201110

İLKÖĞRETİM MATEMATİK ÖĞRETMEN ADAYLARININ İSPATIN MATEMATİK ÖĞRENMEYE KATKISI İLE İLGİLİ GÖRÜŞLERİ VE İSPAT DÜZEYLERİ

Bu çalışma ilköğretim matematik öğretmen adaylarının ispat yapmanın matematik öğretimine katkısı ile ilgili görüşlerini ve ispat düzeylerini belirlemek amacıyla yapılmıştır. Çalışma betimsel yöntem kapsamında özel durum çalışması kullanılarak yürütülmüştür. Veriler, 2010-2011eğitim öğretim yılında Karadeniz Teknik Üniversitesi Fatih Eğitim Fakültesi İlköğretim Bölümü Matematik Öğretmenliği Anabilim Dalı'nda öğrenim gören toplam 99 birinci sınıf öğretmen adayına üç açık uçlu sorudan oluşan bir anket formu uygulanarak elde edilmiştir. Anket formunda kullanılan açık uçlu sorulardan birincisi ilköğretim matematik öğretimindeki önemiyle ilgili görüşlerini ortaya çıkarmak için kullanılmıştır. İkinci soru öğretmen adaylarının ispat yapabilme düzeylerini ortaya çıkarabilecek senaryo tipinde hazırlanmış açık uçlu bir sorudur. Üçüncü soru, ikinci soruya ispat değildir cevabı veren öğretmen adaylarının görüşlerini belirlemek amacıyla kullanılmıştır. Verilerin analizinde; ispat yapabilme düzeyleri Miyazaki (2000)'ninispat ile ilgili sınıflandırması esas alınarak analiz edilirken, ispatın matematik öğretimindeki önemi ve öğrenmeye katkısı ile ilgili görüşlerinden elde edilen veriler ise öğretmen adaylarının cevaplarının benzerlik ve farklılıklarına göre tematik olarak sınıflandırılarak analiz edilmiştir. Çalışma sonunda, öğretmen adaylarının büyük bir kısmının tümdengelimsel muhakeme içeren ve ispatlama yapılırken fonksiyonel dilin kullanıldığı İspat A türüne uygun ispatı tercih ettikleri ortaya çıkmıştır. Ayrıca, çok az öğretmen adayı hariç önemli bir kısmının ispat yapmanın matematik öğretimine katkı sağlayacağına inandıkları ortaya çıkmıştır. Çalışma sonucunda elde edilen sonuçlara dayalı olarak bazı önerilerde bulunulmuştur

PRIMARY MATHEMATICS PRE-SERVICE TEACHERS’ OPINIONS ABOUT THE CONTRIBUTION OF DOING PROOF ON LEARNING MATHEMATICS AND THEIR PROOF

This study was conducted to determine primary mathematics preservice teachers’ opinions about the contribution of doing proof on learning mathematics and their levels of doing mathematical proof. Case study method was used in this descriptive study. The data of the study were obtained by conducting a questionnaire which consists of three open-ended questions to total 99 first grade pre-service teachers enrolled in Department of Primary Mathematics Education in Karadeniz Technical University. Fatih Faculty of Education in 2010-2011 academic year. The first of open-ended question used in questionnaire form is exerted to expose the primary mathematics pre-service teachers’ opinions in mathematics teaching about the importance of proving. The second question is also an open-ended question as a script to expose the primary mathematics pre-service teachers the degree of proving. The third question is exerted to identify the opinions of primary mathematics pre-service teachers who answered the second question is not a proof. In the analysis of the data, primary mathematics preservice teachers’ levels of doing mathmatical proof were analyzed based on Miyazaki’s classification related to the proof. Their views regarding the significance of mathematical proof and the contribution of doing proof on learning mathematics were thematically classified in regard to the similarities and differences among their responses. At the end of the study, it was found that a large portion of pre-service teachers has prefered proof A which is the type of proof in which deductive reasoning is involved and a functional language is used when doing a proof. Also, it can be indicated that a significant part of the pre-service teachers except for a very few pre-service teachers believe in the positive contribution of doing proof on learning mathematics. Some suggestions were based on the results obtained in this study

