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BİR ORTAÖĞRETİM MATEMATİK DERSİNDEKİ İSPAT YAPMA ETKİNLİĞİNE YÖNELİK SINIFİÇİ TARTIŞMA SÜRECİNE ÖĞRENCİ SÖYLEMLERİ ÇERÇEVESİNDE YAKINDAN BAKIŞ

Year 2010, Issue: 28, 134 - 154, 01.12.2010

Abstract

Bu araştırma bir ortaöğretim sınıfının matematik dersinde uygulanan ispat yapma etkinliği esnasındaki iletişim durumlarının incelenmesini kapsamaktadır. Söz konusu iletişim sürecinde tüm sınıf bazında yapılan tartışmalara odaklanılarak özellikle öğrencilerin söylemleri analiz edilmiştir. Özel durum çalışması niteliğindeki bu nitel araştırmada söylem çözümlemesinden yararlanılmıştır. Söylem çözümlemesi, araştırmanın tasarımında, veri toplama aşamasında, verilerin analizinde ve raporlaştırılmasında metodolojik çerçeveyi oluşturmaktadır. Çalışmanın örneklemi özel bir fen lisesinin on birinci sınıfındaki 13 öğrenci ve o sınıfın matematik öğretmeninden (toplam 14 kişi) oluşmaktadır. Teşvik edilmiş söylem (TES) aracılığıyla öğrencilerin ispat ve ispatlamaya yönelik bilgileri ve anlamaları hakkında kayda değer bulguların elde edildiği bu çalışmanın ülkemizde ispatın öğretimi ve ispat yapma becerisinin geliştirilmesine yönelik öğretim anlayışının iyileştirilmesine katkı yapması ve konu ile ilgili araştırmacılara faydalı bilgiler sağlaması amaçlanmaktadır

