-service teacher education
professional noticing of student
mathematical reasoning and strategies
assessment of the validity of student reasoning
and strategies
pre-service teachers’ pedagogical decisions
 
TOPICS
Mathematics Education
 
ABSTRACT
This study sheds light on three teaching competencies: Pre-service teachers’ (PSTs’) professional noticing of student mathematical reasoning and strategies, their ability to assess the validity of student reasoning and strategies, and to select student strategy for class discussion. Our results reveal that PSTs with strong awareness of mathematically significant aspects of student reasoning and strategies (focused noticing) were better positioned to assess the validity of student reasoning and strategies. PSTs with higher strategy evaluation skills were more likely to choose the strategy to engage class in justification or to advance students’ conceptual understanding compared to PSTs with low strategy evaluation skills.
 
REFERENCES (52)
1.
Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2011). Australian Curriculum: Mathematics. Retrieved on August 19, 2017 from https://www.australiancurricul....
Google Scholar
 
 
2.
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/10.1177/002248....
CrossRef
 
Google Scholar
 
 
3.
Bautista, A., Brizuela, B. M., Glennie, C. R., & Caddle, M. C. (2014, July). Mathematics teachers attending and responding to students’ thinking: Diverse paths across diverse assignments. International Journal for Mathematics Teaching and Learning, Retrieved on September 4, 2017 from http://www.cimt.org.uk/journal....
Google Scholar
 
 
4.
Berliner, D. C. (2001). Learning about and learning from expert teachers. International Journal of Educational Research, 35(5), 463-482. https://doi.org/10.1016/S0883-....
CrossRef
 
Google Scholar
 
 
5.
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York, NY: Springer Science + Business Media. https://doi.org/10.1007/978-0-....
CrossRef
 
Google Scholar
 
 
6.
Castro, B. (2004). Pre-service teachers’ mathematical reasoning as an imperative for codified conceptual pedagogy in algebra: A case study of teacher education. Asia Pacific Education Review, 5(2), 157-166. https://doi.org/10.1007/BF0302....
CrossRef
 
Google Scholar
 
 
7.
Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14(5), 355-374. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
8.
Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3-21. https://doi.org/10.1007/BF0098....
CrossRef
 
Google Scholar
 
 
9.
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. https://doi.org/10.1023/A:1009....
CrossRef
 
Google Scholar
 
 
10.
Crespo, S., Oslund, J. A., & Parks, A. N. (2011). Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion. ZDM, 43(1), 119-131. https://doi.org/10.1007/s11858....
CrossRef
 
Google Scholar
 
 
11.
Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339-358). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-....
CrossRef
 
Google Scholar
 
 
12.
Ding, L., & Domínguez, H. (2016). Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. Journal of Mathematics Teacher Education, 19(4), 325-347. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
13.
Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s ‘noticing of students’ mathematical thinking in problem solving. The Mathematics Enthu¬siast, 10(1&2), 441-468.
Google Scholar
 
 
14.
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651.
CrossRef
 
Google Scholar
 
 
15.
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
Google Scholar
 
 
16.
Ingersoll, R. M., & Perda, D. (2008). The status of teaching as a profession. In J. Ballantine & J. Spade (Eds.), Schools and society: A sociological approach to education (pp. 106-118). Los Angeles, CA: Pine Forge Press.
Google Scholar
 
 
17.
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
 
 
18.
Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/414995....
CrossRef
 
Google Scholar
 
 
19.
Knuth, E. J., Choppin, J. M., & Bieda, K. N. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15(4), 206-211.
Google Scholar
 
 
20.
Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning. Hillsdale, NJ: Lawrence Erlbaum.
Google Scholar
 
 
21.
Larsson, M., & Ryve, A. (2011). Effective teaching through problem‐solving by sequencing and connecting student solutions. In G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula‐Sormunen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero, & K. Waege (Eds.), Proceedings of NORMA11: The sixth Nordic conference on mathematics education in Reykjavik (pp. 425–434). Reykjavik: University of Iceland Press.
Google Scholar
 
 
22.
Lee, M. Y., & Choy, B. H. (2017). Mathematical teacher noticing: The key to learning from lesson study. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 121-140). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-....
CrossRef
 
Google Scholar
 
 
23.
Li, Y., & Lappan, G. (Eds.). (2014). Mathematics curriculum in school mathematics. New York, NY: Springer Science + Business Media. https://doi.org/10.1007/978-94....
CrossRef
 
Google Scholar
 
 
24.
Llinares, S. (2013). Professional noticing: A component of the mathematics teacher’s professional practice. Sisyphus Journal of Education, 1(3), 76-93.
Google Scholar
 
 
25.
Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51. https://doi.org/10.2307/749097.
CrossRef
 
Google Scholar
 
 
26.
Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Routledge-Falmer.
Google Scholar
 
