Opinions of Pre-service Elementary School Mathematics Teachers on Misconceptions

Opinions of Pre-service Elementary School Mathematics Teachers on Misconceptions

The aim of this study is to determine the opinions of pre-service elementary school mathematics teachers about misconceptions. For this purpose, case study, which is one of the qualitative research methods, was used. The study was conducted with 54 pre-service elementary school mathematics teachers. The data collection tool of the research consists of written response papers that they give to open-ended questions asked to participants. The views of pre-service elementary school mathematics teachers to open-ended questions were analyzed by content analysis. In order to prevent misconceptions that may arise during the lesson, pre-service elementary school mathematics teachers stated that they would; investigate the misconceptions, prepare for the lesson, study the subject, concretize the subject, visualize, determine the pre-learning, give daily life examples, etc. In order to determine whether their students have misconceptions, they stated that they would ask questions, evaluate the answers, solve the test, examine the mistakes and questions, observe the reactions, etc. It is recommended for further research to examine how pre-service elementary school mathematics teachers take precautions to avoid misconceptions by preparing a lesson plan, and to examine the situations of determining and correcting mistakes in students by observing the lessons of the teachers.

___

  • Adıgüzel, T., Şimşir, F., Çubukluöz, Ö., & Gökkurt-Özdemir, B. (2018). Türkiye’de matematik ve fen eğitiminde kavram yanılgılarıyla ilgili yapılan yüksek lisans ve doktora tezleri: Tematik bir inceleme, [Master's theses and doctoral dissertations on misconceptions in mathematics and science education in Turkey: A thematic analysis]. Journal of Bayburt Education Faculty, 13(25), 57-92.
  • Aktepe, V., Tahiroğlu, M., & Acer, T. (2015). Matematik eğitiminde kullanılan öğretim yöntemlerine ilişkin öğrenci görüşleri [Student opinions on methods used in mathematics education]. Nevşehir Hacı Bektaş Veli University Journal of ISS, 4(2), 127-143.
  • Alkan, R., (2009). İlköğretim 7. sınıf öğrencilerinin matematik dersi rasyonel sayılar konusu ile ilgili hata ve kavram yanılgılarının analizi (Yüksek Lisans Tezi). [Analysis of mistakes and concept regarding the topic of rational numbers in mathematics lesson of the seventh class in the primary education (Master’s Thesis)] Elicited from the National Thesis Center of the Council of Higher Education. (Thesis No. 234392).
  • Ayyıldız, N. (2010). 6. sınıf matematik dersi geometriye merhaba ünitesine ilişkin kavram yanılgılarının giderilmesinde öğrenme günlüklerinin etkisinin incelenmesi (Yüksek Lisans Tezi). [The investigation of effect of learning logs on remedying students? misconceptions concerning `hello to geometry? topic in 6th grade mathematics lesson (Master’s Thesis)], Elicited from the National Thesis Center of the Council of Higher Education. (Thesis No. 263662)
  • Ayyıldız, N., & Altun, S. (2013). Matematik dersine ilişkin kavram yanılgılarının giderilmesinde öğrenme günlüklerinin etkisinin incelenmesi [An investigation of the effect of learning logs on remedying students’ misconceptions concerning mathematics lesson]. Hacettepe University Journal of Education, 28(2), 71-86.
  • Baki, A. (1998). Matematik öğretiminde işlemsel ve kavramsal bilginin dengelenmesi [Balancing procedural and conceptual knowledge in mathematics teaching], Paper Presented at Atatürk University 40th Anniversary Mathematics Symposium, Atatürk University, Erzurum.
  • Baki, A. (1999). Cebirle ilgili işlem yanılgılarının değerlendirilmesi [Evaluation of algebra-related computing misconceptions]. Paper Presented at III. Science Education Symposium. Ministry of National Education, General Directorate of Teacher Training
  • Baki, A., & Bell, A. (1997). Ortaöğretim matematik öğretimi [Secondary school mathematics teaching]. Ankara, Turkey: YÖK Publishing.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Ankara: Harf Eğitim Publishing.
