Research Article
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Year 2024, , 371 - 398, 31.12.2024
https://doi.org/10.52911/itall.1576727

Abstract

References

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172. https://doi.org/10.1023/b:jmte.0000021943.35739.1c
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school teachers’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272. https://doi.org/10.1080/10986060701360910
  • 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
  • Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15. https://doi.org/10.3102/0013189x033008003
  • Brendefur, J. L., Thiede, K., Strother, S., Bunning, K., & Peck, D. (2013). Developing mathematical thinking: Changing teachers’ knowledge and instruction. Journal of Curriculum and Teaching, 2(2), 62–75. https://doi.org/10.5430/jct.v2n2p62
  • Cengiz, N. (2007). What allows teachers to extend student thinking during whole group discussions? [Unpublished doctoral dissertation]. Western Michigan University.
  • Corey, D. L., Williams, S., Monroe, E. E., & Wagner, M. (2020). Teachers’ knowledge of student mathematical thinking in written instructional products. Journal of Mathematics Teacher Education, 24(6), 613–639. https://doi.org/10.1007/s10857-020-09476-y
  • Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124–131. https://doi.org/10.1207/s15430421tip3903_2
  • Empson, S. B., & Junk, D. (2004). Teachers’ knowledge of children’s mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7(2), 121–144. https://doi.org/10.1023/b:jmte.0000021786.32460.7f
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through online discussions. ZDM Mathematics Education, 44(6), 747–759. https://doi.org/10.1007/s11858-012-0425-y
  • Franke, M. L., & Kazemi, E. (2001). Learning to teach mathematics: Focus on student thinking. Theory into Practice, 40(2), 102–109. https://doi.org/10.1207/s15430421tip4002_4
  • Gehrtz, J., Brantner, M., & Andrews, T. C. (2022). How are undergraduate STEM instructors leveraging student thinking? International Journal of STEM Education, 9(1), 1–20. https://doi.org/10.1186/s40594-022-00336-0
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400. https://doi.org/10.5951/jresematheduc.39.4.0372
  • Huang, R., & Shimizu, Y. (2016). Improving teaching, developing teachers and teacher educators, and linking theory and practice through lesson study in mathematics: An international perspective. ZDM, 48(4), 393–409. https://doi.org/10.1007/s11858-016-0795-7
  • Hurd, J., & Licciardo-Musso, L. (2005). Lesson study: Teacher-led professional development in literacy instruction. Language Arts, 82(5), 388–395. https://doi.org/10.58680/la20054415
  • Kelting-Gibson, L. (2013). Analysis of 100 years of curriculum design. International Journal of Instruction, 6(1), 39–58.
  • Kung, D., & Speer, N. (2009). Mathematics teaching assistants learning to teach: Recasting early teaching experiences as rich learning opportunities. Journal of Graduate and Professional Student Development, 12, 1–23.
  • Lee, K. (2006). Teachers’ knowledge of middle school students’ mathematical thinking in algebra word problem solving [Unpublished doctoral dissertation]. Oregon State University.
  • Lewis, C., Perry, R. R., Friedkin, S., & Roth, J. R. (2012). Improving teaching does improve teachers: Evidence from lesson study. Journal of Teacher Education, 63(5), 368–375. https://doi.org/10.1177/0022487112446633
  • Liang, B. (2023). Mental processes underlying a mathematics teacher’s learning from student thinking. Journal of Mathematics Teacher Education, 1–26. https://doi.org/10.1007/s10857-023-09601-7
  • Moon, K. (2023). Developing knowledge of student thinking: Understanding big ideas behind students’ difficulties with connecting representations in algebra. International Journal for Mathematics Teaching and Learning, 24(1), 1–16. https://doi.org/10.4256/ijmtl.v24i1.439
  • National Board for Professional Teaching Standards. (1997). State and local action supporting National Board Certification. Retrieved from https://www.nbpts.org
  • National Comprehensive Center for Teacher Quality. (2011). High-quality professional development for all teachers: Effectively allocating resources. Research & Policy Brief.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  • Pehlivan, C., & Bukova Guzel, E. (2020). Development of mathematics teachers’ moves that support students’ higher order thinking skills through lesson study. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(3), 774–813. https://doi.org/10.16949/turkbilmat.683535
  • Perry, R. R., & Lewis, C. C. (2009). What is successful adaptation of lesson study in the U.S.? Journal of Educational Change, 10(4), 365–391. https://doi.org/10.1007/s10833-008-9069-7
  • Rowland, T., Thwaites, A., & Jared, L. (2011, July). Triggers of contingency in mathematics teaching. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (pp. 73–80). Ankara, Turkey.
  • Schilling, S. G., Blunk, M., & Hill, H. C. (2007). Test validation and the MKT measures: Generalizations and conclusions. Measurement, 5(2–3), 118–128. https://doi.org/10.1080/15366360701487146
  • Takahashi, A. (2014). The role of the knowledgeable other in lesson study: Examining the final comments of experienced lesson study practitioners. Mathematics Teacher Education and Development, 16(1), 4–21.
  • Van Zoest, L. R., Stockero, S. L., & Kratky, J. L. (2010). Beginning mathematics teachers’ purposes for making student thinking public. Research in Mathematics Education, 12(1), 37–52. https://doi.org/10.1080/14794800903569832
  • White, A. L., & Lim, C. S. (2008). Lesson study in Asia Pacific classrooms: Local responses to a global movement. ZDM, 40(6), 915. https://doi.org/10.1007/s11858-008-0138-4
  • Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003
  • Yoshida, M. (1999). Lesson study: A case study of a Japanese approach to improving instruction through school-based teacher development [Unpublished doctoral dissertation]. University of Chicago.

