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Mathematics Student Teachers’ Views about Misconceptions on Fractions

Year 2016, Volume: 4 Issue: 2, 1 - 15, 05.06.2016

Abstract

The purpose of this study is to determine the views of primary school mathematics student teachers regarding possible misconceptions about fractions. Qualitative research method was used for this purpose and the study was conducted with 40 primary school mathematics student teachers. The data was collected from written response papers in which student teachers wrote about the possible misconceptions on fractions and their examples. Misconceptions derived from content analysis were grouped under 12 headings. While most of the student teachers expressed two types of misconceptions, the other types of misconceptions were less expressed. There are also other misconceptions in the literature that are not indicated by teacher candidates. For this reason, it is thought that it is necessary for the student teachers to learn about different kinds of misconceptions and to learn the ways of preventing the formation of the misconceptions and also the educational ways of what they should do when they meet them.

References

  • Alghazo, Y. M. & Alghazo, R. (2017). Exploring Common Misconceptions and Errors about Fractions among College Students in Saudi Arabia. International Education Studies, 10(4), 133.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education. 7, 145–172.
  • Askew, M. & Wiliam, D. (1995). Recent research in mathematics education 5-16. Stationery Office Books (TSO).
  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: knowing and using mathematics. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning, Westport, CT: Ablex.
  • Ball, D. L., & McDiarmid, G. W. (1990). The subject matter preparation of teachers. In R. Houston (Ed.), Handbook of Research on Teacher Education. New York: Macmillan.
  • Bergeson, T. (2000). Teaching and learning mathematics. Retrieved on January, 12, 2008.
  • 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.
  • Bogen, M. (2008). When 1/2 + 1/3 = 2/5. Harvard Education Letter, 1(5), 11 - 14.
  • Booker, G. (1998). Children’s construction of initial fraction concepts. In Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 128-135).
  • Bukova Güzel, E. (2010). An investigation of pre-service mathematics teachers pedagogical content knowledge: Example of solid objects. Scientific Research and Essays, 5(14), 1872-1880.
  • Bukova Güzel, E., Elçi, A. N. & Alkan, H. (2006). Yapılandırmacı Öğrenme Ortamında Fonksiyon Kavramının Öğrenilmesine Yönelik Etkinlikler. Eğitimde Çağdaş Yönelimler – III: Yapılandırmacılık ve Eğitime Yansımaları Sempozyumu (29 Nisan 2006), Tevfik Fikret Okulları, İzmir.
  • Carlsen, W. S. (1999). Domains of teacher knowledge. In J. Gess-Newsome & N.G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education. (pp. 133-144). Springer Netherlands.
  • Charalambous, C. Y. & Pitta-Pantazi, D. (2005). Revisiting a theoretical model on fractions: Implications for teaching and research. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 233-240. Melbourne: PME.
  • Chick, H. L. & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249-256).
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
  • Durkin, K. & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29.
  • Elçi, A. N., Bukova Güzel, E. & Alkan, H. (2006a). Çok Yönlü Etkinlik Yaklaşımları ile Matematiksel Kavram Oluşturma. VII. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi (7 – 9 Eylül 2006), Gazi Üniversitesi, Ankara.
  • Elçi, A. N., Bukova Güzel, E. & Alkan, H. (2006b). Yapılandırmacı Öğrenme Yaklaşımına Uygun Çalışma Yaprakları. Eğitimde Çağdaş Yönelimler – III: "Yapılandırmacılık ve Eğitime Yansımaları Sempozyumu (29 Nisan 2006), Tevfik Fikret Okulları, İzmir.
  • Gelman, R. (2006). Young natural-number arithmeticians. Current Directions in Psychological Science, 15(4), 193-197.
