The Effect of Lesson Study on Pre-service Teachers' Noticing Skills Towards Misconceptions

Year 2024, Volume: 17 Issue: 3, 643 - 675, 25.07.2024

Yasemin Türk Adnan Baki

https://doi.org/10.30831/akukeg.1365907

Abstract

The aim of the study is to examine how lesson study activities affect pre-service classroom teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 pre-service teachers. The data were obtained from the observation form, video recordings, reflection reports and content notes in order to reveal how the lesson study model affected the noticing development of pre-service teachers. In addition to these, the "video exam" at the end of the Teaching Practicum-II course also constituted one of the data collection tools. Descriptive analysis was used in the study. The data obtained were analyzed by adapting the theoretical framework of "Levels of Noticing of Students' Mathematical Thinking" developed by van Es (2011) as "Levels of Noticing of Students' Misconceptions" in order to reveal pre-service teachers' noticing of students' mathematical thinking. As a result of the study, it was concluded that the noticing skills of the lesson study group pre-service teachers, were mainly level 3 or level 4, while the noticing skills of the comparison group pre-service teachers were mainly level 1 and level 2.

Keywords

noticing, lesson study, teacher education, misconception

Ethical Statement

Konu : Etik Kurul Belgesi Sayı : E-81614018-000-2100005124 09.12.2021

References

• Ainley, J., & Luntley, M. (2007). The role of attention in expert classroom practice. Journal of Mathematics Teacher Education, 10(1), 3-22.
• Akbaba-Dağ, S. (2014). Mikroöğretim ders imecesi modeli ile sınıf öğretmeni adaylarının kesir öğretim bilgilerinin geliştirilmesine yönelik bir uygulama. [Doktora tezi, Dumlupınar Üniversitesi]. YÖK Tez Merkezi.
• Alacacı, C. (2012). Öğrencilerin kesirler konusundaki kavram yanılgıları. E. Bingölbali ve M.F. Özmantar (Edt.), Matematiksel zorluklar ve çözüm önerileri (ss. 63-95). PegemA Yayıncılık.
• Arya, P., Christ, T., & Chiu, M. M. (2015). Links between characteristics of collaborative peer video analysis events and literacy teachers’ outcomes. Journal of Technology and Teacher Education, 23(2), 159-183.
• Arya, P., & Christ, T. (2013). An exploration of how professors’ facilitation is related to literacy teachers’ meaning construction process during video-case discussions. Journal of Reading Education, 39, 15-22.
• Ayyıldız, N., & Altun, S. (2013). Matematik dersine ilişkin kavram yanılgılarının giderilmesinde öğrenme günlüklerinin etkisinin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(2), 71-86.
• Baki, A. (2006). Kuramdan uygulamaya matematik eğitimi. Harf Eğitim Yayıncılık.
• Baki, A. (2019). Matematiği öğretme bilgisi. Pegem Akademi Yayıncılık.
• Baki, A., & Aydın Güç, F. (2014). Dokuzuncu sınıf öğrencilerinin devirli ondalık gösterimle ilgili kavram yanılgıları. Turkish Journal of Computer and Mathematics Education. 5(2), 176-206.
• Baki, M. (2012). Sınıf öğretmeni adaylarının matematiği öğretme bilgilerinin gelişiminin incelenmesi: Bir ders imecesi (lesson study) çalışması [Doktora tezi, Karadeniz Teknik Üniversitesi]. YÖK Tez Merkezi.
• 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.
• Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of Professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey-Bass.
• Barnett, M. (2006). Using a web-based professional development system to support preservice teachers in examining authentic classroom practice. Journal of Technology and Teacher Education, 14(4), 701-729.
• Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among preservice science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93.
• Benedict-Chambers, A. (2016). Using tools to promote novice teacher noticing of science teaching practices in post-rehearsal discussions. Teaching and Teacher Education, 59, 28-44.
• Biber, A. Ç., Tuna, A., & Aktaş, O. (2013). Öğrencilerin kesirler konusundaki kavram yanılgıları ve bu yanılgıların kesir problemleri çözümlerine etkisi. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 3(2), 152-162.