PDF

___

ALMEIDA, D. (2000). A survey of mathematicsundergraduates’ interactionwithproof: someimplications form mathematicseducation. International Journal of Mathematical Education in ScienceandTechnology,31(6), 869–890.
ALMEIDA, D. (2001). Pupils’ proofpotential. International Journal of Mathematical Education in ScienceandTechnology, 32(1), 53–60.
ALMEIDA, D. (2003). Engenderingproofattitudes: can thegenesis of mathematicalknowledgeteach us anything? International Journal of Mathematical Education in ScienceandTechnology, 34(4), 479–488.
ANAPA, P. & ŞAMKAR, H. (2010) Investigation of undergraduatestudents’ perceptions of mathematicalprof. ProcediaSocialandBehavioralSciences, 2, 2700–2706.
BAKER, D., & CAMPBELL, C. (2004). Fosteringthedevelopment of mathematicalthinking: Observationsfrom a proofscourse. Primus, 14(4), 345–353.
BAKĠ, A. (2008).Kuramdan Uygulamaya Matematik Eğitimi. Ankara: Harf EğitimYayıncılık..
BAġTÜRK, S. (2010). First-yearsecondaryschoolmathematicsstudents' conceptions mathematical proofs and proving. EducationalStudies, 36(3), 283-298.
BROWN, J.,STILLMAN, G., SCHWARZ,B. & KAISER, G. (2008). Thecase of mathematical proof in lower secondary school: Knowledge and competencies of pre-service teachers. In M. Goos, R. Brown and K. Makar (Eds.), Navigating currents and charting directions, Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane(Vol. 1, pp. 85–91)Adelaide: MERGA.
DE VILLIERS, M. (1990). The role andfunction of proofwithsketchpad. Pythagoras,24, 17–24.
EDWARDS, B.S., & WARD, M.B. (2004). Suprisesfrommathematicseducationresearch: Students (mis)use of mathematicaldefinitions. TheAmerican Mathematical Monthly, 111, 411–424.
ERNEST, P. (1991). Thephilosophy of mathematicseducation. London, UK: TheFalmerPress,.
FITZGERALD, J.F. (1996). Proof in mathematicseducation. Journal of Education, 178(1).
GIBSON, D. (1998). Students’ use of diagramstodevelopproofs in an introductoryanalysiscourse. Students’ proofschemes. In E. Dubinsky, A. Schoenfeld, &J.Kaput (Eds.), Research in CollegiateMathematicsEducation, III, 284–307. AMS.
HANNA, G. (2000). Proof, explanationandexploration: An overview. EducationalStudies in Mathematics,44, 5–23.
HANNA, G., & BARBEAU,E. (2008). Proofs as bearers of mathematicalknowledge. ZDM-The International Journal of MathematicsEducation, 40, 345-353.
İSKENDEROĞLU, T. (2010). İlköğretim Matematik Öğretmeni Adaylarının Kanıtlamayla İlgili Görüşleri ve Kullandıkları Kanıt Semaları (YayınlanmamıĢ Doktora Tezi). Trabzon: KTÜ Fen Bilimleri Enstitüsü,
ALMEIDA, D. (2000). A survey of mathematicsundergraduates’ interactionwithproof: someimplications form mathematicseducation. International Journal of Mathematical Education in ScienceandTechnology,31(6), 869–890.
ALMEIDA, D. (2001). Pupils’ proofpotential. International Journal of Mathematical Education in ScienceandTechnology, 32(1), 53–60.
ALMEIDA, D. (2003). Engenderingproofattitudes: can thegenesis of mathematicalknowledgeteach us anything? International Journal of Mathematical Education in ScienceandTechnology, 34(4), 479–488.
ANAPA, P. & ġAMKAR, H. (2010) Investigation of undergraduatestudents’ perceptions of mathematicalprof. ProcediaSocialandBehavioralSciences, 2, 2700–2706.
BAKER, D., & CAMPBELL, C. (2004). Fosteringthedevelopment of mathematicalthinking: Observationsfrom a proofscourse. Primus, 14(4), 345–353.
BAKĠ, A. (2008).Kuramdan Uygulamaya Matematik Eğitimi. Ankara: Harf EğitimYayıncılık..
BAġTÜRK, S. (2010). First-yearsecondaryschoolmathematicsstudents' conceptions mathematical proofs and proving. EducationalStudies, 36(3), 283-298.
BROWN, J.,STILLMAN, G., SCHWARZ,B. & KAISER, G. (2008). Thecase of mathematical proof in lower secondary school: Knowledge and competencies of pre-service teachers. In M. Goos, R. Brown and K. Makar (Eds.), Navigating currents and charting directions, Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane(Vol. 1, pp. 85–91)Adelaide: MERGA.
DE VILLIERS, M. (1990). The role andfunction of proofwithsketchpad. Pythagoras,24, 17–24.
EDWARDS, B.S., & WARD, M.B. (2004). Suprisesfrommathematicseducationresearch: Students (mis)use of mathematicaldefinitions. TheAmerican Mathematical Monthly, 111, 411–424.
ERNEST, P. (1991). Thephilosophy of mathematicseducation. London, UK: TheFalmerPress,.
FITZGERALD, J.F. (1996). Proof in mathematicseducation. Journal of Education, 178(1).
GIBSON, D. (1998). Students’ use of diagramstodevelopproofs in an introductoryanalysiscourse. Students’ proofschemes. In E. Dubinsky, A. Schoenfeld, &J.Kaput (Eds.), Research in CollegiateMathematicsEducation, III, 284–307. AMS. HANNA, G. (2000). Proof, explanationandexploration: An overview. EducationalStudies in Mathematics,44, 5–23.
HANNA, G., & BARBEAU,E. (2008). Proofs as bearers of mathematicalknowledge. ZDM-The International Journal of MathematicsEducation, 40, 345-353.
İSKENDEROĞLU, T. (2010). İlköğretim Matematik Öğretmeni Adaylarının Kanıtlamayla İlgili Görüşleri ve Kullandıkları Kanıt Semaları (YayınlanmamıĢ Doktora Tezi). Trabzon: KTÜ Fen Bilimleri Enstitüsü,