References

  • Ağlagül, D. (2009). Beşinci Sınıf Sosyal Bilgiler Dersinde Sınıf Öğretmenlerinin Yapılandırmacı Öğrenme Ortamı Düzenleme Becerilerinin Değerlendirilmesi. Yayınlanmamış Yüksek Lisans Tezi, Çukurova Üniversitesi, Sosyal Bilimler Enstitüsü, Adana.
  • Akturan, U. Domaç, B. ve diğer. (2008). Söylem Analizi, (Eds. T. Baş ve U. Akturan) Nitel Araştırma Yöntemleri Nvivo 7.0 ile Nitel Veri Analizi, Ankara: Seçkin Yayıncılık, s. 25- 40.
  • Almeida, D. (2001). Pupils‟ Proof Potential. International Journal of Mathematical Education in Science and Technology, 32(1), pp. 53–60.
  • Ball, D.L., Hoyles, C., Jahnke, H.N., & Movshovitz-Hadar, N. (2002). The Teaching of Proof. In L.I. Tatsien (Ed.). Proceedings of the International Congress of Mathematicians (Vol. III, pp. 907–920). Beijing: Higher Education Press.
  • Barwell, R. (2003). Discursive Psychology and Mathematics Education: Possibilities and Challenges, ZDM, Vol. 35 (5), 201-207.
  • Baş, T., Akturan, U., Ataçkarapınar, M. ve diğer. (2008). Nitel Araştırma Yöntemleri, NVivo 7.0 İle Nitel Veri Analizi, Ankara: Seçkin Yayıncılık.
  • Cazden, C. B. & Beck, S. W. (2003). Classroom Discourse, Handbook of Discourse Processes, (Eds. A. C. Graesser; M, A, Gernsbacher; S. R. Goldman), New Jersey: Lawrence Erlbaum Associates. Inc. Publication.
  • Coe, R. & K. Ruthven. (1994). Proof Practices and Constructs of Advanced Mathematical Students. British Educational Research Journal 20, No. 1, pp. 41–54.
  • Davis, P. J. & Hersh, R. (2002). Matematiğin Seyir Defteri.(Çev. E. Abadoğlu) Ankara: Doruk Yayıncılık.
  • Ellerton, N. F. & Clarkson, P. C. (1996). Language Factors in Mathematics Teaching. (In A. J. Bishop et. al.) International Handbook of Mathematics Education. Netherlands: Kluwer Academic Publishers.
  • Fosnot, C. T. & Perry, R. S. (2007). Oluşturmacılık: Psikolojik Bir Öğrenme Teorisi (Bölüm- 2), Oluşturmacılık. Teori, Perspektifler ve Uygulama, (2. Baskıdan Çev. S. Durmuş), Ankara: Nobel Yayın Dağıtım.
  • Garnier, R. & J. Taylor (1996). 100% Mathematical Proof. John Wiley & Sons, Inc. Press.
  • Günay, V. D. (2010). Söylem Çözümlemeleri, [basımda kitap]
  • Halliday, M. A. K. & Hasan, R. (1989). Language, Context and Text: Aspects of Language in A Social-Semiotic Perspective. (2nd ed.). Oxford: Oxford University Press.
  • Har, Y. B. (2007). The Singapore Mathematics Curriculum and Mathematical Communication, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Harel, G., & Sowder, L (2007). Toward a Comprehensive Perspective on Proof, (Eds. F. Lester), Second Handbook of Research on Mathematics Teaching and Learning, National Council of Teachers of Mathematics, pp. 805-842.
  • Hicks, D. (1996). Discourse, Learning and Teaching, Review of Research in Education, Vol. 21, (1995-1996), 49-95.
  • ICMI Study 19. (2009). Proof and Proving in Matematics Education: Discussion Document, (Eds. F. L. Lin; F. J. Hsieh; G. Hanna & M. de Villiers) Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, (10-15 May) pp. 1-XIX-- 1-XXX,Taipei, Taiwan.
  • Khaing, T. T., Hamaguchi, K. & Ohtani, M. (2007). Development Mathematical Communication in the Classroom, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Knuth, E. J. (2002). Teachers‟ Conceptions of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education. 5, 61-88.
  • Lee, J. K. (2002). Philosophical Perspectives on Proof in Mathematics Education. Philosophy of Mathematics Education Journal, 16.