Expanding on Knowledge of Student Thinking through Mathematics Teachers’ Engagement in Lesson Study

Year 2024, , 371 - 398, 31.12.2024
https://doi.org/10.52911/itall.1576727

Abstract

The purpose of this study is to expand on knowledge of student thinking based on the mathematics teachers’ practices in a lesson study process designed for improving teachers’ knowledge of student thinking. The participants of this qualitative case study were three secondary mathematics teachers. The data were gathered from twenty-two hours lessons observations and field notes. By the data analysis, we got nine main components by constant comparison. The main components of knowledge of student thinking were (a) building on students’ mathematical ideas, (b) promoting students’ thinking of mathematics, (c) triggering and considering divergent thoughts, (d) engaging students in mathematical learning, (e) evaluating students’ understanding, (f) motivating students’ learning, (g) considering students’ misconceptions and errors, (h) considering students’ difficulties, and (i) estimating students’ possible ideas and approaches. This study supported the mathematics teachers in developing professional knowledge and also provided to elaborate the content of teachers’ knowledge of student thinking.

References

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172. https://doi.org/10.1023/b:jmte.0000021943.35739.1c
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school teachers’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272. https://doi.org/10.1080/10986060701360910
  • 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
  • Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15. https://doi.org/10.3102/0013189x033008003
  • Brendefur, J. L., Thiede, K., Strother, S., Bunning, K., & Peck, D. (2013). Developing mathematical thinking: Changing teachers’ knowledge and instruction. Journal of Curriculum and Teaching, 2(2), 62–75. https://doi.org/10.5430/jct.v2n2p62
  • Cengiz, N. (2007). What allows teachers to extend student thinking during whole group discussions? [Unpublished doctoral dissertation]. Western Michigan University.
  • Corey, D. L., Williams, S., Monroe, E. E., & Wagner, M. (2020). Teachers’ knowledge of student mathematical thinking in written instructional products. Journal of Mathematics Teacher Education, 24(6), 613–639. https://doi.org/10.1007/s10857-020-09476-y
  • Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124–131. https://doi.org/10.1207/s15430421tip3903_2
  • Empson, S. B., & Junk, D. (2004). Teachers’ knowledge of children’s mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7(2), 121–144. https://doi.org/10.1023/b:jmte.0000021786.32460.7f
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through online discussions. ZDM Mathematics Education, 44(6), 747–759. https://doi.org/10.1007/s11858-012-0425-y
  • Franke, M. L., & Kazemi, E. (2001). Learning to teach mathematics: Focus on student thinking. Theory into Practice, 40(2), 102–109. https://doi.org/10.1207/s15430421tip4002_4
  • Gehrtz, J., Brantner, M., & Andrews, T. C. (2022). How are undergraduate STEM instructors leveraging student thinking? International Journal of STEM Education, 9(1), 1–20. https://doi.org/10.1186/s40594-022-00336-0
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400. https://doi.org/10.5951/jresematheduc.39.4.0372
  • Huang, R., & Shimizu, Y. (2016). Improving teaching, developing teachers and teacher educators, and linking theory and practice through lesson study in mathematics: An international perspective. ZDM, 48(4), 393–409. https://doi.org/10.1007/s11858-016-0795-7
  • Hurd, J., & Licciardo-Musso, L. (2005). Lesson study: Teacher-led professional development in literacy instruction. Language Arts, 82(5), 388–395. https://doi.org/10.58680/la20054415
  • Kelting-Gibson, L. (2013). Analysis of 100 years of curriculum design. International Journal of Instruction, 6(1), 39–58.
