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ÖĞRENCİLERİN ÖRÜNTÜLERİ GENELLEME SÜREÇLERİ: 7. SINIF ÖRNEĞİ

Yıl 2015, Cilt: 23 Sayı: 2, 523 - 548, 15.05.2015

Öz

Bu çalışmada 7. sınıf öğrencilerinin örüntüleri genelleme süreçleri incelenmiştir. Çalışma dokuz öğrenci ile yürütülmüştür. Veri toplama aracı olarak 10 sorudan oluşan örüntü testi ve beş sorudan oluşan mülakat testi kullanılmıştır. Araştırma sonuçlarına göre öğrenciler yakın uzaklıktaki terimleri bulmak için çoğunlukla yinelemeli ilişki, orta uzaklıktaki terimleri bulmak için kuraldan yapma, örüntülerin kurallarını bulmak için ise belirgin stratejiyi kullanmışlardır. Öğrenciler örüntülerin kurallarını bulmak için tahmin-kontrol, bütüne genişletme stratejilerini çok az kullanmışlar, görsel stratejileri ise hiç kullanmamışlardır. Verilen şekilleri veya şekillerin yapılarını dikkate almamışlar örüntülerin kurallarını bulmak için sadece sayısal ilişkilere odaklanmışlardır. Örüntülerin kuralını bulmada en yüksek başarı tekrarlı, en düşük başarı ise artarak genişleyen örüntü sorularında görülmüştür.