• Bozkuş, F. (2020). Ortaokul matematik öğretmenlerinin öğrencilerin matematiksel düşüncelerini fark etme becerilerinin incelenmesi Yayımlanmamış doktora tezi. Bolu Abant İzzet Baysal Üniversitesi.
• Brouwer, N., & Robijns, F. (2015). Insearch of effective guidance for preservice teachers’ viewing of classroom video. In B. Calandra and P. J. Rich (Eds.), Digital video for teacher education e research and practice (pp.54-67). New York: Routledge.
• Brown, G., & Quinn, R. (2006). Algebra students’ difficulty with fractions: An error analysis. Australian Mathematics Teacher, 62(4), 28-40.
• Budak, G., Budak, A., Bozkurt, I., & Kaygın, B. (2011). Matematik öğretmen adaylarıyla bir ders araştırması uygulaması. e-Journal of New World Sciences Academy, 6(2), 1606-1617.
• Bütün, M. (2012). İlköğretim matematik öğretmeni adaylarının uygulanan zenginleştirilmiş program sürecinde matematiği öğretme bilgilerinin gelişimi Doktora Tezi, Karadeniz Teknik Üniversitesi . YÖK Tez Merkezi.
• Calandra, B. (2015). A process of guided, video-based reflection. In B. Calandra, and P. J. Rich (Eds.), Digital video for teacher education e research and practice (pp. 36-53). New York: Routledge.
• Christ, T., Arya, P., & Chiu, M. M. (2012). Collaborative peer video analysis: Insights about literacy assessment ve instruction. Journal of Literacy Research, 44, 171-199.
• Christ, T., Arya, P., & Chiu, M. M. (2014). Teachers’ reports of learning and application to pedagogy based on engagement in collaborative peer video analysis. Teaching Education, 25(4), 349-374.
• Christ, T., Arya, P., & Chiu, M. M. (2017). Video use in teacher education: An international survey of practices. Teaching and Teacher Education, 63, 22-35.
• Cochran, K.F. (1997). Pedagogical content knowledge: Teachers’ integration of subject matter, pedagogy, students, and learning environments. In R. Sherwood (Eds.), Research matters... To the science teacher (pp. 3-18). Manhattan, KS: NARST.
• Corcoran, D. (2008). Developing mathematical knowlege for teaching: A three-tiered study of irishpreservice primary teachers Doctoral dissertation, University of Cambridge.
• Creswell, J.W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into practice, 39(3), 124-131.
• Darling-Hammond, L. (2003). Teacher learning that supports student learning. In A. Ornstein, L. S. Behar Horenstein and E. Pajak (Eds.), Contemporary issues in curriculum (pp. 277-282). Boston: Pearson Education. Ekiz, D. (2009). Bilimsel araştırma yöntemleri. Anı Yayıncılık.
• Erdik, E. (2014). A comparative analysis of noticing of mathematics teachers with varying teaching experience Master's thesis, Boğaziçi Üniversitesi. YÖK Tez Merkezi.
• Ergöl, H., & Memnun, D. S. (2020). Ortaokul öğrencilerinin kesir kavramına ilişkin ürettikleri metaforlar. OPUS International Journal of Society Researches, 15(23), 1920-1939.
• Eröz-Tuga, P. B. (2013). Reflective feedback session using video recordings. English Language Teaching, 67(2), 175-183.
• Fadde, P., & Sullivan, P. (2013). Using interactive video to develop preservice teachers’ classroom awareness. Contemporary Issues in Technology and Teacher Education, 13(2), 156-174.
• Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
• Fernandez, C. (2005). Lesson study: A means of elementary teachers to develop the knowledge of mathematics needed for reform minded teaching? Mathematical Thinking and Learning, 7(4), 265-289.
• Fernandez, M. L. (2010). Investigating how and what prospective teachers learn through microteaching lesson study. Teaching and Teacher Education, 26(2), 351-562.
• Fernandez, C., Cannon, J., & Chokshi, S. (2003). A US-Japan lesson study collaboration reveals criticallenses for examining practice. Teaching and Teacher Education, 19(2), 171-185.
• Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-upstudy of professional development in mathematics. American Educational Research Journal, 38(3), 653-689.
• Fernandez, C., & Yoshida, M. (2012). Lesson study: A Japanese approach to improving mathematics teaching and learning. Routledge.