  • Kung, D., & Speer, N. (2009). Mathematics teaching assistants learning to teach: Recasting early teaching experiences as rich learning opportunities. Journal of Graduate and Professional Student Development, 12, 1–23.
  • Lee, K. (2006). Teachers’ knowledge of middle school students’ mathematical thinking in algebra word problem solving [Unpublished doctoral dissertation]. Oregon State University.
  • Lewis, C., Perry, R. R., Friedkin, S., & Roth, J. R. (2012). Improving teaching does improve teachers: Evidence from lesson study. Journal of Teacher Education, 63(5), 368–375. https://doi.org/10.1177/0022487112446633
  • Liang, B. (2023). Mental processes underlying a mathematics teacher’s learning from student thinking. Journal of Mathematics Teacher Education, 1–26. https://doi.org/10.1007/s10857-023-09601-7
  • Moon, K. (2023). Developing knowledge of student thinking: Understanding big ideas behind students’ difficulties with connecting representations in algebra. International Journal for Mathematics Teaching and Learning, 24(1), 1–16. https://doi.org/10.4256/ijmtl.v24i1.439
  • National Board for Professional Teaching Standards. (1997). State and local action supporting National Board Certification. Retrieved from https://www.nbpts.org
  • National Comprehensive Center for Teacher Quality. (2011). High-quality professional development for all teachers: Effectively allocating resources. Research & Policy Brief.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  • Pehlivan, C., & Bukova Guzel, E. (2020). Development of mathematics teachers’ moves that support students’ higher order thinking skills through lesson study. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(3), 774–813. https://doi.org/10.16949/turkbilmat.683535
  • Perry, R. R., & Lewis, C. C. (2009). What is successful adaptation of lesson study in the U.S.? Journal of Educational Change, 10(4), 365–391. https://doi.org/10.1007/s10833-008-9069-7
  • Rowland, T., Thwaites, A., & Jared, L. (2011, July). Triggers of contingency in mathematics teaching. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (pp. 73–80). Ankara, Turkey.
  • Schilling, S. G., Blunk, M., & Hill, H. C. (2007). Test validation and the MKT measures: Generalizations and conclusions. Measurement, 5(2–3), 118–128. https://doi.org/10.1080/15366360701487146
  • Takahashi, A. (2014). The role of the knowledgeable other in lesson study: Examining the final comments of experienced lesson study practitioners. Mathematics Teacher Education and Development, 16(1), 4–21.
  • Van Zoest, L. R., Stockero, S. L., & Kratky, J. L. (2010). Beginning mathematics teachers’ purposes for making student thinking public. Research in Mathematics Education, 12(1), 37–52. https://doi.org/10.1080/14794800903569832
  • White, A. L., & Lim, C. S. (2008). Lesson study in Asia Pacific classrooms: Local responses to a global movement. ZDM, 40(6), 915. https://doi.org/10.1007/s11858-008-0138-4
  • Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003
  • Yoshida, M. (1999). Lesson study: A case study of a Japanese approach to improving instruction through school-based teacher development [Unpublished doctoral dissertation]. University of Chicago.
There are 33 citations in total.

Details

Primary Language English
Subjects Other Fields of Education (Other)
Journal Section Research Articles
Authors

Aytuğ Özaltun Çelik 0000-0003-1310-3247

Esra Bukova Guzel 0000-0001-7571-1374

Early Pub Date December 30, 2024
Publication Date December 31, 2024
Submission Date October 31, 2024
Acceptance Date December 12, 2024
Published in Issue Year 2024

Cite

APA Özaltun Çelik, A., & Bukova Guzel, E. (2024). Expanding on Knowledge of Student Thinking through Mathematics Teachers’ Engagement in Lesson Study. Instructional Technology and Lifelong Learning, 5(2), 371-398. https://doi.org/10.52911/itall.1576727

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