TY  - JOUR
T1  - Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions
TT  - Ortaokul Matematik Öğretmeninin 5. Sınıf Kesirler Konusundaki Öğretme Bilgisinin İncelenmesi
AU  - Şen, Ceylan
PY  - 2021
DA  - February
DO  - 10.16949/turkbilmat.742136
JF  - Turkish Journal of Computer and Mathematics Education (TURCOMAT)
PB  - Türkbilmat Eğitim Hizmetleri
WT  - DergiPark
SN  - 1309-4653
SP  - 96
EP  - 138
VL  - 12
IS  - 1
LA  - en
AB  - This study has aimed at revealing the knowledge for teaching a middle-school mathematics teacher has in teaching the 5th-grade subject of fractions. For this purpose, the Mathematics Knowledge for Teaching (MKT) was used. The study adopted the holistic single-case study, one of the qualitative study designs. The study was implemented with a teacher assigned at a public school and who volunteered for the study. The study data were collected by semi-structured interviews held with the teacher and observations during the teaching process of the subject of fractions, on which the teacher’s knowledge was sought to be assessed. Consequent to the study, it was revealed that the middle-school mathematics teacher possesses insufficient content knowledge on fractions, operations with fractions and meanings and models of fractions. It was concluded that his insufficient content knowledge also had an adverse impact on this knowledge for teaching and therefore, restricted the teacher’s teaching process. Based on the study, it was concluded that due to the teacher’s limited content knowledge and pedagogical content knowledge, he has an insufficient mathematical knowledge for teaching.
KW  - Mathematical knowledge for teaching
KW  - fractions
KW  - middle-school mathematics teacher
N2  - Bu çalışmada 5. sınıf kesirler konusunun öğretiminde bir ortaokul matematik öğretmeninin öğretme bilgisinin ortaya konulması amaçlanmıştır. Bu amaç doğrultusunda Öğretmek için Matematik Bilgisi (ÖMB) modeli kullanılmıştır. Araştırmada nitel araştırma desenlerinden bütüncül tek durum çalışması benimsenmiştir. Araştırma, devlet ortaokulunda görev yapan ve çalışmaya katılmaya gönüllü olan bir matematik öğretmeni ile yürütülmüştür. Araştırmanın verileri öğretmen ile gerçekleştirilen yarı yapılandırılmış görüşmeler ve öğretmen bilgisinin incelendiği kesirler konusunun öğretimi sürecinde yapılan gözlemler yolu ile toplanmıştır. Araştırmada elde edilen verilerin analizinde betimsel analiz yöntemi kullanılmıştır. Araştırma sonucunda çalışmada yer alan ortaokul matematik öğretmeninin kesir, kesirlerle işlemler, kesirlerin anlamları ve modellerine ilişkin yetersiz alan bilgisine sahip olduğu ortaya konulmuştur. Yetersiz alan bilgisinin, öğretmenin öğretme bilgisini de olumsuz etkilediği ve öğretim sürecinin de bu doğrultuda kısıtlı kaldığı ortaya konulmuştur. Çalışma sonucunda öğretmenin alan bilgisi ve pedagojik alan bilgisinin kısıtlı olması sonucu matematik öğretme bilgisinin de yeterli olmadığı sonucuna ulaşılmıştır.
CR  - Amato, A. S. (2005). Developing students’ understanding of the concept of fractions as numbers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Australia.
CR  - Aslan-Tutak, F., & Köklü, O. (2016). Öğretmek için matematik bilgisi. E. Bingölbali, S. Arslan & İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler içinde (s. 701-720). Ankara: Pegem Akademi.
CR  - Baek, J. M., Wickstrom, M. H., Tobias, J. M., Miller, A. L., Safak, E., Wessman-Enzinger, N., & Kirwan, J. V. (2017). Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem. The Journal of Mathematical Behavior, 45, 1-14. doi: 10.1016/j.jmathb.2016.10.005
CR  - Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi: 10.1016/j.jecp.2012.06.004
CR  - Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). Washington, DC: American Educational Research Association.
CR  - 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. doi: 10.1177/0022487108324554
CR  - Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Yi-Miau, T. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. doi:10.3102/0002831209345157
CR  - Begle, E. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Washington, DC: The Mathematical Association of America and the National Council of Teachers of Mathematics.
CR  - Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: Macmillan.
CR  - Brownell, M. T., Ross, D. D., Colon, E. P., & McCallum, C. L. (2005). Critical features of special education teacher preparation: A comparison with general teacher education. The Journal of Special Education, 38(4), 242-252.
