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Assessment Of Students Preferred Proof Schemes In The Context Of The Analysis Course

Year 2024, Volume: 13 Issue: 2, 274 - 284, 16.04.2024

Abstract

This study investigated the proof schemes preffered by prospective teachers in the analytics courses. This study is a case study focused on qualitative data. In the study, an open-ended questionaire was applied to 12 prospective teachers. They were asked to describe the most memorable proof that was covered in the analytics 1 and analytic 2 courses. Evaluation of these answers showed that the most memorized proof scheme was the transformational proof scheme. First-year students used their preferred proof method, without any structured form, and because they had adequate prior knowledge, they utilized the transformational proof scheme, despite the fact that this scheme demands upper-class level and strong academic understanding. In conclusion, prospective teachers may show a tendency to display a high-level proof scheme by combining their prior knowledge to the proof with the highest level of memorability.

References

  • Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18. 147-146.
  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. (Ed.), Mathematics, teachers and children. (216-235).
  • Barnard, T. & Tall, D. (1997). Cognitive Units, Connections and Mathematical Proof. Proceeding of PME, 21(2). 41-48.
  • Bell, A.W. (1976). A study of pupils’ proof-explanations in mathematical situations, Educational Studies in Mathematics, 7, 23-40.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2012). Bilimsel araştırma yöntemleri [Scientific research methods] (13. Baskı). Ankara: Pegem Akademi.
  • Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41-53
  • Cusi, A., & Malara, N. (2007). Proofs problems in elementary number theory: Analysis of trainee teachers’ productions. In Proceedings of the Fifth Conference of the European Society for Research in Mathematics Education (pp. 591-600).
  • Doruk, M., & Kaplan, A. (2015). Prospective mathematics teachers’ difficulties in doing proofs and causes of their struggle with proofs. Bayburt Üniversitesi Eğitim Fakültesi Dergisi, 10(2), 315-328
  • Dreyfus, T. (1999). Why Johnny Can’t Prove. Educational Studies in Mathematics, 38(1), 85-109
  • Harel, G.& Sowder, L. (1998). Students' proof schemes. Research on Collegiate Mathematics Education, 3. 234-283. Harel, G., & Sowder, L (2007). Toward comprehensive perspectives on learning and teaching proof, In F. Lester (Ed.), Handbook of Research on Teaching and Learning Mathematics (2nd Ed.). Greenwich, CT: Information Age Publishing.
  • Hartter, B.J. (1995). Concept image and concept definition for the topic of the derivative (Unpublished doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 9603516)
  • Housman, D., & Porter, M. (2003). Proof schemes and learning strategies of above-average mathematics students. Educational Studies in Mathematics, 53(2), 139-158.
  • Heinze, A. & Reiss, K. (2003). Reasoning and proof: Methodological knowledge as a component of proof competence. In M.A. Mariotti (Ed.), Proceedings of the ThirdConference of the European Society for Research in Mathematics Education, Bellaria, Italy.
  • Hersch, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389-399
  • Housman, D.& Porter, M. (2003). Proof schemes and learning strategies of above average mathematics students. Educational Studies in Mathematics, 53, 139–158
  • İskenderoğlu, T. (2010). İlköğretim matematik öğretmeni adaylarının kanıtlamayla ilgili görüşleri ve kullandıkları kanıt şemaları [Primary mathematics teacher candidates' views on proof and the proof schemes they use] (Yayınlanmamış doktora tezi). Karadeniz Teknik Üniversitesi, Trabzon.
  • Jones, K. (2000). The student experience of mathematical proof at university level, International Journal of Mathematical Education in Science and Technology, 31,1, 53-60.
  • Knuth, E. (2002). Teacher’s Conceptions of Proof in the Contex of Secondary School Mathematics. Journal of Mathematics Teacher Education, 5. 61-88.
  • Miyazaki, M. (2000). Levels of Proof in Lover Secondary School Mathematics. Educational Studies in Mathematics. 41, 47-68.
  • Ören, D. (2007). Onuncu sınıf öğrencilerinin geometrideki ispat şemalarının bilişsel stilleri ve cinsiyetlerine göre incelenmesine yönelik bir çalışma.[ A study on examining tenth grade students' proof schemes in geometry according to their cognitive styles and gender.] Yayınlanmamış yüksek lisans tezi, Orta Doğu Teknik Üniversitesi Fen Bilimleri Enstitüsü, Ankara
  • Pektaş, O., & Bilgici, G. (2019). Matematik Öğretmen Adaylarının Trigonometri Konusunda Kullandıkları Kanıt Şemalarının Öğrenme Stillerine Göre İncelenmesi.[ Examining the Proof Schemes Used by Pre-service Mathematics Teachers on Trigonometry According to Their Learning Styles] Kastamonu Eğitim Dergisi, 27(3), 1347-1358.
  • Saeed, R., M. (1996). An Exploratory Study of College Student’s Understanding of Mathematical Proof and the Relationship of this Understanding to their Attitude toward Mathematics. Unpublished PhD Dissetation, Ohio University, USA Sarı, M., Altun, A., & Aşkar, P. (2007). Undergraduate students’ mathematical proof processes in a calculus course: case study, Journal of Faculty of Educational Sciences, 40(2), 295-319.
  • Schabel, C. (2005). An Instructional Model for Teaching proof Writing in the Number Theory Classroom. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 15(1). 45-59.
  • Sowder, L., & Harel, G. (1998). Types of students’ justifications, The Mathematics Teacher, 91(8), 670-675 . Şengül, S., & Güner, P. (2013). DNR tabanlı öğretime göre matematik öğretmen adaylarının ispat şemalarının incelenmesi,[ Examining the proof schemes of pre-service mathematics teachers according to DNR-based teaching,] International Journal of Social Science, 6(2), 869-878
  • Tall, D. (1995). Cognitive Development, Representations and Proof. The conference on Justifying and Proving in School Mathematics, Institute of Education, London, December 1995, 27-3
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101– 119.
  • Weber, K. (2010). Mathematics majors' perceptions of conviction, validity, and proof, Mathematical Thinking and Learning, 12(4), 306-336.
  • Yıldırım, A. & Şimşek, H. (2000). Sosyal Bilimlerde Nitel Araştırma Yöntemleri,[ Qualitative research methods in the social sciences] 2. Baskı, Seçkin Yayınları, Ankara.