  • Lin, C. H., Shann, W. C. & Lin, S. C. (2007). Reflection on Mathematical Communication from Taiwan Math Curriculum Guideline and PISA 2003, Proceeding of APEC- TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • MEB, (2005). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, http://ogm.meb.gov.tr/(alıntı 01 Ekim 2009).
  • Miyagui, M. (2007). Key Questions for Focusing on Mathematical Communication, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical
  • Morgan, C. (2006). What Does Social Semiotics Have to Offer Mathematics Education Research?, Educational Studies in Mathematics, Vol. 61, No.1/2, A PME Special Issue, 219-245.
  • NCTM, (2000). Principles and Standarts for School Mathematics. Reston, VA: NCTM.
  • Özer, Ö. & Arıkan, A. (2002). Lise Matematik Derslerinde Öğrencilerin İspat Yapabilme Düzeyleri, V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Orta Doğu Teknik Üniversitesi, Eğitim Fakültesi, (16-18 Eylül) Ankara.
  • Padraig, M. & McLoughlin, M. M. (2002). The Central Role of Proof in the Mathematics Canon: The Efficacy of Teaching Students to Create Proofs Using a Fusion of Modified Moore, Traditional, and Reform Methods. The Annual Summer Meeting of the Mathematical Association of America, (3 August) Burlington, Vermont.
  • Ryve, A. (2004). Can Colloborative Concept Mapping Create Mathematically Productive Discourses?, Educational Studies in Mathematics, 26, 157-177.
  • Setati, M. (2005). Mathem atics Education and Language: Policy, Research and Practice in Multilingual South Africa, (Eds. R. Vithal, J. Adler, & C. Keitel) Researching Mathematics Education in South Africa. Cape Town: HSRC Press.
  • Sfard, A. (2001). There is More to Discourse Than Meets the Ears: Loking at Thinking as Communicating to Learn More about Mathematical Learning, Educational Studies in Mathematics, Vol. 46, No. 1/3, 13-57.
  • Steele, D. F., (2001). Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective. School Science and Mathematics. 101(8), 404-416.
  • Şimşek, N. (2004). Yapılandırmacı Öğrenme ve Öğretime Eleştirel Bir Yaklaşım, Eğitim Bilimleri ve Uygulama, 3(5), 115-139.
  • Taylor, S. (2001) Locating and Conducting Discourse Analytic Research (Eds. M. Wetherell, S. Taylor and S. J. Yates), Discourse As Data, A Guide for Analysis, London: Sage Publications, pp. 5-48.
  • Uğurel, I. ve Moralı, S. (2010). Matematik Eğitimi ve Dilbilim Etkileşimine Dayalı Bir Araştırma ve Metodoloji Alanı: Söylem Çözümleme, E-Journal of New World Sciences Academy, Vol. 5, No. 1, 173-184.
  • Ulep, S. A. (2007). Developing Mathematical Communication in Philippine Classroom, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Vui, T. (2007). Enhancing Classroom Communication to Develop Students‟ Mathematical Thinking, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical
  • Wang, S. (2007). Research Process, Changes and Implementation of Mathematics Curriculum Standard of China, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Weber, K., (2001),Student Difficulty in Constructing Proofs: The Need For Strategic Knowledge. Educational Studies in Mathematics. 48, 101-119.
  • Wertsch, J. V. & Toma, C. (1995). Discourse and Learning in The Classroom: A Sociocultural Approach, (Eds. L. Steffe & J. Gale) Constructivism in Education, New Jersey: Lawrence Erlbaum, pp. 159-174.
  • Yıldırım, A..& Şimşek, H. (2000). Sosyal Bilimlerde Nitel Araştırma Yöntemleri, (2. Basım) Ankara : Seçkin Yayıncılık.

