Research Article
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Examination of Pre-Service Teachers’ Ability to Eliminate Misconceptions about Fractions in terms of Pedagogical Content Knowledge According to Different Variables

Year 2017, Volume: 6 Issue: 3, 1264 - 1292, 30.10.2017
https://doi.org/10.14686/buefad.337019

Abstract

The aim of this study is to determine the
pre-service teachers' competencies to eliminate possible misconceptions about
fractions and to examine these competencies according to different variables.
 The teaching methods preferred
by the prospective teachers have also been investigated. The study has been conducted
on the mixed method. The study group is composed of 52 teacher candidates who
are senior students of a state university elementary mathematics education
program. Eliminating Misconceptions
Form was used as data collection tool in the study. The analysis of the data was
carried out in four stages. Scoring Scale was used in this process. As a result
of the research, it was seen that the teacher candidates mostly preferred the
method of using a model in order to eliminate the misconceptions. They generally propose valid methods
but they are found to be inadequate to use these methods. Furthermore, there
were no significant relationships/differences between the competencies
according to variables of taking (or not) elective course of Misconceptions in Mathematics Education,
school type and general academic average.

References

  • Akgün, L., Çiltaş, A. vd. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi. 12(6), 1-34.
  • Aksu, M. (1997). Student performance in dealing with fractions. The Journal of Educational Research. 90 (6), 375-380.
  • Alacacı, C., (2010). Öğrencilerin kesirler konusundaki kavram yanılgıları. E. Bingölbali ve M.F. Özmantar (Ed.), Matematiksel zorluklar ve çözüm önerileri içinde (s. 63-95). Ankara: PegemA Yayıncılık.
  • Ball, D. L. (1990a). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education. 21, 132-144.
  • Ball, D. L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal. 90, 449-469.
  • Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. T. P. Carpenter, E. Fennema, & T. A. Romberg (Ed.), In Rational numbers: An integration of research (pp. 157–195). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Bayazit, İ., Aksoy, Y. vd. (2011). Öğretmenlerin matematiksel modelleri anlama ve model oluşturma yeterlilikleri. Nwsa: Education Sciences. 6 (4), 2495-2516.
  • Behr, M. J., Lesh, R. vd. (1983). Rational number concepts. R. Lesh, & M. Landau (Ed.), In Acquisition of mathematics concepts and processes (pp. 91-126). New York: Academic Press.
  • Behr, M., Harel, G. et al. (1993). Rational Number: Towards a semantic analysis. T. Carpenter, E. Fennema, & T. Romberg (Ed.), In Rational numbers: An integration of research (pp. 13-47). Hillsdale, NJ: Erlbaum.
  • Bezuk, N. S., & Bieck, M. (1993). Current research on rational numbers and common fractions: summary and implications for teachers. D. T. Owens (Ed.), In Research ideas for the classroom middle grades mathematics (pp. 118 - 136). New York: MacMillan.
  • Bigalke, H.G., & Hasemann, K. (1978). Zur Didaktik der Mathematik in den Klassen 5 and 6, Band 2. Frankfurt: Diester weg.
  • Booker, G., (1998). Children’s construction of ınitial fraction concepts. In proceedings of the 22. Conference of the International Group for the Psychology of Mathematics Education. Stellenbosh, South Africa. 2, 128-135.
  • Borko, H., & Putnam, R., (1996). Learning to teach. D. Berliner, & R. Calfee (Ed.), In Handbook of educational psychology (pp. 673–708). New York: Macmillan.
  • Borko, H., Eisenhart, M. et al. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education. 23, 194-222.
  • 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.). In Proceedings of the 29th conference of the international group for the psychology of mathematics education, 2, 233-240.
  • Creswell, J., & Plano Clark, V. L. (2007). Understanding mixed methods research. J. Creswell (Ed.), In Designing and conducting mixed methods research (pp. 1-19). Thousand Oaks, CA: Sage.
  • Çelik, B., ve Çiltaş, A. (2016). Beşinci sınıf kesirler konusunun öğretim sürecinin matematiksel modeller açısından incelenmesi. Bayburt Eğitim Fakültesi Dergisi. 10 (1), 180-204.
