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Özel Yetenekli Öğrenciler Ile Anadolu Lisesi Öğrencilerinin Matematik Dersindeki Hatalara Yönelik Bakış Açılarının Karşılaştırılması

Year 2025, Issue: 58, 48 - 64, 08.09.2025
https://doi.org/10.33418/education.1607772

Abstract

Bu çalışmada, üstün yetenekli öğrenciler ile Anadolu Lisesinde öğrenim gören öğrencilerin matematik dersindeki hatalara yönelik bakış açılarının karşılaştırılması amaçlanmıştır. Araştırma, 2020-2021 eğitim-öğretim yılında Niğde ilindeki Bilim Sanat Merkezi proje programında öğrenim gören 15 üstün yetenekli öğrenci ve Anadolu Lisesinde öğrenim gören 15 lise öğrencisi olmak üzere toplam 30 öğrenci ile yürütülmüştür. Veri toplama aracı olarak 6 sorudan oluşan yarı yapılandırılmış görüşme formu kullanılmıştır. Elde edilen verilerin analizinde içerik analizi kullanılmıştır. Görüşmelerde öğrencilere matematik dersinde ne sıklıkla hata yaptıklarını, hata yapmaktan korkmalarını, hatalarını başkaları tarafından dile getirmelerini ve hataların tartışılmasına ilişkin bakış açılarını belirlemelerini sağlayacak sorular sorulmuştur. Bulgulara göre, Anadolu Lisesi öğrencilerinin matematik derslerinde üstün yetenekli öğrencilere göre daha fazla hata yapmaktan kaçındıkları, korktukları ve hata yaptıkları görülmektedir. Anadolu Lisesi öğrencilerinin hata yapmamak için soruları çözmeden veya boş bırakma olasılıkları daha yüksek olup, daha sık hata yaptıkları, yaptıkları hatalardan duygusal olarak daha fazla etkilendikleri görülmüştür. Anadolu Lisesi öğrencilerinin matematik derslerinde hata yapmaktan daha çok korktukları söylenebilir. Üstün yetenekli öğrencilerin tamamı ve Anadolu Lisesi öğrencilerinin çoğunluğu hataları "öğretici" olarak görüyor.

Ethical Statement

Etik kurul onayı Kırşehir Ahi Evran Üniversitesi Sosyal ve Beşeri Bilimler Etik Kurulu'ndan alınmıştır (Tarih: 03.02.2022, Sayı: 2021/6).