A CLOSE VIEW ON THE DISSUSSION IN RELATION TO A ACTIVITY ABOUT PROVING A THEOREM IN A HIGH SCHOOL MATHEMATICS LESSON VIA STUDENTS’ DISCOURSE

Year 2010, Issue: 28, 134 - 154, 01.12.2010

Abstract

This study includes the communication processes occuring during proof activities in mathematics lessons in a high school. The student discourse has been analysed by focusing the discussions realised in the whole class. In this qualitative study, which can be described as a case study as well, discourse analysis has been used. Discourse analysis is the methodological framework used in the design of the research, data collection, the analysis and reporting stages. The study has a sample of 12 people consisting of 13 eleventh-year students from a private science high school and their mathematics teacher. Finally, important findings have been found out concerning the students‟ knowledge and perception of proof and proving via prompt discourse (PD). The study aims at providing the future researchers some useful informations about the subject and contributing to the improvement of the proving skill and teaching proof in our country.

References

  • Ağlagül, D. (2009). Beşinci Sınıf Sosyal Bilgiler Dersinde Sınıf Öğretmenlerinin Yapılandırmacı Öğrenme Ortamı Düzenleme Becerilerinin Değerlendirilmesi. Yayınlanmamış Yüksek Lisans Tezi, Çukurova Üniversitesi, Sosyal Bilimler Enstitüsü, Adana.
  • Akturan, U. Domaç, B. ve diğer. (2008). Söylem Analizi, (Eds. T. Baş ve U. Akturan) Nitel Araştırma Yöntemleri Nvivo 7.0 ile Nitel Veri Analizi, Ankara: Seçkin Yayıncılık, s. 25- 40.
  • Almeida, D. (2001). Pupils‟ Proof Potential. International Journal of Mathematical Education in Science and Technology, 32(1), pp. 53–60.
  • Ball, D.L., Hoyles, C., Jahnke, H.N., & Movshovitz-Hadar, N. (2002). The Teaching of Proof. In L.I. Tatsien (Ed.). Proceedings of the International Congress of Mathematicians (Vol. III, pp. 907–920). Beijing: Higher Education Press.
  • Barwell, R. (2003). Discursive Psychology and Mathematics Education: Possibilities and Challenges, ZDM, Vol. 35 (5), 201-207.
  • Baş, T., Akturan, U., Ataçkarapınar, M. ve diğer. (2008). Nitel Araştırma Yöntemleri, NVivo 7.0 İle Nitel Veri Analizi, Ankara: Seçkin Yayıncılık.
  • Cazden, C. B. & Beck, S. W. (2003). Classroom Discourse, Handbook of Discourse Processes, (Eds. A. C. Graesser; M, A, Gernsbacher; S. R. Goldman), New Jersey: Lawrence Erlbaum Associates. Inc. Publication.
  • Coe, R. & K. Ruthven. (1994). Proof Practices and Constructs of Advanced Mathematical Students. British Educational Research Journal 20, No. 1, pp. 41–54.
  • Davis, P. J. & Hersh, R. (2002). Matematiğin Seyir Defteri.(Çev. E. Abadoğlu) Ankara: Doruk Yayıncılık.
  • Ellerton, N. F. & Clarkson, P. C. (1996). Language Factors in Mathematics Teaching. (In A. J. Bishop et. al.) International Handbook of Mathematics Education. Netherlands: Kluwer Academic Publishers.
  • Fosnot, C. T. & Perry, R. S. (2007). Oluşturmacılık: Psikolojik Bir Öğrenme Teorisi (Bölüm- 2), Oluşturmacılık. Teori, Perspektifler ve Uygulama, (2. Baskıdan Çev. S. Durmuş), Ankara: Nobel Yayın Dağıtım.
  • Garnier, R. & J. Taylor (1996). 100% Mathematical Proof. John Wiley & Sons, Inc. Press.
  • Günay, V. D. (2010). Söylem Çözümlemeleri, [basımda kitap]
  • Halliday, M. A. K. & Hasan, R. (1989). Language, Context and Text: Aspects of Language in A Social-Semiotic Perspective. (2nd ed.). Oxford: Oxford University Press.
  • Har, Y. B. (2007). The Singapore Mathematics Curriculum and Mathematical Communication, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Harel, G., & Sowder, L (2007). Toward a Comprehensive Perspective on Proof, (Eds. F. Lester), Second Handbook of Research on Mathematics Teaching and Learning, National Council of Teachers of Mathematics, pp. 805-842.
  • Hicks, D. (1996). Discourse, Learning and Teaching, Review of Research in Education, Vol. 21, (1995-1996), 49-95.
  • ICMI Study 19. (2009). Proof and Proving in Matematics Education: Discussion Document, (Eds. F. L. Lin; F. J. Hsieh; G. Hanna & M. de Villiers) Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, (10-15 May) pp. 1-XIX-- 1-XXX,Taipei, Taiwan.