Kaynakça

  • Akkan Y., ve Çakıroğlu, Ü. (2012). Doğrusal ve İkinci Dereceden Örüntüleri Genelleştirme Stratejile- ri: 6-8. Sınıf Öğrencilerinin Karşılaştırılması. Eğitim ve Bilim, 37(165), 104-120
  • Baki, A.(2008). Kuramdan Uygulamaya Matematik Eğitimi. Ankara: Harf Eğitim Yayıncılığı.
  • Baş, S., Erbaş, K. A., ve Çetinkaya, B. (2011). Öğretmenlerin Dokuzuncu Sınıf Öğrencilerinin Cebir- sel Düşünme Yapılarıyla İlgili Bilgileri. Eğitim ve Bilim, 36(159), 41-55
  • Becker, J.R., and Rivera, F. (2005). Generalization an Strategies of Beginning High School Algebra Students. In Chick, H.L. ve Vincent, J.L.(Eds). Proceedings of the 29th Conference of the Interna- tional Group for the Psychology of Mathematics Education, Vol. 4, pp. 121-128
  • Becker, J.R., and Rivera, F. (2006). Sixth Graders’ Figural and Numerical Strategies for Generalizing Patterns in Algebra. In Alatorre, S., Cortina, J.L., M. Mendez, A.(Eds). Proceedings of the 28th Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 95-101, Merida, Mexico
  • Bezuska, S. J. and Kenney, M. J. (2008). The Three R’s: Recursive Thinking, Recursion, and Recursive Formu- las. In C. E. Greenes and R. Rubenstein (Eds.), Algebra and Algebraic Thinking in School Mathematics: Seventieth Yearbook, pp. 81 - 97. Reston, VA: National Council of Teachers of Mathematics.
  • Bishop, W. J. (1997). Middle school students’ understanding of mathematical patterns and their symbolic representation. Doctor of Philosophy, Department of Mathematics Illinois State Universiy
  • Blair, S.L. (2001). The Importance of Basic Facts in Mathematics. Dissertation Abstracts Internatio- nal, 62(08), 2705A. (UMI No:3022967)
  • Blanton, M. L., and Kaput, J. J. (2004). Elementary Grades Students’ Capacity for Functional Thin- king. In M. J. Hoines ve A. B. Fuglestad (Eds.). Proceedings of the 28th Conference of the Interna- tional Group for the Psychology of Mathematics Education. Bergen, Norway.
  • Dörfler, W. (1991). Forms and means of generalization in mathematics.in A.J. Bishop(Ed.), Mathematical Knowledge: Its Growth through Teaching, Kluwer AcademicPublishers, Dordrecht, pp. 63–85.
  • Feifei, Y. (2005). Diognastic assesment of urban middle school learning of pre-algebra patterns. Doc- toral Dissertation, Ohio State University, USA
  • Gall, M., Borg, W. and Gall, J.P.(1996). Educational Research an Introduction. USA: Longman Publisher
  • Hargreaves, M., Shorrocks-Taylor, D. and Threlfall, J. (1998). Children’s Strategies with Number Patterns. Educational Studies, 24(3), 315-331
  • Healy, L. and Hoyles, C. (1999). Visual and Symbolic Reasoning in Mathematics: Making Connecti- ons with Computers?. Mathematical Thinking and Learning, 1(1), 59-84
  • Kalaycı, Ş. (2005). SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri. Ankara: Asil Yayın Dağıtım
  • Kaput, J. (1998). Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by “Algebrafying” the K-12 Curriculum, In NCTM, The Nature and role of Algebra in the K-14 Curriculum. Washington, DC: National Academy Press
  • Kaput, J., and Blanton, M. (2001). Algebrafying the Elementary Mathematics Experience. In H. Chick, K. Stacey, J. Vincent, and J. Vincent (Eds.), The Twelfth ICMI Study, on the Future of the Teaching and Learning of Algebra: 1. (pp. 344–352). Melbourne, Australia: University of Melbourne.
  • Karataş, İ. ve Güven, B. (2003). Problem Çözme Davranışlarının Değerlendirilmesinde Kullanılan Yöntemler: Klinik Mülakatın Potansiyeli. İlköğretim Online, 2(2), 2-9
