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Determining secondary school mathematics teachers' errors and misconceptions in geometry

Year 2023, Volume: 4 Issue: 2, 77 - 86, 30.12.2023

Esra Altıntaş Selin Uygun

Abstract

The aim of this study is to determine the mistakes and misconceptions experienced by the teachers on the basis of the definitions and examples of geometry subjects in the error and misconception detection test prepared for elementary school mathematics teachers in secondary school geometry subjects. Errors and misconceptions experienced by teachers will open the door to mistakes and misconceptions that students will experience during the lesson. For this reason, by identifying the errors and misconceptions experienced by primary school mathematics teachers in geometry subjects, producing solutions will ensure the prevention of misconceptions. The study group of the research consists of 20 primary school mathematics teachers working in secondary schools in the center of Kars in the 2021-2022 academic year. Since the teachers who could be reached while forming the study group were included in the research, the appropriate sampling method was used. In the research, the "Error and Misconception Identification Test", which was developed by the researcher and determined by taking expert opinion, was applied. In the results of the research, it was determined that primary school mathematics teachers mostly experienced errors and misconceptions about basic geometric concepts, quadrilaterals and prisms. It was determined that the teachers did not experience the misconception that they only made mistakes in some questions.

Keywords

Elementary mathematics Error Geometry teaching Mathematics education Math teachers’ misconceptions