• Garet, M., Porter, A., Desimone, L., Birman, B., & Yoon, K. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(3), 915-945.
• Gilbert, J.K., Osborne, R.J., & Fensham, P.J. (1982). Children's science and its consequences for teaching. Science Education. 66(4), 623-633.
• Gözel, E. (2016). Ders imecesi çalışmalarıyla sınıf öğretmenlerinin problem çözmeye dayalı matematiği öğretme bilgilerinin gelişiminin incelenmesi Doktora tezi, Pamukkale Üniversitesi. YÖK Tez Merkezi.
• Güner, P. (2017). Investigating preservice middle school mathematics teachers noticing of students mathematical thinking in the context of lesson study Doctoral dissertation], Middle East Technical University. YÖK Tez Merkezi.
• Güner, P., & Akyüz, D. (2017). Ders imecesi mesleki gelişim modeli: Öğretmen adaylarının fark etme becerilerinin incelenmesi. İlköğretim Online, 16(2), 428-452.
• Gür, H., & Seyhan, G. (2004). İlköğretim 7 ve 8. sınıf öğrencilerinin ondalık sayılar konusundaki hataları ve kavram yanılgıları. Retrieved April, 14, 2019 from http://citeseerx.ist.psu.edu/showciting?cid=61957684 Hansen, A. (2014). Children’s errors in mathematics. London: Sage Publications.
• Harford, J., & MacRuairc, G. (2008). Engaging student inservice-teachers in meaningful reflective practice. Teaching and Inservice-Teacher Education, 24, 1884-1892.
• Hart, K.M. (1993) Fractions. In K. M. Hart (Eds.), Children’s understanding of mathematics (pp. 66-81). London: John Murray.
• Haser, Ç., & Ubuz, B. (2003). Students’ conception of fractions: A study of 5th grade students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 64-69.
• Hawley, D. W., & Valli, L. (1999). The essentials of effective professional development: A newconsensus. In D. L. Hammond ve H. G. Sykes (Eds.), Teaching as the learning profession: Handbook o f policy and practice (pp. 127-150). San Francisco, CA: Jossey-Bass.
• Hiebert, J., Morris, A. K., Berk, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47-61.
• Hollingsworth, H., & Clarke, D. (2017). Video as a tool for focusing teacher self-reflection: Supporting and provoking teacher learning. Journal of Mathematics Teacher Education, 20(5), 457-475.
• Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers’ noticing of mathematics classroom events. School Science and Mathematics, 112(7), 420-432.
• Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
• Işık, C., & Kar, T. (2012). Analyzing problems posed by 7th-grade students for addition operation with fractions. Elementary Education Online. 11(4), 1021-1035.
• Jacob, F., John, S.& Gwany, D. M. (2020). Teachers’ pedagogical content knowledge and students’ academic achievement: a theoretical overview. Journal of Global Research in Education and Social Science, 14(2), 14-44.
• Jacobs, V.R., Lamb, L.C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
• Karasar, N. (2009). Bilimsel araştırma yöntemi. Nobel Yayın Dağıtım.
• Kennedy, M. M. (1999). The role of preservice teacher education. In l. Darling hammond and G. Sykes (Eds.), Teaching as the learning profession: Handbook of teaching and policy (pp. 54-86). San Francisco: Jossey Bass.
• Kleinknecht, M., & Gröschner, A. (2016). Fostering preservice teachers’ noticing with structured video feedback: Results of an online- and video-based intervention study. Teaching and Teacher Education, 59, 45-56.
• Kocaoğlu, T., & Yenilmez, K. (2010). Beşinci sınıf öğrencilerinin kesir problemlerinde yaptıkları hatalar ve kavram yanılgıları. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 14, 71-85.
• Lee, M. Y. (2018). Further investigation into the quality of teachers’ noticing expertise: A proposed framework fore valuating teachers’ models of students’ mathematical thinking. EURASIA Journal of Mathematics, Science, and Technology Education, 14(9), 1-15.
• Lee, Y., Capraro, R.M. & Capraro, M.M. (2018). Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing. International Electronic Journal Of Mathematics Education, 13(2), 75-90.
