In this study, the participants were asked to create
figural patterns (figural representations) of two sequences, where the
presentation is in the form of an algebraic formula. Those algebraic formulas
were representing linear and quadratic (non-linear) patterns, in which
pre-service primary teachers were asked to generate figural patterns based on
those algebraic formulas. In total, 127 pre-service primary teachers
participated in the study. The obtained data were analysed at two levels
including both semantic and descriptive analyzes. The results of the study
indicated that of 127 participants, 88 could generate a correct figural pattern
of some kind for the given arithmetic sequence expressed via a linear function
of n, while 72 were able to do so for the given non-linear sequence expressed
via a quadratic function of n. Follow-up individual interviews were conducted
with 9 volunteer participants, reflecting a cross-section of types of
responses, including some who were unable to respond and had some issues.

Algebraic formula, figural pattern, linear pattern, non-linear pattern

- Anthony, G., & Hunter, J. (2008). Developing algebraic generalisation strategies. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX. Cinvestav, Mexico (Vol. 2, pp. 65 - 72). Mexico: Cinvestav UMSNH.
- Bassarear, T. (2008). Mathematics for elementary school teachers. (5th ed.). CA: Brooks/Cole.
- Bennett, A. B., & Nelson, T. L. (1998). Mathematics for elementary teachers: An activity approach. (4th ed.). Boston, MA: Mc Graw Hill.
- Blitzer, R. (2011). Thinking mathematically. (5th ed.). London, England: Pearson Education Limited.
- Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R. , S., Reed, B., & 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. (3rd ed.). 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.
- Fraenkel, J., R., & Wallen, N. E. (2005). How to design and evaluate research in education. (6th ed.). New York, NY: Mc Graw Hill.
- 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.
- 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, England: Cassell.
- Gay, L. R., Mills, G. E., & Airasian, P. (2006). Educational research: Competencies for analysis and applications (8th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
- 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.
- Increasing patterns (2009, February 15). Retrieved from http://www.learnalberta.ca/content/mepg2/html/pg2_increasingpatterns/index.html Janvier, B. D., & Bednarz, N. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed), Problems of representation in the teaching and learning of mathematics (pp. 67-72). New Jersey, NJ: Lawrence Erlbaum Associates.
- Lawrence A., & Hennessy, C. (2002). Lessons for algebraic thinking: Grades 6–8. CA: Math Solutions Publications.
- 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 Associates.
- Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage Publication.
- 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.
- Merriam, S. B. (1998). Qualitative research and case study applications in education. (1st ed.). San Francisco, SF: Jossey-Bass.
- Miller, C. D., Heeren, V. E., & Hornsby, J. (2012). Mathematical ideas. (12th ed.). Boston, MA: Pearson Education.
- Miles, M. B., & Huberman, A. M. (1994). An expanded sourcebook qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage.
- Nathan, M. J., & Kim, S. (2007). Pattern generalization with graphs and words: A cross-sectional and longitudinal analysis of middle school students' representational fluency. Mathematical Thinking and Learning, 9(3), 193-219.
- Orton, A., & Orton, J. (1999). Pattern and the approach to algebra. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp.104-120). London, England: Cassell. Reys, R. E., Suydam, M. N., Lindquist, M. M., & Smith, N. L. (1998). Helping children learn mathematics. (5th ed.). Boston, MA: 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(2), 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.
- Rivera, F. D., & Becker, J. R. (2011). Formation of pattern generalization involving linear figural patterns among middle school students: Results of a three-year study. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives. Advances in mathematics education (pp.323-366). Berlin Heidelberg, Germany: Springer-Verlag.
- Rivera, F. (2013). Teaching and learning patterns in school mathematics. New York, NY: Springer.
- Souviney, R. J. (1994). Learning to teach mathematics (2nd ed.). New York, NY: Merrill.
- Smith, S. P. (1997). Early childhood mathematics. Needham Heights, MA: Allyn & Bacon.
- 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. & Özdaş, A. (2009). İlköğretim Beşinci Sınıf Öğrencilerinin Örüntüleri Genellemede Kullandıkları Stratejiler. KUYEB, 1455-1497.
- 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). NY: Casse.
- Van de Walle J. A. (2004). Elementary and middle school mathematics. Teaching developmentally. (5th ed.). Boston, MA: Allyn &Bacon. 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, England: Cassel.
- Warren, E., & Cooper, T. (2006). Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom, 11(1), 9-14.
- Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379 – 402.

Konular | Sosyal ve Beşeri Bilimler |
---|---|

Dergi Bölümü | Araştırma Makaleleri |

Yazarlar |

Bibtex | ```
@araştırma makalesi { turkbilmat329067,
journal = {Turkish Journal of Computer and Mathematics Education (TURCOMAT)},
issn = {1309-4653},
address = {Türkbilmat Eğitim Hizmetleri},
year = {2017},
volume = {8},
pages = {261 - 283},
doi = {10.16949/turkbilmat.329067},
title = {The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas},
key = {cite},
author = {Kılıç, Çiğdem}
}
``` |

APA | Kılıç, Ç . (2017). The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8 (2), 261-283. DOI: 10.16949/turkbilmat.329067 |

MLA | Kılıç, Ç . "The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 8 (2017): 261-283 <http://dergipark.gov.tr/turkbilmat/issue/29685/329067> |

Chicago | Kılıç, Ç . "The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 8 (2017): 261-283 |

RIS | TY - JOUR T1 - The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas AU - Çiğdem Kılıç Y1 - 2017 PY - 2017 N1 - doi: 10.16949/turkbilmat.329067 DO - 10.16949/turkbilmat.329067 T2 - Turkish Journal of Computer and Mathematics Education (TURCOMAT) JF - Journal JO - JOR SP - 261 EP - 283 VL - 8 IS - 2 SN - 1309-4653- M3 - doi: 10.16949/turkbilmat.329067 UR - http://dx.doi.org/10.16949/turkbilmat.329067 Y2 - 2017 ER - |

EndNote | %0 Turkish Journal of Computer and Mathematics Education (TURCOMAT) The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas %A Çiğdem Kılıç %T The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas %D 2017 %J Turkish Journal of Computer and Mathematics Education (TURCOMAT) %P 1309-4653- %V 8 %N 2 %R doi: 10.16949/turkbilmat.329067 %U 10.16949/turkbilmat.329067 |