  • Davis, E. G. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior. 22, 107–111.
  • de Castro, B. (2008). Cognitive models: the missing link to learning fraction multiplication and division. Asia Pacific Education Review. 9(2), 101-112. http://dx.doi.org/10.1007/BF03026491
  • Dickson, L., Brown, B. et al. (1993). Children Learning Mathematics: A Teacher’s Guide to Recent Research. London: Cassell.
  • Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude. (Unpublished doctoral dissertation). Ataturk University, Erzurum.
  • Gökkurt, B., Şahin, Ö. vd. (2012). Matematik öğretmenlerinin matematiksel alan bilgileri ile pedagojik alan bilgileri arasındaki ilişkinin incelenmesi. The Journal of Academic Social Science Studies. 5(8), 997-1012.
  • Gökkurt, B., Şahin, Ö. vd. (2016). Öğretmen adaylarının değişken kavramına yönelik pedagojik alan bilgilerinin öğrenci hataları bağlamında incelenmesi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi. 39, 17-31.
  • Gökkurt, B., Şahin, Ö. vd. (2013). Öğretmen adaylarının kesirlerle ilgili pedagojik alan bilgilerinin öğrenci hataları açısından incelenmesi. International Online Journal of Educational Sciences. 5(3), 719-735.
  • Hanson, D. (1995). Understanding Fractions (Grades 5 to 8). http://mathcentral.uregina.ca/RR/database/RR.09.95/hanson4.html
  • Hart, K. M. (1987). Practical work and formalisation, too great a gap. J. C. Bergeron, N. Herscovicsi, & C. Kieran (Ed.). In Proceedings of the eleventh international conference psychology of mathematics education. (pp. 408-415). Montreal: The University of Montreal.
  • Hart, K.M., (1993). Fractions. In K. M. Hart (Ed.,), In Children’s understanding of mathematics: 11-16, (pp. 66-81). London: John Murray.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics. 12(1), 71–87.
  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education. 28, 524–549.
  • Işık, C. ve Kar, T. (2012). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online. 11(4), 1021-1035.
  • Işıksal M. & Osmanoğlu, A. (2016). Pedagojik alan bilgisi. Erhan Bingölbali, Selahattin Arslan, İsmail Özgür Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 677-699). Ankara: Pegem.
  • Işıksal, M. (2006). İlköğretim matematik öğretmen adaylarının kesirlerde çarpma ve bölmeye ilişkin alan ve pedagojik içerik bilgileri üzerine bir çalışma. (Yayımlanmamış doktora tezi). Orta Doğu Teknik Üniversitesi, Ankara.
  • Kabapınar, F. (2003). Kavram yanılgılarının ölçülmesinde kullanılabilecek bir ölçeğin bilgi-kavrama düzeyini ölçmeyi amaçlayan ölçekten farklılıkları. Kuram ve Uygulamada Eğitim Yönetimi. 35(35), 398-417.
  • Karaağaç, M. K., ve Köse, L. (2015). Öğretmen ve öğretmen adaylarının öğrencilerin kesirler konusundaki kavram yanılgıları ile ilgili bilgilerinin incelenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi. 30, 72-92.
  • Kılcan, S. (2006). İlköğretim matematik öğretmenlerinin kavramsal bilgileri: Kesirlerle bölme. (Yayınlanmamış Yüksek Lisans Tezi). Abant İzzet Baysal Üniversitesi, Bolu.
  • Kinach, B. M., (2002a). 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, 153–186.
  • Kinach, B.M. (2002b). A cognitive strategy for developing prospective teachers‟ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education. 18(1), 51–71.
  • Kovarik, K. (2008). Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge. (Unpublished doctoral dissertation). Columbia University, New York.
  • Lamon, S. J. (1996). The development of unizing: its role in children’s partitioning strategies. Journal for Research in Mathematics Education. 27(2), 170–193. http://dx.doi.org/10.2307/749599
  • Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology. 77, 247-271.
  • Lubinski, C.A., Fox, T. et al. (1998). Learning to make sense of division of fractions: one K-8 pre-service teacher’s perspective. School Science and Mathematics. 98(5), 247–253.
  • Ma, L. (1996). Profound understanding of fundamental mathematics: What is it, why is it important, and how is it attained. (Unpublished doctoral dissertation). Stanford University, CA.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in china and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education. 21, 16-32.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education. 26(5), 422-441.
  • Mason, J. (2006) Mixing methods in a qualitatively driven way. Qualitative Research. 6 (1), 9–25.