  • Baki, A., & Kartal, T. (2004). Kavramsal ve işlemsel bilgi bağlamında lise öğrencilerinin cebir bilgilerinin karakterizasyonu [Characterizing high school students’ algebra knowledge in terms of procedural and conceptual knowledge]. The Journal of Turkish Educational Sciences, 2(1), 27-50.
  • Baykul, Y. (2003). İlköğretimde matematik öğretimi [Teaching mathematics in primary education]. Ankara, Turkey: Pegem A Publishing.
  • Berg, T., & Brouwer, W. (1991), Teacher awareness of student alternate conceptions about rotational motion and gravity. Journal of Research Science Teaching, 28, 3-18.
  • Birgin, O., & Gürbüz, R. (2009). İlköğretim II. kademe öğrencilerinin rasyonel sayılar konusundaki işlemsel ve kavramsal bilgi düzeylerinin incelenmesi [Investigate the procedural and conceptual knowledge of students between grade 6 and grade 8 about the rational numbers.]. Journal of Uludag University Faculty of Education, 22(2), 529-550.
  • Cornu, B. (1991). Limits. In D. Tall (Eds.), Advanced mathematical thinking (153-166). Dordrect, The Netherlands: Kluwer Academic.
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
  • Çetin, İ., (2009). 7. ve 9. sınıf öğrencilerinin oran ve orantı konusundaki kavram yanılgıları (Yüksek Lisans Tezi). [Seventh and nineth grade students’ misconceptions about ratio and proportion (Master’s Thesis)] Elicited from the National Thesis Center of the Council of Higher Education. (Thesis No. 245751)
  • Duatepe Paksu, A. (2013). Üslü ve köklü sayılar konularındaki öğrenme güçlükleri [Learning difficulties in exponents and radicals]. In E. Bingölbali & M. F. Özmantar (Eds.), İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri [Mathematical challenges encountered in primary education and suggestions for solutions] (pp. 9-39). Ankara, Turkey: Pegem A Publishing.
  • Duru, A. (2011). Pre-service teachers' perception about the concept of limit, Educational Sciences: Theory and Practice, 11(3), 1710-1715.
  • Ersoy, Y. (2002). Matematik okur yazarlığı-I: Genel amaçlar ve yeterlikler [Mathematical literacy-I: General objectives and competencies]. Paper presented at Mathematics Activities Symposium, Ankara.
  • Ersoy, Y. (2006). İlköğretim matematik öğretim programındaki yenilikler-I: Amaç, içerik ve kazanımlar [Innovations in mathematics curricula of elementary schools-I: Objective, content and acquisition]. Elementary Education Online, 5(1), 30-44.
  • Geddis, A. N. (1993). Transforming subject-matter knowledge: the role of pedagogical content knowledge in learning to reflect on teaching. International Journal of Science Education, 15(6), 673–683.
  • 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: Tirosh, D. (eds) Forms of Mathematical Knowledge. Springer, Dordrecht.
  • Grouws, D. & Schultz, K. (1996). Mathematics teacher education in: J. Sikula (Ed) Handbook of research on teacher education, 2nd edition (USA: Macmillan).
  • Gökkurt Özdemir, B., Bayraktar, R., & Yılmaz, M. (2017). Sınıf ve matematik öğretmenlerinin kavram yanılgılarına ilişkin açıklamaları [Explanations of primary and middle school mathematics teachers on misconceptions]. Trakya Journal of Education, 7(2), 284-305.
  • Guba, E.G., & Lincoln, Y.S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Technology Research and Development, 30(4), 233–252.
  • Güneş, B. (2007). Fizikteki kavram yanılgıları [Misconceptions in physics]. Kişisel web sayfası [Personal web page]. Retrieved from http://w3.gazi.edu.tr/~bgunes/files/kavramyanilgilari/kavramyanilgilari.html 10 Mayıs 2007
  • 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.