  • Gess-Newsome, J. (1999). Secondary teachers’ knowledge and beliefs about subject matter and their impact on instructıon. In J. Gess-Newsome & N. G. Lederman (Eds.), Examining pedagogical content knowledge (pp. 51-94). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  • Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. In Forms of Mathematical Knowledge (pp. 189-208). Springer Netherlands. Grossman, P. L. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York: Teachers College Press.
  • Halim, L. & Meerah, S. M. M. (2002). Science trainee teachers' pedagogical content knowledge and its influence on physics teaching. Research in Science & Technological Education, 20(2), 215-225.
  • Ho, J. C. (2009). "Why Do We Need a Common Denominator?": Using Fraction Bars to Help Improve Students' Conceptual Understanding of Adding and Subtracting Fractions in an Eighth Grade Pre-Algebra Class. University of California, Davis.
  • Işıksal, M. & Çakıroğlu, 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.
  • Jordaan, T. (2005). Misconceptions of the Limit Concept in a Mathematics Course for Engineering Students. Unpublished Master of Science Dissertation, University of South Africa, Pretoria.
  • Kula, S. & Bukova Güzel, E. (2014). Misconceptions emerging in mathematics student teachers’ limit instruction and their reflections. Quality & Quantity, 48(6), 3355-3372.
  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for research in mathematics education, 16-32.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for research in mathematics education, 422-441.
  • Mayer, R. E. (1987). Educational psychology: A cognitive approach. Scott Foresman & Co.
  • 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(2), 93-103.
  • McLeod, R. & Barbara N. (2006). Maths4Life: Fractions. London, UK: National Research and Development Centre for Adult Literacy and Numeracy.
  • Nesher, P. (1987). Towards an instructional theory: The role of learners’ misconception for the learning of mathematics. For the Learning of Mathematics, 7(3), 33-39.
  • Özgen, K. (2016). Rasyonel sayılar. Elçi, A. N., Bukova Güzel, E., Cantürk Günhan, B. & Ev
  • Çimen, E. (Edt.) Temel Matematiksel Kavramlar ve Uygulamaları (s. 57-70). Ankara, Pegem Akademi.
  • Peck, D. M. & Jencks, S. M. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 12(5), 339-348.
  • Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5, 1-7.
  • Shulman, L. S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
  • Smith, D. C., & Neale, D. C. (1989). The construction of subject matter knowledge in primary science teaching. Teaching and Teacher Education, 5, 1-20.
  • Smith, J. P., diSessa, A.A. & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3, 115–163.
  • Soylu, Y. & Soylu, C. (2005). İlköğretim Beşinci Sınıf Öğrencilerinin Kesirler Konusundaki Öğrenme Güçlükleri: Kesirlerde Sıralama, Toplama, Çıkarma, Çarpma ve Kesirlerle İlgili Problemler. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 7(2), 101-117.
  • Stafylidou, S. & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and instruction, 14(5), 503-518.
  • Swan, M. (2001). 10 Dealing with misconceptions in mathematics. Issues in mathematics teaching, 147.
  • Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258-276.
  • Tirosh, D. & Graeber, A. O. (1989). Preservice elementary teachers' explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96.
  • 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.
  • Türkdoğan, A., Güler, M., Bülbül, B. Ö. & Danişman, Ş. (2015). Türkiye’de Matematik Eğitiminde Kavram Yanılgılarıyla İlgili Çalışmalar: Tematik Bir İnceleme. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 11(2), 215-236.
  • Van Steenbrugge, H., Lesage, E., Valcke, M. & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?. Journal of Curriculum Studies, 46(1), 138-161.
  • Yıldırım, A. & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin Yayıncılık.

