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Development of Pre-service Middle School Mathematics Teachers’ Skills in Interpretation of Student Thinking in the Context of Lesson Study

Year 2019, Volume: 14 , 67 - 72, 20.09.2019

Abstract

Mathematics
teachers’ knowledge of students’ thinking has an important effect on the
teaching-learning process (Cai, Ding & Wang, 2014; Clarkson & Presmeg,
2008). Teachers who understand student thinking sufficiently can interpret
student thinking effectively and can anticipate student misconceptions,
difficulties, and errors. Furthermore, they can overcome these challenges with
appropriate explanations (An, Kulm & Wu, 2004; Ball, Thames & Phelps,
2008). The research revealed, however, that teachers/pre-service teachers have
difficulty interpreting student thinking (Crepso, 2000; 2003). This led to the
conclusion that pre-service teachers need to develop skills in understanding
and interpreting the student perspective (Hiebert, Morris & Glass 2003).
The scope of this study was to improve pre-service middle school mathematics
teachers’ knowledge and interpretation of student thinking through lesson
study. Three senior pre-service teachers participated in this study.
Pre-service teachers implemented three practice lesson study cycles in a real
classroom. Data was obtained from documents, video recordings, observations,
field notes, and reflective papers. In order to analyze data, content analysis
was used. Results showed that the pre-service teachers had some challenges
knowing and interpreting student thinking at the beginning of the study. As
lesson study cycles proceeded, pre-service teachers began to take into account
student thinking, design and implement lesson plans according to students’
needs and difficulties

References

  • An, S.,Kulm, G. & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teacher in China and the U. S. Journal of Mathematics Teacher Education, 7,145-172. Ball, D. L.,& Forzani. F. (2009). The work of teaching and challenge for teacher education. Journal of Teacher Education, 60(5), 497-511. 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. Bergqvist, T. (2005). How students verify conjectures: Teachers’ expectations. Journal of Mathematics Teacher Education, 8, 171–191. Berk, D. & Hiebert, J. (2009). Improving the mathematics preparation of elementary teachers, one lesson at a time. Teachers and Teaching: Theory and Practice, 15, 337-356. Cai, J., Ding, M., & Wang, T. (2014). How do exemplary Chinese and U.S. mathematics teachers view instructional coherence? Educational Studies in Mathematics, 85(2), 265–280. Carpenter, T. P.,Fennema, E., Peterson, P. L., Chiang, C. P., &Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531. Clarkson, P.,& Presmeg, N. C. (2008). Critical issues in mathematics education: Major contributions of Alan Bishop. Dordrecht, the Netherlands: Springer. Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3, 155–181. Crespo, S. (2003) Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243—270. Creswell, J. W. (2013). Qualitative inquiry & research design: Choosing among five approaches (3rd ed.). Thousand Oaks, CA: SAGE. Doerr, H. M.,& English, L. D. (2004). Learning throughinteractingwithstudents' ways of thinking. In I. Putt, R. Faragher, & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australia. Mathematics Education for the Third Millenium: Towards 2010 (pp. 215–222). Townsville, Queensland: James CookUniversity. Fennema, E., Carpenter, T.P., Franke, M.L., Levi. L.,Jacobs, V. &Empson, S. (1996). A longitudinalstudy of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27 (4), 403-434. Driel, J. H.,&Berry, A. (2010). The Teacher education knowledge base: Pedagogical content knowledge. In B. McGraw, P. L. Peterson, E. Baker, (Eds.). International encyclopaedia of education (pp. 656-661). Elsevier, Oxford. Empson, S. B.,& Junk, D. L. (2004). Teachers' knowledge of children's mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7, 121–144. Fennema, E., M. L. Franke, T. P. Carpenter, & D. A. Carey. (1993). Using children’s knowledge in instruction. American Educational Research Journal. 30(3), 555–583. Franke M.L. & Kazemi E. (2001). Learning to teach Mathematics: Focus on student thinking. Theory into Practice, 40(2), 102-109. Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press. Guskey, T. R. (2003). What makes Professional development effective? Phi Delta Kappan, 84(10), 748-750. Hadjidemetriou, C. & Williams, J. (2002). Teachers' pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group forPsychology of MathematicsEducation (Vol. 3, pp. 57–64). Norwich, UK. Hiebert, J., Morris, A. K., & Glass, B. (2003). Learning to learn to teach: An “experiment” model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222. 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. Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17–35. Nathan, M. J. &Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190. NationalCouncil of Teachers of Mathematics. [NCTM] (2000). Principles and Standards for School Mathematics. Reston, VA. Masingila, J. O. &Doerr, H. M. (2002). Understanding pre-service teachers’ emerging practices through their analyses of multimedia case study of practice. Journal of Mathematics Teacher Education, 5, 235–263. Mcdonald, M., Kazemi, E., & Kavanagh, S. S. (2013). Core practices and pedagogies of teacher education: A call for a common language and collective activity. Journal of TeacherEducation, 64(5), 378-386. McDuffie, A. R. (2014). Mathematics teaching as deliberate practice: An investigation of elementary pre-Service teachers’ reflective thinking during student teaching. Journal of MathematicsTeacher Education, 7, 33–61. Ministry of National Education [MoNE]. (2017a). Öğretmenlik Mesleği Genel Yeterlikleri. M.E.B.: Ankara, otmg.meb.gov.tr/YetOzel.html (01.02.2019 tarihinde erişilmiştir.) Ministry of National Education [MoNE]. (2017b). İlköğretim Matematik Öğretmeni Özel Alan Yeterlikleri. M.E.B.: Ankara, otmg.meb.gov.tr/alanmatematik.html (01.02.2019 tarihinde erişilmiştir.) Ministry of National Education (MoNE) (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar. Ankara, Türkiye Schorr, R. Y. & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 159–174). Mahwah, NJ: Lawrence Erlbaum. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. EducationalResearcher, 15(2), 4-14. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25. Wallach, T.,&Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.
Year 2019, Volume: 14 , 67 - 72, 20.09.2019