• Lee, M. Y., & Cross Francis, D. (2018). Investigating the relationship among elementary teachers’ perception about the use of students’ thinking, their professional noticing skills and their teaching practice. Journal of Mathematical Behavior, 51, 118-128.
• Lee, M.Y. (2019). The development of elementary preservice teachers’ professional noticing of students’ thinking through adapted lesson study. Asia-Pacific Journal of Teacher Education, 47(4), 383-398. Lewis, C. (2016). How does lesson study improve mathematics instruction? ZDM: The International Journal on Mathematics Education, 48(4), 571-580.
• Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river. American Educator, 12-17, 50-52. Lewis, C., Friedkin, S., Baker, E., & Perry, R. (2011). Learning from the key tasks of lesson study. In O. Zaslavsky and P. Sullivan (Eds), Constructing knowledge for teaching secondary mathematics (pp. 161-176). US: Springer. Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35(3), 3-14.
• Liu, Y. (2014). Teachers’ in-the-moment noticing of students’ mathematical thinking: A case study of two teachers Unpublished doctoral dissertation. University of North Carolina.
• Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates Press.
• Magnusson, S., Borko, H., & Krajcik, J. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In Gress-Newsome, J., and Ledermen, N.G. (Eds.), Examining pedagogical content knowledge (pp. 95-132). Boston: Kluwer Akademic Publishers.
• Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to modified conception. Journal of Teacher Education, 41, 3-11.
• Mason, J. (2002). Researching your own practice: The discipline of noticing. New York: Springer.
• MEB, (2017). Öğretmenlik mesleği genel yeterlikleri, öğretmen yetiştirme ve geliştirme genel müdürlüğü, Ankara.
• MEB, (2018). Matematik dersi öğretim programı, ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar, Ankara. Merriam, S. B. (1998). Qualitative research and case study applications in education. CA: Jossey-Bass Publishers.
• Merriam, S.B. (2013). Nitel araştırma desen ve uygulama için bir rehber. (Selahattin Turan, Trans.Eds), Nobel Yayınları.
• Meyer, R. (2005). Lesson study: The effects on teachers and students in urban middleschools Unpublished doctoral dissertation. Baylor University.
• Meyer, R. D., & Wilkerson, T. L. (2011). Lesson Study: The impact on teachers’ knowledge for teaching mathematics. In L. C. Hart, A. S. Alston and A. Murata, (Eds.), Lesson study research and practice in mathematic seducation: Learning together (pp. 15-26). New York: Springer.
• Mitchell, R. N., & Marin, K. A. (2014). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education, 18(6), 551-575.
• Mohr, D. J., & Townsend, J. S. (2002). Research to practice: Using comrehensive teaching models to enhance pedagogical content knowledge. Teaching Elementary Physical Education, 13(4), 36-37.
• Mostofo, J. (2013). Using lesson study with preservice secondary mathematics teachers: Effects on instruction, planning, and efficacy to teach mathematics Unpublished doctoral dissertation. Arizona State University. National Council of Teachers of Mathematics (NCTM). (2000). Learning mathematics for a new century (2000 Yearbook). Reston, VA: Author.
• Nesher, P., & Peled, I. (1986). Shifts in reasoning: The case of extending number concepts. Educational Studies in Mathematics, 17, 67-79.
• Osmanoğlu, A. (2010). Preparing preservice teachers for reform-minded teaching through online video case discussions: Change innoticing Unpublished doctoral dissertation. Middle East Technical University.
• Osmanoğlu, A., Işıksal, M., & Koç, Y. (2012). Prospective teachers' noticing with respect to the student roles underlined in the elementary mathematics program: Use of video-cases. Eğitim ve Bilim, 37(165), 336-347.
• Ojose, B. (2015). Students’ misconceptions in mathematics: analysis of remedies and what research says.Ohio Journal of School Mathematics, 72, 30-34.
• Halil, Ö. N. A. L., & Yorulmaz, A. (2017). İlkokul Dördüncü Sinif Öğrencilerinin Kesirler Konusunda Yaptiklari Hatalar. Eğitim ve Toplum Araştırmaları Dergisi, 4(1), 98-113.
