-

Öz

The purpose of this study was to determine the performances of elementary 3, 4, 5, 6 and 7th grade level students on mathematical patterns according to presentation forms. The implementation was carried out to 317 students from two elementary schools that were middle socioeconomic level in Ankara city center. The data were collected through 12-item test -called as Mathematical Pattern Achievement Test- developed by the researcher. The reliability coefficient was found as 0, 88. As a result of this study, it was found that there are significant differences between students’ performances according to presentation forms of mathematical pattern in terms of grade levels. Students received the highest score from pattern questions presented in the table format in the “Mathematical Pattern Achievement Test”. It was found that the other pattern presentation forms were ranked as respectively “Figural”, “Word Problem” and “Numeric Sequence”.

Anahtar Kelimeler

• pattern, generalization, pattern presentation formats

İlköğretim Öğrencilerinin Sunum Biçimlerine Göre Matematiksel Örüntüleri Algılayışları

Öz

Bu çalışmanın amacı, ilköğretim 3, 4, 5, 6 ve 7. sınıf öğrencilerinin örüntü sunum biçimlerine göre matematiksel örüntüleri algılayışları ve performanslarının belirlenmesidir. Uygulama Ankara şehir merkezindeki sosyoekonomik düzeyi orta seviyede olan iki ilköğretim okulundaki 317 öğrenci üzerinde gerçekleştirilmiştir. Araştırma verilerinin toplanması için, araştırmacı tarafından “Matematiksel Örüntü Başarı Testi” adı altında 12 soruluk bir test geliştirilmiştir. Geliştirilen testin güvenirlik katsayısı 0,88 olarak bulunmuştur. Araştırma sonucunda öğrencilerin sınıf seviyeleri açısından örüntülerin sunum biçimlerine göre matematiksel örüntüler ile ilgili performansları arasında anlamlı farklılıklar olduğu bulunmuştur. “Matematiksel Örüntü Başarı Testi”nde, öğrenciler en yüksek puanı “Tablo” biçiminde sunulan örüntü sorularında almışlardır. Diğer sunum biçimlerinde de puan sıralamasının “Şekil”, “Sözel Problem” ve “Sayı Dizisi” biçiminde devam ettiği görülmüştür.

Anahtar Kelimeler

• örüntü, genelleme, örüntü sunum biçimleri.

Kaynakça

1. Burns, M. (2000). About teaching mathematics. Sausalito, CA: Math Solutions Publications
2. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge Mass: Harvard University Press.
3. Devlin, K. (1998). Life by The Numbers. Canada: John Wiley ve Sons
4. English, L. & Warren, E. (1998). Introducing the variable through pattern exploration. Mathematics Teacher. 91, 2, 166-171 Ferrini-Mundy, J., Lappan, G. & Phillips, E. (1997). Experiences with patterning. Teaching Children Mathematics, (3)6, 28228
5. Fouche, K. K. (1997). Algebra for everyone: Start early. Mathematics Teaching in the Middle School, (2)4, 226-229.
6. Fraenkel, J. R. & Wallen, N. E. (2006). How to Design and Evaluate Research in Education (6th edition). USA: Mc Graw Hill, Inc.
7. Jones, L. (1993) Algebra in the primary school. Education, 3-13, June, s. 27-31.
8. Lannin, J. K. (2002). Developing middle school students’ understanding of recursive and explicit reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA

9. Lannin, J. K. (2003). Developing algebraic reasoning through generalization. Mathematics Teaching in the Middle School, 8(7). 342-348
10. Ley, A. F. (2005). A cross-sectional investigation of elementary school student’s ability to work with linear generalizing patterns: The impact of format and age on accuracy and strategy choice. Yayınlanmamış Yüksek Lisans Tezi, Toronto, Kanada
11. Looney, C. L. (2004). A study of students’ understanding of patterns and functions in grades 3-5. Yayınlanmamış Doktora Tezi, Boston, USA
12. MacGregor, M. & Stacey, K. (1995). The effect of different approaches to algebra on students’ perceptions of functional relationships. Mathematics Education Research Journal. Vol. 7, No. 1, 69-85
13. Martinez, M. & Brizuela, B. M. (2006). A third grader’s way of thinking about linear function tables. Journal of Mathematical Behavior. 25, 285-298.
14. Mottershead. L. (1995). Investigations in Mathematics. Oxford, Basil Blackwell.
15. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM
16. Olkun, S. ve Toluk-Uçar, Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi. Ankara: Maya Akademi
17. Orton, A. & Orton, J. (1999). Pattern and the approach to algebra. In A. Orton (Ed.), Pattern in the Teaching and Learning of Mathematics. s. 104-120. London: Cassel
18. Orton, J., Orton, A. & Roper, T. (1999). Pictorial and Practical Context and the Presentation of Pattern. . In A. Orton (Ed.), Pattern in the Teaching and Learning of Mathematics. s. 121-136. London: Cassel
19. Pegg, J. & Redden, E. (1990). Procedures for, and experiences in introducing algebra in New South Wales. Mathematics Teacher. 83, 5, 386-391
20. Schliemann, A.D., Carraher, D. W. & Brizuella, B. (2001). When tables become function tables. Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education. Vol. 4 (s.145-152). Utrecht, The Netherlands
21. Schultz, J. E. (1991). Teaching informal algebra. Arithmetic Teacher, (38), 34-37.
22. Smith, E.. (2003). Stasis and change: Integrating pattern, functions, and algebra throughout the K-12 curriculum. In J.Kilpatrick, W. G.Martin, & D.Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 136-150). Reston , VA : National Council of Teachers of Mathematics.
23. Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics. 20, 14716
24. Steele, D. (2005). Using writing to access students’ schemata knowledge for algebraic thinking. School Science and Mathematics. 103(3), 142-154.
25. Tanışlı, D. (2008). İlköğretim beşinci sınıf öğrencilerinin örüntülere ilişkin anlama ve kavrama biçimlerinin belirlenmesi. Yayınlanmamış Doktora Tezi, Eskişehir, Türkiye
26. Türk Dil Kurumu Sözlüğü, http://www.tdk.gov.tr adresinden 12.03.2009 tarihinde alınmıştır.
27. Van De Walle, J. A. (2004). Elementary and Middle School Mathematics: Teaching Developmentally. 5th ed. Boston: Allyn and Bacon.
28. Willoughby, S.S. (1997). Functions from kindergarten through sixth grade. Teaching Children Mathematics, 3, 314-318
29. Zaskis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics. 49, 379-402