Children’s capacity for algebraic thinking in the early grades

Abstract

Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children’s algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and looking at the capacity of learners for algebraic thinking in the early grades. Data was gathered using Grade 3 learner tests and focus group interviews based on pattern tasks. The data analysis process examined learners’ pattern matching and building explanations related to each data collection instrument using Blanton, Brizuela, Gardiner, Sawrey and Newman-Owens’s (2015. A learning trajectory in 6-year-old’s thinking about generalising functional relationships. Journal for Research in Mathematics Education, 46, 511–558) levels of sophistication in learner’s thinking about functional relationships. The results of the study suggest that young learners have the potential to think algebraically when offered opportunities to do so, particularly in terms of recursive and functional thinking when solving pattern problems. Traditionally instructional practice emphasises lengthy exposure to recursive thinking as a first route to algebraic thinking: this recent research suggests that young children also have the capacity to engage in functional thinking. Thus, we may need to rethink our approach to algebraic thinking through the development of a pattern-based approach to algebra.