Pre-Service Mathematics Teachers’ Pattern Conversion Ability: Generating Figural Patterns Based on Number Patterns
In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different figural patterns effectively, mostly by using geometric shapes. Moreover, most of the participants could generate linear figural patterns successfully compared with non-linear patterns based on number patterns and used different pattern generating strategies. In that study, some of the participants had issues while generating figural patterns.
Brenner, M. E., Mayer,R. E., Moseley, B. , Brar, T., Durán, R. , S., B. Reed &Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663-689.
Cathcart, W. G., Pothier, Y. M., Vance, J. H. & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. Englewood Cliffs, N.J.: Merrill/Prentice Hall.
Chua, L. B. & Hoyles,C. (2010). Generalisation and perceptual agility: how did teachers fare in a quadratic generalising problem?, Research in Mathematics Education,12(1), 71-72.
Clement, L. (2004). A model for understanding, using, and connecting representations. Teaching Children Mathematics, 11(2), 97-102.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61,103–131.
Fielding, H. (2014). An exploration of primary student teachers’ understanding of fractions. Pope, S. (Ed.) Proceedings of the 8th British Congress of Mathematics Education. (pp.143-150). UK, University of Nottingham.
Fox, J. 2005. Child-initiated mathematical patterning in the pre-compulsory years. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2 , pp. 313-320). Melbourne, Australia: University of Melbourne.
Fraenkel, J., R. & Wallen, N. E. (2005). How to design and evaluate research in education. New York, NY: Mc Graw Hill.
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.
Goldin G. & Shteingold, N. (2001).Systems of representations and the development of mathematical concepts. In Cuoco, A.A & Curcio, F. R. (Eds.), The Roles of Representation in School Mathematics. (pp. 1-23 ). Va: Reston Virginia, NCTM.
Gregg, D. U. (2002).Building students’ sense of linear relationships by stacking cubes. Mathematics Teacher, 95(5), 330–333.
Hallagan,J. E., Rule, A.C.& Carlson, L. F. (2009). Elementary school pre-service teachers’ understandings of algebraic generalizations. The Montana Mathematics Enthusiast, 6 (1&2), 201- 206.
Houssart, J. (2000). Perceptions of mathematical pattern amongst primary teachers. Educational Studies, 26 (4), 489-502.
Hunting, R. P. (1997). Clinical interview methods in mathematics education research and practice. Journal of Mathematical Behavior, 16(2), 145-165.
Janvier, B. D. & Bednarz, N.& Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp.109-122). Hillsdale, NJ: Lawrence Erlbaum.
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.
Larsson, J. & Holmström, I. (2007). Phenomenographic or phenomenological analysis: does it matter? Examples from a study on anaesthesiologists’ work. International Journal of Qualitative Studies on Health and Well-being, 2, 55-64.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
Lincoln, Y.S.& Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage Publication.
McGarvey, L. M. (2012). What is a pattern? Criteria used by teachers and young children, Mathematical Thinking and Learning, 14 (4), 310-337.
Miles, M.B. & Huberman, A.M. (1994). An expanded sourcebook qualitative data analysis. Thousand Oaks, CA: Sage.
MONE (2013). Ortaokul matematik dersi (5,6,7,8. Sınıflar) öğretim programı. [Middle School Mathematics Curriculum (5-8. grades)]. Ankara Devlet Kitapları Basımevi.
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. Boston, MA: Allyn&Bacon.
Rivera, F. D. & Becker, J. R. (2003). The effects of numerical and figural cues on the induction processes of preservice elementary teachers. Editors: Pateman, N. A., Dougherty, B. J., Zilliox, J. T. Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of PME-NA. 4,63-70.
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.
Smith, S. P. (1997). Early Childhood Mathematics. Needham Heights, MA: Allyn & Bacon.
Souviney, R. J. (1994). Learning to teach mathematics.New York, NY: Merrill.
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.
Tanışlı, D. & Köse, N. (2011). Generalization strategies about linear figural patterns: Effect of figural and numerical clues. Education and Science, 36 (160), 184-198.
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, MA: Allyn &Bacon.
Vogel, R.(2005). Patterns – a fundamental idea of mathematical thinking and learning. ZDM, 37(5), 445-449.
Walkowiak, T. A. (2014). Elementary and middle school students’ analysis 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.
Wicket, M., Kharas, K.&Burns, M. (2002). Grades 3-5 Lessons for Algebraic Thinking. Sausalito, CA: Math Solution Publications.
Warren, E. & Cooper, T. (2006). Using repeating patterns to explore functional thinking. APMC ,11 (1), 9-14.
Yeşildere, S. & Akkoç, H. (2010). Algebraic generalization strategies of number patterns used by pre-service elementary mathematics teachers. Procedia Social and Behavioral Sciences, 2, 1142–1147.
Yeşildere, S. &Akkoç, H. (2011). Pre-service mathematics teachers’ generalization process of visual patterns. Pamukkale University Education Faculty Journal, 30,141-153.
Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379–402.