 
27.
Meikle, E. (2014). Preservice teachers’ competencies to select and sequence students’ solution strategies for productive whole-class discussions. Mathematics Teacher Educator, 3(1), 27-57. https://doi.org/10.5951/mathte....
CrossRef
 
Google Scholar
 
 
28.
Monoyiou, A., Xistouri, X., & Philippou, G. (2006). Primary students’ reasoning in problem solving and teachers’ evaluation of their arguments. In J. Novotna, H., Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 177-184). Prague: PME.
Google Scholar
 
 
29.
Morris, A. K. (2007). Factors affecting pre-service teachers’ evaluations of the validity of students’ mathematical arguments in classroom contexts. Cognition and Instruction, 25(4), 479-522. https://doi.org/10.1080/073700....
CrossRef
 
Google Scholar
 
 
30.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
Google Scholar
 
 
31.
National Council of Teachers of Mathematics. (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: Author.
Google Scholar
 
 
32.
NGA & CCSSO (National Governors Association Center for Best Practices & Council of Chief State School Officers). (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. Retrieved on August 19, 2017 from http://www.corestandards.org/w....
Google Scholar
 
 
33.
Peterson, B. E., & Leatham, K. R. (2009). Learning to use students’ mathematical thinking to orchestrate a class discussion. In L. Knott (Ed.), The role of mathematics discourse in producing leaders of discourse (pp. 99-128). Charlotte, NC: Information Age Publishing.
Google Scholar
 
 
34.
Phillipp, R., Fredenberg, M., & Hawthorn, C. (2017). Examining student thinking thought teacher noticing: Commentary. In E.O. Schack, M. H. Fisher, & J. A. Williams (Eds.). Teacher Noticing: Bridging and broadening perspectives, contexts, and frameworks. (pp. 113-120). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-....
CrossRef
 
Google Scholar
 
 
35.
Reiss, K., Klieme, E., & Heinze, A. (2001). Prerequisites for the understanding of proofs in the geometry classroom. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 97-104). Utrecht, the Netherlands: Utrecht University.
Google Scholar
 
 
36.
Roller, S. A. (2016). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education, 19(5), 477-498. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
37.
Salinas, T. M. (2009). Beyond the right answer: Exploring how preservice elementary teachers evaluate student-generated algorithms. Mathematics Educator, 19(1), 27-34.
Google Scholar
 
 
38.
Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305-1329. https://doi.org/10.1007/s10763....
CrossRef
 
Google Scholar
 
 
39.
Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379-397. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
40.
Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20-37. https://doi.org/10.1177/002248....
CrossRef
 
Google Scholar
 
 
41.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.....
CrossRef
 
Google Scholar
 
 
42.
Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49-70. https://doi.org/10.1007/s10649....
CrossRef
 
Google Scholar
 
 
43.
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. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
44.
Steinberg, R. M., Empson, S. B., & Carpenter, T. P. (2004). Inquiry into children’s mathematical thinking as a means to teacher change. Journal of Mathematics Teacher Education, 7(3), 237-267. https://doi.org/10.1023/B:JMTE....
CrossRef
 
Google Scholar
 
 
45.
Stiff, L. (Ed.). (1999). Developing mathematical reasoning in grades K-12. 1999 NCTM Yearbook. Reston, VA: NCTM.
Google Scholar
 
 
46.
Stockero, S. L., & van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16(2), 125-147. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
47.
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. https://doi.org/10.1177/002248....
CrossRef
 
Google Scholar
 
 
48.
Thompson, D., & Schultz-Farrel, K. (2008). Introduction to reasoning and proof. Grades 6-8. Portsmouth, NH: Heinemann.
Google Scholar
 
 
49.
Toulmin, S. (1958/2003). The uses of argument. Cambridge: Cambridge University Press.
Google Scholar
 
 
50.
Tyminski, A. M., Zambak, V. S., Drake, C., & Land, T. J. (2014). Using representations, decomposition, and approximations of practices to support prospective elementary mathematics teachers’ practice of organizing discussions. Journal of Mathematics Teacher Education, 17(5), 463-487. https://doi.org/10.1007/s10857....
CrossRef
 
Google Scholar
 
 
51.
van den Kieboom, L., Magiera, M. T., & Moyer, J. (2017). Learning to notice student thinking about the equal sign: K-8 pre-service teachers’ experiences in a teacher preparation program. In E. O., Schack, M. H., Fisher, & J. Wilhelm, (Eds.), Teacher noticing – Bridging and broadening perspectives, contexts, and frameworks, (pp. 141-159). New York, NY: Springer. https://doi.org/10.1007/978-3-....
CrossRef
 
Google Scholar
 
 
52.
Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516-551. https://doi.org/10.3102/003465....
CrossRef
 
Google Scholar
 
 
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