GENERALIZING REPEATING PATTERNS: A STUDY WITH CHILDREN AGED FOUR

Abstract

This paper presents part of a study that aimed to understand how the emergence of algebraic thinking takes place in a group of four-year-old children, as well as its relationship to the exploration of children’s literature. To further deepen and guide this study the following research questions were formulated: (1) How can children's literature help preschoolers identify patterns?; (2) What strategies and thinking processes do children use to create, analyze and generalize repeating and growing patterns?; (3) What strategies do children use to identify the unit of repeat of a pattern? and (4) What factors influence the identification of patterns? The paper focuses only on the strategies and thinking processes that children use to create, analyze and generalize repeating patterns. The present study was developed with a group of 14 preschoolers in a private school in Lisbon, and it was carried out with all children. In order to develop the research, a qualitative research methodology under the interpretive paradigm was chosen, emphasizing meanings and processes. The researcher took the dual role of teacher-researcher, conducting the study with her own group and in her own natural environment. Participant observation and document analysis (audio and video recordings, photos and children productions) were used as data collection methods. Data collection took place from October 2013 to April 2014. The results of the study indicate that children master the concept of repeating patterns, and they are able to identify the unit of repeat, create and analyze various repeating patterns, evolving from simpler to more complex forms.

Keywords

• children’s literature,repeating patterns,algebraic thinking in four-year-old children

References

1. Blanton, M., & Kaput, J (2011). Funtional thinking as a route into algebra in the elementary grades. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 5-23). Berlin: Springer. Bogdan, R., & Biklen, S. (1994). Investigação qualitativa em educação: Uma introdução à teoria e aos métodos. Porto: Porto Editora. Borralho, A., Cabrita, I., Palhares, P., & Vale, I. (2007). Os padrões no ensino e aprendizagem da álgebra. In I. Vale, T. Pimentel, A. Barbosa, Fonseca, L. Santos & P. Canavarro (Orgs.), Números e álgebra (pp. 193-211). Lisboa: SEM-SPCE. Carraher, D., Schliemann, A., & Schwartz, J. (2008). Early algebra is not the same as algebra early. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 235-271). New York: Lawrence Erlbaum Associates. DEB (1997). Orientações curriculares para a educação pré-escolar. Lisboa: Ministério da Educação. Garrick, R., Threlfall, J., & Orton, A. (1999). Pattern in the nursery. In A. Orton (Ed.), Patterns in the teaching and learning of mathematics (pp. 1-17). London: Cassell. Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5-17). New York: Lawrence Erlbaum Associates. Loureiro, C. (2006). Os livros de histórias e a matemática. In APM (Ed.), Actas do Profmat 2006. Lisboa: APM. Mulligan, J. (2013). Reconceptualizing early mathematics learning. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 139-142). Kiel, Germany: PME. National Council of Teachers of Mathematics. (2007). Princípios e normas para a matemática escolar. (APM, Trans.) Lisboa: APM. (Original work published 2000) Palhares, P., & Mamede, E. (2002). Os padrões na matemática do pré-escolar. Educare-Educere, 10(1), 107-123. Papic, M., Mulligan, T., & Mitchelmore, M. (2011). Assessing the developing of preescholers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237-268. Serra, P. (2014). Lendo e explorando histórias: A emergência do pensamento algébrico em crianças de 4 anos. Lisboa: APM. Smole, K., Rocha, G., Cândido, P., & Stancanelli, R. (2007). Era uma vez na matemática: Uma conexão com a literatura infantil (6th ed.). S. Paulo: CAEM. Suh, J. M. (2007). Developing algebra: “Rithmetic” in the elementary grades. Teaching Children Mathematics, 246- 253. Threlfall, J. (1999). Repeating patterns in the early primary years. In A. Orton (Ed.), Patterns in the teaching and learning of mathematics (pp. 18-30). London: Cassell. Vale, I., Pimentel, T., Barbosa, A., Borralho, A., Cabrita, I., & Fonseca, L. (2011). Padrões em matemática: Uma proposta didática do novo programa para o ensino básico. Lisboa: Texto Editores. Warren, E., & Cooper, T. (2008). Generalising the pattern rule for visual growth: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics, 67(2), 171-185.