Research Article
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Öğretmen Adaylarının Matematiksel Anlayışlarının Ck¢ Teorisine Göre Modellenmesi: Bilgi Transferi Anlayışı / Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The “Knowledge Transfer” Conception

Year 2023, Volume: 14 Issue: 1, 71 - 95, 28.02.2023

Selcen Çalık Uzun , Selahattin Arslan

https://doi.org/10.19160/e-ijer.1168980

Abstract

Öğrenenlerin zihinlerinde neler olduğu, bilgiyi nasıl yapılandırdıkları, nasıl kullandıkları gibi sorular araştırmacılar için her zaman merak konusu olmuştur. Bu sorulara açıklık getirmek amacıyla, çeşitli teorilerden yararlanılarak birçok araştırma yapılmaktadır. Bu çalışmada ise sınıf öğretmeni adaylarının temel matematiksel bilgilerini Ck¢ teorisinin anlayış aşamasına göre incelemek amaçlanmıştır. Nitel araştırma yöntemine uygun olarak tasarlanan çalışmanın verileri; öğretmen adaylarına uygulanan sınavlar ve yapılan klinik mülakatlar yardımıyla toplanmıştır. Öğretmen adaylarının matematiksel anlayışlarını belirlemek için Küme, Denklem, Fonksiyon ve Sayılar konularında hazırlanan sınavlar 61 sınıf öğretmeni adayına uygulanmış, sınavların ardından 26 öğretmen adayı ile mülakatlar yürütülmüştür. Uygulanan sınavlarda sorulan soruların ayrıntılı analizi yapılarak öğretmen adaylarının bu soruları çözerken kullandıkları her türlü bilgi belirlenmiştir. cK¢ teorisinin anlayış aşamasında “operatör” olarak ifade edilen bu bilgilerin, birbirleri ile ilgili olanlarının sınıflanmasıyla, adayların sahip oldukları genel matematiksel anlayışlara ulaşılmıştır. Bu çalışmada belirlenen anlayışlardan bilgi transferi anlayışı tanıtılmıştır. Bu anlayış bize, öğrencinin problemleri çözerken yaptıklarının matematiksel geçerliliğinin olmadığını fark etse bile, kendi mantığına, önceki birikimlerine, kendi matematiksel düşüncesine uygun düşen bilgileri kullanma eğiliminde olduğunu göstermektedir. Bu nedenle öğrencilerin matematiksel düşünme biçimlerini ortaya koyması ve öğretmenlerin öğrenme ortamlarını tasarlarken nelere dikkat etmesi gerektiğini göstermesi açısından alan yazına katkı sağlayacağı düşünülmektedir.

