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Ortaokul Matematik Öğretmen Adaylarının Sabit Değişen Şekil Örüntüsü Genellemesini Öğretmek İçin Matematik Bilgileri

Yıl 2019, Cilt: 9 Sayı: 3, 396 - 414, 30.09.2019

Dilek Girit Yildiz Funda Gündoğdu Alaylı

Öz

Öğretmen adaylarının cebirsel düşünme ile ilgili hem kendi bilgilerini
hem de öğrenciler hakkında bilgilerini ortaya koymak, kavramsal bilgiye sahip
olan öğretmenler yetiştirmek için ilk aşama sayılabilir. Bu amaçla bu
çalışmada, ortaokul matematik öğretmeni adaylarının örüntü genellemesi
hakkındaki konu alan ve pedagojik alan bilgileri incelenmiştir. Nitel araştırma
tasarımı kapsamında, 26 öğretmen adayına sabit değişen şekil örüntüsü problemi
ve bu problemle ilişkili olarak açık uçlu sorular sorulmuştur. Elde edilen
veriler, Ball, Thames ve Phelps (2008) tarafından geliştirilen “Öğretmek için
Matematiksel Bilgi (ÖMB)” modeli kullanılarak içerik analizi ile incelenmiştir.
Bulgular, öğretmen adaylarının tümünün örüntüyü cebirsel olarak doğru
genelleyebildiklerini ortaya koymuştur. Çoğunun genellemeye ulaşırken sayısal
akıl yürütme kullandığı tespit edilmiştir. Öğretmen adaylarının, öğrencilerin
problem çözme konusundaki bilgilerinin, genellikle kendi çözüm yöntemlerine
dayandığı görülmüştür. Öğretmen adaylarının, öğrencilerin yaşayabileceği zorluk
ve kavram yanılgılarına yönelik tahminleri oldukça sınırlıdır. Dolayısıyla
bunları gidermek için yaptıkları öneriler de yetersiz kalmıştır. Bulgulara
dayanarak, öğretmen adaylarını yetiştirmeye yönelik öneriler yapılmıştır.

Anahtar Kelimeler

Ortaokul matematik öğretmen adayları öğretmek için matematik bilgisi şekil örüntüsü cebirsel genelleme

Kaynakça

  • Akyüz, D., Coşkun, Ş., & Hacıömerliğlu, E. S. (2009). An investigation into two preservice teachers’ use of different representations in solving a pattern task. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.). Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1261-1265). Atlanta, GA: Georgia State University.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172.
  • Aslan-Tutak, F. & Köklü, O. (2016). Öğretmek için matematik bilgisi. In E. Bingölbali, A. Arslan, & İ. Ö. Zembat (Eds.). Matematik eğitiminde teoriler (pp. 701- 719). Ankara: Pegem Akademi.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389- 407.
  • Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization: Potential and challenges. Journal of the European Teacher Education Network, 10, 57-70.
  • Becker, J. R., & Rivera, F. (2005). Generalization schemes in algebra of beginning high school students. In H. Chick, & J. Vincent (Eds.), Proceedings of the 29th conference of the international group for psychology of mathematics education (vol. 4, pp. 121–128). Melbourne, Australia: University of Melbourne.
  • Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers: Algebra eyes and ears, Teaching children mathematics, 10, 70-77.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4). 309-333.
  • Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. International Journal of Educational Research, 17(5), 457-470.
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44, 263-272.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Thousand Oaks, CA: Sage Publications.
  • Çayır, M. Y., & Akyüz, G. (2015). 9. sınıf öğrencilerinin örüntü genelleme problemlerini çözme stratejilerinin belirlenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(2), 205-229.
  • Depeape, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. & Van Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92.
  • El Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379-396.
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York, NY: McGraw-Hill.
  • Girit, D. & Akyüz, D. (2016). Algebraic thinking in middle school students at different grades: Conceptions about generalization of patterns. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED), 10(2), 243-272.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College.
  • Hargreaves, M., Threlfall, J., Frobisher, L. & Shorrocks Taylor, D. (1999). Children's strategies with linear and quadratic sequences. In A. Orton (Eds.), Pattern in the Teaching and Learning of Mathematics (pp. 67-83). London: Cassell.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
  • İmre, S. Y., & Akkoç, H. (2012). Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum. Journal of Mathematics Teacher Education, 15(3), 207-226.
  • Jurdak, M. E., & El Mouhayar, R. R. (2014). Trends in the development of student level of reasoning in pattern generalization tasks across grade level. Educational Studies in Mathematics, 85(1), 75-92.
  • Kirwan, J. V. (2015). Preservice secondary mathematics teachers' knowledge of generalization and justification on geometric-numerical patterning tasks (Unpublished Doctoral Dissertation). Illinois State University, ABD.
  • Magiera, M. T., van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84, 93–113.
  • Malara, N. A., & Navarra, G. (2009). The analysis of classroom-based processes as a key task in teacher training for the approach to early algebra. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in Primary Mathematics Teacher Education (pp. 235–262). Berlin: Springer.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation: Revised and expanded from qualitative research and case study applications in education. San Franscisco: Jossey-Bass.
  • Milli Eğitim Bakanlığı (2017). İlkokul ve ortaokul 1-8.sınıflar matematik öğretim programı. 15 Ekim 2017 tarihinde, http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=191 adresinden alınmıştır.
  • Moss, J., Beatty, R., Barkin, S., & Shillolo, G. (2008). “What is your theory? what is your rule?” fourth graders build an understanding of functions through patterns and generalizing problems. In C. Greenes, & R. Rubenstein (Eds.), Algebra and Algebraic Thinking in School Mathematics: 70th NCTM Yearbook (pp. 155–168). Reston, VA: National Council of Teachers of Mathematics.
  • Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalization of patterns in different contexts. ZDM Mathematics Education, 40, 83–96.
  • Rivera, F., & Becker, J. R. (2007). Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra. The Journal of Mathematical Behavior, 26, 140–155.
  • Rowland, T., Turner, F., Thwaites, & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the Knowledge Quartet. London: Sage.Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Strauss, A. L. & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newburry Park, CA: Sage.
  • Tanışlı, D., & Köse, N. Y. (2011). Lineer şekil örüntülerine ilişkin genelleme stratejileri: Görsel ve sayısal ipuçlarının etkisi. Eğitim ve Bilim, 36(160).
  • Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428.
  • Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9.baskı). Ankara: Seçkin Yayıncılık.
  • Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379–402.