  • Kutluk, B. (2011). İlköğretim matematik öğretmenlerinin örüntü kavramına ilişkin öğrenci güçlükleri bilgilerinin incelenmesi. Yüksek Lisans Tezi, Dokuz Eylül Üniversitesi, İzmir
  • Lan-Ma, H. (2007). The Potential of Patterning Activities to Generalizations. In Woo, J.H. , Lew, H.C., Park, K.S., and Seo, D.Y. (Eds). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 225-232, Seoul: PME
  • Lannin, J.K. (2003). Developing Algebraic Reasoning Through Generalization. Mathematics Teac- hing in the Middle School, 8(7), 342-348
  • Lannin, J.K. (2005). Generalization and Justification: The Challenge of İntroducting Algebraic Reaso- ning through Patterning Activities, Mathematical Thinking and Learning, 7(3), 231-258
  • Lannin, J.K., Barker, D.D. and Townsend, B.E. (2006a). Recursive and Explicit Rules: How can We Build Student Algebraic Understanding?. Journal of Mathematical Behavior, 25, 299-317
  • Lannin, J.K., Barker, D. and Townsend, B. (2006b). Algebraic Generalization Strategies: Factors Inf- luencing Student Strategy Selection. Mathematics Education Research Journal, 18(3), 3-28
  • Lesley, L. and Freiman, V. (2004). Tracking Primary Students’ Understanding of Patterns. In M. J. Hoines ve A. B. Fuglestad (Eds.). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. 2, 415–422. Bergen, Norway.
  • Ley, F. A. (2005). A Cross-Sectional İnvestigation of Elementary School Students’ Ability to Work with Linear Generalizing Patterns: The İmpact of Format and Age on Accuracy and Strategy Choice. Mas- ter of Arts Department of Human Development and Applied Psychology University of Toronto
  • Liljedahl, P. (2004). Repeating Pattern or Number Pattern: The Distinction is Blurred. Focus on Lear- ning Problems in Mathematics, 26(3), 24–42.
  • Linchevski, L., 1995. Algebra with Numbers and Arithmetic with Letters: A Definition of Pre-algebra, The Journal of Mathematical Behaviour, 14, 113-120.
  • Markworth, A. K. (2010). Growing and Growing: Promoting Functional Thinking with Geometric Growing Pattern. Doctor of Philosophy, University of North Carolina at Chapel Hill
  • Milli Eğitim Bakanlığı, (MEB), (2005a). İlköğretim Matematik Dersi 1-5. Sınıflar Öğretim Programı. Ankara: Devlet Kitapları Müdürlüğü.
  • Milli Eğitim Bakanlığı, (MEB), (2005b). İlköğretim Matematik Dersi Öğretim Programı ve Klavuzu 6-8. Sınıflar. Ankara: Talim ve Terbiye Kurulu Başkanlığı
  • National Council of Teachers of Mathematics.(2000). Principles and Standards for School Mathema- tics, NCTM, Reston, VA.
  • Ndlovu, C. W. (2011). Learners’ mathematical reasoning when generalizing from number patterns in the general education and training phase, wired.wits.ac.za adresinden alınmıştır.
  • Noss, R., Healy, L., and Hoyles, C. (1997). The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic. Educational Studies in Mathematics, 33(2), 203-233.
  • Olkun, S. ve Toluk Uçar, Z. (2004). İlköğretimde Etkinlik Temelli Matematik Öğretimi. Ankara:Anı Yayıncılık (3. Baskı)
  • Olkun, S. ve Toluk Uçar, Z. (2006). Temel Matematik II, Ankara: Tekağaç Eylül Yayıncılık.
  • Olkun, S. ve Toluk-Uçar, Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi, Ankara: Maya Akademi Yayıncılık (Genişletilmiş 3. Baskı),
  • Orton, A. and Orton, J. (2005). Pattern and the Apprach to Algebra. In A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics (Chapter 7, pp.104-120) London: Cassell
  • Orton, J., Orton, A. and Roper, T (2005). Pictorial and Practical Contexts and the Perception of Pat- tern. In A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics (Chapter 8, pp.121- 136) London: Cassell
