# EXAMINING MATHEMATICS DEPARTMENT STUDENTS’ VIEWS ON THE USE OF MATHEMATICS IN DAILY LIFE

## Main Article Content

## Abstract

Some researchers report that especially the students of the faculty of science and letters do not have sufficient knowledge of the practicability of mathematics since they are mostly interested in the pure aspect of mathematics, and they have difficulty in using their pure mathematical knowledge properly. So, this study aims to examine the views of mathematics students registered in the pedagogical formation program about the use of mathematics in daily life. To this end, an interview form with open-ended questions was administered to 86 pre-service mathematics teachers. The findings showed that pre-service teachers viewed mathematics as an indispensable part of life, but they treated real-life math and school math as separate types of math and had difficulty in relating them to each other. We recommend the use of real or real-like situations in the classroom environment in order to train individuals who can associate mathematics with everyday life and use it more effectively.

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## References

Aksu, M., Demir, C., & Sümer, Z. (1998). Mathematics teachers and students’ beliefs about mathematics. III. National Science Education Conference. Karadeniz Technical University, Trabzon, Turkey.

Arslan, S., & Yildiz, C. (2010). Reflections from the experiences of 11th graders during the stages of mathematical thinking. Egitim ve Bilim. 35 (156), 17-31.

Baki, A. (2014). Kuramdan uygulamaya matematik eğitimi (5. Basım).Trabzon: Derya Kitabevi.

Ball, D. L. (1988). Research on teaching mathematics: Making subject matter knowledge part of the equation (pp. 1-48). National Center for Research on Teacher Education, Michigan State University.

Baydar, C. S. (2000). Beliefs of pre-service mathematics teachers at the Middle East Technical University and Gazi University about the nature of mathematics and the teaching of mathematics. (Unpublishhed master’s thesis). Middle East Technical University, Ankara.

Baydar, S. C., & Bulut, S. (2002). Importance of teachers’ beliefs about nature of mathematics and teaching of mathematics in mathematics education. Journal of Hacettepe University Education Faculty. 23, 62-66.

Beaton, A. E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., Smith, T.A. (1996). Mathematics achievement in the middle school years. IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: Boston College, Center for the Study of Testing, Evaluation, and Educational Policy.

Beswick, K., Watson, J., & Brown, N. (2006). Teachers’ confidence and beliefs and their students’ attitudes to mathematics. Identities, Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia, 68-75.

Blitzer, R. (2003). Thinking mathematically. New Jersey: Prentice Hall.

Bondi, C. (1991). New applications of mathematics. London: Penguin.

Büyüköztürk, Ş., Çakmak, E. Kılıç, A., Özcan, E., Karadeniz, Ş. ve Demirel, F. (2011). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi Yayınları.

Carter, G., & Norwood, K. S. (1997). The relationship between teacher and student beliefs about mathematics. School Science and Mathematics. 97(2), 62-67.

Civelek, Ş., Meder, M., Tüzen, H., & Aycan, C. (2003). Matematik öğretiminde karşılaşılan aksaklıklar. Retrieved from http://www.matder.org.tr/index.php?option=com_content&view=article&catid=8:matematik-kosesi-makaleleri&id=62:matematik-ogretiminde-karsilasilan-aksakliklar-&Itemid=38

Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th ed.). London: Routledge Falmer.

Cooney, T. J. (1985). A beginning teacher's view of problem solving. Journal for Research in Mathematics Education. 16 (5), 324-336.

Çontay, E. G., and İymen, E. (2011). İlköğretim 3. sınıf öğrencilerinin okul matematiğini günlük hayata uygulama becerileri. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi. 30(30), 63-77.

De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491–549). NewYork, NY: Macmillan.

Dede, Y., & Karakus, F. (2014). The effect of teacher training programs on pre-service mathematics teachers' beliefs towards mathematics. Educational Sciences: Theory and Practice. 14(2), 804-809.

Duatepe Paksu, A. (2008). Comparing teachers' beliefs about mathematics in terms of their branches and gender. Hacettepe University Journal of Education. 35, 87-97.

Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: amodel. Journal of Education for Teaching. 15(1), 13-33.

Erturan, D. (2007). 7. sınıf öğrencilerinin sınıf içindeki matematik başarıları ile günlük hayatta matematiği fark edebilmeleri arasındaki ilişki. (Unpublished Master’s Thesis). Hacettepe University, Ankara.

Feiman-Nemser, S., McDiarmid, G. W., Melnick, S., & Parker, M. (1988). Changing beginning teachers’ conceptions: A study of an introductory teacher education course. East Lansing: National Center for Research on Teacher Education and Department of Teacher Education, Michigan State University.

Felbrich, A., Müller, C., & Blömeke, S. (2008). Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics. ZDM. 40(5), 763-776.

Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? The Arithmetic Teacher. 37(5), 10–12.

Gainsburg, J. (2008). Real world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education. 11(3), 199-219.

Greer, B. (1993). The modelling perspective on wor(l)d problems. Journal of Mathematical Behavior. 12, 239-250.

Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction. 7 (4), 293-307.

Gülten, D. Ç., İlgar, L., & Gülten, İ. (2009). Lise 1. sınıf öğrencilerinin matematik konularının günlük yaşamda kullanımı konusundaki fikirleri üzerine bir araştırma. Hasan Ali Yücel Eğitim Fakültesi Dergisi. 11(1), 51-62.

Güzel, E. B. (2008). Yapılandırmacı öğrenme yaklaşımına dayalı matematik öğreniminin bilimi tanıma, yaşam ile ilişki kurma, öğrenmeyi öğrenme, sorgulayarak ve iletişim kurarak öğrenme üzerindeki etkisinin belirlenmesi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi. 135-149.

Henderson, P. B., Hitchner, L., Fritz, S. J., Marion, B., Scharff, C., Hamer, J., & Riedesel, C. (2002, June). Materials development in support of mathematical thinking. In ACM SIGCSE Bulletin (Vol. 35, No. 2, pp. 185-190). ACM.

Henn, H. W. (2007). Modelling in school-chances and obstacles. The Monhana Mathematics Enthusiast, Monograph 3. 125-138.

Inoue, N. (2005).The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction. 15, 69-83.

Kılıç, Ç. (2011). İlköğretim matematik öğretmen adaylarının standart olmayan sözel problemlere verdikleri yanıtlar ve yorumlar. Journal of Kirsehir Education Faculty. 12(3), 55-74.

Kirk, J., & Miller, M. L. (1986). Reliability and Validity in Qualitative Research. Beverly Hills: Sage.

Köller, O., Baumert, J., & Neubrand, J. (2000). Epistemologische Überzeugungen und Fachverständnis im Mathematik- und Physikunterricht. In Mathematische und physikalische Kompetenzen am Ende der gymnasialen Oberstufe (pp. 229-269). Opladen: Leske + Budrich.

LeCompte, M. D., & Goetz, J. P. (1982). Ethnographic data collection in evaluation research. Educational evaluation and policy analysis. 4(3), 387-400.

Lester, F., Garofalo, J., & Kroll, D. (1989). The role of metacognition in mathematical problem solving: A study of two grade seven classes. Final report to the National Science Foundation of NSF Project, MDR 85-50346.

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry (Vol. 75). Beverly Hills, CA: Sage.

Manouchehri, A. (1997). School mathematics reform: Implications for mathematics teacher preparation. Journal of Teacher Education. 48(3), 197-209.

Masingila, J.O. (1995). Examining students’ perceptions of their everyday mathematics practice. Proceedings of the Annual Meeting of the American Educational Research Association. San Francisco. Retrieved from

http://files.eric.ed.gov/fulltext/ED387347.pdf

Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: A sourcebook. Beverly Hills: Sage Publications.

Muller E., & Burkhardt, H. (2007). Applications and modelling for mathematics-overview. In W. Blum, P.L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI-study (pp. 265-275). NewYork: Springer.

National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston , VA : Author.

Neyland, J. (1994). Mathematics education: a handbook for teachers. Wellington: Wellington College Press.

OECD (2013). PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy. OECD Publishing.