References

  • Ay, Y. (2014). Yedinci sınıf öğrencilerinin çokgenlerle ilgili kavram yanılgıları ve nedenlerinin belirlenmesi (Determining seventh grade students' misconceptions about polygons and their reasons). Master thesis. Ege University, Izmir
  • Berkant, H. G., & Çadırlı, G. (2019). Ortaokul öğrencilerinin geometri öz-yeterlik inançlarının ve geometric düşünme becerilerinin incelenmesi (Examining secondary school students' geometry self-efficacy beliefs and geometric thinking skills). Turkish Journal of Educational Studies, 6(3), 29-52.
  • Blanco, L. J. (2001). Errors in the teaching/learning of the basic concepts of geometry. International Journal for Mathematics Teaching and Learning, 24.
  • Borasi, R. (1987). Exploring mathematics through the analysis of errors. For the learning of Mathematics, 7(3), 2-8.
  • Bozkurt, A., & Koç, Y. (2012). İlköğretim matematik öğretmenliği birinci sınıf öğrencilerinin prizma kavramına dair bilgilerinin incelenmesi (Examining the knowledge of first-year primary school mathematics teaching students about the concept of prism). Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2941-2952.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2020). Örnekleme yöntemleri (Sampling methods). Pegem Yayıncılık. Çakmak, Z., Konyalıoğlu, A. C., & Işık, A. (2014). İlköğretim matematik öğretmen adaylarının üç boyutlu cisimlere ilişkin konu alan bilgilerinin incelenmesi (Examining the subject knowledge of primary school mathematics teacher candidates regarding three-dimensional object). MiddleEastern & African Journal of EducationalResearch, 8(1), 28-44.
  • Cunningham, R. F., and Roberts, A. (2010). Reducing the mismatch of geometry concept definitions andconcept images held by pre-service teachers. Issuesin the Undergraduate Mathematics Preparationof School Teachers, 1.
  • Doyuran, G. (2014). Ortaokul öğrencilerinin temel geometri konularında sahip oldukları kavram yanılgıları (Misconceptions of secondary school students about basic geometry ). Master thesis. Dokuz Eylül Unversity, İzmir.
  • Erbaş, A. K., Çetinkaya, B., & Ersoy, Y. (2010). Öğrencilerin basit doğrusal denklemlerin çözümünde karşılaştıkları güçlükler ve kavram yanılgıları (Difficulties and misconceptions encountered by students in solving simple linear equations). Eğitim ve Bilim, 34(152).
  • Erdem, Z., & Gürbüz, R. (2017) . Öğrencilerin hata ve kavram yanılgıları üzerine bir inceleme: Denklem örneği (An investigation on students' mistakes and misconceptions: Equation example). YYÜ Eğitim Fakültesi Dergisi (YYU Journal Of Education Faculty), 14(1), 640-670.
  • Erdoğan, T. (2006). Van Hiele modeline dayalı öğretim sürecinin sınıf öğretmenliği öğretmen adaylarının yeni geometri konularına yönelik hazırbulunuşluk düzeylerine etkisi (The effect of the teaching process based on the Van Hiele model on the readiness levels of classroom teacher candidates for new geometry subjects). Master thesis. Abant İzzet Baysal Unievrsity, Bolu.
  • Erdoğan, E. O. & Dur, Z. (2014). Preservice mathematics teachers’ personel figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6), 107-133.
  • Fischbein, E. (1993). The Theory of Figural Concepts. Educational studies in mathematics, 24(2), 139-162.
  • Gülkılık, H. (2008). Öğretmen adaylarının bazı geometrik kavramlarla ilgili sahip oldukları kavram imajlarının ve imaj gelişiminin incelenmesi üzerinefenomenografik bir çalışma (A phenomenographic study on examining the concept images and image development of prospective teachers regarding some geometric concepts). Master thesis, Gazi University, Ankara.
  • Gutierrez, A., and Jaime, A. (1999). Preservice primary teachers' understanding of theconcept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253-275.
  • İncikabı, L., & Kılıç, Ç. (2013). İlköğretim öğrencilerinin geometrik cisimlerle ilgili kavram bilgilerinin analizi (Analysis of primary school students' conceptual knowledge about geometric objects). Kuramsal Eğitim Bilim Dergisi, 6(3), 343-358.
  • Jones K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the BritishSociety for Research into Learning Mathematics, 20(3), 109-114.
  • Kartal, B., & Çınar, C. (2017). İlköğretim matematik öğretmen adaylarının çokgenlere dair geometri bilgilerinin incelenmesi (Examination of primary school mathematics teacher candidates' geometry knowledge of polygons). Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(2), 375-399.
  • Kiriş, B. (2008). İlköğretim altıncı sınıf öğrencilerinin nokta, doğru, doğruparçası, işın ve düzlem konularında sahip oldukları kavram yanılgıları ve bu yanılgı nedenlerinin belirlenmesi (Determining the misconceptions of primary school sixth grade students about point, line, line segment, ray and plane and the reasons for these misconceptions). Master thesis. Adnan Menderes University, Aydın.
  • Köprücü, M. (2020). Ortaokul düzeyinde geometri kavram yanılgıları üzerine yapılan lisansüstü tezlerin betimsel içerik analizi (Descriptive content analysis of postgraduate theses on geometry misconceptions at secondary school level). In International Marmara Social Sciences Congress (Autumn 2020) (p. 447).
  • Ojose, B. (2015). Students’ misconceptions in mathematics: analysis of remedies and what research says. Ohio Journal of School Mathematics, 70, 30-34. Paksu, A. D., Musan, M., İymen, E., & Pakmak, G. S. (2012). Sınıf öğretmeni adaylarının boyut konusundaki kavram görüntüleri (Concept images of classroom teacher candidates about size). Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (34), 52-68.
  • Skordoulis, C., Vitsas, T., Dafermos, V., and Koleza, E. (2009). The system of coordinates as an obstacle in understanding the concept of dimension. International Journal of Science and Mathematics Education, 7(2), 253-272.
  • Şengün, K. Ç., & Yılmaz, S. (2021). Ortaokul 8. sınıf öğrencilerinin üçgende açıortay ve kenarortay belirleme durumlarının incelenmesi (Concept images of classroom teacher candidates about size). International Journal of Active Learning, 6(1), 81-97.
  • Tall, D. and Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169. Türk Dil Kurumu, (2011). Türkçe sözlükleri (Turkish dictionaries). Ankara: Türk Dil Kurumu Yayınları.
  • Türnüklü, E., & Ergin, A. S. (2016). 8. sınıf öğrencilerinin görsel tanıma ve tanımlamaları: cisim imgeleri (Visual recognition and definitions of 8th grade students: object images). İlköğretim Online, 15(1). Ulusoy, F. (2022). Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments. International Journal of Mathematical Education in Science and Technology, 1-20.
  • Usta, N. (2018). Öğretmen adaylarının ölçüler konusunda öğrenci hatalarını tespit etme becerileri vehataların giderilmesine ilişkin önerileri (Teacher candidates' skills in detecting student errors regarding measurements and their suggestions for eliminating errors). Journal of Computer and Education Research, 6(12), 247-284.
  • Yazıcı, N. (2019). Temel geometri kavramlarına ilişkin matematik öğretmen adaylarının genel alan bilgisi (General field knowledge of mathematics teacher candidates regarding basic geometry concepts). Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 21(1), 135-155.