  • McDiarmid, G. W., & Wilson, S. M. (1991). An exploration of the subject matter knowledge of alternate route teachers: Can we assume they know their subject? Journal of Teacher Education. 42, 93-103.
  • McDiarmid, G. W., Ball, D. L. et al. (1989). Why staying one chapter ahead doesn’t really work: Subject-specific pedagogy. In M. C. Reynolds (Ed.), In Knowledge base for the beginning teacher (pp. 193-205). New York: Pergamon Press.
  • Miles, M. B., & Huberman, A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. United States of America: Sage Publications.
  • 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.
  • 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, 122-147.
  • Nagle, L. M., & Mccoy, L. P. (1999). Division of fractions: procedural versus conceptual knowledge. In McCoy, L.P. (Ed.), In Studies in teaching: 1999 research digest (pp.81-85). Research projects presented at annual Research Forum (Winston-Salem, NC). ERIC Document Reproduction Service No: ED 443 814.
  • Newstead, K. and Murray, H. (1998). Young student’s construction of fractions. Proceeding of the 22nd Conference of the International Group for the Psychology of Mathematics Education. Stellenbosh, South Africa, 295-302.
  • Padberg, F., & Wartha, S. (1978). Didaktik der Bruchrechnung. Freiburg: Herder.
  • Pantziara, M., & Philippou, G. (2011). Levels of students’ “conception” of fractions. Educational Studies in Mathematics. 79 (1), 61-83.
  • Parmar, R. (2003). Understanding the concept of “division”: assessment considerations. Exceptionality. 11(3), 177-189. http://dx.doi.org/10.1207/S15327035EX1103_05
  • Patton, M. Q. (1987). How to use qualitative methods in evaluation (No. 4). California: Sage Publications, Inc.
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (Çeviri Editörleri: Mesut Bütün ve Selçuk Beşir Demir). Ankara: Pegem Akademi.
  • Post, T. R., Harel, G. et al. (1991). Intermediate teachers’ knowledge of rational number concepts. E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), In Integrating research on teaching and learning mathematics (pp. 177-198). Albany, NY: State University Press of New York.
  • Prawat, R. S. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American Journal of Education. 100 (3), 354–395. Reys, R. E., Suydam, M.N. et al. (1998). Helping Children Learn Mathematics. Boston: Allen and Bacon.
  • Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. J. Sikula (Ed.), In Handbook of research on teacher education (pp. 102–119). New York: Macmillan.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher. 15 (2), 4-14.
  • Soylu, Y. ve Soylu, C. (2005). İlköğretim beşinci sınıf öğrencilerinin kesirler konusundaki öğrenme güçlükleri: kesirlerde sıralama, toplama, çıkarma, çarpma ve kesirlerle ilgili problemler. Erzincan Eğitim Fakültesi Dergisi. 7(2), 101-117.
  • Stoddart, T., Connell, M. Et al. (1993). Reconstructing elementary teacher candidates’ understanding of mathematics and science content. Teacher and Teacher Education. 9, 229-241.
  • Thompson, A. G. (1992). Teachers‟ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), In Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
  • Thompson, A. G. (1993). Quantitative reasoning, complexity and additive structures. Educational Studies in Mathematics. 25(3), 165-208.
  • Tirosh, D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education. 31(1), 5-25.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education. 25, 166–175.
  • Toluk-Ucar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education. 2(2), 87-102.
  • Tuna, A., Biber, A. Ç., & Yurt, N. (2013). Matematik Öğretmeni Adaylarının Matematiksel Modelleme Becerileri. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi. 33(1), 129-146.
  • Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Allyn and Bacon.
  • Van Driel, J., Beijaard, D. et al. (2001). Professional development and reform in science education: The role of teachers’ practical knowledge. Journal of Research in Science Teaching. 38, 137-158.
  • Van-Steenbrugge, H., Lesage, E. et al. (2014). Preservice elementary school teachers’ knowledge of fractions: A mirror of students’ knowledge. Journal of Curriculum Studies. 46(1), 138-161.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.