  • Harwood, T. G., & Garry, T. (2003). An overview of content analysis. The Marketing Review, 3(4), 479-498. İpekoğlu, A. (2017). Ortaokul matematik öğretmenlerinin kavram yanılgılarının giderilmesine yönelik çözüm önerilerinin incelenmesi (Yüksek Lisans Tezi). [An examination of secondary school teachers' solution proposals towards removal of misconseptions (Master’s Thesis)], Elicited from the National Thesis Center of the Council of Higher Education. (Thesis No. 485959)
  • 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. Retrieved from https://uir.unisa.ac.za/bitstream/handle/10500/2102/dissertation.pdf;sequence=1
  • Kaynak, M., Narlı, S., Köroğlu, H., Çelik, A., & Alkan, H. (2000). 9., 10. ve 11. sınıf öğrencilerinin 9. sınıf matematik dersinde düştükleri bazı kavram yanılgılarının belirlenmesi ve çözüme yönelik öneriler [Determination of some misconceptions of 9th, 10th and 11th grade students in 9th grade mathematics lesson and suggestions for solutions]. Paper presented at IV. Science Education Congress. Hacettepe University Education Faculty, Ankara.
  • Kula, S., & Bukova Güzel, E. (2014). Misconceptions emerging in mathematics student teachers’ limit instruction and their reflections. Quality & Quantity, 48(6), 3355-3372.
  • Mayer, R. E. (1987). Educational psychology: A cognitive approach. Scott Foresman & Co.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.
  • Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd ed). Thousand Oaks, CA: Sage.
  • 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.
  • Okur, M., & Gürel, Z. Ç. (2016). Ortaokul 6. ve 7. sınıf öğrencilerinin kesirler konusundaki kavram yanılgıları [6 th and 7th grade secondary school students’ misconceptions about fractions]. Erzincan University Journal of Education Faculty, 18(2), 922-952.
  • Özdemir Fincan, K. (2021). İlköğretim matematik öğretiminde kavram yanılgıları ile ilgili lisansüstü tezlerin incelenmesi (Yüksek Lisans Tezi). [A review of graduate theses related to misconceptions ın primary education mathematics teaching (Master’s Thesis)], Elicited from the National Thesis Center of the Council of Higher Education. (Thesis No. 701979)
  • Patton, M. Q. (2014). Qualitative Research & Evaluation Methods. 3rd edition. Sage Publications, Inc. Ryan, J., & Williams, J. (2007). Children’s mathematics 4–15: Learning from errors and misconceptions. Open University Press, Maidenhead
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • 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., & Aydın, S. (2006). Matematik derslerinde kavramsal ve işlemsel öğrenmenin dengelenmesinin önemi üzerine bir çalışma [A study on ımportance of the conceptual and operatıonal knowledge are balanced ın mathematıcs lessons]. Erzincan University Journal of Education Faculty, 8(2), 83-95.
  • Şandır, H., & Aztekin, S. (2013). Pre-service teachers' opinions and methods about finding students' misconceptions, Mediterranean Journal for Research in Mathematics Education, 12(1-2), 23-37.
  • Van de Walle, J., Karp, K., & Bay-Williams, J. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim [Elementary and middle school mathematics: Teaching developmentally]. (S. Durmuş Trans.). Ankara, Turkey: Nobel Publishing.
  • Williams, S. R. (2001). Predications of the limit concept: an application of repertory grids. Journal for Research in Mathematics Education 32(4), 343-367.
  • Yavuz Mumcu, H. (2017). Pedagojik alan bilgisi bağlamında öğretmen adaylarının kesirlerle ilgili kavram yanılgılarını giderme yeterliklerinin farklı değişkenlere göre incelenmesi [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.
  • Yenilmez, K., & Yaşa, E. (2008). İlköğretim öğrencilerinin geometrideki kavram yanılgıları [Secondary school students' misconceptions in geometry]. Journal of Uludag University Faculty of Education, 21(2) , 461-483.
  • Zembat, İ, Ö. (2013). Kavram yanılgısı nedir?[What is misconception?]. In M.F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri [Mathematical misconceptions and solution suggestions] (pp. 1-8). Ankara, Turkey: Pegem A Publishing.