Keywords

Ck¢ teorisi Anlayış Bilgi transferi anlayışı Sınıf öğretmeni adayları

Supporting Institution

KTÜ Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

735

References

  • Altun, M., & Yılmaz, A. (2008). High school students’ process of construction of the knowledge of the greatest ınteger function. Ankara University Journal of Faculty of Educational Sciences (JFES), 41 (2), 237-271. https://doi.org/10.1501/Egifak_0000001125
  • Aydın, H. (2008). A phenomenographic study on the usage of mathematical modelling by the teachers and the students teaching and studying in the secondary schools in London. [Unpublished master’s thesis] Gazi University, Ankara.
  • Balacheff N. (2000) A modelling challenge: untangling learner knowledge. Retrieved September, 25, 2008 from https://telearn.archivesouvertes.fr/file/index/docid/190292/filename/Balacheff2000.pdf
  • Balacheff N., & Gaudin N. (2002). Students conceptions: an introduction to a formal characterization Retrieved September, 25, 2008 from https://hal.archives-ouvertes.fr/hal-00190425
  • Balacheff, N., & Gaudin, N. (2003). Baghera assessment project, in S. Soury-Lavergne (ed.), Baghera Assessment Project: Designing an Hybrid and Emergent Educational Society. Les Cahiers du Laboratoire Leibniz, Grenoble.
  • Balacheff, N. (2013). cK¢, a model to reason on learners' conceptions. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 2–15). Chicago: University of Illinois at Chicago.
  • Baki, A. (1998, October 21-23). Cebirle ilgili işlem yanılgılarının değerlendirilmesi [Evaluation of misconceptions about algebra]. [Paper presentation]. 3rd National Symposium Of Science Education, Karadeniz Thecnical University, Trabzon, Türkiye
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory into practice]. Harf Eğitim Yayıncılık.
  • Biber, A. Ç., Abdulkadir, T., & Aktaş, O. (2013). Students’ misconceptions of fractions and its effect on solving fractions problems. Trakya University Journal of Education, 3(2), 152-162. https://dergipark.org.tr/en/download/article-file/200350
  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Kluwer. Cambridge Dictionary (n.d.) Conception. In Cambridge dictionary. Retrieved 12 June 2022, from https://dictionary.cambridge.org/tr/s%C3%B6zl%C3%BCk/ingilizce/conception?q=Conception
  • Cengiz, Ö. M., (2006). A study on the misconception and mistake of a part of high school students in the teaching of real numbers. [Unpublished Master’s thesis]. Atatürk University, Erzurum.
  • Çalık Uzun, S. (2012). Determining preservice elementary teachers? mathemetical conceptions according to cK¢ theory. [Unpublished doctoral thesis]. Karadeniz Technical University, Trabzon.
  • Çalık Uzun S., & Arslan S. (2016). Öğrenci Anlayışlarını Modellemek İçin Bir Teori: CK¢ [A Theory for Modeling Student Understandings: CK¢]. In E. Bingölbali, S. Arslan, İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in Mathematics Education]. (pp. 85-99). PegemA
  • Çelik, D. (2016). Matematiksel düşünme [Mathematical thinking]. In E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in Mathematics Education]. (pp. 17-42). PegemA.
  • Doğan, M., & Yeniterzi, B. (2011). Attainment level of seventh grade students for rational numbers. Selçuk University Journal of the Ahmet Keleşoğlu Faculty of Education, 31, 217-237.
  • Dubinsky, E., & McDonald, M. (2001). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. In D. Hilton et. all. (Eds.) The teaching and learning of mathematics at University level: An ICMI Study, Kluwer Academic Publishers, 273-280.
  • Duval, R. (1993). Register de representations semiotique et fonctionnement cognitif de la pense [registers of semiotic representation and cognitive function of thought]. Annales de Didactique et de Sciences Cognitizes, 5, 37-65
  • Duval, R. (2000). Basic ıssues for research in mathematics education. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (PME) Vol 1. (pp. 55-69). Eric. https://eric.ed.gov/?id=ED452031
  • Gökçek, T., & Güneş G. (2011). Determine teachers candidates’ levels of concept learning in mathematics with attitudes of mathematics. Kastamonu Education Journal, 19(3), 849-858. Retrieved from https://dergipark.org.tr/en/pub/kefdergi/issue/49049/625723
  • Harel, G., & Sowder, L. (2005). Advanced mathematical- thinking at any age: Its nature and its development. Mathematical Thinking and Learning, 7(1), 27-50.
  • Işık, A., Çiltaş A., & Bekdemir, M. (2008). Matematik eğitiminin gerekliliği ve önemi [The importance and necessity of mathematics education]. Journal of Kazım Karabekir Education Faculty, 17, 174-184. Retrieved from https://dergipark.org.tr/en/pub/ataunikkefd/issue/2770/37025
  • Kandemir, M. (2006). Learning level of concepts and views about basic mathematics of class, Pamukkale University Journal of Education. 19, 29-36. Retrieved from https://dergipark.org.tr/en/pub/pauefd/issue/11124/133035
