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The Proof Schemes of Preservice Middle School Mathematics Teachers and Investigating the Expressions Revealing These Schemes

Year 2019, Volume: 10 Issue: 1, 59 - 100, 10.04.2019

Emine Gaye Çontay , Asuman Duatepe Paksu

https://doi.org/10.16949/turkbilmat.397109

Abstract

The aim of this study is to investigate preservice middle
school teachers’ proof schemes and how they presented their proof schemes.
Clinical method was used to identify the proof schemes of preservice
teachers.  For this purpose, clinical
interviews about the nature of proof and task based interviews were conducted
with the participants in the field of numbers. The Task Based Interview
Questions Form and Interview Questions Form about the Nature of Proof were
conducted with three female preservice teachers in a single session. Using the
content analysis report, it was found that preservice teachers used external
proof schemes more frequently than analytic proof schemes, and they used
empirical proof schemes less often. It was determined that showing responses on
analytical proof schemes was higher in those preservice teachers when compared
to the ones with lower level achievements. It was found that the external based
opinions of the preservice teachers were found to be related with their
characteristics which revealed external based proof scheme. It was also noticed
that there could be a relationship between already acquired opinions which were
memorized and superficial and the ones which block transforming ideas while
making proofs.      

Keywords

Preservice middle school mathematics teachers numbers task based interviews proof scheme nature of proof

References

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Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi

Year 2019, Volume: 10 Issue: 1, 59 - 100, 10.04.2019

Emine Gaye Çontay , Asuman Duatepe Paksu

https://doi.org/10.16949/turkbilmat.397109

Abstract

Mevcut çalışma ile ortaokul matematik öğretmeni adaylarının
ispat şemalarının neler olduğunu ve bu şemaları nasıl ortaya koyduklarını
araştırmak amaçlanmıştır. Öğretmen adaylarının ispat şemalarının
belirlenebilmesi için klinik yöntem kullanılmıştır. Bu amaçla öğretmen
adaylarıyla sayılar alanında görev temelli görüşmeler ve ispatın doğasına
ilişkin klinik görüşmeler yapılmıştır. 3 kız öğretmen adayına tek bir oturumda
Görev Temelli Görüşme Formu ve İspatın Doğasına İlişkin Görüşme Formu
yöneltilmiştir. İçerik analizi yöntemi kullanılarak öğretmen adaylarının en çok
dışsal, daha sonra analitik ve en az deneysel ispat şemalarını ortaya koyan
tepkiler verdikleri belirlenmiştir. Çalışmada daha yüksek başarı düzeyindeki
öğretmen adaylarının daha düşük başarı düzeyindeki öğretmen adayına göre
analitik ispat şemasını ortaya koyan tepkileri daha sık gösterdikleri
belirlenmiştir. Öğretmen adaylarının dışsal kaynaklı fikirlerinin, çoğunlukla
onların dışsal alışkanlık edinilmiş ispat şemalarını ortaya çıkaran özellikleri
ile ilişkili olduğu belirlenmiştir. Öğretmen adaylarının ispatın doğasına
ilişkin önceden edinilmiş ezbere ve yüzeysel fikirleri ile onların ispatı
yapılandırırken dönüşüm yapmalarına engel olan fikirlerinin ilişkili
olabileceği belirlenmiştir.

Keywords

Ortaokul matematik öğretmeni adayları sayılar görev temelli görüşmeler ispat şeması ispatın doğası