OECD (2014). PISA 2012 Results: What Students Know and Can Do: Student Performance in Mathematics, Reading and Science. OECD Publishing.

Öktem, S. P. (2009). İlköğretim ikinci kademe öğrencilerinin gerçekçi cevap gerektiren matematiksel sözel problemleri çözme becerileri. (Yayınlanmamış Yüksek Lisans Tezi). Çukurova Üniversitesi Sosyal Bilimler Enstitüsü, Adana.

Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. (1989). Teacher's pedagogical content beliefs in mathematics. Cognition and instruction. 6(1), 1-40.

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education. 28 (5), 550-576.

Raymond, A. M., & Santos, V. (1995). Preservice elementary teachers and self-reflection: How innovation in mathematics teacher preparation challenges mathematics beliefs. Journal of Teacher Education. 46(1), 58-70.

Restıvo, S., Van Bendegen, J.P., and Fısher, R. (1993). Maths World: Philosophical Social Studies of Mathematics and Mathematical Education. New York: New York State University Press.

Reusser, K.., and Stebler, R. (1997). Every word problem has a solution – The social rationality of mathematical modeling in schools. Learning and Instruction. 7, 309-327.

Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

Staub, F. C., & Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology. 94(2), 344.

Tavşancıl, E., & Aslan, E. (2001). Content Analyse and Application Examples. İstanbul: Epsilon Yayıncılık.

Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.

Treffers, A., & De Moor, E. (1990). Proeve van een nationaal programma van het reken-wiskundeonderwijs op de basisschool. Deel 2: Basisvaardigheden en cijferen [Specimen of a national program for primary mathematics teaching. Part 2: Basic mental strategies and written computation]. Tilburg, The Netherlands: Zwijsen.

Underhill, R.G. (1988). Focus on research into practice in diagnostic and prescriptive nıathematics. Focus on Learning Problems in Mathematies. 10(3), 43-58.

Verschaffel, L, De Corte, E., & Borghart, I. (1997). Pre-service teachers’conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction. 7(4), 339-359.

Verschaffel, L., De Corte E. and Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction. 4, 273-294.

Wallace, C. S., & Kang, N. H. (2004). An investigation of experienced secondary science teachers' beliefs about inquiry: An examination of competing belief sets. Journal of Research in Science Teaching. 41(9), 936-960.

Yıldırım, A., & Şimşek, H. (2005). Qualitative Research Methods in Social Sciences. Ankara: Seçkin Publishing.

Yin, R.K (2009). Case study research: Design and methods. London: Sage

Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties. Learning and Instruction. 7 (4), 329-338.

Arslan, S., & Yildiz, C. (2010). Reflections from the experiences of 11th graders during the stages of mathematical thinking. Egitim ve Bilim. 35 (156), 17-31.

Baki, A. (2014). Kuramdan uygulamaya matematik eğitimi (5. Basım).Trabzon: Derya Kitabevi.

Ball, D. L. (1988). Research on teaching mathematics: Making subject matter knowledge part of the equation (pp. 1-48). National Center for Research on Teacher Education, Michigan State University.

Baydar, C. S. (2000). Beliefs of pre-service mathematics teachers at the Middle East Technical University and Gazi University about the nature of mathematics and the teaching of mathematics. (Unpublishhed master’s thesis). Middle East Technical University, Ankara.

Baydar, S. C., & Bulut, S. (2002). Importance of teachers’ beliefs about nature of mathematics and teaching of mathematics in mathematics education. Journal of Hacettepe University Education Faculty. 23, 62-66.

Beaton, A. E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., Smith, T.A. (1996). Mathematics achievement in the middle school years. IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: Boston College, Center for the Study of Testing, Evaluation, and Educational Policy.

Beswick, K., Watson, J., & Brown, N. (2006). Teachers’ confidence and beliefs and their students’ attitudes to mathematics. Identities, Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia, 68-75.

Blitzer, R. (2003). Thinking mathematically. New Jersey: Prentice Hall.

Bondi, C. (1991). New applications of mathematics. London: Penguin.

