Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study

Vecihi S. Zambak; Marta T. Magiera

doi:10.29333/ejmste/92021

Full Text (PDF)

Vecihi S. Zambak ¹, Marta T. Magiera ¹ ^*

More Detail

¹ Marquette University, Department of Mathematics, Statistics and Computer Science, Milwaukee, WI, USA^* Corresponding Author

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.

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

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2018, Volume 14, Issue 11, Article No: em1572

https://doi.org/10.29333/ejmste/92021

Publication date: 06 Jun 2018

Article Views: 2711

Article Downloads: 1006

Open Access References How to cite this article

References

Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2011). Australian Curriculum: Mathematics. Retrieved on August 19, 2017 from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/rationale/.
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.
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/.
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/S0883-0355(02)00004-6.
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York, NY: Springer Science + Business Media. https://doi.org/10.1007/978-0-387-09742-8.
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/BF03024953.
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/s10857-011-9179-7.
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/BF00988593.
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:100999901.
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/s11858-010-0296-z.
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/10.1007/978-3-319-46753-5_20.
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/s10857-015-9301-3.
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.
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.
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
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.
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.
Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959.
Knuth, E. J., Choppin, J. M., & Bieda, K. N. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15(4), 206-211.
Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning. Hillsdale, NJ: Lawrence Erlbaum.
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.
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/10.1007/978-3-319-46753-5_8.
Li, Y., & Lappan, G. (Eds.). (2014). Mathematics curriculum in school mathematics. New York, NY: Springer Science + Business Media. https://doi.org/10.1007/978-94-007-7560-2_1.
Llinares, S. (2013). Professional noticing: A component of the mathematics teacher’s professional practice. Sisyphus Journal of Education, 1(3), 76-93.
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.
Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Routledge-Falmer.
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/mathteaceduc.3.1.0027.
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.
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/10.1080/07370000701632405.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: Author.
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/wp-content/uploads/Math_Standards1.pdf.
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.
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/10.1007/978-3-319-46753-5_7.
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.
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/s10857-015-9307-x.
Salinas, T. M. (2009). Beyond the right answer: Exploring how preservice elementary teachers evaluate student-generated algorithms. Mathematics Educator, 19(1), 27-34.
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/s10763-014-9544-y.
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/s10857-013-9240-9.
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/10.1177/0022487108328155.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.57.1.j463w79r56455411.
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/s10649-013-9475-5.
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/s10857-007-9063-7.
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.0000033083.04005.d3.
Stiff, L. (Ed.). (1999). Developing mathematical reasoning in grades K-12. 1999 NCTM Yearbook. Reston, VA: NCTM.
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/s10857-012-9222-3.
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/10.1177/0022487115574103.
Thompson, D., & Schultz-Farrel, K. (2008). Introduction to reasoning and proof. Grades 6-8. Portsmouth, NH: Heinemann.
Toulmin, S. (1958/2003). The uses of argument. Cambridge: Cambridge University Press.
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/s10857-013-9261-4.
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/10.1007/978-3-319-46753-5_9.
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/10.3102/0034654308320292.

How to cite this article

APA

Zambak, V. S., & Magiera, M. T. (2018). Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), em1572. https://doi.org/10.29333/ejmste/92021

Vancouver

Zambak VS, Magiera MT. Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study. EURASIA J Math Sci Tech Ed. 2018;14(11):em1572. https://doi.org/10.29333/ejmste/92021

AMA

Zambak VS, Magiera MT. Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study. EURASIA J Math Sci Tech Ed. 2018;14(11), em1572. https://doi.org/10.29333/ejmste/92021

Chicago

Zambak, Vecihi S., and Marta T. Magiera. "Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 11 (2018): em1572. https://doi.org/10.29333/ejmste/92021

Harvard

Zambak, V. S., and Magiera, M. T. (2018). Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), em1572. https://doi.org/10.29333/ejmste/92021

MLA

Zambak, Vecihi S. et al. "Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 11, 2018, em1572. https://doi.org/10.29333/ejmste/92021