BibTex RIS Kaynak Göster

Pre-Service Mathematics Teachers’ Generalization Processes of Visual Patterns

Yıl 2011, Cilt: 30 Sayı: 30, 141 - 153, 01.02.2011

Öz

The aim of this study is to investigate pre-service mathematics teachers’ generalization processes and models used in these processes. 145 elementary pre-service mathematics teachers were asked four openended problems which requires to generalize linear and non-linear pictorial patterns. Pre-service teachers' written responses were analyzed to investigate their generalization processes and how they used pictorial models in these processes. Radford’s (2006) framework is used for the analysis. The analysis of data indicated that pre-service teachers used pictorial models more effectively for linear patterns when compared to non-linear patterns. It was also found that they tend to represent pictorial patterns numerically first and then generalize the numerical pattern. In addition to that it was observed that the way they discovered the commonalities among the terms of the patterns were not helpful in generalization process since they looked for commonalities by focusing on the consecutive terms of the patterns.

Kaynakça

  • Becker, J. R., & Rivera, F. (2006). Sixth graders’ figural and numerical strategies for generalizing patterns in algebra. In S. Alatorre, J. Cortina, M. Sa´iz, & A. Me´ndez (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). Me´rida, Me´xico: Universidad Pedago´gica Nacional.
  • Carraher, D. W., Martinez, M. V. ve Schliemann, A. D. (2008). Early algebra and mathematical generalization, Education, 40: 3–22.
  • Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. London: Routledge.
  • 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. London: Cassell.
  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. Romnberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahway: Lawrence Erlbaum.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. (J. Kilpatrick, & I. Wirszup, Trans.) Chicago: University of Chicago Press.
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp.65–86). Dordrecht: Kluwer.
  • Orton, A. (1999). Pattern and the approach to algebra. London: Cassell.
  • Orton, A., & Orton J. (1999). Pattern and the approach to algebra. In A. Orton (Ed.), Patterns in the Teaching and Learning of Mathematics (pp. 104–120). London: Cassell.
  • Papic, M. (2007). Promoting repeating patterns with young children--more than just alternating colours . Australian Primary Mathematics Classroom, 12(3), 8–13.
  • Polya, G. (1957). How to solve it (2nd ed.). Princeton: Princeton University Press.
  • Radford, L. (2006). Algebraic thinking and the generalization of patterns: a semiotic perspective. In J. L. C. S. Alatorre, M. Sa´iz, Iconicity and contraction A. Me´ndez (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter (Vol. 1, pp. 2–21). Mexico: Me´rida.
  • Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts, ZDM Mathematics Education, 40, 83–96.
  • Rico, L. (1996). The role of representation systems in the learning of numerical structures. In L. Puig, & A. Gutierrez (Eds.), Proceedings of the 20th conference of the international group for the psychology of mathematics education (Vol. 1, pp. 87–102). Valencia: University of Valencia.
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20, 147–164.
  • Steele, D.F.& Johanning, D.I. (2004). A Schematic- Theoretic View of Problem Solving and Development of Algebraic Thinking, Educational Studies in Mathematics, 57(1), 65–90
  • Uygur-Kabael, T., & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. İlköğretim Online, 9(1), 213–228.
  • Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402.

Matematik Öğretmen Adaylarının Şekil Örüntülerini Genelleme Süreçleri

Yıl 2011, Cilt: 30 Sayı: 30, 141 - 153, 01.02.2011

Öz

Bu araştırmanın amacı matematik öğretmen adaylarının örüntüleri genelleme süreçlerini incelemek ve bu süreçte model kullanımında tercih ettikleri görsel kalıpları belirlemektir. 145 ilköğretim matematik öğretmen adayına lineer olan ve lineer olmayan şekil örüntülerini genellemeye yönelik dört tane açık uçlu problem yöneltilmiştir. Öğretmen adaylarının problemlere verdikleri yanıtlar, örüntüyü genelleme süreçleri ve şekil örüntülerini bu süreçte nasıl kullandıkları analiz edilmiştir. Cebirsel genelleme sürecinin analizinde Radford (2006) tarafından ortaya konulan kuramsal çerçeve kullanılmıştır. Veriler analiz edildiğinde öğretmen adaylarının genelleme sürecinde lineer şekil örüntülerinden lineer olmayanlara göre daha çok yararlandıkları belirlenmiştir. Ayrıca, öğretmen adaylarının şekil örüntüsünü nümerik olarak belirterek genelleme yapmaya yatkın oldukları görülmüştür. Bunun yanı sıra verilen örüntüdeki ortak özelliği belirleme bağlamında genelleme yapmaya yardımcı olacak seçimlerde bulunmadıkları, sadece bir sonraki terimi bulmayı sağlayacak şekilde ortak bir özellik araştırdıkları gözlemlenmiştir.

Kaynakça

  • Becker, J. R., & Rivera, F. (2006). Sixth graders’ figural and numerical strategies for generalizing patterns in algebra. In S. Alatorre, J. Cortina, M. Sa´iz, & A. Me´ndez (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). Me´rida, Me´xico: Universidad Pedago´gica Nacional.
  • Carraher, D. W., Martinez, M. V. ve Schliemann, A. D. (2008). Early algebra and mathematical generalization, Education, 40: 3–22.
  • Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. London: Routledge.
  • 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. London: Cassell.
  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. Romnberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahway: Lawrence Erlbaum.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. (J. Kilpatrick, & I. Wirszup, Trans.) Chicago: University of Chicago Press.
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp.65–86). Dordrecht: Kluwer.
  • Orton, A. (1999). Pattern and the approach to algebra. London: Cassell.
  • Orton, A., & Orton J. (1999). Pattern and the approach to algebra. In A. Orton (Ed.), Patterns in the Teaching and Learning of Mathematics (pp. 104–120). London: Cassell.
  • Papic, M. (2007). Promoting repeating patterns with young children--more than just alternating colours . Australian Primary Mathematics Classroom, 12(3), 8–13.
  • Polya, G. (1957). How to solve it (2nd ed.). Princeton: Princeton University Press.
  • Radford, L. (2006). Algebraic thinking and the generalization of patterns: a semiotic perspective. In J. L. C. S. Alatorre, M. Sa´iz, Iconicity and contraction A. Me´ndez (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter (Vol. 1, pp. 2–21). Mexico: Me´rida.
  • Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts, ZDM Mathematics Education, 40, 83–96.
  • Rico, L. (1996). The role of representation systems in the learning of numerical structures. In L. Puig, & A. Gutierrez (Eds.), Proceedings of the 20th conference of the international group for the psychology of mathematics education (Vol. 1, pp. 87–102). Valencia: University of Valencia.
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20, 147–164.
  • Steele, D.F.& Johanning, D.I. (2004). A Schematic- Theoretic View of Problem Solving and Development of Algebraic Thinking, Educational Studies in Mathematics, 57(1), 65–90
  • Uygur-Kabael, T., & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. İlköğretim Online, 9(1), 213–228.
  • Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Sibel Yeşildere Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2011
Gönderilme Tarihi 1 Ağustos 2014
Yayımlandığı Sayı Yıl 2011 Cilt: 30 Sayı: 30

Kaynak Göster

APA Yeşildere, S. (2011). Matematik Öğretmen Adaylarının Şekil Örüntülerini Genelleme Süreçleri. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 141-153.