Supporting Institution

Kırşehir Ahi Evran Üniversitesi

Thanks

Teşekkürler

References

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  • Berman, W. (2006). When will they ever learn? Learning and teaching from mistakes in the clinical context. Clinical Law Review, 13, 115-141. https://ssrn.com/abstract=874070
  • Bickhard, M. H. (2004). The social ontology of persons. In J. I. M. Carpendale & U. Muller (Eds.), Social interaction and the development of knowledge, (111-132). Psychology Press.
  • Bilgili, S., Özkaya, M., Çiltaş, A. & Konyalıoğlu, A. C. (2020). Examining middle school mathematics teachers' error approaches to modeling. Journal of Social Sciences of Mus Alparslan University, 8(3), 871-882. https://doi.org/10.18506/anemon.637049
  • Booth, J. L., Begolli, K. N. & McCann, N. (2016). The effect of worked examples on student learning and error anticipation in Algebra. In M. B. Wood, E. E. Turner, M. Civil & J. A. Eli (Eds.), Psychology of Mathematics & Education of North America (pp. 551-556). Tucson, University of Arizona.
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  • Borasi, R. (1988). Towards a reconceptualization of the role of errors in education: The need for new metaphors. Annual Meeting of the American Educational Research Association, New Orleans, LA.
  • Borasi, R. (1989, March). Students’ constructive uses of mathematical errors: A taxonomy. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA, USA.
  • Borasi, R. (1994). Capitalizing on errors as “Springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 25(2) 166–208. https://doi.org/10.2307/749507
  • Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex Publishing.
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  • Cockburn, A. D. (2005). Teaching mathematics within sight. Falmer Press.
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  • Dede, Y. & Peker, M. (2007). Students’ errors and misunderstandings regarding algebra: predictive skills and solution suggestions of prospective mathematics teachers. Elementary Education Online, 6(1), 35-49. Dweck, C.S. (2012). Teaching Mathematics for a Growth. In Personal Communication. Mindset workshop, Stanford, CA.
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  • Hansen, A. (2014). Children’s errors in mathematics. Learning Matters Publishing.
  • Heemsoth, T. & Heinze, A. (2016). Secondary school students learning from reflections on the rationale behind self-made errors: a field experiment. The Journal of Experimental Education, 84(1), 98-118. https://doi.org/10.1080/00220973.2014.963215
  • Heinze, A. & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: effects of an ın-service teacher training on students’ performance in geometry. In J.-H. Woo, H.-C. Lew, K.-S. Park & D.-Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, 9-16). Seoul: PME.
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  • Kline, M. (1980). Mathematics: The loss of certainty. Oxford University Press. London.
  • Koca, S. (2011). Investigation of the differences in mathematics achievement, attitudes and anxieties of 8th grade primary school students according to their learning styles [Unpublished master's thesis, Afyon Kocatepe University-Afyonkarahisar]. Council of Higher Education National Thesis Centre. No: 296359
  • Konyalıoğlu, A., C., Kaplan, A., Selvitopu, H.,Işık, A. & Tortumlu, N. (2011). Some determinations on conceptual learning of the concept of derivative. Kazım Karabekir Faculty of Education Journal, 22, 317-328.
  • Kuhn, T. S. (1970). Criticism and the growth of knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London. Cambridge University Press.
  • Lakatos, I. (1976). Falsification and the methodology of scientific research programmes. In Can theories be refuted? (pp. 205–259). Springer.
  • Lannin, J. K., Barker, D. D. & Townsend, B. E. (2007). How students view the general nature of their errors. Educational Studies in Mathematics, 66(1), 43-59. https://doi.org/10.1007/s10649-006-9067-8
  • Mathan, S. A., & Koedinger, K. R. (2018). Fostering the intelligent novice: Learning from errors with metacognitive tutoring. In Computers as Metacognitive Tools for Enhancing Learning (pp. 257-265). Routledge.
  • Miles, M. B. & Huberman A. M. (1994). Qualitative data analysis: An expanded source book. (2nd Edition). Sage Publications.
  • Melis, E. (2004). Erroneous examples as a source of learning in mathematics. CELDA, 311–318. https://pdfs.semanticscholar.org/17be/73f009cf0df2a4523f099fbf0db42180679a.pdf
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  • Mirasyedioğlu, Ş. & Peker, M. (2008). Pre-service elementary school teachers’ learning styles and attitudes towards mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 4(1), 21-26. https://doi.org/10.12973/ejmste/75302
  • Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P. & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive post error adjustments. Psychological Science, 22(12), 1484-1489. https://doi.org/10.1177/0956797611419520
  • Movshovitz-Hadar, N., Zaslavsky, O. & Inbar, S. (1987). An empirical classification model for errors in highschool mathematics. Journal for research in mathematics Education, 18(1), 3-14. https://doi.org/10.2307/749532
  • Oflaz, G., & Polat, K. (2022). Error analysis of eighth grade students' non-routine problem solutions. Mehmet Akif Ersoy University Journal of Education Faculty, 62, 1-41.
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  • Önal, H. & Aydın, O. (2018). Misconceptions and error examples in primary school mathematics lesson, Journal of Educational Theory and Practice, 4(2), 1-9. https://dergipark.org.tr/tr/pub/ekuad/issue/38280/442698
  • Özkaya, M., & Konyalıoğlu, A. C. (2019). Error-based activities in the development of subject matter knowledge of secondary school mathematics teachers: Addition with fractions. Journal of Bayburt Education Faculty, 14(27), 23-52.
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Comparison of Gifted Students and Anatolian High School Students' Perspectives on Errors in Mathematics Lesson

Year 2025, Issue: 58, 48 - 64, 08.09.2025
https://doi.org/10.33418/education.1607772

Abstract

In this study, it is aimed to compare the perspectives of gifted students and students studying at Anatolian High School towards errors in mathematics lessons. The research was conducted with 30 students, including 15 gifted students studying in the project program at the Science and Art Center in Niğde, and 15 high school students studying at Anatolian High School during the 2020-2021 academic year. A semi-structured interview form consisting of 6 questions was used as a data collection tool. Content analysis was used in the analysis of the obtained data. In the interviews, the students were asked questions that would enable them to determine how often they made errors in the mathematics lesson, their fear of making errors, the expression of their errors by others, and their perspectives on the discussion of errors. Based of the findings, it is seen that Anatolian High School students avoid, fear and make errors more than gifted students in mathematics lessons. The Anatolian High School students were more likely to leave the questions unsolved or blank not to make errors, they make errors more frequently, they are more emotionally affected by the errors they make. It can be said that Anatolian High School students are more afraid of making errors in mathematics lessons. All of the gifted students and the majority of Anatolian High School students see the errors "instructive”.

Ethical Statement

Ethics committee approval was obtained from Kırşehir Ahi Evran University Social and Humanitarian Ethics Committee (Date: 03.02.2022, Number: 2021/6).