Pedagojik Alan Bilgisi Bağlamında Öğretmen Adaylarının Kesirlerdeki Kavram Yanılgılarını Giderme Yeterliklerinin Farklı Değişkenlere Göre İncelenmesi

Year 2017, Volume: 6 Issue: 3, 1264 - 1292, 30.10.2017
https://doi.org/10.14686/buefad.337019

Abstract

Bu araştırmanın amacı öğretmen adaylarının,
kesirlerle ilgili olarak öğrencilerde görülmesi muhtemel kavram yanılgılarını
gidermeye yönelik yeterlik durumlarını belirleyerek, bu yeterlikleri farklı
değişkenlere göre incelemektir. Bu kapsamda ayrıca öğretmen adaylarının söz
konusu yanılgıları gidermeye yönelik tercih ettikleri öğretim yöntemleri de
araştırılmıştır. Araştırma karma desende yürütülmüştür. Çalışma grubunu bir
devlet üniversitesinin ilköğretim matematik öğretmenliği lisans programının son
sınıfına devam etmekte olan 52 öğretmen adayı oluşturmaktadır. Çalışmada veri
toplama aracı olarak araştırmacı tarafından geliştirilmiş olan ve iki bölümden
oluşan Kavram Yanılgıları Giderme
Formu 
(KYGF) kullanılmıştır. Verilerin analizi dört aşamada
gerçekleştirilmiştir. Bu süreçte iki bölümden oluşan Puanlama Ölçeği (PÖ)
kullanılmıştır. Araştırma sonucunda öğretmen adaylarının kesirlerde görülen
kavram yanılgılarını gidermek amacıyla çoğunlukla model kullanma yöntemini
tercih ettikleri ve genel olarak geçerli yöntemler önerdikleri fakat bu
yöntemleri söz konusu duruma uygun olarak kullanma noktasında yetersiz
kaldıkları görülmüştür.  Ayrıca Matematik Eğitiminde Kavram Yanılgıları
seçmeli dersini alma-almama, mezun olunan okul türü ve genel akademik not
ortalaması değişkenlerine göre öğretmen adaylarının kavram yanılgıları giderme
yeterlikleri arasında anlamlı ilişkiler/farklılıklar gözlenmemiştir.