Yıl 2019, Cilt: 9 Sayı: 3, 396 - 414, 30.09.2019

Dilek Girit Yildiz Funda Gündoğdu Alaylı

Öz

Kaynakça

  • Akyüz, D., Coşkun, Ş., & Hacıömerliğlu, E. S. (2009). An investigation into two preservice teachers’ use of different representations in solving a pattern task. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.). Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1261-1265). Atlanta, GA: Georgia State University.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172.
  • Aslan-Tutak, F. & Köklü, O. (2016). Öğretmek için matematik bilgisi. In E. Bingölbali, A. Arslan, & İ. Ö. Zembat (Eds.). Matematik eğitiminde teoriler (pp. 701- 719). Ankara: Pegem Akademi.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389- 407.
  • Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization: Potential and challenges. Journal of the European Teacher Education Network, 10, 57-70.
  • Becker, J. R., & Rivera, F. (2005). Generalization schemes in algebra of beginning high school students. In H. Chick, & J. Vincent (Eds.), Proceedings of the 29th conference of the international group for psychology of mathematics education (vol. 4, pp. 121–128). Melbourne, Australia: University of Melbourne.
  • Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers: Algebra eyes and ears, Teaching children mathematics, 10, 70-77.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4). 309-333.
  • Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. International Journal of Educational Research, 17(5), 457-470.
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44, 263-272.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Thousand Oaks, CA: Sage Publications.
  • Çayır, M. Y., & Akyüz, G. (2015). 9. sınıf öğrencilerinin örüntü genelleme problemlerini çözme stratejilerinin belirlenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(2), 205-229.
  • Depeape, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. & Van Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92.
  • El Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379-396.
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York, NY: McGraw-Hill.
  • Girit, D. & Akyüz, D. (2016). Algebraic thinking in middle school students at different grades: Conceptions about generalization of patterns. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED), 10(2), 243-272.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College.
  • Hargreaves, M., Threlfall, J., Frobisher, L. & Shorrocks Taylor, D. (1999). Children's strategies with linear and quadratic sequences. In A. Orton (Eds.), Pattern in the Teaching and Learning of Mathematics (pp. 67-83). London: Cassell.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
  • İmre, S. Y., & Akkoç, H. (2012). Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum. Journal of Mathematics Teacher Education, 15(3), 207-226.
  • Jurdak, M. E., & El Mouhayar, R. R. (2014). Trends in the development of student level of reasoning in pattern generalization tasks across grade level. Educational Studies in Mathematics, 85(1), 75-92.
  • Kirwan, J. V. (2015). Preservice secondary mathematics teachers' knowledge of generalization and justification on geometric-numerical patterning tasks (Unpublished Doctoral Dissertation). Illinois State University, ABD.
  • Magiera, M. T., van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84, 93–113.
  • Malara, N. A., & Navarra, G. (2009). The analysis of classroom-based processes as a key task in teacher training for the approach to early algebra. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in Primary Mathematics Teacher Education (pp. 235–262). Berlin: Springer.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation: Revised and expanded from qualitative research and case study applications in education. San Franscisco: Jossey-Bass.
  • Milli Eğitim Bakanlığı (2017). İlkokul ve ortaokul 1-8.sınıflar matematik öğretim programı. 15 Ekim 2017 tarihinde, http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=191 adresinden alınmıştır.
  • Moss, J., Beatty, R., Barkin, S., & Shillolo, G. (2008). “What is your theory? what is your rule?” fourth graders build an understanding of functions through patterns and generalizing problems. In C. Greenes, & R. Rubenstein (Eds.), Algebra and Algebraic Thinking in School Mathematics: 70th NCTM Yearbook (pp. 155–168). Reston, VA: National Council of Teachers of Mathematics.
  • Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalization of patterns in different contexts. ZDM Mathematics Education, 40, 83–96.
  • Rivera, F., & Becker, J. R. (2007). Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra. The Journal of Mathematical Behavior, 26, 140–155.
  • Rowland, T., Turner, F., Thwaites, & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the Knowledge Quartet. London: Sage.Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Strauss, A. L. & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newburry Park, CA: Sage.
  • Tanışlı, D., & Köse, N. Y. (2011). Lineer şekil örüntülerine ilişkin genelleme stratejileri: Görsel ve sayısal ipuçlarının etkisi. Eğitim ve Bilim, 36(160).
  • Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428.
  • Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9.baskı). Ankara: Seçkin Yayıncılık.
  • Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379–402.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Eğitim Üzerine Çalışmalar
Bölüm Makaleler
Yazarlar

Dilek Girit Yildiz 0000-0003-3406-075X

Funda Gündoğdu Alaylı 0000-0002-0382-9610

Yayımlanma Tarihi 30 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 3

Kaynak Göster

APA Girit Yildiz, D., & Gündoğdu Alaylı, F. (2019). Ortaokul Matematik Öğretmen Adaylarının Sabit Değişen Şekil Örüntüsü Genellemesini Öğretmek İçin Matematik Bilgileri. Trakya Eğitim Dergisi, 9(3), 396-414.
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