Abstract
The origins of algebraic thinking precede understanding of arithmetic, as shown in a study of children aged 4–7. A mathematics curriculum introduced in some New Zealand schools in 1999, The New Zealand Numeracy Project, now encourages this algebraic thinking within arithmetic. The underlying framework for this curriculum is described, with examples of the type of thinking encouraged. The effect of this emphasis on the algebra underpinning arithmetic operations was examined in two further studies. One of these involved students in their final year of elementary and intermediate school, at age 12. This study showed that on a test that focused on students’ awareness of the underlying algebraic structure of arithmetic, those students who had been included in the new curriculum in its early stages outperformed those who had received a traditional curriculum. A later study followed a cohort of students who received the new curriculum through their two intermediate school years (aged 11–12) and into their first year of high school at age 13, when traditional algebra is introduced. The results of this study showed that students who had developed their understanding of the interrelationship of mathematical relationships for additive, multiplicative and proportional operations could display this understanding algebraically. The ramifications of these findings for further teaching algebraic thinking with or without algebraic representation led to a proposal for a ‘pathway for algebraic thinking’ accessible to all students.
We are grateful to the New Zealand Ministry of Education for funding this research and to R. J. Irwin for help with the statistical analysis. This chapter is a revised version of an article published in ZDM—International Reviews on Mathematical Education), 40(1), 39–53. DOI 10.1007/s11858-007-0064-x.
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Britt, M.S., Irwin, K.C. (2011). Algebraic Thinking with and without Algebraic Representation: A Pathway for Learning. In: Cai, J., Knuth, E. (eds) Early Algebraization. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_10
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