Analyzing Middle School Students’ Figural Pattern Generating Strategies Dependıng on a Linear Number Pattern/Ortaokul Öğrencilerinin Lineer Sayı Örüntüsüne Bağlı Olarak Şekil Örüntüsü Oluşturma Stratejilerinin Analizi

In this study strategies used by middle school students while creating figural patterns based on a linear number pattern was investigated. In total, 474 middle school students attended to study. Data were collected from a pattern task, in which participants were asked to generate figural patterns based on a 3,5,7,9,11,… linear number pattern. The obtained data were analysed at two levels. The results of the study indicated that participants produced different figural patterns and used different generating pattern strategies. The nature of the strategies that participants used was both visual and non-visual. Most of the participants preferred counting strategy while creating figural patterns. Moreover, in that study in addition to counting strategy, determining a figure+counting, recursive, drawing, explicit and chunking the numbers strategies were used. During the generating figural patterns, some of the participants had issues while generating figural patterns.

PDF

___

REFERENCES
Akkan, Y. (2013). Comparison of 6th-8th graders’ efficiencies, strategies and representations regarding generalization patterns. Bolema, 27 (47), 703-732.
Amit, M &Neria, D. (2008). Rising to the challenge’’: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40, 111–129.
Barbosa, A.&Vale, I. (2015). Visualization in pattern generalization: Potential and Challenges. Journal of the European Teacher Education Network, 10, 57-70.
Bassarear, T. (2008). Mathematics for elementary school teachers. Belmont, CA:Brooks/Cole.
Bishop, J. (2000). Linear geometric number patterns: Middle school students' strategies. Mathematics Education Research Journal, 12(2), 107-126.
Cathcart, W. G., Pothier, Y. M., Vance, J. H. & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. Upper Saddle River, N.J. : Merrill/Prentice Hall.
Fox, J. (2005). Child-initiated mathematical patterning in the pre-compulsory years. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 2, pp. 313-320). Melbourne: PME.
Frobisher, L & Threlfall, J. (1999). Teaching and assessing patterns in number in the primary years. In A. Orton (Ed.). Pattern in the teaching and learning of mathematics (pp.84-103). London and New York: Casse.
Gregg, D. U. (2002).Building students’ sense of linear relationships by stacking cubes. Mathematics Teacher, 95(5), 330–333.
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, 85,75–92.
Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.
Lin, F-L., Yang, K-L &Chen, C-Y.(2004). The features and relationships of reasoning, proving and understanding proof in number patterns. International Journal of Science and Mathematics Education, 2, 227–256.
McGarvey, L. M. (2012). What is a pattern? Criteria used by teachers and young children, Mathematical Thinking and Learning, 14 (4), 310-337.
MONE (2013). Ortaokul matematik dersi (5,6,7,8. Sınıflar) öğretim programı. [Middle School Mathematics Curriculum (5-8. grades)]. Ankara Devlet Kitapları Basımevi.
Miles, M.B. & Huberman, A.M. (1994). An expanded sourcebook qualitative data analysis. Beverly Hills, CA:SAGE.
Mulligan, J. & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49.
Orton,J. Orton, A. & Roper, T. (1999). Pictorial and practical contexts and the perception of pattern. In A. Orton (Ed.). Pattern in the teaching and learning of mathematics (pp.18-30). London and New York: Casse.
Radford, L. (2008). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM Mathematics Education. DOI 10.1007/s11858-007-0061-0.
Radford, L. (2010). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2–7.
Reys, R. E., Suydam, M. N., Lindquist, M. M. &Smith, N. L. (1998). Helping children learn mathematics. Needham Heights: Allyn&Bacon.
Rivera, F. D. & Becker, J. R. (2007). Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra. Journal of Mathematical Behavior, 26, 140–155.
Rivera, F. D. & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM Mathematics Education, 40, 65–82.
Smith, S. P. (1997). Early Childhood Mathematics. Needham Heights: Ally&Bacon.
Souviney, R. J. (1994). Learning to teach mathematics. Englewood Cliffs: Macmillan Publishing Company.
Stacey, K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics, 20, 147–164.
Steele, D. (2008). Seventh-grade students’ representations for pictorial growth and change problems. ZDM Mathematics Education, 40, 97–110.
Threlfall, J. (1999). Repeating patterns in the early primary years. In A. Orton (Ed.). Pattern in the teaching and learning of mathematics (pp.18-30). London and New York: Casse.
Van de Walle J. A. (2004). Elementary and Middle School Mathematics. Teaching Developmentally. Boston: Allyn &Bacon.
Walkowiak, T. A. (2014). Elementary and middle school students’ analyses of pictorial growth. Journal of Mathematical Behavior, 33, 56– 71.
Waring, S., Orton, A. & Roper, T. (1999). Pattern and proof. In A. Orton (Ed.). Pattern in the teaching and learning of mathematics (pp.18-30). London and New York: Casse.
Warren, E. (2005). Young children’s ability to generalise the pattern rule for growing patterns. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 305-312). Melbourne: PME.
Warren, E. & Cooper, T. (2006). Using repeating patterns to explore functional thinking. APMC, 11 (1), 9-14.
Wicket, M., Kharas, K.&Burns, M. (2002). Grades 3-5 Lessons for Algebraic Thinking. Sausalito, CA: Math Solution Publications.
Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379–402.