The Korea Society Of Educational Studies In Mathematics
[ Special ]
Journal of Educational Research in Mathematics - Vol. 30, No. SP1, pp.185-198
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 Aug 2020
DOI: https://doi.org/10.29275/jerm.2020.08.sp.1.185

Korean Teachers’ Mathematical Knowledge for Teaching in Algebraic Reasoning

Yeon Kim*
*Professor, Silla University, South Korea

Email: yeonkim10@silla.ac.kr

Please cite this article as: Kim, Y. Korean teachers’ mathematical knowledge for teaching in algebraic reasoning.

Abstract

To collect information about teachers concerning mathematical knowledge for teaching and find out what needs to be considered in developing a curriculum to teach it, the current study surveyed 137 secondary teachers and interviewed thirteen of them in Korea. The survey and interviews used the assessment of mathematical knowledge for teaching about algebra I, which was developed as part of the Measures of Effective Teaching project. The correct response rate of Korean teachers was very high, but there were some differences found in the areas of algebraic reasoning. Furthermore, mathematical analysis is important in assessing students’ algebraic reasoning, and each teacher’s typical teaching method is formidable in evaluating students’ reasoning. Implication is discussed for the improvement of teachers’ mathematical knowledge for teaching algebra.

Keywords:

Mathematical knowledge for teaching, Mathematical reasoning, The Measures of Effective Teaching project, Algebra, South Korea

Acknowledgments

Earlier versions of this paper were presented at the annual meeting of the American Educational Research Association, New York, NY, 2018 and at a conference of 2016 Korea Society of Educational Studies in Mathematics. This paper is part of broader research on mathematical knowledge for teaching, conducted in collaboration with Soo Jin Lee and Inah Ko, whom I wish to thank for their help in initiating this research.

Endnotes

There was a significant difference in the rates of Korean teachers’ correct answers for all items (M=0.80, SD=0.21) and those of U.S. teachers (M=0.60, SD=0.25); t(28)=3.25, p=0.001. Analysis of the rates of correct answers for U.S. teachers are based on the data from Phelps et al. (2014).