  • Rivera, F. and Becker, J.R. (2007). Abduction-Iinduction (generalization) Processes of Preservice Ele- mentary Majors on Patterns in Algebra. Journal of Mathemetical Behavior, 26(2), 140-155
  • Rivera, F. D., and Becker, J. R. (2009). Algebraic Reasoning through Patterns. Mathematics Teaching in the Middle School, 15(4), 213-221.
  • Ross, M. K. (2011). Fıfth graders’ representations and reasoning on constant growth function prob- lems: Connections between problem representations, student work and ability to generalize, Deg- ree of Doctor of Philosophy, the University of Arizona
  • Sasman, C. M., Linchevski, L. and Olivier, A. (1999). The Influence of Different Representations on Children’s Generalization Thinking Processes. In J. Kupier (Ed), Proceedings of the 7th Annual Conference of the Southern African Association for Research in Mathematics and Science Edu- cation (pp. 406-415). Harare, Zimbabwe
  • Sharon, V.V. (2010). Pre-service elementary teachers’ understanding of pattern and function. the Deg- ree of Doctor of Philosophy, Oklahoma State University
  • Sorkin, E.J. (2011). Young children’s abilities to make generalizations about functional relations using cube tower. The Degree of Doctor Philosophy, Columbia University
  • Stacey, K. (1989). Finding and Using Patterns in Linear Generalising Problems, Educational Studies in Mathematics, 20, 147-164
  • Steele, D. (2005). Using Writing to Access Students’ Schemata Knowledge for Algebraic Thinking. School Science and Mathematics, 103(3), 142-154
  • Swafford, O. J., and Langrall, W. C. (2000). Grade 6 Students’ Preinstructional Use of Equations to Describe and Represent Problem Situations. Journal for Research in Mathematics Education, 31(1), 89-112
  • Tanışlı, D. (2008). İlköğretim 5. sınıf öğrencilerinin örüntülere ilişkin anlama ve kavrama biçimlerinin belirlenmesi. Anadolu Üniversitesi Eğitim Bilimleri Enstitüsü İlköğretim Ana Bilim Dalı Sınıf Öğretmenliği Doktora Tezi, Eskişehir
  • Tanışlı, D. ve Köse, Y.N. (2010). Sınıf Öğretmeni Adaylarının Örüntüleri Genellemeleri: Görsel Stra- tejilerin Etkisi: 9. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu (s. 220-225), Elazığ
  • Tanışlı, D. ve Köse, Y.N. (2011). Lineer Şekil Örüntülerine İlişkin Genelleme Stratejileri: Görsel Ve Sayısal İpuçlarının Etkisi. Eğitim ve Bilim, 36(160), 184-198
  • Warren, E. A., and Cooper, T. J. (2006). Using Repeating Patterns to Explore Functional Thinking. Australian Primary Mathematics Classroom, 11(1), 9-14.
  • Yaman, H (2010). İlköğretim öğrencilerinin matematiksel örüntülerdeki ilişkileri algılayışları üzerine bir inceleme. Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü İlköğretim Anabilim Dalı, Dok- tora Tezi, Ankara
  • Yeşildere, S. ve Akkoç, H. (2010a). Matematik Öğretmen Adaylarının Sayı Örüntülerine İlişkin Pe- dagojik Alan Bilgilerinin Konuya Özel Stratejiler Bağlamında İncelenmesi. On Dokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 125-149
  • Yeşildere, S. ve Akkoç, H. (2010b). Algebraic Generalization Strategies of Number Patterns Used by Pre- Service Elementary Mathematics Teachers. Procedia Social and Behavioral Sciences 2, 1142-1147
  • Yıldırım, A. ve Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayınları
  • Zaskis, R. and Liljedahl, P. (2002). Generalization of Patterns: The Tension between Algebraic Thin- king and Algebraic Notation. Educational Studies in Mathematics, 49, 379-402