References

  • Akgün, L., Çiltaş, A. vd. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi. 12(6), 1-34.
  • Aksu, M. (1997). Student performance in dealing with fractions. The Journal of Educational Research. 90 (6), 375-380.
  • Alacacı, C., (2010). Öğrencilerin kesirler konusundaki kavram yanılgıları. E. Bingölbali ve M.F. Özmantar (Ed.), Matematiksel zorluklar ve çözüm önerileri içinde (s. 63-95). Ankara: PegemA Yayıncılık.
  • Ball, D. L. (1990a). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education. 21, 132-144.
  • Ball, D. L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal. 90, 449-469.
  • Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. T. P. Carpenter, E. Fennema, & T. A. Romberg (Ed.), In Rational numbers: An integration of research (pp. 157–195). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Bayazit, İ., Aksoy, Y. vd. (2011). Öğretmenlerin matematiksel modelleri anlama ve model oluşturma yeterlilikleri. Nwsa: Education Sciences. 6 (4), 2495-2516.
  • Behr, M. J., Lesh, R. vd. (1983). Rational number concepts. R. Lesh, & M. Landau (Ed.), In Acquisition of mathematics concepts and processes (pp. 91-126). New York: Academic Press.
  • Behr, M., Harel, G. et al. (1993). Rational Number: Towards a semantic analysis. T. Carpenter, E. Fennema, & T. Romberg (Ed.), In Rational numbers: An integration of research (pp. 13-47). Hillsdale, NJ: Erlbaum.
  • Bezuk, N. S., & Bieck, M. (1993). Current research on rational numbers and common fractions: summary and implications for teachers. D. T. Owens (Ed.), In Research ideas for the classroom middle grades mathematics (pp. 118 - 136). New York: MacMillan.
  • Bigalke, H.G., & Hasemann, K. (1978). Zur Didaktik der Mathematik in den Klassen 5 and 6, Band 2. Frankfurt: Diester weg.
  • Booker, G., (1998). Children’s construction of ınitial fraction concepts. In proceedings of the 22. Conference of the International Group for the Psychology of Mathematics Education. Stellenbosh, South Africa. 2, 128-135.
  • Borko, H., & Putnam, R., (1996). Learning to teach. D. Berliner, & R. Calfee (Ed.), In Handbook of educational psychology (pp. 673–708). New York: Macmillan.
  • Borko, H., Eisenhart, M. et al. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education. 23, 194-222.
  • 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.). In Proceedings of the 29th conference of the international group for the psychology of mathematics education, 2, 233-240.
  • Creswell, J., & Plano Clark, V. L. (2007). Understanding mixed methods research. J. Creswell (Ed.), In Designing and conducting mixed methods research (pp. 1-19). Thousand Oaks, CA: Sage.
  • Çelik, B., ve Çiltaş, A. (2016). Beşinci sınıf kesirler konusunun öğretim sürecinin matematiksel modeller açısından incelenmesi. Bayburt Eğitim Fakültesi Dergisi. 10 (1), 180-204.
  • Davis, E. G. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior. 22, 107–111.
  • de Castro, B. (2008). Cognitive models: the missing link to learning fraction multiplication and division. Asia Pacific Education Review. 9(2), 101-112. http://dx.doi.org/10.1007/BF03026491
  • Dickson, L., Brown, B. et al. (1993). Children Learning Mathematics: A Teacher’s Guide to Recent Research. London: Cassell.
  • Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude. (Unpublished doctoral dissertation). Ataturk University, Erzurum.
  • Gökkurt, B., Şahin, Ö. vd. (2012). Matematik öğretmenlerinin matematiksel alan bilgileri ile pedagojik alan bilgileri arasındaki ilişkinin incelenmesi. The Journal of Academic Social Science Studies. 5(8), 997-1012.
  • Gökkurt, B., Şahin, Ö. vd. (2016). Öğretmen adaylarının değişken kavramına yönelik pedagojik alan bilgilerinin öğrenci hataları bağlamında incelenmesi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi. 39, 17-31.
  • Gökkurt, B., Şahin, Ö. vd. (2013). Öğretmen adaylarının kesirlerle ilgili pedagojik alan bilgilerinin öğrenci hataları açısından incelenmesi. International Online Journal of Educational Sciences. 5(3), 719-735.
  • Hanson, D. (1995). Understanding Fractions (Grades 5 to 8). http://mathcentral.uregina.ca/RR/database/RR.09.95/hanson4.html
  • Hart, K. M. (1987). Practical work and formalisation, too great a gap. J. C. Bergeron, N. Herscovicsi, & C. Kieran (Ed.). In Proceedings of the eleventh international conference psychology of mathematics education. (pp. 408-415). Montreal: The University of Montreal.
  • Hart, K.M., (1993). Fractions. In K. M. Hart (Ed.,), In Children’s understanding of mathematics: 11-16, (pp. 66-81). London: John Murray.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics. 12(1), 71–87.
  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education. 28, 524–549.
  • Işık, C. ve Kar, T. (2012). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online. 11(4), 1021-1035.
  • Işıksal M. & Osmanoğlu, A. (2016). Pedagojik alan bilgisi. Erhan Bingölbali, Selahattin Arslan, İsmail Özgür Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 677-699). Ankara: Pegem.
  • Işıksal, M. (2006). İlköğretim matematik öğretmen adaylarının kesirlerde çarpma ve bölmeye ilişkin alan ve pedagojik içerik bilgileri üzerine bir çalışma. (Yayımlanmamış doktora tezi). Orta Doğu Teknik Üniversitesi, Ankara.
  • Kabapınar, F. (2003). Kavram yanılgılarının ölçülmesinde kullanılabilecek bir ölçeğin bilgi-kavrama düzeyini ölçmeyi amaçlayan ölçekten farklılıkları. Kuram ve Uygulamada Eğitim Yönetimi. 35(35), 398-417.
  • Karaağaç, M. K., ve Köse, L. (2015). Öğretmen ve öğretmen adaylarının öğrencilerin kesirler konusundaki kavram yanılgıları ile ilgili bilgilerinin incelenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi. 30, 72-92.
  • Kılcan, S. (2006). İlköğretim matematik öğretmenlerinin kavramsal bilgileri: Kesirlerle bölme. (Yayınlanmamış Yüksek Lisans Tezi). Abant İzzet Baysal Üniversitesi, Bolu.
  • Kinach, B. M., (2002a). 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, 153–186.