Year 2023, Volume: 4 Issue: 2, 77 - 86, 30.12.2023

Esra Altıntaş Selin Uygun

Abstract

References

  • Ay, Y. (2014). Yedinci sınıf öğrencilerinin çokgenlerle ilgili kavram yanılgıları ve nedenlerinin belirlenmesi (Determining seventh grade students' misconceptions about polygons and their reasons). Master thesis. Ege University, Izmir
  • Berkant, H. G., & Çadırlı, G. (2019). Ortaokul öğrencilerinin geometri öz-yeterlik inançlarının ve geometric düşünme becerilerinin incelenmesi (Examining secondary school students' geometry self-efficacy beliefs and geometric thinking skills). Turkish Journal of Educational Studies, 6(3), 29-52.
  • Blanco, L. J. (2001). Errors in the teaching/learning of the basic concepts of geometry. International Journal for Mathematics Teaching and Learning, 24.
  • Borasi, R. (1987). Exploring mathematics through the analysis of errors. For the learning of Mathematics, 7(3), 2-8.
  • Bozkurt, A., & Koç, Y. (2012). İlköğretim matematik öğretmenliği birinci sınıf öğrencilerinin prizma kavramına dair bilgilerinin incelenmesi (Examining the knowledge of first-year primary school mathematics teaching students about the concept of prism). Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2941-2952.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2020). Örnekleme yöntemleri (Sampling methods). Pegem Yayıncılık. Çakmak, Z., Konyalıoğlu, A. C., & Işık, A. (2014). İlköğretim matematik öğretmen adaylarının üç boyutlu cisimlere ilişkin konu alan bilgilerinin incelenmesi (Examining the subject knowledge of primary school mathematics teacher candidates regarding three-dimensional object). MiddleEastern & African Journal of EducationalResearch, 8(1), 28-44.
  • Cunningham, R. F., and Roberts, A. (2010). Reducing the mismatch of geometry concept definitions andconcept images held by pre-service teachers. Issuesin the Undergraduate Mathematics Preparationof School Teachers, 1.
  • Doyuran, G. (2014). Ortaokul öğrencilerinin temel geometri konularında sahip oldukları kavram yanılgıları (Misconceptions of secondary school students about basic geometry ). Master thesis. Dokuz Eylül Unversity, İzmir.
  • Erbaş, A. K., Çetinkaya, B., & Ersoy, Y. (2010). Öğrencilerin basit doğrusal denklemlerin çözümünde karşılaştıkları güçlükler ve kavram yanılgıları (Difficulties and misconceptions encountered by students in solving simple linear equations). Eğitim ve Bilim, 34(152).
  • Erdem, Z., & Gürbüz, R. (2017) . Öğrencilerin hata ve kavram yanılgıları üzerine bir inceleme: Denklem örneği (An investigation on students' mistakes and misconceptions: Equation example). YYÜ Eğitim Fakültesi Dergisi (YYU Journal Of Education Faculty), 14(1), 640-670.
  • Erdoğan, T. (2006). Van Hiele modeline dayalı öğretim sürecinin sınıf öğretmenliği öğretmen adaylarının yeni geometri konularına yönelik hazırbulunuşluk düzeylerine etkisi (The effect of the teaching process based on the Van Hiele model on the readiness levels of classroom teacher candidates for new geometry subjects). Master thesis. Abant İzzet Baysal Unievrsity, Bolu.
  • Erdoğan, E. O. & Dur, Z. (2014). Preservice mathematics teachers’ personel figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6), 107-133.
  • Fischbein, E. (1993). The Theory of Figural Concepts. Educational studies in mathematics, 24(2), 139-162.
  • Gülkılık, H. (2008). Öğretmen adaylarının bazı geometrik kavramlarla ilgili sahip oldukları kavram imajlarının ve imaj gelişiminin incelenmesi üzerinefenomenografik bir çalışma (A phenomenographic study on examining the concept images and image development of prospective teachers regarding some geometric concepts). Master thesis, Gazi University, Ankara.
  • Gutierrez, A., and Jaime, A. (1999). Preservice primary teachers' understanding of theconcept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253-275.