STUDENTS’ PATTERN GENERALIZATION PROCESS: THE 7TH GRADE SAMPLE

Yıl 2015, Cilt: 23 Sayı: 2, 523 - 548, 15.05.2015

Öz

This study examines 7th grade students’ pattern generalization process. The study was conducted with nine students. A pattern test composing of ten questions and an interview test composing of five questions were used as the data collection tool. According to research results, the students mostly used the recursive relationship strategy to find near distance terms; the rule-based strategy to find medium distance terms; and the explicit strategy to find the rule of the patterns. The students rarely used the guess-and-check and whole object strategies in order to find the rules of the patterns. They did not use the visual strategies at all. They did not consider the given figures or the structures of those figures. They focused on only numerical relationships in order to find the rules of the patterns. The highest success rate in finding the rule of the patterns was observed in repeated pattern questions whereas the lowest success rate was observed in quadratic growing pattern questions.

Kaynakça

  • Akkan Y., ve Çakıroğlu, Ü. (2012). Doğrusal ve İkinci Dereceden Örüntüleri Genelleştirme Stratejile- ri: 6-8. Sınıf Öğrencilerinin Karşılaştırılması. Eğitim ve Bilim, 37(165), 104-120
  • Baki, A.(2008). Kuramdan Uygulamaya Matematik Eğitimi. Ankara: Harf Eğitim Yayıncılığı.
  • Baş, S., Erbaş, K. A., ve Çetinkaya, B. (2011). Öğretmenlerin Dokuzuncu Sınıf Öğrencilerinin Cebir- sel Düşünme Yapılarıyla İlgili Bilgileri. Eğitim ve Bilim, 36(159), 41-55
  • Becker, J.R., and Rivera, F. (2005). Generalization an Strategies of Beginning High School Algebra Students. In Chick, H.L. ve Vincent, J.L.(Eds). Proceedings of the 29th Conference of the Interna- tional Group for the Psychology of Mathematics Education, Vol. 4, pp. 121-128
  • Becker, J.R., and Rivera, F. (2006). Sixth Graders’ Figural and Numerical Strategies for Generalizing Patterns in Algebra. In Alatorre, S., Cortina, J.L., M. Mendez, A.(Eds). Proceedings of the 28th Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 95-101, Merida, Mexico
  • Bezuska, S. J. and Kenney, M. J. (2008). The Three R’s: Recursive Thinking, Recursion, and Recursive Formu- las. In C. E. Greenes and R. Rubenstein (Eds.), Algebra and Algebraic Thinking in School Mathematics: Seventieth Yearbook, pp. 81 - 97. Reston, VA: National Council of Teachers of Mathematics.
  • Bishop, W. J. (1997). Middle school students’ understanding of mathematical patterns and their symbolic representation. Doctor of Philosophy, Department of Mathematics Illinois State Universiy
  • Blair, S.L. (2001). The Importance of Basic Facts in Mathematics. Dissertation Abstracts Internatio- nal, 62(08), 2705A. (UMI No:3022967)
  • Blanton, M. L., and Kaput, J. J. (2004). Elementary Grades Students’ Capacity for Functional Thin- king. In M. J. Hoines ve A. B. Fuglestad (Eds.). Proceedings of the 28th Conference of the Interna- tional Group for the Psychology of Mathematics Education. Bergen, Norway.
  • Dörfler, W. (1991). Forms and means of generalization in mathematics.in A.J. Bishop(Ed.), Mathematical Knowledge: Its Growth through Teaching, Kluwer AcademicPublishers, Dordrecht, pp. 63–85.
  • Feifei, Y. (2005). Diognastic assesment of urban middle school learning of pre-algebra patterns. Doc- toral Dissertation, Ohio State University, USA
  • Gall, M., Borg, W. and Gall, J.P.(1996). Educational Research an Introduction. USA: Longman Publisher
  • Hargreaves, M., Shorrocks-Taylor, D. and Threlfall, J. (1998). Children’s Strategies with Number Patterns. Educational Studies, 24(3), 315-331
  • Healy, L. and Hoyles, C. (1999). Visual and Symbolic Reasoning in Mathematics: Making Connecti- ons with Computers?. Mathematical Thinking and Learning, 1(1), 59-84
  • Kalaycı, Ş. (2005). SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri. Ankara: Asil Yayın Dağıtım
  • Kaput, J. (1998). Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by “Algebrafying” the K-12 Curriculum, In NCTM, The Nature and role of Algebra in the K-14 Curriculum. Washington, DC: National Academy Press