Matematik Öğretmeni Adaylarının Kesirler Konusundaki Olası Kavram Yanılgılarına İlişkin Görüşleri

Year 2016, Volume: 4 Issue: 2, 1 - 15, 05.06.2016

Abstract

Bu çalışmanın amacı ilköğretim matematik öğretmeni adaylarının kesirler konusundaki olası kavram yanılgılarına ilişkin görüşlerini belirlemektir. Amaç doğrultusunda nitel araştırma yönteminden yararlanılmış ve çalışma 40 ilköğretim matematik öğretmeni adayı ile gerçekleştirilmiştir. Veriler öğretmen adaylarının kesirler konusunda sahip olunabilecek kavram yanılgılarını ve örneklerini yazdıkları cevap kağıtlarından derlenmiştir. İçerik analizinden yararlanılarak elde edilen yanılgılar 12 başlık altında toplanmıştır. Öğretmen adaylarının büyük kısmı iki yanılgı türünü ifade ederken, geri kalan yanılgı türleri daha az ifade edilmiştir. Alanyazında yer alan ancak öğretmen adaylarınca belirtilmeyen kavram yanılgısı türleri bulunmaktadır. Bu nedenle öğretmen adaylarının farklı yanılgı türlerine ilişkin bilgi edinmelerinin ve söz konusu yanılgıların oluşumunu engelleme yolları ile bu yanılgılarla karşılaştıklarında nasıl bir yol izlemeleri gerektiğini öğrenmelerinin gerekli olduğu düşünülmektedir.

