Young Children's Mathematical Patterning
Fox, Jillian L. (2005) Young Children's Mathematical Patterning. In Lloyd, G. M., Wilson, M. R., Wilkins, J. L. M., & Behm, S. L. (Eds.) 27th Conference of Psychology of Mathematical Education - North America, October, 2005, Roanoke, Virginia, United States of America.
YOUNG CHILDREN'S MATHEMATICAL PATTERNING
Queensland University of Technology, Brisbane, Australia
Mathematical patterning is fundamental to the development of mathematics. Steen (1990), in fact, argued that "Mathematics is the science and language of patterns" (p. 5). The years prior to formal schooling (pre-compulsory education and care services) are widely recognised as a period of critical development where the salient role of patterning features significantly.
In a multi-case study children’s engagement in mathematical patterning experiences was investigated as was the teachers’ involvement in, and influence on these experiences. The study was conducted in one preschool and one preparatory year setting. These sites were typical learning environments for Queensland children in the year prior to compulsory schooling. Multiple sources of data were collected. These data comprised semi-structured interviews with each teacher, copies of their daily programs and video-taped observation of the classes. Ten episodes of mathematical patterning were identified and categorised as teacher-planned, teacher-initiated, or child-initiated. Two episodes were initiated by children and the other eight were guided by the teachers. The nature of the teacher intervention in the child-initiated activities was of particular interest. Frameworks were developed to guide the examination of these episodes, with these frameworks being informed by the conceptual framework of Stein, Grover and Henningsen (1996).
The findings of this case study suggest that child-initiated episodes containing mathematical patterning are productive learning occurrences. During unstructured play times, children initiated activities that explored repeating patterns, pattern language, and the elements of linear patterns. These episodes were rich opportunities where children shared, refined, and developed their knowledge of patterns. Thus, child-initiated experiences can be powerful learning opportunities with the potential to develop children’s knowledge of mathematical patterning in meaningful contexts.
The findings also suggest that teachers’ understanding of patterning as well as their engagement in, and influence on child-initiated episodes impacts significantly on the outcomes of the event. Teachers play a myriad of salient roles to assist the development of mathematical patterning. The role of the teacher in questioning, providing resources, being involved, and offering encouragement has the potential to enrich mathematical patterning experiences and extend the children’s existing knowledge. Likewise, teachers’ limited knowledge of patterning concepts and processes, and the confines of their teaching competencies can hinder the outcomes of patterning events.
The poster will illustrate some of the above findings and will include a focus on how teachers’ intervention can either extend or inhibit children’s development of mathematical patterning. Many early childhood professionals now agree that children should be "guided if not taught" to do some mathematics (Ginsburg et. al., 1999). When teachers understand what to teach, when to teach, and how to teach, they can provide rich opportunities for children to engage in patterning experiences, and capitalise on child-initiated learning activities. Ginsburg, H. P., Inoue, N. & Seo, K. H. (1999). Young children doing mathematics: Observations of everyday activities. In J. Copely (Ed.). Mathematics in the early years (pp.88-99). Reston, VA. National Council of Teachers of Mathematics. Steen, L. A. (Ed.). (1990). On the shoulders of giants: New approaches to numeracy. Washington DC: National Academy Press in Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Education Research Journal, 33, 455-488.
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|Item Type:||Conference Item (Poster)|
|Keywords:||early childhood, mathematical patterning|
|Subjects:||Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)|
|Divisions:||Current > QUT Faculties and Divisions > Faculty of Education|
|Copyright Owner:||Copyright 2005 (please consult author)|
|Deposited On:||24 May 2006|
|Last Modified:||03 Mar 2011 05:47|
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