  • İncikabı, L., & Kılıç, Ç. (2013). İlköğretim öğrencilerinin geometrik cisimlerle ilgili kavram bilgilerinin analizi (Analysis of primary school students' conceptual knowledge about geometric objects). Kuramsal Eğitim Bilim Dergisi, 6(3), 343-358.
  • Jones K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the BritishSociety for Research into Learning Mathematics, 20(3), 109-114.
  • Kartal, B., & Çınar, C. (2017). İlköğretim matematik öğretmen adaylarının çokgenlere dair geometri bilgilerinin incelenmesi (Examination of primary school mathematics teacher candidates' geometry knowledge of polygons). Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(2), 375-399.
  • Kiriş, B. (2008). İlköğretim altıncı sınıf öğrencilerinin nokta, doğru, doğruparçası, işın ve düzlem konularında sahip oldukları kavram yanılgıları ve bu yanılgı nedenlerinin belirlenmesi (Determining the misconceptions of primary school sixth grade students about point, line, line segment, ray and plane and the reasons for these misconceptions). Master thesis. Adnan Menderes University, Aydın.
  • Köprücü, M. (2020). Ortaokul düzeyinde geometri kavram yanılgıları üzerine yapılan lisansüstü tezlerin betimsel içerik analizi (Descriptive content analysis of postgraduate theses on geometry misconceptions at secondary school level). In International Marmara Social Sciences Congress (Autumn 2020) (p. 447).
  • Ojose, B. (2015). Students’ misconceptions in mathematics: analysis of remedies and what research says. Ohio Journal of School Mathematics, 70, 30-34. Paksu, A. D., Musan, M., İymen, E., & Pakmak, G. S. (2012). Sınıf öğretmeni adaylarının boyut konusundaki kavram görüntüleri (Concept images of classroom teacher candidates about size). Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (34), 52-68.
  • Skordoulis, C., Vitsas, T., Dafermos, V., and Koleza, E. (2009). The system of coordinates as an obstacle in understanding the concept of dimension. International Journal of Science and Mathematics Education, 7(2), 253-272.
  • Şengün, K. Ç., & Yılmaz, S. (2021). Ortaokul 8. sınıf öğrencilerinin üçgende açıortay ve kenarortay belirleme durumlarının incelenmesi (Concept images of classroom teacher candidates about size). International Journal of Active Learning, 6(1), 81-97.
  • Tall, D. and Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169. Türk Dil Kurumu, (2011). Türkçe sözlükleri (Turkish dictionaries). Ankara: Türk Dil Kurumu Yayınları.
  • Türnüklü, E., & Ergin, A. S. (2016). 8. sınıf öğrencilerinin görsel tanıma ve tanımlamaları: cisim imgeleri (Visual recognition and definitions of 8th grade students: object images). İlköğretim Online, 15(1). Ulusoy, F. (2022). Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments. International Journal of Mathematical Education in Science and Technology, 1-20.
  • Usta, N. (2018). Öğretmen adaylarının ölçüler konusunda öğrenci hatalarını tespit etme becerileri vehataların giderilmesine ilişkin önerileri (Teacher candidates' skills in detecting student errors regarding measurements and their suggestions for eliminating errors). Journal of Computer and Education Research, 6(12), 247-284.
  • Yazıcı, N. (2019). Temel geometri kavramlarına ilişkin matematik öğretmen adaylarının genel alan bilgisi (General field knowledge of mathematics teacher candidates regarding basic geometry concepts). Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 21(1), 135-155.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Math Teacher Education
Authors

Esra Altıntaş

Selin Uygun

Early Pub Date December 22, 2023
Publication Date December 30, 2023
Submission Date October 14, 2023
Acceptance Date December 22, 2023
Published in Issue Year 2023 Volume: 4 Issue: 2

Cite

APA Altıntaş, E., & Uygun, S. (2023). Determining secondary school mathematics teachers’ errors and misconceptions in geometry. Journal for the Mathematics Education and Teaching Practices, 4(2), 77-86.
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