  • Kaput, J., and Blanton, M. (2001). Algebrafying the Elementary Mathematics Experience. In H. Chick, K. Stacey, J. Vincent, and J. Vincent (Eds.), The Twelfth ICMI Study, on the Future of the Teaching and Learning of Algebra: 1. (pp. 344–352). Melbourne, Australia: University of Melbourne.
  • Karataş, İ. ve Güven, B. (2003). Problem Çözme Davranışlarının Değerlendirilmesinde Kullanılan Yöntemler: Klinik Mülakatın Potansiyeli. İlköğretim Online, 2(2), 2-9
  • Kutluk, B. (2011). İlköğretim matematik öğretmenlerinin örüntü kavramına ilişkin öğrenci güçlükleri bilgilerinin incelenmesi. Yüksek Lisans Tezi, Dokuz Eylül Üniversitesi, İzmir
  • Lan-Ma, H. (2007). The Potential of Patterning Activities to Generalizations. In Woo, J.H. , Lew, H.C., Park, K.S., and Seo, D.Y. (Eds). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 225-232, Seoul: PME
  • Lannin, J.K. (2003). Developing Algebraic Reasoning Through Generalization. Mathematics Teac- hing in the Middle School, 8(7), 342-348
  • Lannin, J.K. (2005). Generalization and Justification: The Challenge of İntroducting Algebraic Reaso- ning through Patterning Activities, Mathematical Thinking and Learning, 7(3), 231-258
  • Lannin, J.K., Barker, D.D. and Townsend, B.E. (2006a). Recursive and Explicit Rules: How can We Build Student Algebraic Understanding?. Journal of Mathematical Behavior, 25, 299-317
  • Lannin, J.K., Barker, D. and Townsend, B. (2006b). Algebraic Generalization Strategies: Factors Inf- luencing Student Strategy Selection. Mathematics Education Research Journal, 18(3), 3-28
  • Lesley, L. and Freiman, V. (2004). Tracking Primary Students’ Understanding of Patterns. In M. J. Hoines ve A. B. Fuglestad (Eds.). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. 2, 415–422. Bergen, Norway.
  • Ley, F. A. (2005). A Cross-Sectional İnvestigation of Elementary School Students’ Ability to Work with Linear Generalizing Patterns: The İmpact of Format and Age on Accuracy and Strategy Choice. Mas- ter of Arts Department of Human Development and Applied Psychology University of Toronto
  • Liljedahl, P. (2004). Repeating Pattern or Number Pattern: The Distinction is Blurred. Focus on Lear- ning Problems in Mathematics, 26(3), 24–42.
  • Linchevski, L., 1995. Algebra with Numbers and Arithmetic with Letters: A Definition of Pre-algebra, The Journal of Mathematical Behaviour, 14, 113-120.
  • Markworth, A. K. (2010). Growing and Growing: Promoting Functional Thinking with Geometric Growing Pattern. Doctor of Philosophy, University of North Carolina at Chapel Hill
  • Milli Eğitim Bakanlığı, (MEB), (2005a). İlköğretim Matematik Dersi 1-5. Sınıflar Öğretim Programı. Ankara: Devlet Kitapları Müdürlüğü.
  • Milli Eğitim Bakanlığı, (MEB), (2005b). İlköğretim Matematik Dersi Öğretim Programı ve Klavuzu 6-8. Sınıflar. Ankara: Talim ve Terbiye Kurulu Başkanlığı
  • National Council of Teachers of Mathematics.(2000). Principles and Standards for School Mathema- tics, NCTM, Reston, VA.
  • Ndlovu, C. W. (2011). Learners’ mathematical reasoning when generalizing from number patterns in the general education and training phase, wired.wits.ac.za adresinden alınmıştır.
  • Noss, R., Healy, L., and Hoyles, C. (1997). The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic. Educational Studies in Mathematics, 33(2), 203-233.
  • Olkun, S. ve Toluk Uçar, Z. (2004). İlköğretimde Etkinlik Temelli Matematik Öğretimi. Ankara:Anı Yayıncılık (3. Baskı)
  • Olkun, S. ve Toluk Uçar, Z. (2006). Temel Matematik II, Ankara: Tekağaç Eylül Yayıncılık.
  • Olkun, S. ve Toluk-Uçar, Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi, Ankara: Maya Akademi Yayıncılık (Genişletilmiş 3. Baskı),
  • Orton, A. and Orton, J. (2005). Pattern and the Apprach to Algebra. In A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics (Chapter 7, pp.104-120) London: Cassell