  • Kara, G. (2021). Türkiye’de yayınlanan ortaokul matematik eğitimindeki kavram yanılgıları çalışmalarının incelenmesi [Unpublished master’s thesis]. Hacettepe University, Ankara
  • Karasar, N. (2009). Bilimsel araştırma yöntemi [Scientific Research Method]. (20th ed.). Nobel
  • Katrancı, Y., Yılmaz, A., & Kahraman, S. (2009, May 1-3). Partly correct information structures observed in the process of forming knowledge of functions. [Paper presentation]. The first international congress of educational research, Çanakkale, Turkiye.
  • Kerslake, D. (1986). Fractions: children's strategies and errors. a report of the strategies and errors in secondary mathematics project. Eric https://eric.ed.gov/?id=ED295826
  • Kurdal, C. (2016). Student's errors on ratio and proportions done in dynamic and interactive mathematics environments. [Unpublished master’s thesis]. University of Bayburt.
  • Maracci, M. (2006). On students’ conceptions in vector space theory. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.). Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (PME) Vol 4. (pp. 129-136). https://www.igpme.org/publications/current-proceedings/
  • Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40(1), 1–24. https://doi.org/10.1023/A:1003715913784
  • Okur, M., & Gürel, Z. Ç. (2016). 6 th and 7th grade secondary school students’ misconceptions about fractions. Erzincan University Journal of Education Faculty 18(2), 922-952. https://doi.org/10.17556/jef.30116
  • Özçifçi, R. (2007). Diagnosing the errors in teaching rational numbers and taking the required measures. [Unpublished master’s thesis]. Selçuk University, Konya.
  • Ryan, J., & Williams, J. (2007). Children’s Mathematics 4-15 Learning From Errors and Misconception. Open University Press
  • Soylu, Y., & Soylu, C. (2005). Learning difficulties of 5fh class in primary education at fraction: ordering, adding, subtraction, multiplication in fraction and problems related to fraction. Erzincan University Journal of Education Faculty. 7(2), 101-117. Retrieved from https://dergipark.org.tr/tr/pub/erziefd/issue/6005/80075
  • Sertöz, S. (1998). Matematiğin Aydınlık Dünyası. (8th ed). Tubitak Popular Scicence Book
  • Toluk Uçar, Z. (2011). Preservice teachers’ pedagogical content knowledge: Instructional Explanations, Turkish Journal of Computer and Mathematics Education, 2 (2), 87-102. Retrieved from https://dergipark.org.tr/tr/pub/turkbilmat/issue/21564/231439
  • Turkish Language Association. (n.d). Conception. In TLA current Turkish Dictionary. Retrieved 12 June 2022, from https://sozluk.gov.tr/
  • Umay, A. (1996). Matematik eğitimi ve ölçülmesi [Mathematics education and its measurement]. Hacettepe University Journal of Education 12, 145-149. Retrieved from http://www.efdergi.hacettepe.edu.tr/yonetim/icerik/makaleler/1277-published.pdf
  • Vittori, T. (2018). Analyzing the use of history in mathematics education: Issues and challenges around Balacheff’s cKȼ model. Educational Studies in Mathematics, 99(2), 125-136. https://doi.org/10.1007/s10649-018-9831-6
  • Webber, C., Pesty S., & Balacheff N. (2002). A multi-agent and emergent approach to learner modelling. In F. van Harmelen (ed.), Proceedings of the 15th European Conference on Artificial Intelligence (ECAI 2002). (pp.98-102). Amsterdam: IOS Press
  • Webber, C. (2004). From errors to conceptions an approach to student diagnosis. In J. C. Lester, R. M. Vicari, & F. Paraguacu (Eds.), Intelligent tutoring systems, lecture notes in computer science. 3220, (pp 710–719). Springer, https://doi.org/10.1007/978-3-540-30139-4_124
  • Wu, H. (1999). Some remarks on the teaching of fractions ın elementary school. Retrieved from http://math.berkeley.edu/~wu/fractions2.pdf
  • Yazgan, G. (2006). A quantitative research of 10th year students's conceptions on geometric locus concept by using the Ck¢ model. [Unpublished Master’s Thesis]. Gazi University, Ankara.
  • Yenilmez, K., & Uysal, E. (2007). The primary school students' level of the ability of establishing relation the mathematical expression and symbols with daily life. Ondokuz Mayıs University Journal of Education Faculty, (24), 89-98. Retrieved from https://app.trdizin.gov.tr/makale/TnpBek9EYzM/ilkogretim-ogrencilerinin-matematiksel-kavram-ve-sembolleri-gunluk-hayatla-iliskilendirme-duzeyi
  • Yürekli, Ü. B. (2008). The relationship between pre-service elementary school teachers? self-efficacy perceptions and attitudes towards mathematics. [Unpublished Master’s Thesis]. Pamukkale University, Denizli.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Seçkin.
  • Yujing, N., & Zhou, Y. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias, Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326985ep4001_3
  • Zembat, İ. Ö. (2008). Kavram yanılgısı nedir? [What is misconception?]. In M. F. Özmantar, E. Bingölbali & H. Akkoç (Eds.) Matematiksel Kavram Yanılgıları ve Çözüm Önerileri [Matmematical misconceptions and suggestion for solution]. (pp 1-8). PegemA

Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The “Knowledge Transfer” Conception / Öğretmen Adaylarının Matematiksel Anlayışlarının Ck¢ Teorisine Göre Modellenmesi: Bilgi Transferi Anlayışı

Year 2023, Volume: 14 Issue: 1, 71 - 95, 28.02.2023

Selcen Çalık Uzun , Selahattin Arslan

https://doi.org/10.19160/e-ijer.1168980

Abstract

This study aims to examine the basic mathematical knowledge of primary education student teachers according to the Ck¢ theory. The data of this qualitative study is collected through exams applied and clinical interviews undertaken with student teachers. To determine mathematical conceptions of student teachers, examinations on the subjects of Sets, Equations, Functions, and Numbers were applied to 61 classroom teachers, and then 26 of them were interviewed. A detailed analysis of the exam questions was undertaken and all types of knowledge that student teachers used whilst solving these problems were identified. Student teachers’ general mathematical conceptions were revealed through the classification of the related parts of such knowledge that were expressed as “operator” in the conception phase of Ck¢ theory. In this study, the conception of knowledge transfer is presented as one of the determined conceptions. It has been identified that student teachers use the knowledge they have previously experienced as effective in problems, whilst they solve problems, and that they thus think that they will be effective in future problems as well. Operators involving such knowledge underpin the ‘knowledge transfer’ conception. Yet, it has also been found that this knowledge transfer leads students to make mistakes as they usually rely on the idea that a rule leading them to the correct result in a situation, which occasionally leads them to the correct result, will be applicable in any other situations. This conception shows that students tend to use the knowledge that seems appropriate for their logic, their existing knowledge, and their mathematical thinking, even if they notice that what they do in solving problems does not have any mathematical validity. Therefore, this study contributes to the literature in terms of revealing students’ ways of mathematical thinking and addressing the important areas to be covered by teachers in designing learning environments.