CR  - Charalambous, C.  Y., & Pitta-Pintazi, D. (2005). Revisiting a theoretical model on fractions: Implications for teaching and research. Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education, 2, 233-240.
CR  - Chestnut-Andrews, A. (2007). Pedagogical content knowledge and scaffolds: Measuring teacher knowledge of equivalent fractions in a didactic setting. (Doctoral Dissertation). City University of New York.
CR  - Clarke, D. M., Roche, A., & Mitchell, A. (2008). 10 practical tips for making fractions come alive and make sense. Mathematics Teaching in The Middle School, 13(7), 372-380.
CR  - Cramer, K., Wyberg, T., & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics Teaching in The Middle School, 13(8), 490-496. doi: 10.5951/MTMS.13.8.0490
CR  - Davis, G. E. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. The Journal of Mathematical Behavior, 22(2), 107-111. doi:10.1016/S0732-3123(03)00016-6
CR  - Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12-25. doi: 10.1016/j.tate.2013.03.001
CR  - Donnelly, V., & Watkins, A. (2011). Teacher education for inclusion in Europe. Prospects, 41(3), 341-353. doi: 10.1007/s11125-011-9199-1
CR  - Eli, J. A., Mohr‐Schroeder, M. J., & Lee, C. W. (2013). Mathematical connections and their relationship to mathematics knowledge for teaching geometry. School Science and Mathematics, 113(3), 120-134.  doi:10.1111/ssm.12009
CR  - Fazio, L. K., DeWolf, M., & Siegler, R. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42(1), 1-16. doi: 10.1037/xlm0000153
CR  - Fazio, L. K., & Siegler, R. S. (2011). Teaching fractions. Educational Practices Series 22. Geneva:  International Academy of Education International Bureau of Education.
CR  - Fernandez, M. L. (2005). Learning through microteaching lesson study in teacher preparation. Action in Teacher Education, 26(4), 37-47.  doi:10.1080/01626620.2005.10463341
CR  - Ferrini-Mundy, J., & Findell, B. (2001). The mathematical education of prospective teachers of secondary school mathematics: Old assumptions, new challenges. In CUPM discussion papers about mathematics and the mathematical sciences in 2010: What should students know? (pp. 31-41). Washington, DC: Mathematical Association of America.
CR  - Flores, A., Samson, J., & Yanık, H. B. (2006). Quotient and measurement interpretations of rational numbers. Teaching Children Mathematics, 13(1), 34-39.
CR  - Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education. New York: McGraw-Hill.
CR  - Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., ... Changas, P. (2013). Improving at risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683-700. doi: 10.1037/a0032446
CR  - Goulding, M., Hatch, G., & Rodd, M. (2003). Undergraduate mathematics experience: Its significance in secondary mathematics teacher preparation. Journal of Mathematics Teacher Education, 6(4), 361-393.   doi:10.1023/A:1026362813351
CR  - Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
CR  - Hanselman C. A. (1997). Stop using foul language in the mathematics classroom. Mathematics Teaching in the Middle School, 3(2), 154-160.
CR  - Hanson, D. (1995). Understanding fractions (Grades 5 to 8). Retrieved from http://mathcentral.uregina.ca/RR/ database/RR.09.95/hanson4.html
CR  - Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351. doi:10.2307/30034819
CR  - 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.
CR  - Hill, H. C., Rowan, R., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
CR  - Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.
CR  - Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111-155). Charlotte, NC: Information Age.
CR  - Holm, J., & Kajander, A. (2011). “I finally get it": Developing mathematical understanding during
teacher education. International Journal of Mathematical Education in Science and Technology, 43(5), 563-574. doi: 10.1080/0020739X.2011.62280
CR  - Işık, C., & Kar, T. (2012). An error analysis in division problems in fractions posed by preservice elementary mathematics teachers. Educational Sciences: Theory and Practice, 12(3), 2303-2309.
CR  - Işıksal, M., & Çakıroglu, E. (2011). The nature of prospective mathematics teachers’ pedagogical content knowledge: the case of multiplication of fractions. Journal of Mathematics Teacher Education, 14(3), 213-230. doi:10.1007/s10857-010-9160-x
CR  - Joyner, V. (1994). Elementary school teachers’ knowledge of rational number concepts. A paper presented at the Annual Conference of the National Council of Teachers of Mathematics in Indianapolis, Indiana.
CR  - Kajander, A., & Boland, T. (2014). Mathematical models for teaching: Reasoning without
memorization. Toronto, ON: Canadian Scholars’ Press.