Büyüköztürk, Ş., Çakmak, E. Kılıç, A., Özcan, E., Karadeniz, Ş. ve Demirel, F. (2011). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi Yayınları.

Carter, G., & Norwood, K. S. (1997). The relationship between teacher and student beliefs about mathematics. School Science and Mathematics. 97(2), 62-67.

Civelek, Ş., Meder, M., Tüzen, H., & Aycan, C. (2003). Matematik öğretiminde karşılaşılan aksaklıklar. Retrieved from http://www.matder.org.tr/index.php?option=com_content&view=article&catid=8:matematik-kosesi-makaleleri&id=62:matematik-ogretiminde-karsilasilan-aksakliklar-&Itemid=38

Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th ed.). London: Routledge Falmer.

Cooney, T. J. (1985). A beginning teacher's view of problem solving. Journal for Research in Mathematics Education. 16 (5), 324-336.

Çontay, E. G., and İymen, E. (2011). İlköğretim 3. sınıf öğrencilerinin okul matematiğini günlük hayata uygulama becerileri. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi. 30(30), 63-77.

De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491–549). NewYork, NY: Macmillan.

Dede, Y., & Karakus, F. (2014). The effect of teacher training programs on pre-service mathematics teachers' beliefs towards mathematics. Educational Sciences: Theory and Practice. 14(2), 804-809.

Duatepe Paksu, A. (2008). Comparing teachers' beliefs about mathematics in terms of their branches and gender. Hacettepe University Journal of Education. 35, 87-97.

Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: amodel. Journal of Education for Teaching. 15(1), 13-33.

Erturan, D. (2007). 7. sınıf öğrencilerinin sınıf içindeki matematik başarıları ile günlük hayatta matematiği fark edebilmeleri arasındaki ilişki. (Unpublished Master’s Thesis). Hacettepe University, Ankara.

Feiman-Nemser, S., McDiarmid, G. W., Melnick, S., & Parker, M. (1988). Changing beginning teachers’ conceptions: A study of an introductory teacher education course. East Lansing: National Center for Research on Teacher Education and Department of Teacher Education, Michigan State University.

Felbrich, A., Müller, C., & Blömeke, S. (2008). Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics. ZDM. 40(5), 763-776.

Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? The Arithmetic Teacher. 37(5), 10–12.

Gainsburg, J. (2008). Real world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education. 11(3), 199-219.

Greer, B. (1993). The modelling perspective on wor(l)d problems. Journal of Mathematical Behavior. 12, 239-250.

Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction. 7 (4), 293-307.

Gülten, D. Ç., İlgar, L., & Gülten, İ. (2009). Lise 1. sınıf öğrencilerinin matematik konularının günlük yaşamda kullanımı konusundaki fikirleri üzerine bir araştırma. Hasan Ali Yücel Eğitim Fakültesi Dergisi. 11(1), 51-62.

Güzel, E. B. (2008). Yapılandırmacı öğrenme yaklaşımına dayalı matematik öğreniminin bilimi tanıma, yaşam ile ilişki kurma, öğrenmeyi öğrenme, sorgulayarak ve iletişim kurarak öğrenme üzerindeki etkisinin belirlenmesi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi. 135-149.

Henderson, P. B., Hitchner, L., Fritz, S. J., Marion, B., Scharff, C., Hamer, J., & Riedesel, C. (2002, June). Materials development in support of mathematical thinking. In ACM SIGCSE Bulletin (Vol. 35, No. 2, pp. 185-190). ACM.

Henn, H. W. (2007). Modelling in school-chances and obstacles. The Monhana Mathematics Enthusiast, Monograph 3. 125-138.

Inoue, N. (2005).The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction. 15, 69-83.

Kılıç, Ç. (2011). İlköğretim matematik öğretmen adaylarının standart olmayan sözel problemlere verdikleri yanıtlar ve yorumlar. Journal of Kirsehir Education Faculty. 12(3), 55-74.

Kirk, J., & Miller, M. L. (1986). Reliability and Validity in Qualitative Research. Beverly Hills: Sage.