References

  • American Educational Research Association, American Psychological Association, & National Council on Measurement in Education (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
  • Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272. [https://doi.org/10.1080/10986060701360910]
  • Attorps, I. (2003). Teachers’ images of the ‘equation’ concept. European Research in Mathematics Education, 3, 1-8.
  • Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey-Bass.
  • 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]
  • Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458-474. [https://doi.org/10.1086/596996]
  • Belfort, E., Guimaraes, L., & Barbastefano, R. (2001). Tertiary algebra and secondary classroom practices in number and algebra: Closing the gap. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra(Proceedings of the 12th ICMI Study Conference, (pp. 79-86). Melbourne, Australia: The University of Melbourne.
  • Blömeke, S., & Paine, L. W. (2008). Getting the fish out of the water: Considering benefits and problems of doing research on teacher education at an international level. Teaching and Teacher Education, 24(8), 2027-2037. [https://doi.org/10.1016/j.tate.2008.05.006]
  • Caglayan, G. (2013). Prospective mathematics teachers’ sense making of polynomial multiplication and factorization modeled with algebra tiles. Journal of Mathematics Teacher Education, 16(5), 349-378. [https://doi.org/10.1007/s10857-013-9237-4]
  • Cai, J., & Knuth, E. (Eds.). (2011). Early algebraization: A global dialogue from multiple perspectives. Heidelberg, Germany: Springer. [https://doi.org/10.1007/978-3-642-17735-4]
  • Chazan, D. (1999). On teachers’ mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra. International Journal of Computers for Mathematical Learning, 4(2–3), 121-149. [https://doi.org/10.1023/A:1009875213030]
  • Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.
  • Chazan, D., Larriva, C., & Sandow, D. (1999). What kind of mathematical knowledge supports teaching for "conceptual understanding"? Preservice teachers and the solving of equations. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 193-200). Haifa, Israel: Technion Printing Center.
  • Chazan, D., Yerushalmy, M., & Leikin, R. (2008). An analytic conception of equation and teachers’ views of school algebra. The Journal of Mathematical Behavior, 27(2), 87-100. [https://doi.org/10.1016/j.jmathb.2008.07.003]
  • Chinnappan, M., & Thomas, M. (2001). Prospective teachers’ perspectives on function representations. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and beyond. Proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia (pp. 155-162). Sydney: MERGA.
  • Cohen, D. K. (2011). Teaching and its predicaments. Cambridge, MA: Harvard University Press. [https://doi.org/10.4159/harvard.9780674062788]
  • Cole, Y. (2012). Assessing elemental validity: the transfer and use of mathematical knowledge for teaching measures in Ghana. ZDM, 44(3), 415-426. [https://doi.org/10.1007/s11858-012-0380-7]
  • Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197. [https://doi.org/10.1007/s10857-008-9072-1]
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94-116. [https://doi.org/10.5951/jresematheduc.24.2.0094]
  • Haimes, D. H. (1996). The implementation of a “function” approach to introductory algebra: A case study of teacher cognitions, teacher actions, and the intended curriculum. Journal for Research in Mathematics Education, 27(5), 582-602. [https://doi.org/10.5951/jresematheduc.27.5.0582]
  • Heid, M. K., Blume, G. W., Zbiek, R. M., & Edwards, B. S. (1999). Factors that influence teachers learning to do interviews to understand students’ mathematical understandings. Educational Studies in Mathematics, 37(3), 223–249. [https://doi.org/10.1023/A:1003657820047]
  • Hiebert, J., & Morris, A. K. (2012). Teaching, rather than teachers, as a path toward improving classroom instruction. Journal of Teacher Education, 63(2), 92-102. [https://doi.org/10.1177/0022487111428328]
  • 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., Umland, K., Litke, E., & Kapitula, L. R. (2012). Teacher quality and quality teaching: Examining the relationship of a teacher assessment to practice. American Journal of Education, 118(4), 489-519. [https://doi.org/10.1086/666380]
  • Hitt, F. (1994). Teachers’ difficulties with the construction of continuous and discontinuous functions. Focus on Learning Problems in Mathematics, 16(4), 10–20.
  • Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematical Behavior, 31(4), 417-430. [https://doi.org/10.1016/j.jmathb.2012.06.001]
  • Izsák, A., Çağlayan, G., & Olive, J. (2009). Meta-representation in an algebra I classroom. The Journal of the Learning Sciences, 18(4), 549-587. [https://doi.org/10.1080/10508400903191912]
  • Kim, Y. (2014). A comparison study of curricular of teacher education for elementary teachers in South Korea and the United States: Focusing on opportunities to learn teaching mathematics. Journal of Educational Research in Mathematics, 24(4), 555-572.
  • Kim, Y. (2016). Interview prompts to uncover mathematical knowledge for teaching: focus on providing written feedback. The Mathematics Enthusiast, 13(1), 71-92.
  • Koellner, K., Jacobs, J., Borko, H., Schneider, C., Pittman, M. E., Eiteljorg, E., . . . Frykholm, J. (2007). The problem-solving cycle: A model to support the development of teachers' professional knowledge. Mathematical Thinking and Learning, 9(3), 273-303. [https://doi.org/10.1080/10986060701360944]
  • Lewis, J., & Blunk, M. (2012). Reading between the lines: Teaching linear algebra. Journal of Curriculum Studies, 44(4), 515-536. [https://doi.org/10.1080/00220272.2012.716975]
  • Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274. [https://doi.org/10.5951/jresematheduc.29.3.0248]
  • Lynch, K., & Star, J. R. (2014). Teachers’ views about multiple strategies in middle and high school mathematics. Mathematical Thinking and Learning, 16(2), 85-108. [https://doi.org/10.1080/10986065.2014.889501]
  • McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584-615. [https://doi.org/10.5951/jresematheduc.43.5.0584]
  • Moses, R. P., & Cobb, C. E. (2001). Math literacy and civil rights. Boston: Beacon Press.
  • Mosvold, R., & Fauskanger, J. (2009). Challenges of translating and adapting the MKT measures for Norway. Paper presented at the American Educational Research Annual Meeting in San Diego, CA.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education.
  • Ng, D. (2012). Using the MKT measures to reveal Indonesian teachers’ mathematical knowledge: challenges and potentials. ZDM, 44(3), 401-413. [https://doi.org/10.1007/s11858-011-0375-9]
  • Norman, A. (1992). Teachers’ mathematical knowledge of the concept of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (Vol. 25, MAA Notes, pp. 215-232). Washington, DC: Mathematical Association of America.
  • Phelps, G., Weren, B., Croft, A., & Gitomer, D. (2014). Developing content knowledge for teaching assessments for the Measures of Effective Teaching study (ETS Research Report No. RR-14-33). Princeton, NJ: Educational Testing Service. [https://doi.org/10.1002/ets2.12031]
  • Postelnicu, V. (2011). Student difficulties with linearity and linear functions and teachers' understanding of student difficulties. Unpublished doctoral dissertation, Arizona State University, Tempe.
  • Rockoff, J. E., Jacob, B. A., Kane, T. J., & Staiger, D. O. (2011). Can you recognize an effective teacher when you recruit one? Education Finance and Policy, 6(1), 43-74. [https://doi.org/10.1162/EDFP_a_00022]
  • Sato, M. (2014). What is the underlying conception of teaching of the edTPA? Journal of Teacher Education, 65(5), 421-434. [https://doi.org/10.1177/0022487114542518]
  • Schmidt, W. H., Houang, R. T., Cogan, L., Blömeke, S., Tatto, M. T., Hsieh, F. J., ...Paine, L. (2008). Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries. ZDM, 40(5), 735-747. [https://doi.org/10.1007/s11858-008-0115-y]
  • Sherin, M. G. (2002). When teaching becomes learning. Cognition and Instruction, 20(2), 119-150. [https://doi.org/10.1207/S1532690XCI2002_1]
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. [https://doi.org/10.3102/0013189X015002004]
  • Stein, M. K., Baxter, J., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27(4), 639-663. [https://doi.org/10.3102/00028312027004639]
  • Strauss, A. L., & Corbin, J. M. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage Publications.
  • Stump, S. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11(2), 124-144. [https://doi.org/10.1007/BF03217065]
  • Stump, S. (2001). Developing preservice teachers’ pedagogical content knowledge of slope. Journal of Mathematical Behavior, 20, 207-227. [https://doi.org/10.1016/S0732-3123(01)00071-2]
  • Tanisli, D., & Kose, N. Y. (2013). Pre-Service Mathematics Teachers' Knowledge of Students about the Algebraic Concepts. Australian Journal of Teacher Education, 38(2), 1-18. [https://doi.org/10.14221/ajte.2013v38n2.1]
  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64. [https://doi.org/10.1023/A:1003011913153]
  • Wilson, M. R. (1994). One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25(4), 346-370. [https://doi.org/10.5951/jresematheduc.25.4.0346]
  • Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching: perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12, 263-281. [https://doi.org/10.1080/10986061003786349]