Abstract

References

  • An, S.,Kulm, G. & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teacher in China and the U. S. Journal of Mathematics Teacher Education, 7,145-172. Ball, D. L.,& Forzani. F. (2009). The work of teaching and challenge for teacher education. Journal of Teacher Education, 60(5), 497-511. 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. Bergqvist, T. (2005). How students verify conjectures: Teachers’ expectations. Journal of Mathematics Teacher Education, 8, 171–191. Berk, D. & Hiebert, J. (2009). Improving the mathematics preparation of elementary teachers, one lesson at a time. Teachers and Teaching: Theory and Practice, 15, 337-356. Cai, J., Ding, M., & Wang, T. (2014). How do exemplary Chinese and U.S. mathematics teachers view instructional coherence? Educational Studies in Mathematics, 85(2), 265–280. Carpenter, T. P.,Fennema, E., Peterson, P. L., Chiang, C. P., &Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531. Clarkson, P.,& Presmeg, N. C. (2008). Critical issues in mathematics education: Major contributions of Alan Bishop. Dordrecht, the Netherlands: Springer. Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3, 155–181. Crespo, S. (2003) Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243—270. Creswell, J. W. (2013). Qualitative inquiry & research design: Choosing among five approaches (3rd ed.). Thousand Oaks, CA: SAGE. Doerr, H. M.,& English, L. D. (2004). Learning throughinteractingwithstudents' ways of thinking. In I. Putt, R. Faragher, & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australia. Mathematics Education for the Third Millenium: Towards 2010 (pp. 215–222). Townsville, Queensland: James CookUniversity. Fennema, E., Carpenter, T.P., Franke, M.L., Levi. L.,Jacobs, V. &Empson, S. (1996). A longitudinalstudy of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27 (4), 403-434. Driel, J. H.,&Berry, A. (2010). The Teacher education knowledge base: Pedagogical content knowledge. In B. McGraw, P. L. Peterson, E. Baker, (Eds.). International encyclopaedia of education (pp. 656-661). Elsevier, Oxford. Empson, S. B.,& Junk, D. L. (2004). Teachers' knowledge of children's mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7, 121–144. Fennema, E., M. L. Franke, T. P. Carpenter, & D. A. Carey. (1993). Using children’s knowledge in instruction. American Educational Research Journal. 30(3), 555–583. Franke M.L. & Kazemi E. (2001). Learning to teach Mathematics: Focus on student thinking. Theory into Practice, 40(2), 102-109. Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press. Guskey, T. R. (2003). What makes Professional development effective? Phi Delta Kappan, 84(10), 748-750. Hadjidemetriou, C. & Williams, J. (2002). Teachers' pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group forPsychology of MathematicsEducation (Vol. 3, pp. 57–64). Norwich, UK. Hiebert, J., Morris, A. K., & Glass, B. (2003). Learning to learn to teach: An “experiment” model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222. 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. Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17–35. Nathan, M. J. &Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190. NationalCouncil of Teachers of Mathematics. [NCTM] (2000). Principles and Standards for School Mathematics. Reston, VA. Masingila, J. O. &Doerr, H. M. (2002). Understanding pre-service teachers’ emerging practices through their analyses of multimedia case study of practice. Journal of Mathematics Teacher Education, 5, 235–263. Mcdonald, M., Kazemi, E., & Kavanagh, S. S. (2013). Core practices and pedagogies of teacher education: A call for a common language and collective activity. Journal of TeacherEducation, 64(5), 378-386. McDuffie, A. R. (2014). Mathematics teaching as deliberate practice: An investigation of elementary pre-Service teachers’ reflective thinking during student teaching. Journal of MathematicsTeacher Education, 7, 33–61. Ministry of National Education [MoNE]. (2017a). Öğretmenlik Mesleği Genel Yeterlikleri. M.E.B.: Ankara, otmg.meb.gov.tr/YetOzel.html (01.02.2019 tarihinde erişilmiştir.) Ministry of National Education [MoNE]. (2017b). İlköğretim Matematik Öğretmeni Özel Alan Yeterlikleri. M.E.B.: Ankara, otmg.meb.gov.tr/alanmatematik.html (01.02.2019 tarihinde erişilmiştir.) Ministry of National Education (MoNE) (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar. Ankara, Türkiye Schorr, R. Y. & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 159–174). Mahwah, NJ: Lawrence Erlbaum. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. EducationalResearcher, 15(2), 4-14. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25. Wallach, T.,&Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.
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Details

Primary Language English
Journal Section Articles
Authors

Nadide Yılmaz This is me

İ. Elif Yetkın Ozdemır This is me

Publication Date September 20, 2019
Published in Issue Year 2019 Volume: 14

Cite

APA Yılmaz, N., & Yetkın Ozdemır, İ. E. (2019). Development of Pre-service Middle School Mathematics Teachers’ Skills in Interpretation of Student Thinking in the Context of Lesson Study. The Eurasia Proceedings of Educational and Social Sciences, 14, 67-72.