References

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  • Aydoğdu İskenderoğlu, T. (2016). Kanıt ve kanıt şemaları. E. Bingölbali, S. Arslan, ve İ.Ö. Zembat (Eds.), Matematik Eğitiminde Teoriler içinde (s. 65-83). Pegem Akademi, Ankara.
  • Aydoğdu İskenderoğlu, T. (2003). Farklı sınıf düzeylerindeki öğrencilerin matematik problemlerini kanıtlama süreçleri. (Yüksek Lisans Tezi, Abant İzzet Baysal Üniversitesi, Sosyal Bilimleri Enstitüsü, Bolu). http://tez2.yok.gov.tr/ adresinden edinilmiştir.
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  • Baştürk, S. (2010). First-year secondary school mathematics students' conceptions mathematical proofs and proving. Educational Studies, 36(3), 283-298.
  • Bieda, K.N. (2008). The pedagogy of proving in middle school mathematics. (Doctoral dissertation, University of Wisconsin, Madison, USA).
  • Boyle, J.D. (2012). Study of prospective secondary mathematics teachers’ evolving understanding of reasoning-and-proving. (Doctoral dissertation, University of Pittsburgh, USA). Retrieved from https://search.proquest.com/pqdtglobal/docview/1222084018.
  • CadwalladerOlsker, T. (2007). Proof schemes and proof writing. (Doctoral dissertation, Claremont Graduate University, California, USA).
  • Chazan, D. (1993). High school geometry students’ justification for their views of empirial evidence and mathematical proof, Educational Studies in Mathematics, 24(4), 359-387.
  • Ceylan, T. (2002). Geogebra yazılımı ortamında ilköğretim matematik öğretmen adaylarının geometrik ispat biçimlerinin incelenmesi. (Yüksek Lisans Tezi, Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara). http://tez2.yok.gov.tr/ adresinden edinilmiştir.
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  • Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students, British Educational Research Journal, 20(1), 41–54.
  • Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics (CCSSM). Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/Math/ internet adresinden 5.03.2017 tarihinde elde edildi.
  • Demiray, E. (2013). An investigation of pre-service middle school mathematics teachers’ achievement levels in mathematical proof and the reasons of their wrong interpretations. (Doctoral Dissertation, Orta Doğu Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara). http://tez2.yok.gov.tr/ adresinden edinilmiştir.
  • Ellis, A.B. (2007). Connections between generalizing and justifiying; Students’ reasoning with linear relationships, Journal for Research in Mathematics Education, 38(3), 194-229.
  • Flores, A. (2006). How do students know what they learn in middle school mathematics is true?, School Science and Mathematics, 106(3), 124-132.
  • Gholamazad, S., Liljedahl, P., & Zazkis, R. (2004, October). What Counts as Proof? Investigation of Preservice Elementary Teachers' Evaluation of Presented 'Proofs’, Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Toronto, Canada.
  • Goetting, M. M. (1995). The college students' understanding of mathematical proof. (Unpublished doctoral dissertation). The University of Maryland, USA.
  • Goldin, G. A. (2000). A scientific perspective on structured, task based interviews in mathematics education research. İçinde A. E. Kelly , & R.A. Lesh (Ed.), Handbook of research design in mathematics and science education (517-545). Mahwah: Lawrence Erlbaum Associates Publishers.
  • Grigoriadou, O. (2012). Reasoning in geometry. How first learning to appreciate the generality of arguments helps students come to grips with the notion of proof. (Unpublished master’s thesis). University of Amsterdam, Holland.
  • Güler, G. (2013). Matematik öğretmeni adaylarının cebir öğrenme alanındaki ispat süreçlerinin incelenmesi, (Doktora Tezi, Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum). http://tez2.yok.gov.tr/ adresinden edinilmiştir.
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There are 80 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Emine Gaye Çontay 0000-0002-6446-9217

Asuman Duatepe Paksu

Publication Date April 10, 2019
Published in Issue Year 2019 Volume: 10 Issue: 1

Cite

APA Çontay, E. G., & Duatepe Paksu, A. (2019). Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(1), 59-100. https://doi.org/10.16949/turkbilmat.397109
AMA Çontay EG, Duatepe Paksu A. Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). April 2019;10(1):59-100. doi:10.16949/turkbilmat.397109
Chicago Çontay, Emine Gaye, and Asuman Duatepe Paksu. “Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları Ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 1 (April 2019): 59-100. https://doi.org/10.16949/turkbilmat.397109.
EndNote Çontay EG, Duatepe Paksu A (April 1, 2019) Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 1 59–100.
IEEE E. G. Çontay and A. Duatepe Paksu, “Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 1, pp. 59–100, 2019, doi: 10.16949/turkbilmat.397109.
ISNAD Çontay, Emine Gaye - Duatepe Paksu, Asuman. “Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları Ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10/1 (April 2019), 59-100. https://doi.org/10.16949/turkbilmat.397109.
JAMA Çontay EG, Duatepe Paksu A. Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10:59–100.
MLA Çontay, Emine Gaye and Asuman Duatepe Paksu. “Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları Ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 1, 2019, pp. 59-100, doi:10.16949/turkbilmat.397109.
Vancouver Çontay EG, Duatepe Paksu A. Ortaokul Matematik Öğretmeni Adaylarının İspat Şemaları ve Bu Şemaları Ortaya Koyan İfadelerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10(1):59-100.