• Özdemir-Baki, G. (2017) Ortaokul matematik öğretmenlerinin matematiği öğretme bilgilerinin gelişim sürecinin incelenmesi: Ders imecesi modeli Doktora tezi, Atatürk Üniversitesi. YÖK Tez Merkezi.
• Özdemir-Baki, G. (2020). Video kulüp sürecine katılan öğretmenlerin deneyimlerini yansıtan bir fenomenografi araştırması. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 14(2), 1142-1188.
• Özen, D. (2015). Ortaokul matematik öğretmenlerinin geometrik düşünmelerinin geliştirilmesi: Bir ders imecesi Doktora tezi, Anadolu Üniversitesi. YÖK Tez Merkezi.
• Özen, D., & Köse, N. (2013, Haziran 20-22). Geometrik cisimler konusunda bir ders imecesi örneği Sözlü Bildiri. 1. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu, Trabzon, Türkiye.
• Özen, D., & Köse, N. Y. (2014, Eylül 11-14). Ortaokul matematik öğretmenlerinin geometrik düşünmeyi geliştirme üzerine gerçekleştirdikleri ders imecesinin bireysel öğretimlerine yansımaları Sölzü Bildiri. XI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Adana, Türkiye.
• Pesen, C. (2007). Öğrencilerin kesirlerle ilgili kavram yanılgıları. Dicle Üniversitesi Eğitim ve Bilim, 32(143), 79-88. Philipp R. A. (2014). Commentary on section 3: Research on teachers’ focusing on children’s thinking in learning to teach: Teacher noticing and learning trajectories. In J. Cai and J. Middleton (Eds.), Research trends in mathematics teacher education (pp. 285-293). Newyork: Springer.
• Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27. Richert, A. (2005). Inquiring about practice: Using web-based materials to develop teacher inquiry. Teaching Education, 16, 297-310.
• Sackur-Grisvard, C., Leonard, F. (1985). Intermediate cognitive organization in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2, 157-174. Sadi, A. (2007), Misconceptions in numbers. UGRU Journal, 5, 1-7.
• Santagata, R., Yeh, C., & Mercado, J. (2018). Preparing elementary school teachers to learn from teaching: A comparison of two approaches to mathematics methods instruction. Journal of the Learning Sciences, 27(3), 474-516.
• Santagata, R., Zannoni, C., & Stigler, J.W. (2007). The role of lesson analysis in preservice teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10, 123-140.
• Sartono, S. & Karso, K. (2020). Are the fractions difficult? A case study at Elementary School 033 Asmi. In International Conference on Elementary Education, 2(1), 1029-1043.
• Seidel, T., Blomberg, G., & Renkl, A. (2013). Instructional strategies for using video in teacher education. Teaching and Teacher Education, 34(1), 56-65.
• Shanahan, L. E., & Tochelli, A. L. (2014). Examining the use of video study groups for developing literacy pedagogical content knowledge for critical elements of strategy instruction with elementary teachers. Literacy Research and Instruction, 53(1), 1-24.
• Sherin, M. G. (2007). The development of teachers’ professional vision in video clubs. In R. Goldman, R. Pea, B. Barron and S. J. Derry (Eds.), Video research in the learning sciences (pp. 383-396). Mahwah, NJ: Erlbaum. Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.), Situating the study of teacher noticing (pp. 3-15). New York: Taylor and Francis.
• Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers' ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
• 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.
• Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
• Stacey, K., & Steinle, V. (1998). Refining the classification of students’ interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 1-21.
• Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125.
• Steffe, L. P., & Olive, J. (2010). The construction of fraction schemes using the generalized number sequence. Children’s Fractional Knowledge, Springer US.
• Steinle, V., & Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in Grades 5 to 10. Retrieved April, 15, 2019 from https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/backinfo/refs/merga98stst.pdf.
• Stigler, J., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.