Keywords

Ck¢ theory Conception Knowledge transfer conception Student teachers

Project Number

735

References

  • Altun, M., & Yılmaz, A. (2008). High school students’ process of construction of the knowledge of the greatest ınteger function. Ankara University Journal of Faculty of Educational Sciences (JFES), 41 (2), 237-271. https://doi.org/10.1501/Egifak_0000001125
  • Aydın, H. (2008). A phenomenographic study on the usage of mathematical modelling by the teachers and the students teaching and studying in the secondary schools in London. [Unpublished master’s thesis] Gazi University, Ankara.
  • Balacheff N. (2000) A modelling challenge: untangling learner knowledge. Retrieved September, 25, 2008 from https://telearn.archivesouvertes.fr/file/index/docid/190292/filename/Balacheff2000.pdf
  • Balacheff N., & Gaudin N. (2002). Students conceptions: an introduction to a formal characterization Retrieved September, 25, 2008 from https://hal.archives-ouvertes.fr/hal-00190425
  • Balacheff, N., & Gaudin, N. (2003). Baghera assessment project, in S. Soury-Lavergne (ed.), Baghera Assessment Project: Designing an Hybrid and Emergent Educational Society. Les Cahiers du Laboratoire Leibniz, Grenoble.
  • Balacheff, N. (2013). cK¢, a model to reason on learners' conceptions. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 2–15). Chicago: University of Illinois at Chicago.
  • Baki, A. (1998, October 21-23). Cebirle ilgili işlem yanılgılarının değerlendirilmesi [Evaluation of misconceptions about algebra]. [Paper presentation]. 3rd National Symposium Of Science Education, Karadeniz Thecnical University, Trabzon, Türkiye
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory into practice]. Harf Eğitim Yayıncılık.
  • Biber, A. Ç., Abdulkadir, T., & Aktaş, O. (2013). Students’ misconceptions of fractions and its effect on solving fractions problems. Trakya University Journal of Education, 3(2), 152-162. https://dergipark.org.tr/en/download/article-file/200350
  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Kluwer. Cambridge Dictionary (n.d.) Conception. In Cambridge dictionary. Retrieved 12 June 2022, from https://dictionary.cambridge.org/tr/s%C3%B6zl%C3%BCk/ingilizce/conception?q=Conception
  • Cengiz, Ö. M., (2006). A study on the misconception and mistake of a part of high school students in the teaching of real numbers. [Unpublished Master’s thesis]. Atatürk University, Erzurum.
  • Çalık Uzun, S. (2012). Determining preservice elementary teachers? mathemetical conceptions according to cK¢ theory. [Unpublished doctoral thesis]. Karadeniz Technical University, Trabzon.
  • Çalık Uzun S., & Arslan S. (2016). Öğrenci Anlayışlarını Modellemek İçin Bir Teori: CK¢ [A Theory for Modeling Student Understandings: CK¢]. In E. Bingölbali, S. Arslan, İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in Mathematics Education]. (pp. 85-99). PegemA
  • Çelik, D. (2016). Matematiksel düşünme [Mathematical thinking]. In E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in Mathematics Education]. (pp. 17-42). PegemA.
  • Doğan, M., & Yeniterzi, B. (2011). Attainment level of seventh grade students for rational numbers. Selçuk University Journal of the Ahmet Keleşoğlu Faculty of Education, 31, 217-237.
  • Dubinsky, E., & McDonald, M. (2001). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. In D. Hilton et. all. (Eds.) The teaching and learning of mathematics at University level: An ICMI Study, Kluwer Academic Publishers, 273-280.
  • Duval, R. (1993). Register de representations semiotique et fonctionnement cognitif de la pense [registers of semiotic representation and cognitive function of thought]. Annales de Didactique et de Sciences Cognitizes, 5, 37-65
  • Duval, R. (2000). Basic ıssues for research in mathematics education. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (PME) Vol 1. (pp. 55-69). Eric. https://eric.ed.gov/?id=ED452031
  • Gökçek, T., & Güneş G. (2011). Determine teachers candidates’ levels of concept learning in mathematics with attitudes of mathematics. Kastamonu Education Journal, 19(3), 849-858. Retrieved from https://dergipark.org.tr/en/pub/kefdergi/issue/49049/625723
  • Harel, G., & Sowder, L. (2005). Advanced mathematical- thinking at any age: Its nature and its development. Mathematical Thinking and Learning, 7(1), 27-50.
  • Işık, A., Çiltaş A., & Bekdemir, M. (2008). Matematik eğitiminin gerekliliği ve önemi [The importance and necessity of mathematics education]. Journal of Kazım Karabekir Education Faculty, 17, 174-184. Retrieved from https://dergipark.org.tr/en/pub/ataunikkefd/issue/2770/37025
  • Kandemir, M. (2006). Learning level of concepts and views about basic mathematics of class, Pamukkale University Journal of Education. 19, 29-36. Retrieved from https://dergipark.org.tr/en/pub/pauefd/issue/11124/133035
  • Kara, G. (2021). Türkiye’de yayınlanan ortaokul matematik eğitimindeki kavram yanılgıları çalışmalarının incelenmesi [Unpublished master’s thesis]. Hacettepe University, Ankara
  • Karasar, N. (2009). Bilimsel araştırma yöntemi [Scientific Research Method]. (20th ed.). Nobel
  • Katrancı, Y., Yılmaz, A., & Kahraman, S. (2009, May 1-3). Partly correct information structures observed in the process of forming knowledge of functions. [Paper presentation]. The first international congress of educational research, Çanakkale, Turkiye.