References

  • Alghazo, Y. M. & Alghazo, R. (2017). Exploring Common Misconceptions and Errors about Fractions among College Students in Saudi Arabia. International Education Studies, 10(4), 133.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education. 7, 145–172.
  • Askew, M. & Wiliam, D. (1995). Recent research in mathematics education 5-16. Stationery Office Books (TSO).
  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: knowing and using mathematics. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning, Westport, CT: Ablex.
  • Ball, D. L., & McDiarmid, G. W. (1990). The subject matter preparation of teachers. In R. Houston (Ed.), Handbook of Research on Teacher Education. New York: Macmillan.
  • Bergeson, T. (2000). Teaching and learning mathematics. Retrieved on January, 12, 2008.
  • 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.
  • Bogen, M. (2008). When 1/2 + 1/3 = 2/5. Harvard Education Letter, 1(5), 11 - 14.
  • Booker, G. (1998). Children’s construction of initial fraction concepts. In Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 128-135).
  • Bukova Güzel, E. (2010). An investigation of pre-service mathematics teachers pedagogical content knowledge: Example of solid objects. Scientific Research and Essays, 5(14), 1872-1880.
  • Bukova Güzel, E., Elçi, A. N. & Alkan, H. (2006). Yapılandırmacı Öğrenme Ortamında Fonksiyon Kavramının Öğrenilmesine Yönelik Etkinlikler. Eğitimde Çağdaş Yönelimler – III: Yapılandırmacılık ve Eğitime Yansımaları Sempozyumu (29 Nisan 2006), Tevfik Fikret Okulları, İzmir.
  • Carlsen, W. S. (1999). Domains of teacher knowledge. In J. Gess-Newsome & N.G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education. (pp. 133-144). Springer Netherlands.
  • Charalambous, C. Y. & Pitta-Pantazi, D. (2005). Revisiting a theoretical model on fractions: Implications for teaching and research. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 233-240. Melbourne: PME.
  • Chick, H. L. & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249-256).
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
  • Durkin, K. & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29.
  • Elçi, A. N., Bukova Güzel, E. & Alkan, H. (2006a). Çok Yönlü Etkinlik Yaklaşımları ile Matematiksel Kavram Oluşturma. VII. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi (7 – 9 Eylül 2006), Gazi Üniversitesi, Ankara.
  • Elçi, A. N., Bukova Güzel, E. & Alkan, H. (2006b). Yapılandırmacı Öğrenme Yaklaşımına Uygun Çalışma Yaprakları. Eğitimde Çağdaş Yönelimler – III: "Yapılandırmacılık ve Eğitime Yansımaları Sempozyumu (29 Nisan 2006), Tevfik Fikret Okulları, İzmir.
  • Gelman, R. (2006). Young natural-number arithmeticians. Current Directions in Psychological Science, 15(4), 193-197.
  • Gess-Newsome, J. (1999). Secondary teachers’ knowledge and beliefs about subject matter and their impact on instructıon. In J. Gess-Newsome & N. G. Lederman (Eds.), Examining pedagogical content knowledge (pp. 51-94). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  • Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. In Forms of Mathematical Knowledge (pp. 189-208). Springer Netherlands. Grossman, P. L. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York: Teachers College Press.
  • Halim, L. & Meerah, S. M. M. (2002). Science trainee teachers' pedagogical content knowledge and its influence on physics teaching. Research in Science & Technological Education, 20(2), 215-225.
  • Ho, J. C. (2009). "Why Do We Need a Common Denominator?": Using Fraction Bars to Help Improve Students' Conceptual Understanding of Adding and Subtracting Fractions in an Eighth Grade Pre-Algebra Class. University of California, Davis.
  • Işıksal, M. & Çakıroğlu, 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.
  • Jordaan, T. (2005). Misconceptions of the Limit Concept in a Mathematics Course for Engineering Students. Unpublished Master of Science Dissertation, University of South Africa, Pretoria.
  • Kula, S. & Bukova Güzel, E. (2014). Misconceptions emerging in mathematics student teachers’ limit instruction and their reflections. Quality & Quantity, 48(6), 3355-3372.
  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for research in mathematics education, 16-32.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for research in mathematics education, 422-441.
  • Mayer, R. E. (1987). Educational psychology: A cognitive approach. Scott Foresman & Co.
  • 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(2), 93-103.
  • McLeod, R. & Barbara N. (2006). Maths4Life: Fractions. London, UK: National Research and Development Centre for Adult Literacy and Numeracy.
  • Nesher, P. (1987). Towards an instructional theory: The role of learners’ misconception for the learning of mathematics. For the Learning of Mathematics, 7(3), 33-39.
  • Özgen, K. (2016). Rasyonel sayılar. Elçi, A. N., Bukova Güzel, E., Cantürk Günhan, B. & Ev
  • Çimen, E. (Edt.) Temel Matematiksel Kavramlar ve Uygulamaları (s. 57-70). Ankara, Pegem Akademi.
  • Peck, D. M. & Jencks, S. M. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 12(5), 339-348.
  • Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5, 1-7.
  • Shulman, L. S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
  • Smith, D. C., & Neale, D. C. (1989). The construction of subject matter knowledge in primary science teaching. Teaching and Teacher Education, 5, 1-20.
  • Smith, J. P., diSessa, A.A. & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3, 115–163.
  • Soylu, Y. & Soylu, C. (2005). İlköğretim Beşinci Sınıf Öğrencilerinin Kesirler Konusundaki Öğrenme Güçlükleri: Kesirlerde Sıralama, Toplama, Çıkarma, Çarpma ve Kesirlerle İlgili Problemler. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 7(2), 101-117.
  • Stafylidou, S. & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and instruction, 14(5), 503-518.
  • Swan, M. (2001). 10 Dealing with misconceptions in mathematics. Issues in mathematics teaching, 147.
  • Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258-276.
  • Tirosh, D. & Graeber, A. O. (1989). Preservice elementary teachers' explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96.
  • 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.
  • Türkdoğan, A., Güler, M., Bülbül, B. Ö. & Danişman, Ş. (2015). Türkiye’de Matematik Eğitiminde Kavram Yanılgılarıyla İlgili Çalışmalar: Tematik Bir İnceleme. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 11(2), 215-236.
  • Van Steenbrugge, H., Lesage, E., Valcke, M. & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?. Journal of Curriculum Studies, 46(1), 138-161.
  • Yıldırım, A. & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin Yayıncılık.
There are 48 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Semiha Kula Ünver

Publication Date June 5, 2016
Submission Date October 2, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Kula Ünver, S. (2016). Matematik Öğretmeni Adaylarının Kesirler Konusundaki Olası Kavram Yanılgılarına İlişkin Görüşleri. Manisa Celal Bayar Üniversitesi Eğitim Fakültesi Dergisi, 4(2), 1-15.