  • Orton, J., Orton, A. and Roper, T (2005). Pictorial and Practical Contexts and the Perception of Pat- tern. In A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics (Chapter 8, pp.121- 136) London: Cassell
  • Rivera, F. and Becker, J.R. (2007). Abduction-Iinduction (generalization) Processes of Preservice Ele- mentary Majors on Patterns in Algebra. Journal of Mathemetical Behavior, 26(2), 140-155
  • Rivera, F. D., and Becker, J. R. (2009). Algebraic Reasoning through Patterns. Mathematics Teaching in the Middle School, 15(4), 213-221.
  • Ross, M. K. (2011). Fıfth graders’ representations and reasoning on constant growth function prob- lems: Connections between problem representations, student work and ability to generalize, Deg- ree of Doctor of Philosophy, the University of Arizona
  • Sasman, C. M., Linchevski, L. and Olivier, A. (1999). The Influence of Different Representations on Children’s Generalization Thinking Processes. In J. Kupier (Ed), Proceedings of the 7th Annual Conference of the Southern African Association for Research in Mathematics and Science Edu- cation (pp. 406-415). Harare, Zimbabwe
  • Sharon, V.V. (2010). Pre-service elementary teachers’ understanding of pattern and function. the Deg- ree of Doctor of Philosophy, Oklahoma State University
  • Sorkin, E.J. (2011). Young children’s abilities to make generalizations about functional relations using cube tower. The Degree of Doctor Philosophy, Columbia University
  • Stacey, K. (1989). Finding and Using Patterns in Linear Generalising Problems, Educational Studies in Mathematics, 20, 147-164
  • Steele, D. (2005). Using Writing to Access Students’ Schemata Knowledge for Algebraic Thinking. School Science and Mathematics, 103(3), 142-154
  • Swafford, O. J., and Langrall, W. C. (2000). Grade 6 Students’ Preinstructional Use of Equations to Describe and Represent Problem Situations. Journal for Research in Mathematics Education, 31(1), 89-112
  • Tanışlı, D. (2008). İlköğretim 5. sınıf öğrencilerinin örüntülere ilişkin anlama ve kavrama biçimlerinin belirlenmesi. Anadolu Üniversitesi Eğitim Bilimleri Enstitüsü İlköğretim Ana Bilim Dalı Sınıf Öğretmenliği Doktora Tezi, Eskişehir
  • Tanışlı, D. ve Köse, Y.N. (2010). Sınıf Öğretmeni Adaylarının Örüntüleri Genellemeleri: Görsel Stra- tejilerin Etkisi: 9. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu (s. 220-225), Elazığ
  • Tanışlı, D. ve Köse, Y.N. (2011). Lineer Şekil Örüntülerine İlişkin Genelleme Stratejileri: Görsel Ve Sayısal İpuçlarının Etkisi. Eğitim ve Bilim, 36(160), 184-198
  • Warren, E. A., and Cooper, T. J. (2006). Using Repeating Patterns to Explore Functional Thinking. Australian Primary Mathematics Classroom, 11(1), 9-14.
  • Yaman, H (2010). İlköğretim öğrencilerinin matematiksel örüntülerdeki ilişkileri algılayışları üzerine bir inceleme. Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü İlköğretim Anabilim Dalı, Dok- tora Tezi, Ankara
  • Yeşildere, S. ve Akkoç, H. (2010a). Matematik Öğretmen Adaylarının Sayı Örüntülerine İlişkin Pe- dagojik Alan Bilgilerinin Konuya Özel Stratejiler Bağlamında İncelenmesi. On Dokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 125-149
  • Yeşildere, S. ve Akkoç, H. (2010b). Algebraic Generalization Strategies of Number Patterns Used by Pre- Service Elementary Mathematics Teachers. Procedia Social and Behavioral Sciences 2, 1142-1147
  • Yıldırım, A. ve Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayınları
  • Zaskis, R. and Liljedahl, P. (2002). Generalization of Patterns: The Tension between Algebraic Thin- king and Algebraic Notation. Educational Studies in Mathematics, 49, 379-402
Toplam 57 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA43CY55JK
Bölüm Derleme Makale
Yazarlar

Ercan Özdemir Bu kişi benim

Ramazan Dikici Bu kişi benim

M.Nuri Kültür Bu kişi benim

Yayımlanma Tarihi 15 Mayıs 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 23 Sayı: 2

Kaynak Göster

APA Özdemir, E., Dikici, R., & Kültür, M. (2015). STUDENTS’ PATTERN GENERALIZATION PROCESS: THE 7TH GRADE SAMPLE. Kastamonu Education Journal, 23(2), 523-548.

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