  • Khaing, T. T., Hamaguchi, K. & Ohtani, M. (2007). Development Mathematical Communication in the Classroom, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Knuth, E. J. (2002). Teachers‟ Conceptions of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education. 5, 61-88.
  • Lee, J. K. (2002). Philosophical Perspectives on Proof in Mathematics Education. Philosophy of Mathematics Education Journal, 16.
  • Lin, C. H., Shann, W. C. & Lin, S. C. (2007). Reflection on Mathematical Communication from Taiwan Math Curriculum Guideline and PISA 2003, Proceeding of APEC- TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • MEB, (2005). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, http://ogm.meb.gov.tr/(alıntı 01 Ekim 2009).
  • Miyagui, M. (2007). Key Questions for Focusing on Mathematical Communication, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical
  • Morgan, C. (2006). What Does Social Semiotics Have to Offer Mathematics Education Research?, Educational Studies in Mathematics, Vol. 61, No.1/2, A PME Special Issue, 219-245.
  • NCTM, (2000). Principles and Standarts for School Mathematics. Reston, VA: NCTM.
  • Özer, Ö. & Arıkan, A. (2002). Lise Matematik Derslerinde Öğrencilerin İspat Yapabilme Düzeyleri, V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Orta Doğu Teknik Üniversitesi, Eğitim Fakültesi, (16-18 Eylül) Ankara.
  • Padraig, M. & McLoughlin, M. M. (2002). The Central Role of Proof in the Mathematics Canon: The Efficacy of Teaching Students to Create Proofs Using a Fusion of Modified Moore, Traditional, and Reform Methods. The Annual Summer Meeting of the Mathematical Association of America, (3 August) Burlington, Vermont.
  • Ryve, A. (2004). Can Colloborative Concept Mapping Create Mathematically Productive Discourses?, Educational Studies in Mathematics, 26, 157-177.
  • Setati, M. (2005). Mathem atics Education and Language: Policy, Research and Practice in Multilingual South Africa, (Eds. R. Vithal, J. Adler, & C. Keitel) Researching Mathematics Education in South Africa. Cape Town: HSRC Press.
  • Sfard, A. (2001). There is More to Discourse Than Meets the Ears: Loking at Thinking as Communicating to Learn More about Mathematical Learning, Educational Studies in Mathematics, Vol. 46, No. 1/3, 13-57.
  • Steele, D. F., (2001). Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective. School Science and Mathematics. 101(8), 404-416.
  • Şimşek, N. (2004). Yapılandırmacı Öğrenme ve Öğretime Eleştirel Bir Yaklaşım, Eğitim Bilimleri ve Uygulama, 3(5), 115-139.
  • Taylor, S. (2001) Locating and Conducting Discourse Analytic Research (Eds. M. Wetherell, S. Taylor and S. J. Yates), Discourse As Data, A Guide for Analysis, London: Sage Publications, pp. 5-48.
  • Uğurel, I. ve Moralı, S. (2010). Matematik Eğitimi ve Dilbilim Etkileşimine Dayalı Bir Araştırma ve Metodoloji Alanı: Söylem Çözümleme, E-Journal of New World Sciences Academy, Vol. 5, No. 1, 173-184.
  • Ulep, S. A. (2007). Developing Mathematical Communication in Philippine Classroom, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Vui, T. (2007). Enhancing Classroom Communication to Develop Students‟ Mathematical Thinking, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical
  • Wang, S. (2007). Research Process, Changes and Implementation of Mathematics Curriculum Standard of China, Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication, (9-14 December), Tokyo and Kanazawa, Japon.
  • Weber, K., (2001),Student Difficulty in Constructing Proofs: The Need For Strategic Knowledge. Educational Studies in Mathematics. 48, 101-119.
  • Wertsch, J. V. & Toma, C. (1995). Discourse and Learning in The Classroom: A Sociocultural Approach, (Eds. L. Steffe & J. Gale) Constructivism in Education, New Jersey: Lawrence Erlbaum, pp. 159-174.
  • Yıldırım, A..& Şimşek, H. (2000). Sosyal Bilimlerde Nitel Araştırma Yöntemleri, (2. Basım) Ankara : Seçkin Yayıncılık.
There are 41 citations in total.

Details

Other ID JA45ER33CK
Journal Section Articles
Authors

İşıkhan Uğurel This is me

H. Sevgi Moralı This is me

Publication Date December 1, 2010
Published in Issue Year 2010 Issue: 28

Cite

APA Uğurel, İ., & Moralı, H. S. (2010). BİR ORTAÖĞRETİM MATEMATİK DERSİNDEKİ İSPAT YAPMA ETKİNLİĞİNE YÖNELİK SINIFİÇİ TARTIŞMA SÜRECİNE ÖĞRENCİ SÖYLEMLERİ ÇERÇEVESİNDE YAKINDAN BAKIŞ. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(28), 134-154.