Jodie Miller

Date of Submission



There is limited research that focuses on young Australian Indigenous students learning specific mathematical concepts (Meaney, McMurchy-Pilkington, & Trinick, 2012). To date, there has been no study conducted within an Australian context that considers how young Australian Indigenous students engage in mathematical generalisation of growing patterns. Mathematical growing patterns are a sequence of shapes or numbers characterised by the relationship between elements, which can increase or decrease by a constant difference (linear growing pattern). Additionally, growing patterns can also exhibit quadratic and exponential growth. The purpose of this study is to explore how young Australian Indigenous students generalise growing patterns. Patterns are a common route for young students to engage with in early algebraic thinking. Algebra has been labelled as a mathematical gatekeeper for all students, having the potential to provide both economic opportunity and equal citizenship (Satz, 2007). It has been proposed that algebra is one link in reducing the exacerbated inequalities between ethnicity and socioeconomic groups (Greenes, 2008). Concerns about students’ poor understanding of algebra in secondary school have contributed to early algebra becoming a focal point for mathematics education. Early algebra is its own unique subject, and is not to be confused with the teaching of algebra early. Rather, the concept of early algebra is integrated with other early mathematical concepts as students engage in the gradual introduction to formal notation (Carraher, Schliemann, & Schwartz, 2008). In addition, early algebraic thinking leads to a deeper understanding of mathematical structures (Blanton & Kaput, 2011; Carraher, Schliemann, Brizuela & Ernest, 2006; Cooper & Warren, 2011). Recent studies indicate that young students are capable of engaging with early algebraic concepts (e.g., Blanton & Kaput, 2011; Cooper & Warren, 2011; Cooper & Warren, 2008; Radford, 2010a; Rivera, 2006)...


School of Education

Document Type


Access Rights

Open Access


327 pages

Degree Name

Doctor of Philosophy (PhD)


Faculty of Education