  • Kerslake, D. (1986). Fractions: children's strategies and errors. a report of the strategies and errors in secondary mathematics project. Eric https://eric.ed.gov/?id=ED295826
  • Kurdal, C. (2016). Student's errors on ratio and proportions done in dynamic and interactive mathematics environments. [Unpublished master’s thesis]. University of Bayburt.
  • Maracci, M. (2006). On students’ conceptions in vector space theory. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.). Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (PME) Vol 4. (pp. 129-136). https://www.igpme.org/publications/current-proceedings/
  • Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40(1), 1–24. https://doi.org/10.1023/A:1003715913784
  • Okur, M., & Gürel, Z. Ç. (2016). 6 th and 7th grade secondary school students’ misconceptions about fractions. Erzincan University Journal of Education Faculty 18(2), 922-952. https://doi.org/10.17556/jef.30116
  • Özçifçi, R. (2007). Diagnosing the errors in teaching rational numbers and taking the required measures. [Unpublished master’s thesis]. Selçuk University, Konya.
  • Ryan, J., & Williams, J. (2007). Children’s Mathematics 4-15 Learning From Errors and Misconception. Open University Press
  • Soylu, Y., & Soylu, C. (2005). Learning difficulties of 5fh class in primary education at fraction: ordering, adding, subtraction, multiplication in fraction and problems related to fraction. Erzincan University Journal of Education Faculty. 7(2), 101-117. Retrieved from https://dergipark.org.tr/tr/pub/erziefd/issue/6005/80075
  • Sertöz, S. (1998). Matematiğin Aydınlık Dünyası. (8th ed). Tubitak Popular Scicence Book
  • Toluk Uçar, Z. (2011). Preservice teachers’ pedagogical content knowledge: Instructional Explanations, Turkish Journal of Computer and Mathematics Education, 2 (2), 87-102. Retrieved from https://dergipark.org.tr/tr/pub/turkbilmat/issue/21564/231439
  • Turkish Language Association. (n.d). Conception. In TLA current Turkish Dictionary. Retrieved 12 June 2022, from https://sozluk.gov.tr/
  • Umay, A. (1996). Matematik eğitimi ve ölçülmesi [Mathematics education and its measurement]. Hacettepe University Journal of Education 12, 145-149. Retrieved from http://www.efdergi.hacettepe.edu.tr/yonetim/icerik/makaleler/1277-published.pdf
  • Vittori, T. (2018). Analyzing the use of history in mathematics education: Issues and challenges around Balacheff’s cKȼ model. Educational Studies in Mathematics, 99(2), 125-136. https://doi.org/10.1007/s10649-018-9831-6
  • Webber, C., Pesty S., & Balacheff N. (2002). A multi-agent and emergent approach to learner modelling. In F. van Harmelen (ed.), Proceedings of the 15th European Conference on Artificial Intelligence (ECAI 2002). (pp.98-102). Amsterdam: IOS Press
  • Webber, C. (2004). From errors to conceptions an approach to student diagnosis. In J. C. Lester, R. M. Vicari, & F. Paraguacu (Eds.), Intelligent tutoring systems, lecture notes in computer science. 3220, (pp 710–719). Springer, https://doi.org/10.1007/978-3-540-30139-4_124
  • Wu, H. (1999). Some remarks on the teaching of fractions ın elementary school. Retrieved from http://math.berkeley.edu/~wu/fractions2.pdf
  • Yazgan, G. (2006). A quantitative research of 10th year students's conceptions on geometric locus concept by using the Ck¢ model. [Unpublished Master’s Thesis]. Gazi University, Ankara.
  • Yenilmez, K., & Uysal, E. (2007). The primary school students' level of the ability of establishing relation the mathematical expression and symbols with daily life. Ondokuz Mayıs University Journal of Education Faculty, (24), 89-98. Retrieved from https://app.trdizin.gov.tr/makale/TnpBek9EYzM/ilkogretim-ogrencilerinin-matematiksel-kavram-ve-sembolleri-gunluk-hayatla-iliskilendirme-duzeyi
  • Yürekli, Ü. B. (2008). The relationship between pre-service elementary school teachers? self-efficacy perceptions and attitudes towards mathematics. [Unpublished Master’s Thesis]. Pamukkale University, Denizli.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Seçkin.
  • Yujing, N., & Zhou, Y. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias, Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326985ep4001_3
  • Zembat, İ. Ö. (2008). Kavram yanılgısı nedir? [What is misconception?]. In M. F. Özmantar, E. Bingölbali & H. Akkoç (Eds.) Matematiksel Kavram Yanılgıları ve Çözüm Önerileri [Matmematical misconceptions and suggestion for solution]. (pp 1-8). PegemA
There are 47 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Issue Articles
Authors

Selcen Çalık Uzun 0000-0002-2178-6642

Selahattin Arslan 0000-0001-8557-2507

Project Number 735
Publication Date February 28, 2023
Published in Issue Year 2023Volume: 14 Issue: 1

Cite

APA Çalık Uzun, S., & Arslan, S. (2023). Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The “Knowledge Transfer” Conception / Öğretmen Adaylarının Matematiksel Anlayışlarının Ck¢ Teorisine Göre Modellenmesi: Bilgi Transferi Anlayışı. E-Uluslararası Eğitim Araştırmaları Dergisi, 14(1), 71-95. https://doi.org/10.19160/e-ijer.1168980
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