Supporting Institution

Kırşehir Ahi Evran University

Thanks

Thanks

References

  • Altun, M. (2001). Teaching mathematics in the second stage of primary education. Alfa.
  • Arı, K., Savaş, E. & Konca, Ş. (2010). Examining the causes of mathematics anxiety among 7th grade primary school students. Journal of Ahmet Kelesoglu Education Faculty, 29(1), 211-230.
  • Berman, W. (2006). When will they ever learn? Learning and teaching from mistakes in the clinical context. Clinical Law Review, 13, 115-141. https://ssrn.com/abstract=874070
  • Bickhard, M. H. (2004). The social ontology of persons. In J. I. M. Carpendale & U. Muller (Eds.), Social interaction and the development of knowledge, (111-132). Psychology Press.
  • Bilgili, S., Özkaya, M., Çiltaş, A. & Konyalıoğlu, A. C. (2020). Examining middle school mathematics teachers' error approaches to modeling. Journal of Social Sciences of Mus Alparslan University, 8(3), 871-882. https://doi.org/10.18506/anemon.637049
  • Booth, J. L., Begolli, K. N. & McCann, N. (2016). The effect of worked examples on student learning and error anticipation in Algebra. In M. B. Wood, E. E. Turner, M. Civil & J. A. Eli (Eds.), Psychology of Mathematics & Education of North America (pp. 551-556). Tucson, University of Arizona.
  • Borasi, R. (1987). Exploring matematics through the analysis of errors. For the Learning of Mathematics, 7(3), 2-8.
  • Borasi, R. (1988). Towards a reconceptualization of the role of errors in education: The need for new metaphors. Annual Meeting of the American Educational Research Association, New Orleans, LA.
  • Borasi, R. (1989, March). Students’ constructive uses of mathematical errors: A taxonomy. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA, USA.
  • Borasi, R. (1994). Capitalizing on errors as “Springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 25(2) 166–208. https://doi.org/10.2307/749507
  • Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex Publishing.
  • Bransford, J. D., Brown, A. L. & Cocking, R. R. (2000). How people learn. National Academy Press.
  • Brown, S. I. & Callahan, L. (Eds) (1985). Using Errors as Springboards for the Learning of Mathematics [Special Issue]. Focus on Learning Problems in Mathematics, 7(3-4).
  • Burns, M. (2007). About Teaching Mathematics: A K-8 Resource (3rd ed.). Math Solutions.
  • Christensen, L. B., Johnson, B. & Turner, L. A. (2011). Measuring variables and sampling. Research Methods, Design, and Analysis. Boston, Pearson.
  • Cockburn, A. D. (2005). Teaching mathematics within sight. Falmer Press.
  • Colaizzi, P.F. (1978). Psychological research as the phenomenologist views it. In Valle RS, King M (Eds.) Existential phenomenological alternatives for psychology. Oxford University Press, New York.
  • Civelek, Ş., Meder, M. & Tüzen, H. (2001). Problems encountered in teaching mathematics. http://www.matder.org.tr/index.php?option=com_content&view=article&catid=8: matematik-kosesi-makaleleri&id=62:matematik-ogretiminde-karsilasilanaksakliklar-&Itemid=38
  • Creswell, J. W. (2007). Quantitative, qualitative and mixed methods approach research design (SB Demir, Trans. Ed). Anı.
  • Çiftçi, Ş. (2010). Problems of mathematics education in rural areas: an evaluation study from the perspective of teachers and students. [Unpublished master's thesis,. Osmangazi University-Eskişehir] Council of Higher Education National Thesis Centre. No: 266403
  • Dede, Y. & Peker, M. (2007). Students’ errors and misunderstandings regarding algebra: predictive skills and solution suggestions of prospective mathematics teachers. Elementary Education Online, 6(1), 35-49. Dweck, C.S. (2012). Teaching Mathematics for a Growth. In Personal Communication. Mindset workshop, Stanford, CA.
  • Dursun, Ş. & Bindak, R. (2011). Investigation of mathematics anxiety of primary school second stage students. Cumhuriyet University Journal of Social Sciences, 35(1), 18-21.
  • Fisher, K. M. & Lipson J. I. (1986). Twenty questions about student errors. Journal of Research Science Teaching, 23(9), 783-803. https://doi.org/10.1002/tea.3660230904
  • Gardner, D. & Wood, R. (2009). Errors, feedback, learning and performance. The Australasian Journal of Organisational Psychology. 2(1),30-43. https://doi.org/10.1375/ajop.2.1.30
  • Gartmeier, M., Bauer, J., Gruber, H. & Heid, H. (2008). Negative knowledge: Understanding professional learning and expertise. Vocations and Learn, 1(2), 87- 103. https://doi.org/10.1007/s12186-008-9006-1
  • Ginat, D. (2003, February). The Greedy Trap And Learning From Mistakes, Proc of the 34th ACM Computer Science Education Symposium - SIGCSE, Nevada, 11-15. https://doi.org/10.1145/792548.611920
  • Hansen, A. (2014). Children’s errors in mathematics. Learning Matters Publishing.
