Supporting Pre-service Mathematics Teachers’ Professional Noticing of Students’ Reasoning About Length

Busra Caylan Ergene 1 * , Mine Isiksal Bostan 2
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1 Department of Science and Mathematics Education, Sakarya University, Sakarya, TURKEY
2 Department of Science and Mathematics Education, Middle East Technical University, Ankara, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 1, pp. 50-70. https://doi.org/10.30935/scimath/11384
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ABSTRACT

This study examined how the levels-of-sophistication framework supports pre-service mathematics teachers’ professional noticing of students’ reasoning about length measurement. Three pre-service teachers were asked to analyse students’ written solutions in the tasks that reflected different characteristics of students’ reasoning before and after participating in an intervention based on the “Levels of Sophistication in Students’ Reasoning about Length” (Battista, 2006) conceptual framework The findings indicated that the levels-of-sophistication framework enabled the pre-service teachers to give their full attention to students’ mathematical understanding and to provide proper instruction to support students’ learning and hence, it had a significant role in the improvement of the professional noticing skills of these pre-service teachers. Thus, it is suggested that the levels-of-sophistication framework can be used to support pre-service teachers’ professional noticing skills and to better prepare them to teach length measurement based on students’ reasoning.

CITATION

Caylan Ergene, B., & Isiksal Bostan, M. (2022). Supporting Pre-service Mathematics Teachers’ Professional Noticing of Students’ Reasoning About Length. European Journal of Science and Mathematics Education, 10(1), 50-70. https://doi.org/10.30935/scimath/11384