CR  - Kajander, A., & Holm, J. (2016). What math matters? Types of mathematics knowledge and relationships to methods course performance. Canadian Journal of Science, Mathematics and Technology Education, 16(3), 273-283. doi: 10.1080/14926156.2016.1183837
CR  - Kamii C., & Dominick, A. (1998). The harmful effects of algorithms in grades 1-4. In L. J. Morrow, M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 130-140). Reston (VA): NCTM.
CR  - Kellman, P. J., Massey, C. M., Roth, Z., Burke, T., Zucker, J., Saw, A., ... Wise, J. (2008). Perceptual learning and the technology of expertise: Studies in fraction learning and algebra. Learning Technologies and Cognition: Special issue of Pragmatics & Cognition, 16(2), 356-405.
CR  - Khoury, H. A., & Zazkis, R. (1994). On fractions and non-standard representations: Pre-service teachers’ concepts. Educational Studies in Mathematics, 27(2), 191-204.
CR  - Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101-144). Columbus, OH: ERIC/SMEAC.
CR  - Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49 -84). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
CR  - Kinach, B.  M.  (2002). Understanding and learning-to-explain by representing mathematics: Epistemological dilemmas facing teacher educators in the Secondary mathematics “methods” course. Journal of Mathematics Teacher Education, 5(2), 153-186. doi: 10.1023/A:1015822104536
CR  - Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ content and pedagogical content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 64(1), 90-106. doi: 10.1177/0022487112460398
CR  - Klemer, A., Rapoport, S., & Lev-Zamir, H. (2019). The missing link in teachers’ knowledge about common fractions division. International Journal of Mathematical Education in Science and Technology, 50(8), 1256-1272.  doi:10.1080/0020739X.2018.1522677
CR  - Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte: Information Age Publishing.
CR  - Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM Mathematics Education, 40(5), 833-843. doi:10.1007/s11858-008-0148-2
CR  - Lo, J. J., & Luo, F. (2012). Prospective elementary teachers' knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500. doi: 10.1007/s10857-012-9221-4
CR  - Luo, F., Lo, J.-J., & Leu, Y.-C. (2011). Fundamental fraction knowledge of preservice elementary teachers: A cross-national study in the United States and Taiwan. School Science and Mathematics, 111(4), 164-177. doi: 10.1111/j.1949-8594.2011.00074.x
CR  - Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
CR  - Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In J. Gess-Newsome & N. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education (pp. 95-132). Dordrecht, The Netherlands: Kluwer Academic Publishers.
CR  - McMullen, J., Laakkonen, E., Hannula-Sormunen, M., & Lehtinen, E. (2015). Modeling the developmental trajectories of rational number concept(s). Learning and Instruction, 37, 14-20. doi: 10.1016/j.learninstruc.2013.12.004
CR  - Merenluoto, K., & Lehtinen, E. (2004). Number concept and conceptual change: towards a systemic model of the processes of change. Learning and Instruction, 14(5), 519-534. doi: 10.1016/j.learninstruc.2004.06.016.
CR  - Milli Eğitim Bakanlığı (MEB). (2018). Matematik dersi (İlkokul ve Ortaokul 1, 2, 3, 4,
5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara: Talim Terbiye Kurulu Başkanlığı.
CR  - Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
CR  - Mitchell, R., Charalambous, C., & Hill, H. (2014). Examining the task and knowledge demands
needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37-60. doi: 10.1007/s10857-013-9253-4.
CR  - Mok, I., Cai, J., & Fong-Fung, A. (2008). Missing learning opportunities in classroom instruction: evidence from an analysis of a well-structured lesson on comparing fractions. The Mathematics Educator,11(1-2), 111-126.
CR  - Monk, D. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125-145. doi: 10.1016/0272-7757(94)90003-5
CR  - Morris, A. K., Hiebert, J., & Spitzer, S. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can pre-service teachers learn? Journal for Research in Mathematics Education, 40(5), 491-521.
CR  - Moss, J., & Case, R. (1999). Developing children's understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 127-147.
CR  - National Council of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
CR  - National Mathematics Advisory Panel (NMP). (2008). Foundations for success. Jessup, MD: U. S. Department of Education. Retrieved from www.ed.gov/MathPanel.
CR  - Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning an Instruction, 28, 64-72. doi: 10.1016/j.learninstruc.2013.05.003.