  • Heemsoth, T. & Heinze, A. (2016). Secondary school students learning from reflections on the rationale behind self-made errors: a field experiment. The Journal of Experimental Education, 84(1), 98-118. https://doi.org/10.1080/00220973.2014.963215
  • Heinze, A. & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: effects of an ın-service teacher training on students’ performance in geometry. In J.-H. Woo, H.-C. Lew, K.-S. Park & D.-Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, 9-16). Seoul: PME.
  • Ingram, J., Pitt, A. & Baldry, F. (2015). Handling errors as they arise in whole class interactions. Research in Mathematics Education, 17(3), 183–197. http://dx.doi.org/10.1080/14794802.2015.1098562
  • Keklikçi, H. & Yılmazer, Z. (2013). Determining the relationship between primary school students' levels of fear of mathematics and their views on mathematics teachers. Journal of Education and Teaching Research, 2(3), 198-204.
  • Kline, M. (1980). Mathematics: The loss of certainty. Oxford University Press. London.
  • Koca, S. (2011). Investigation of the differences in mathematics achievement, attitudes and anxieties of 8th grade primary school students according to their learning styles [Unpublished master's thesis, Afyon Kocatepe University-Afyonkarahisar]. Council of Higher Education National Thesis Centre. No: 296359
  • Konyalıoğlu, A., C., Kaplan, A., Selvitopu, H.,Işık, A. & Tortumlu, N. (2011). Some determinations on conceptual learning of the concept of derivative. Kazım Karabekir Faculty of Education Journal, 22, 317-328.
  • Kuhn, T. S. (1970). Criticism and the growth of knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London. Cambridge University Press.
  • Lakatos, I. (1976). Falsification and the methodology of scientific research programmes. In Can theories be refuted? (pp. 205–259). Springer.
  • Lannin, J. K., Barker, D. D. & Townsend, B. E. (2007). How students view the general nature of their errors. Educational Studies in Mathematics, 66(1), 43-59. https://doi.org/10.1007/s10649-006-9067-8
  • Mathan, S. A., & Koedinger, K. R. (2018). Fostering the intelligent novice: Learning from errors with metacognitive tutoring. In Computers as Metacognitive Tools for Enhancing Learning (pp. 257-265). Routledge.
  • Miles, M. B. & Huberman A. M. (1994). Qualitative data analysis: An expanded source book. (2nd Edition). Sage Publications.
  • Melis, E. (2004). Erroneous examples as a source of learning in mathematics. CELDA, 311–318. https://pdfs.semanticscholar.org/17be/73f009cf0df2a4523f099fbf0db42180679a.pdf
  • Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68, 465-489. https://doi.org/10.1146/annurev-psych-010416-044022
  • Mirasyedioğlu, Ş. & Peker, M. (2008). Pre-service elementary school teachers’ learning styles and attitudes towards mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 4(1), 21-26. https://doi.org/10.12973/ejmste/75302
  • Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P. & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive post error adjustments. Psychological Science, 22(12), 1484-1489. https://doi.org/10.1177/0956797611419520
  • Movshovitz-Hadar, N., Zaslavsky, O. & Inbar, S. (1987). An empirical classification model for errors in highschool mathematics. Journal for research in mathematics Education, 18(1), 3-14. https://doi.org/10.2307/749532
  • Oflaz, G., & Polat, K. (2022). Error analysis of eighth grade students' non-routine problem solutions. Mehmet Akif Ersoy University Journal of Education Faculty, 62, 1-41.
  • Oiler, C. (1982). The phenomenological approach in nursing research. Nursing Research, 31(3), 178-181. https://doi.org/10.1097/00006199-198205000-00013
  • Önal, H. & Aydın, O. (2018). Misconceptions and error examples in primary school mathematics lesson, Journal of Educational Theory and Practice, 4(2), 1-9. https://dergipark.org.tr/tr/pub/ekuad/issue/38280/442698
  • Özkaya, M., & Konyalıoğlu, A. C. (2019). Error-based activities in the development of subject matter knowledge of secondary school mathematics teachers: Addition with fractions. Journal of Bayburt Education Faculty, 14(27), 23-52.
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There are 71 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Research Articles
Authors

Zekiye Morkoyunlu 0000-0002-1978-4525

Gülşah Saltık Ayhanöz 0000-0003-0174-9999

Early Pub Date September 3, 2025
Publication Date September 8, 2025
Submission Date December 26, 2024
Acceptance Date May 5, 2025
Published in Issue Year 2025 Issue: 58

Cite

APA Morkoyunlu, Z., & Saltık Ayhanöz, G. (2025). Comparison of Gifted Students and Anatolian High School Students’ Perspectives on Errors in Mathematics Lesson. Educational Academic Research(58), 48-64. https://doi.org/10.33418/education.1607772

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