Öğrencilerin Analiz Dersi Kapsamında Tercih Ettikleri İspat Şemaları Üzerine Bir İnceleme

Year 2024, Volume: 13 Issue: 2, 274 - 284, 16.04.2024

Abstract

Bu araştırmada öğretmen adaylarının analiz dersinde tercih ettikleri ispat şemaları incelenmiştir. Nitel araştırma yaklaşımın benimsendiği bu çalışma bir durum çalışmasıdır. Araştırmada, 12 öğretmen adayına açık uçlu soru formu uygulanmıştır. Uygulama kapsamında öğrencilere analiz 1 ve analiz 2 dersi kapsamında akıllarında en çok kalan ispat sorulmuş ve yanıtlarındaki ispat şemaları incelenmiştir. Buna göre öğretmen adaylarının akıllarında en çok kalan ispat şeması dönüşümsel ispat şeması olmuştur. Dönüşümsel ispat şeması üst sınıf düzeyi ve yüksek akademik bilgi düzeyi gerektiren bir yaklaşım olmasına karşın, bu çalışma kapsamında birinci sınıf öğrencilerinin dönüşümsel ispat şemasını tercih etmesinin sebebi öğrencilerin herhangi bir yapılandırılmış format olmadan, kendi tercih ettikleri ispatı yapmaları ve dolayısı ile yeterli ön bilgiye sahip olmaları ile açıklanabilir. Sonuç olarak öğretmen adayları akılda kalıcılık düzeyi en yüksek ispatı ön bilgileri ile birleştirerek üst düzey bir ispat şeması sergileme eğilimi gösterebilirler.