Köller, O., Baumert, J., & Neubrand, J. (2000). Epistemologische Überzeugungen und Fachverständnis im Mathematik- und Physikunterricht. In Mathematische und physikalische Kompetenzen am Ende der gymnasialen Oberstufe (pp. 229-269). Opladen: Leske + Budrich.

LeCompte, M. D., & Goetz, J. P. (1982). Ethnographic data collection in evaluation research. Educational evaluation and policy analysis. 4(3), 387-400.

Lester, F., Garofalo, J., & Kroll, D. (1989). The role of metacognition in mathematical problem solving: A study of two grade seven classes. Final report to the National Science Foundation of NSF Project, MDR 85-50346.

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry (Vol. 75). Beverly Hills, CA: Sage.

Manouchehri, A. (1997). School mathematics reform: Implications for mathematics teacher preparation. Journal of Teacher Education. 48(3), 197-209.

Masingila, J.O. (1995). Examining students’ perceptions of their everyday mathematics practice. Proceedings of the Annual Meeting of the American Educational Research Association. San Francisco. Retrieved from

http://files.eric.ed.gov/fulltext/ED387347.pdf

Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: A sourcebook. Beverly Hills: Sage Publications.

Muller E., & Burkhardt, H. (2007). Applications and modelling for mathematics-overview. In W. Blum, P.L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education, The 14th ICMI-study (pp. 265-275). NewYork: Springer.

National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston , VA : Author.

Neyland, J. (1994). Mathematics education: a handbook for teachers. Wellington: Wellington College Press.

OECD (2013). PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy. OECD Publishing.

OECD (2014). PISA 2012 Results: What Students Know and Can Do: Student Performance in Mathematics, Reading and Science. OECD Publishing.

Öktem, S. P. (2009). İlköğretim ikinci kademe öğrencilerinin gerçekçi cevap gerektiren matematiksel sözel problemleri çözme becerileri. (Yayınlanmamış Yüksek Lisans Tezi). Çukurova Üniversitesi Sosyal Bilimler Enstitüsü, Adana.

Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. (1989). Teacher's pedagogical content beliefs in mathematics. Cognition and instruction. 6(1), 1-40.

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education. 28 (5), 550-576.

Raymond, A. M., & Santos, V. (1995). Preservice elementary teachers and self-reflection: How innovation in mathematics teacher preparation challenges mathematics beliefs. Journal of Teacher Education. 46(1), 58-70.

Restıvo, S., Van Bendegen, J.P., and Fısher, R. (1993). Maths World: Philosophical Social Studies of Mathematics and Mathematical Education. New York: New York State University Press.

Reusser, K.., and Stebler, R. (1997). Every word problem has a solution – The social rationality of mathematical modeling in schools. Learning and Instruction. 7, 309-327.

Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

Staub, F. C., & Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology. 94(2), 344.

Tavşancıl, E., & Aslan, E. (2001). Content Analyse and Application Examples. İstanbul: Epsilon Yayıncılık.

Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.

Treffers, A., & De Moor, E. (1990). Proeve van een nationaal programma van het reken-wiskundeonderwijs op de basisschool. Deel 2: Basisvaardigheden en cijferen [Specimen of a national program for primary mathematics teaching. Part 2: Basic mental strategies and written computation]. Tilburg, The Netherlands: Zwijsen.

Underhill, R.G. (1988). Focus on research into practice in diagnostic and prescriptive nıathematics. Focus on Learning Problems in Mathematies. 10(3), 43-58.

Verschaffel, L, De Corte, E., & Borghart, I. (1997). Pre-service teachers’conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction. 7(4), 339-359.

Verschaffel, L., De Corte E. and Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction. 4, 273-294.

Wallace, C. S., & Kang, N. H. (2004). An investigation of experienced secondary science teachers' beliefs about inquiry: An examination of competing belief sets. Journal of Research in Science Teaching. 41(9), 936-960.

Yıldırım, A., & Şimşek, H. (2005). Qualitative Research Methods in Social Sciences. Ankara: Seçkin Publishing.

Yin, R.K (2009). Case study research: Design and methods. London: Sage

Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties. Learning and Instruction. 7 (4), 329-338.