REFERENCES

  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analysis misconceptions in homework. International Journal of Science and Mathematics Education, 10, 717-753. https://doi.org/10.1007/s10763-011-9324-x
  • Baldinger, E. E. (2019). Reasoning about student written work through self-comparison: How pre-service secondary teachers use their own solutions to analyze student work. Mathematical Thinking and Learning, 22(1), 56-78, https://doi.org/10.1080/10986065.2019.1624930
  • Barrett, J. E., Clements, D. H., & Sarama, J. (2017). Children’s measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume (JRME Monograph No. 16). National Council of Teachers of Mathematics.
  • Barrett, J. E., Clements, D. H., Klanderman, D., Pennisi, S. J., & Polaki, M. V. (2006). Students’ coordination of geometric reasoning and measuring strategies on a fixed perimeter task: Developing mathematical understanding of linear measurement. Journal for Research in Mathematics Education, 37(3), 187-221.
  • Battista, M. T. (2003, July). Levels of sophistication in elementary students’ reasoning about length [Paper presentation]. 27th annual conference of the International Group for the Psychology of Mathematics Education, Honolulu, HI.
  • Battista, M. T. (2006). Understanding the development of students’ thinking about length. Teaching Children Mathematics, 13(3), 140-146. https://doi.org/10.5951/TCM.13.3.0140
  • Battista, M. T. (2017). Reasoning and sense making in the elementary grades: 6-8. National Council of Teachers of Mathematics.
  • Bragg, P., & Outhred, N. L. (2004). A measure of rulers—the importance of units in a measure. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 159-166). PME.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20, 309-333. https://doi.org/10.1007/s10857-016-9343-1
  • Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. In D. H. Clements, J. Sarama, & A. M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 299-317). Erlbaum. https://doi.org/10.4324/9781410609236
  • Cooper, S. (2009). Preservice teachers’ analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355-362. https://doi.org/10.1111/j.1949-8594.2009.tb18105.x
  • Corcoran, D. (2012). Knowledge quartet. http://www.knowledgequartet.org/391/atb-scenario-2/
  • Curry, M., Mitchelmore, M, & Outhred, L. (2006). Development of children’s understanding of length, area, and volume principles. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 377-384). PME.
  • Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassell, J. (2018). Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30, 209-232. https://doi.org/10.1007/s13394-017-0228-0
  • Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225-256). Information Age Publishing.
  • Goodell, J. E. (2006). Using critical incident reflections: A self-study as a mathematics teacher educator. Journal of Mathematics Teacher Education, 9(3), 221-248. https://doi.org/10.1007/s10857-006-9001-0
  • Grant, T. J., & Kline, K. (2003). Developing building blocks of measurement with young children. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 Yearbook (pp. 46-56). National Council of Teachers of Mathematics.
  • Ivars, P., Fernández, C., & Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18, 529-548. https://doi.org/10.1007/s10763-019-09973-4
  • 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(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
  • 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). Routledge.
  • Jaworski, B. (2004). Insiders and outsiders in mathematics teaching development: The design and study of classroom activity. Research in Mathematics Education, 6(1), 3-22. https://doi.org/10.1080/14794800008520127
  • Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.
  • Lee, M. Y. (2021). Using a technology tool to help pre-service teachers notice students’ reasoning and errors on a mathematics problem. ZDM Mathematics Education, 53, 135-149. https://doi.org/10.1007/s11858-020-01189-z
  • Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179-192). National Council of Teachers of Mathematics.
  • Luna, M., Russ, R., & Colestock, A. (2009, April). Teacher noticing in-the-moment of instruction: The case of one high-school teacher [Paper presentation]. Annual meeting of the National Association for Research in Science Teaching (NARST), Garden Grove, CA.
  • Martin, G. W., & Strutchens, M. E. (2000). Geometry and measurement. In E. A. Silver & P. A. Kenney (Eds.), Results from the seventh mathematics assessment of the national assessment of educational progress (pp. 193-234). National Council of Teachers of Mathematics.
  • Martin, J. D. (2007). Fourth graders concurrently investigating perimeter, area, surface area, and volume [Unpublished doctoral dissertation]. Tufts University.
  • Mason, J. (2011). Noticing: Roots and branches. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35-50). Routledge.
  • Ministry of National Education (MoNE) (2018). Matematik dersi öğretim programı (Ilkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) [Mathematics curriculum (Primary and middle school Grades 1, 2, 3, 4, 5, 6, 7 and 8)]. MEB.
  • Monson, D., Krupa, E., Lesseig, K., & Casey, S. (2020). Developing secondary prospective teachers’ ability to respond to student work. Journal of Mathematics Teacher Education, 23, 209-232. https://doi.org/10.1007/s10857-018-9420-8
  • Moreno, M., Sánchez-Matamoros, G., Callejo, M. L., Pérez-Tyteca, P., & Llinares, S. (2021). How prospective kindergarten teachers develop their noticing skills: The instrumentation of a learning trajectory. ZDM Mathematics Education, 53, 57-72. https://doi.org/10.1007/s11858-021-01234-5
  • Moyer-Packenham, M. S. (2001). Links to literature: using representations to explore perimeter and area. Teaching Children Mathematics, 8(1), 52-59. https://doi.org/10.5951/TCM.8.1.0052
  • Outhred, L., Mitchelmore, M., McPhail, D., & Gould, P. (2003). Count me into measurement: A program for the early elementary school. In D. H. Clements (Ed.), Learning and teaching measurement (Vol. 1, pp. 81-99). National Council of Teachers of Mathematics.
  • 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, 1305-1329. https://doi.org/10.1007/s10763-014-9544-y
  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123-140. https://doi.org/10.1007/s10857-007-9029-9
  • Sarama, J., & Clements, D. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. https://doi.org/10.4324/9780203883785
  • 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
  • Shin, D. (2020). Prospective mathematics teachers’ professional noticing of students’ reasoning about mean and variability. Canadian Journal of Science, Mathematics and Technology Education, 20, 423-440. https://doi.org/10.1007/s42330-020-00091-w
  • Shin, D. (2021). Preservice mathematics teachers’ selective attention and professional knowledge–based reasoning about students’ statistical thinking. International Journal of Science and Mathematics Education, 19, 1037-1055. https://doi.org/10.1007/s10763-020-10101-w
  • Simpson, A., & Haltiwanger, L. (2017). “This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20, 335-355. https://doi.org/10.1007/s10857-016-9352-0
  • Son, J. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49-70. https://doi.org/10.1007/s10649-013-9475-5
  • Stockero, S. L., Leatham, K. R., Van Zoest, L. R., & Peterson, B. E. (2017a). Noticing distinctions among and within instances of student mathematical thinking. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 467-480). Springer. https://doi.org/10.1007/978-3-319-46753-5_27
  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017b). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395. https://doi.org/10.1016/j.tate.2017.01.006
  • Strauss, A., & Corbin, J. (1994). Grounded theory methodology: An overview. In N. K. Denzin, & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 273-285). Sage Publications, Inc.
  • Tan Sisman, G., & Aksu, M. A. (2016). Study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14, 1293-1319. https://doi.org/10.1007/s10763-015-9642-5
  • Tasdan, B. T., Erduran, A., & Çelik, A. (2015). A daunting task for pre-service mathematics teachers: Developing students’ mathematical thinking. Educational Research and Reviews, 10(16), 2276-2289. https://doi.org/10.5897/ERR2015.2361
  • Tirosh, D., & Stavy, S. (1999). Intuitive rules: A way to explain and predict students reasoning. Educational Studies in Mathematics, 38, 51-61. https://doi.org/10.1023/A:1003436313032
  • Tsamir, P., & Mandel, N. (2000). The intuitive rule same A - same B: The case of area and perimeter. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 225-232). PME.
  • Ulusoy, F. (2020). Prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Teaching and Teacher Education, 94, 103103. https://doi.org/10.1016/j.tate.2020.103103
  • Ulusoy, F., & Çakıroğlu, E. (2020). Exploring prospective teachers’ noticing of students’ understanding through micro-case videos. Journal of Mathematics Teacher Education, 24, 253-282. https://doi.org/10.1007/s10857-020-09457-1
  • van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Information Technology for Teacher Education, 10(4), 571-596.
  • Warshauer, H. K., Starkey, C., Herrera, C. A., & Smith, S. (2021). Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematics Teacher Education, 24, 89-121. https://doi.org/10.1007/s10857-019-09451-2
  • Yang, Y., & Ricks, T. E. (2012). How crucial incidents analysis support Chinese lesson study. International Journal for Lesson and Learning Studies, 1(1), 41-48. https://doi.org/10.1108/20468251211179696