References

  • Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18. 147-146.
  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. (Ed.), Mathematics, teachers and children. (216-235).
  • Barnard, T. & Tall, D. (1997). Cognitive Units, Connections and Mathematical Proof. Proceeding of PME, 21(2). 41-48.
  • Bell, A.W. (1976). A study of pupils’ proof-explanations in mathematical situations, Educational Studies in Mathematics, 7, 23-40.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2012). Bilimsel araştırma yöntemleri [Scientific research methods] (13. Baskı). Ankara: Pegem Akademi.
  • Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41-53
  • Cusi, A., & Malara, N. (2007). Proofs problems in elementary number theory: Analysis of trainee teachers’ productions. In Proceedings of the Fifth Conference of the European Society for Research in Mathematics Education (pp. 591-600).
  • Doruk, M., & Kaplan, A. (2015). Prospective mathematics teachers’ difficulties in doing proofs and causes of their struggle with proofs. Bayburt Üniversitesi Eğitim Fakültesi Dergisi, 10(2), 315-328
  • Dreyfus, T. (1999). Why Johnny Can’t Prove. Educational Studies in Mathematics, 38(1), 85-109
  • Harel, G.& Sowder, L. (1998). Students' proof schemes. Research on Collegiate Mathematics Education, 3. 234-283. Harel, G., & Sowder, L (2007). Toward comprehensive perspectives on learning and teaching proof, In F. Lester (Ed.), Handbook of Research on Teaching and Learning Mathematics (2nd Ed.). Greenwich, CT: Information Age Publishing.
  • Hartter, B.J. (1995). Concept image and concept definition for the topic of the derivative (Unpublished doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 9603516)
  • Housman, D., & Porter, M. (2003). Proof schemes and learning strategies of above-average mathematics students. Educational Studies in Mathematics, 53(2), 139-158.
  • Heinze, A. & Reiss, K. (2003). Reasoning and proof: Methodological knowledge as a component of proof competence. In M.A. Mariotti (Ed.), Proceedings of the ThirdConference of the European Society for Research in Mathematics Education, Bellaria, Italy.
  • Hersch, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389-399
  • Housman, D.& Porter, M. (2003). Proof schemes and learning strategies of above average mathematics students. Educational Studies in Mathematics, 53, 139–158
  • İskenderoğlu, T. (2010). İlköğretim matematik öğretmeni adaylarının kanıtlamayla ilgili görüşleri ve kullandıkları kanıt şemaları [Primary mathematics teacher candidates' views on proof and the proof schemes they use] (Yayınlanmamış doktora tezi). Karadeniz Teknik Üniversitesi, Trabzon.
  • Jones, K. (2000). The student experience of mathematical proof at university level, International Journal of Mathematical Education in Science and Technology, 31,1, 53-60.
  • Knuth, E. (2002). Teacher’s Conceptions of Proof in the Contex of Secondary School Mathematics. Journal of Mathematics Teacher Education, 5. 61-88.
  • Miyazaki, M. (2000). Levels of Proof in Lover Secondary School Mathematics. Educational Studies in Mathematics. 41, 47-68.
  • Ören, D. (2007). Onuncu sınıf öğrencilerinin geometrideki ispat şemalarının bilişsel stilleri ve cinsiyetlerine göre incelenmesine yönelik bir çalışma.[ A study on examining tenth grade students' proof schemes in geometry according to their cognitive styles and gender.] Yayınlanmamış yüksek lisans tezi, Orta Doğu Teknik Üniversitesi Fen Bilimleri Enstitüsü, Ankara
  • Pektaş, O., & Bilgici, G. (2019). Matematik Öğretmen Adaylarının Trigonometri Konusunda Kullandıkları Kanıt Şemalarının Öğrenme Stillerine Göre İncelenmesi.[ Examining the Proof Schemes Used by Pre-service Mathematics Teachers on Trigonometry According to Their Learning Styles] Kastamonu Eğitim Dergisi, 27(3), 1347-1358.
  • Saeed, R., M. (1996). An Exploratory Study of College Student’s Understanding of Mathematical Proof and the Relationship of this Understanding to their Attitude toward Mathematics. Unpublished PhD Dissetation, Ohio University, USA Sarı, M., Altun, A., & Aşkar, P. (2007). Undergraduate students’ mathematical proof processes in a calculus course: case study, Journal of Faculty of Educational Sciences, 40(2), 295-319.
  • Schabel, C. (2005). An Instructional Model for Teaching proof Writing in the Number Theory Classroom. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 15(1). 45-59.
  • Sowder, L., & Harel, G. (1998). Types of students’ justifications, The Mathematics Teacher, 91(8), 670-675 . Şengül, S., & Güner, P. (2013). DNR tabanlı öğretime göre matematik öğretmen adaylarının ispat şemalarının incelenmesi,[ Examining the proof schemes of pre-service mathematics teachers according to DNR-based teaching,] International Journal of Social Science, 6(2), 869-878
  • Tall, D. (1995). Cognitive Development, Representations and Proof. The conference on Justifying and Proving in School Mathematics, Institute of Education, London, December 1995, 27-3
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101– 119.
  • Weber, K. (2010). Mathematics majors' perceptions of conviction, validity, and proof, Mathematical Thinking and Learning, 12(4), 306-336.
  • Yıldırım, A. & Şimşek, H. (2000). Sosyal Bilimlerde Nitel Araştırma Yöntemleri,[ Qualitative research methods in the social sciences] 2. Baskı, Seçkin Yayınları, Ankara.
There are 28 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Articles
Authors

Bahar Dinçer 0000-0003-4767-7791

Early Pub Date March 25, 2024
Publication Date April 16, 2024
Published in Issue Year 2024 Volume: 13 Issue: 2

Cite

APA Dinçer, B. (2024). Assessment Of Students Preferred Proof Schemes In The Context Of The Analysis Course. Bartın University Journal of Faculty of Education, 13(2), 274-284.

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