• Stockero, S. L. Rupnow, R L., & Pascoe A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395.
• Sudejamnong, A., Robsouk, K., Loipha, S., & Inprasitha, M. (2014). Development of teachers’ mathematical knowledge for teaching by using the innovation of lesson study and open approach. Sociology Mind, 4, 317-327.
• Takahashi, A., & Yoshida, M. (2004). Ideas for establishing lesson study communities. Teaching Children Mathematics, 10(9), 436-443.
• Taşkın, D., & Yıldız, C. (2011, Nisan 27-29). Kesirlerde toplama ve çıkarma işlemlerinin öğretiminde common knowledge construction modele uygun materyal geliştirme. Sözlü Bildiri. 2. International Conference on New Trends in Education and Their Implications Congress, Antalya, Turkey.
• Tripp, T. R., & Rich, P. J. (2012). The influence of video analysis on the process of teacher change. Teaching and Teacher Education, 28(5), 728-739.
• Türker Biber, B. (2017). İstatistikle ilgili modelleme etkinlikleri bağlamında öğretmen farkındalığı: Bir durum çalışması Doktora tezi, Hacettepe Üniversitesi. YÖK Tez Merkezi.
• Van Driel, J. H., Verloop, N., & de Vos, w. (1998). Developing science teachers’ pedagogical content knowledge. Journal of Research in Science Teaching. 35, 673-695.
• van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, and R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134-151). New York, NY: Routledge.
• van Es, E. A., Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers' interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571-576.
• van Es, E. A., & Sherin, M. G. (2006). How different video club designs support teachers in “learning to notice”. Journal of Computing in Teacher Education, 22(4), 125-135.
• van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers “learning to notice” in the context of a video club. Teaching and Teacher Education, 24, 244-276.
• van Es, E. A., & Sherin, M. G. (2010). The influence of video clubs on teachers' thinking and practice. Journal of Mathematics Teacher Education, 13(2), 155-176.
• Verhoef, N.C., Tall, D.O. (2011). Lesson study: The effect on teacher’s professional development. In B. Ubuz (Eds.), Proceedings of the 35th conference of the international for the psychology of mathematics education (Vol. 4, pp. 297-304). Ankara: PME.
• Vrikki, M. Warwick, P. Vermunt, J. D. Mercer, N., & Van Halem, N. (2017). Teacher learning in the context of Lesson Study: A video-based analysis of teacher discussions. Teaching and Teacher Education, 61, 211-224.
• Wise, A. F., Padmanabhan, P., & Duffy, T. M. (2009). Connecting online learners with diverse local practices: The design of effective common reference points for conversation. Distance Education, 30(3), 317-338.
• Yaffe, E. (2010). The reflective beginner: Using theory and practice to facilitate reflection among newly qualified teachers. Reflective Practice: International and Multidisciplinary Perspectives, 11(3), 381-391.
• Yetim, S., & Alkan R. (2010). İlköğretim 7. sınıf öğrencilerinin rasyonel sayılar ve bu sayıların sayı doğrusundaki gösterimleri konusundaki yaygın yanlışları ve kavram yanılgıları. Kırgızistan-Türkiye Manas Üniversitesi Fen Bilimleri Dergisi, 11, 87-109.
• Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemi. Seçkin Yayınları. Yılmaz, Z., & Yenilmez, K. (2007). İlköğretim 7. ve 8. sınıf öğrencilerinin ondalık sayılar konusundaki kavram yanılgıları. Afyon Kocatepe Üniversitesi Fen Bilimleri Dergisi, 8(1), 269-290.
• Yoshida, M., & Jackson, W., C. (2011). Ideas for developing mathematical pedagogical content knowledge through lesson study. In L, C, Hart., A., Alston and A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 279-288). Dordrecht, The Netherlands: Springer.
• Zembat, İ, Ö. (2010). Kavram yanılgısı nedir? M.F. Özmantar, E. Bingölbali ve H. Akkoç (Edt.), Matematiksel kavram yanılgıları ve çözüm önerileri PegemA Yayıncılık.
• Zembat, İ. Ö. (2013). Sayıların farklı algılanması-sorun sayılarda mı, öğrencilerde mi? M. F. Özmantar, E. Bingölbali, ve H. Akkoç (Edt.), Matematiksel kavram yanılgıları ve çözüm önerileri (ss. 41-60). Pegem Akademi.