Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes

References

• Baykul Y. Elementary mathematics education. Ankara: Pegem Academy Publication; 2009.
   Google Scholar
• Van de Walle JA, Karp KS, Bay-Williams JM. Elementary and middle school mathematics: teaching developmentally. 7th ed. Boston (MA): Pearson Education; 2010.
   Google Scholar
• Cengiz A. Student's misconceptions on the concept of fraction. In: Bingölbali E, Özmantar MF, editors. Mathematical difficulties in elementary level and suggestions for solution. 1st ed. Ankara: Pegem Academy Publication; 2009.
   Google Scholar
• Dorgan K. What textbooks offer for instruction in fraction concepts. Teach Math. 1994;1(3):150–155.
   Google Scholar
• Soylu Y. Mistakes and misconceptions of students in the subject of fractions and prospective class teachers’ prediction skills. Çağdaş Eğitim Dergisi. 2008;33(356):31–39.
   Google Scholar
• Stafylidou S, Vosniadou S. The development of students’ understanding of the numerical value of fractions. Learn Instruct. 2004;14(5):503–518.
   Web of Science ®Google Scholar
• Şiap İ, Duru A. Skills of using geometrical models in fractions. Kastamonu Educ J. 2004;12(1):89–96.
   Google Scholar
• Behr MJ, Wachsmuth I, Post RT. Construct a sum: a measure of children's understanding of fraction size. J Res Math Educ. 1985;21(2):132–144.
   Google Scholar
• Tirosh D. Enhancing prospective teachers' knowledge of children's conceptions: the case of division of fractions. J Res Math Educ. 2000;31(1):5–25.
   Web of Science ®Google Scholar
• Davis EG. Teaching and classroom experiments dealing with fractions and proportional reasoning. J Math Behav. 2003;22:107–111.
   Google Scholar
• Soylu Y, ve Soylu C. Learning difficulties of 5th class in primary education at fraction: ordering, adding, subtraction, multıplication in fraction and problems related to fraction. Erzincan Univ J Educ. 2005;(2):101–117.
   Google Scholar
• Temur ÖD. Opinions of teachers of fourth and fifth grade about teaching fractions: a phenomenograhic research. Dumlupınar Univ Soc Sci J. 2011;29(20):3–212.
   Google Scholar
• Hill HC, Ball DL. Learning mathematics for teaching: results from California's mathematics professional development institutes. J Res Math Educ. 2004;35(5):330–351.
   Web of Science ®Google Scholar
• Baki M. Pre-service classroom teachers’ mathematical knowledge and instructional explanations associated with division. Educ Sci. 2013;38(167):300–311.
   Web of Science ®Google Scholar
• Tanisli D, Kose NY. Pre-service mathematic teachers’ knowledge of students about the algebraic concepts. Australian J Teach Educ. 2013;38(2): 1–18.
   Google Scholar
• Aydın M. Examining changes in mathematics teachers’ beliefs towards mathematics education [unpublished doctoral dissertation]. Trabzon: Karadeniz Technical University; 2010.
   Google Scholar
• Staley KN. Tracing the development of understanding rate of change: a case study of changes in a pre-service teacher's pedagogical content knowledge [unpublished doctoral dissertation]. Raleigh (NC): North Carolina State University; 2004.
   Google Scholar
• An S, Kulm G, Wu Z. The pedagogical content knowledge of middle school, mathematics teachers in China and the U.S. J Math Teach Educ. 2004;7:145–172.
   Google Scholar
• Cochran KF, DeRuiter JA, King RA. Pedagogical content knowing: an integrative model for teacher preparation. J Teach Educ. 1993;44(4):263–272.
   Web of Science ®Google Scholar
• Grossman PL. The making of a teacher: teacher knowledge and teacher education. New York (NY): Teachers College Press; 1990.
   Google Scholar
• Marks R. Pedagogical content knowledge: from a mathematical case to a modified conception. J Teach Educ. 1990;41(3):3–11.
   Web of Science ®Google Scholar
• Tamir P. Subject matter and related pedagogical knowledge in teacher education. Teach Teach Educ. 1988;4(2):99–110.
   Web of Science ®Google Scholar
• Shulman LS. Those who understand: knowledge growth in teaching. Educ Res. 1986;15:4–14.
   Google Scholar
• Park S, Oliver JS. National Board Certification (NBC) as a catalyst for teachers' learning about teaching: the effects of the NBC process on candidate teachers' PCK development. J Res Sci Teach. 2008;45(7):812–834.
