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Observations of Structure Within Shape Patterns

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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Constructing general terms for shape patterns supports children in reasoning algebraically about relationships between quantities and relative rates of change. This chapter describes a research project wherein I investigated the strategies children attending Irish schools used when asked to solve shape-patterning tasks. The research instrument was a task-based group interview, and the children’s interactions shed light on a number of catalysts for the broadening of their observations of the pattern structure . Such catalysts included peer interactions, concrete materials, and teacher prompts. In this chapter I draw attention to children’s observations of structure, and seek to trace the thinking of children whose observations broadened from an initially narrow or limited perspective.

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Notes

  1. 1.

    In Ireland children attend primary school for eight years, typically from the age of four or five. The classes are referred to as Junior Infants, Senior Infants, and 1st through to 6th class. As such, Senior Infants would be equivalent to 1st grade, 1st class to 2nd grade, etc. The children who participated in this study were attending 4th class, and for ease of reference I refer to their grade as 5th grade throughout this chapter. In the study of Nic MhuirĂ­ (2014) the children attended 6th class, and in this chapter their grade is referred to as 7th grade.

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Authors and Affiliations

  1. DCU Institute of Education, CASTeL, Dublin City University, Drumcondra, Dublin 9, Dublin, Ireland

    Aisling Twohill

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  1. Aisling Twohill
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Correspondence to Aisling Twohill .

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  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec, Canada

    Carolyn Kieran

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Twohill, A. (2018). Observations of Structure Within Shape Patterns. In: Kieran, C. (eds) Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68351-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-68351-5_9

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