  • Kinach, B.M. (2002b). A cognitive strategy for developing prospective teachers‟ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education. 18(1), 51–71.
  • Kovarik, K. (2008). Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge. (Unpublished doctoral dissertation). Columbia University, New York.
  • Lamon, S. J. (1996). The development of unizing: its role in children’s partitioning strategies. Journal for Research in Mathematics Education. 27(2), 170–193. http://dx.doi.org/10.2307/749599
  • Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology. 77, 247-271.
  • Lubinski, C.A., Fox, T. et al. (1998). Learning to make sense of division of fractions: one K-8 pre-service teacher’s perspective. School Science and Mathematics. 98(5), 247–253.
  • Ma, L. (1996). Profound understanding of fundamental mathematics: What is it, why is it important, and how is it attained. (Unpublished doctoral dissertation). Stanford University, CA.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in china and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education. 21, 16-32.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education. 26(5), 422-441.
  • Mason, J. (2006) Mixing methods in a qualitatively driven way. Qualitative Research. 6 (1), 9–25.
  • McDiarmid, G. W., & Wilson, S. M. (1991). An exploration of the subject matter knowledge of alternate route teachers: Can we assume they know their subject? Journal of Teacher Education. 42, 93-103.
  • McDiarmid, G. W., Ball, D. L. et al. (1989). Why staying one chapter ahead doesn’t really work: Subject-specific pedagogy. In M. C. Reynolds (Ed.), In Knowledge base for the beginning teacher (pp. 193-205). New York: Pergamon Press.
  • Miles, M. B., & Huberman, A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. United States of America: Sage Publications.
  • 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.
  • 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, 122-147.
  • Nagle, L. M., & Mccoy, L. P. (1999). Division of fractions: procedural versus conceptual knowledge. In McCoy, L.P. (Ed.), In Studies in teaching: 1999 research digest (pp.81-85). Research projects presented at annual Research Forum (Winston-Salem, NC). ERIC Document Reproduction Service No: ED 443 814.
  • Newstead, K. and Murray, H. (1998). Young student’s construction of fractions. Proceeding of the 22nd Conference of the International Group for the Psychology of Mathematics Education. Stellenbosh, South Africa, 295-302.
  • Padberg, F., & Wartha, S. (1978). Didaktik der Bruchrechnung. Freiburg: Herder.
  • Pantziara, M., & Philippou, G. (2011). Levels of students’ “conception” of fractions. Educational Studies in Mathematics. 79 (1), 61-83.
  • Parmar, R. (2003). Understanding the concept of “division”: assessment considerations. Exceptionality. 11(3), 177-189. http://dx.doi.org/10.1207/S15327035EX1103_05
  • Patton, M. Q. (1987). How to use qualitative methods in evaluation (No. 4). California: Sage Publications, Inc.
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (Çeviri Editörleri: Mesut Bütün ve Selçuk Beşir Demir). Ankara: Pegem Akademi.
  • Post, T. R., Harel, G. et al. (1991). Intermediate teachers’ knowledge of rational number concepts. E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), In Integrating research on teaching and learning mathematics (pp. 177-198). Albany, NY: State University Press of New York.
  • Prawat, R. S. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American Journal of Education. 100 (3), 354–395. Reys, R. E., Suydam, M.N. et al. (1998). Helping Children Learn Mathematics. Boston: Allen and Bacon.
  • Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. J. Sikula (Ed.), In Handbook of research on teacher education (pp. 102–119). New York: Macmillan.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher. 15 (2), 4-14.
  • Soylu, Y. ve Soylu, C. (2005). İlköğretim beşinci sınıf öğrencilerinin kesirler konusundaki öğrenme güçlükleri: kesirlerde sıralama, toplama, çıkarma, çarpma ve kesirlerle ilgili problemler. Erzincan Eğitim Fakültesi Dergisi. 7(2), 101-117.
  • Stoddart, T., Connell, M. Et al. (1993). Reconstructing elementary teacher candidates’ understanding of mathematics and science content. Teacher and Teacher Education. 9, 229-241.
  • Thompson, A. G. (1992). Teachers‟ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), In Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
  • Thompson, A. G. (1993). Quantitative reasoning, complexity and additive structures. Educational Studies in Mathematics. 25(3), 165-208.
  • Tirosh, D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education. 31(1), 5-25.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education. 25, 166–175.
  • Toluk-Ucar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education. 2(2), 87-102.
  • Tuna, A., Biber, A. Ç., & Yurt, N. (2013). Matematik Öğretmeni Adaylarının Matematiksel Modelleme Becerileri. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi. 33(1), 129-146.
  • Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Allyn and Bacon.
  • Van Driel, J., Beijaard, D. et al. (2001). Professional development and reform in science education: The role of teachers’ practical knowledge. Journal of Research in Science Teaching. 38, 137-158.
  • Van-Steenbrugge, H., Lesage, E. et al. (2014). Preservice elementary school teachers’ knowledge of fractions: A mirror of students’ knowledge. Journal of Curriculum Studies. 46(1), 138-161.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
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Details

Journal Section Articles
Authors

Hayal Yavuz Mumcu

Publication Date October 30, 2017
Published in Issue Year 2017 Volume: 6 Issue: 3

Cite

APA Yavuz Mumcu, H. (2017). Examination of Pre-Service Teachers’ Ability to Eliminate Misconceptions about Fractions in terms of Pedagogical Content Knowledge According to Different Variables. Bartın University Journal of Faculty of Education, 6(3), 1264-1292. https://doi.org/10.14686/buefad.337019

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