   Web of Science ®Google Scholar
• Shulman LS. Knowledge and teaching: foundations of the new reform. Harvard Educ Rev. 1987;57(1):1–22.
   Web of Science ®Google Scholar
• Magnusson S, Krajcik J, Borko H. Nature, sources, and development of PCK for science teaching. In: Gess-Newsome J, Lederman NG, editors. Examining PCK: the construct and its implications for science education. Boston (MA): Kluwer Academic Press; 1999. p. 95–120.
   Google Scholar
• Kleickmann T, Richter D, Kunter M, et al. Teachers’ content knowledge and pedagogical content knowledge: the role of structural differences in teacher education. J Teach Educ. 2013;64(1):90–106.
   Web of Science ®Google Scholar
• Lederman NG, Newsome JG. Do subject matter knowledge, pedagogical knowledge and pedagogical content knowledge constitute the ideal gas law of science teaching? J Sci Teach Educ. 1992;3(1):16–20.
   Google Scholar
• Loughran J. Pedagogy: making sense of the complex relationship between teaching and learning. Curriculum Inq. 2013;43(1):118–141.
   Web of Science ®Google Scholar
• Even R. Subject-matter knowledge and pedagogical content knowledge: prospective secondary teachers and the function concept. J Res Math Educ. 1993;24(2):94–116.
   Web of Science ®Google Scholar
• Tall DO, Razali MR. Diagnosing students’ difficulties in learning mathematics. Int J Math Educ Sci Teach. 1993;24(2):209–222.
   Google Scholar
• Dikici R, İşleyen T. The study of learning diffıculties in relation and function from the poınt view of certain variables. Kastamonu Educ J. 2004;11(2):105–116.
   Google Scholar
• Kinach BM. A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: toward a model of effective practice. Teach Teach Educ. 2002;18:51–71.
   Web of Science ®Google Scholar
• Baştürk S, Dönmez G. Investigating mathematics student teachers’ pedagogical content knowledge in the context of knowledge of assessment. Ahi Evran Univ J Educ. 2011;12(3):17–37.
   Google Scholar
• Şahin Ö, Gökkurt B, Başıbüyük K, et al. The comparison of preservice elementary and mathematıcs teachers’ pedagogical content knowledge. J Acad Soc Sci Stud. 2013;6(4):693–713.
   Google Scholar
• Creswell JW. Educational research: planning, conducting, and evaluating quantitative and qualitative research. 4th ed. Boston (MA): Pearson Publications; 2011.
   Google Scholar
• Yıldırım A, Şimşek H. Qualitative research methods in social sciences. 8th ed. Ankara: Seçkin Publication; 2011.
   Google Scholar
• Cepni S. Introduction to research and project studies. Trabzon: Celepler Press; 2007.
   Google Scholar
• Patton MQ. How to use qualitative methods in evaluation. Thousand Oaks (CA): Sage Publications; 1987.
   Google Scholar
• Hsieh HF, Shannon SE. Three approaches to qualitative content analysis. Qual Health Res. 2005;15(9):1277–1288.
   PubMed Web of Science ®Google Scholar
• Ma L. Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah (NJ): Erlbaum; 1999.
   Google Scholar
• Gökkurt B, Şahin Ö, Soylu Y. An analysis on the relationship between the pedagogical and mathematical content knowledge of mathematics teachers. J Acad Soc Sci Stud. 2012;5(8):997–1012.
   Google Scholar
• Gökkurt B, Şahin Ö, Soylu Y, et al. Examining pre-service teachers' pedagogical content knowledge on fractions in terms of students’ errors. Int Online J Educ Sci. 2013;5(3):719–735.
   Google Scholar
• Şahin Ö, Erdem E, Başıbüyük K, et al. Examining the development of secondary mathematics teachers’ pedagogical content knowledge on numbers. Turkish J Comput Math Educ. 2014;5(3):207–230.
   Google Scholar
• Ball DL. The mathematical understandings that prospective teachers bring to teacher education. Elementary School J. 1990;90(4):449–466.
   Web of Science ®Google Scholar
• Cavin RM. Developing technological pedagogical content knowledge in preservice teachers through microteaching lesson study [doctoral dissertation]. Tallahassee (FL): The Florida State University; 2007.
   Google Scholar
• Jenkins OF. Developing teachers’ knowledge of students as learners of mathematics through structured interviews. J Math Teach Educ. 2010;13:141–154.
   Google Scholar
• Stewart MT. The effect of elementary mathematics coaching on student achievement in fourth, fifth, and sixth grade [doctoral dissertation]. Minneapolis (MN): Walden University; 2013.
   Google Scholar