CR  - Ölmez, İ. B., & Izsák, A. (2020). Characterizing reasoning about fraction arithmetic of middle grades teachers in three latent classes. Mathematical Thinking and Learning, 1-29.  doi: 10.1080/10986065.2020.1780368
CR  - Özel, S. (2013). An analysis of in-service teachers’ pedagogical content knowledge of division of fractions. The Anthropologist, 16(1-2), 1-5.  doi:10.1080/09720073.2013.11891330
CR  - Pantziara, M., & Philippou, G. (2011). Levels of students’ “conception” of fractions. Educational Studies in Mathematics,79(1), 61-83. doi: 10.1007/s10649-011-9338-x
CR  - Petocz, P., & Reid, A.  (2003). What on earth is sustainability in mathematics? New Zealand Journal of Mathematics, 32, 135-144.
CR  - Reys, R.  E., Suydam, M. N., & Lindquist, M.  M., & Smith, N. L. (1998). Helping children learn mathematics. Boston: Allen and Bacon.
CR  - Rowan, B., Chiang, F. S., & Miller, R. J. (1997). Using research on employees’ performance to study the effects of teachers on student achievement. Sociology of Education, 70(4), 256-284. doi: 10.2307/2673267
CR  - Sahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551.  doi:10.1080/0020739X.2015.1092178
CR  - Savolainen, H. (2009). Responding to diversity and striving for excellence. An analysis of international comparison of learning outcomes with a particular focus in Finland. In C. Acedo, M. Amadio, R. Opertti (Eds), Defining an inclusive education agenda: Reflections around the 48th session of the International Conference on Education (pp. 49-59). Geneva, UNESCO-IBE.
CR  - Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. doi: 10.17763/haer.57.1.j463w79r56455411
CR  - Shulman, L., S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. doi: 10.3102/0013189X015002004
CR  - Siebert, D., & Gaskin, N. (2006). Creating, naming, and justifying fractions. Teaching Children Mathematics, 12(8), 394-400.
CR  - Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 219-233). Reston, VA: National Council of Teachers of Mathematics.
CR  - Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE 2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/fractions_pg_093010.pdf
CR  - Simon, M. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254. doi: 10.2307/749346
CR  - Smith, J. P. (2002). The development of students’ knowledge of fractions and ratios. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 3-17). Reston, VA: NCTM.
CR  - Soylu Y, & Soylu C. (2002). Learning difficulties of 5th class in primary education at fraction: ordering,
adding, subtraction, multiplication in fraction and problems related to fraction. Erzincan University Journal of Education, 7(2), 101-117.
CR  - Tanışlı, D., & Köse, N. Y. (2013). Preservice mathematics teachers' knowledge of students about the algebraic concepts. Australian Journal of Teacher Education, 38(2), 1-18.
CR  - 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. doi:10.2307/749817
CR  - Toluk, Z. (2002). İlkokul öğrencilerinin bölme işlemi ve rasyonel sayıları ilişkilendirme süreçleri. Boğaziçi Üniversitesi Eğitim Dergisi, 19(2), 81-101.
CR  - Vamvakoussi, X. & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction, 14(5), 453-467. doi: 10.1016/j.learninstruc.2004.06.013
CR  - Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344-355. doi: 10.1016/j.jmathb.2012.02.001
CR  - Van de Walle, Karp, & Bay-Williams (2013). Elementary and middle school mathematics: Teaching developmentally (8th Edition). Boston: Pearson.
CR  - Van Dooren, W., Lehtinen, E., & Verschaffel, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction, 37, 1-4. https://doi.org/10.1016/j.learninstruc.2015.01.001
CR  - Warrington, M. A. (1997). How children think about division with fractions. Mathematics Teaching in the Middle School, 2(6), 390-94.
CR  - Webel, C., & DeLeeuw, W. W. (2016). Meaning for fraction multiplication: Thematic analysis of mathematical talk in three fifth grade classes. The Journal of Mathematical Behavior, 41, 123-140. doi: 10.1016/j.jmathb.2015.12.003
CR  - Wu, H. H. (2011). Understanding elementary school mathematics. Washington, DC: Mathematical Association of America.
CR  - Yanık, H. B. (2013). Rasyonel sayılar. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır & A. Delice (Eds.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar içinde (s. 95-110). Ankara: Pegem Akademi.
CR  - Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
CR  - Yin, R. K. (2003). Applications of case study research. Beverly Hills, CA: Sage Publishing.Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross cultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31(4), 438-457.  doi:10.1016/j.cedpsych.2006.02.001
UR  - https://doi.org/10.16949/turkbilmat.742136
L1  - https://dergipark.org.tr/en/download/article-file/1117916
ER  -