There is compelling international evidence that demonstrates participation in high quality early education and transition to school programs are particularly beneficial for children from disadvantaged backgrounds (see van Smeerdijk et al. 2014). The evidence indicates that participation enhances social ability and improvements in academic achievement in areas such as mathematics and language learning. Long term benefits include less likelihood of the need for special education, lower juvenile delinquency and, higher high school completion rates.
For Indigenous children, particularly those living in rural and remote Australia, equity of education in terms of access to high quality education is problematic (Sarra 2011). A range of challenges with the provision of education services are faced by children and families particularly those outside metropolitan regions. A lack of access to high quality education in the early years increases the likelihood of remedial education and limited future life opportunities.
Frigo and Adams (2002) identify many issues that exist for Indigenous students transitioning to school and argue that these are further perpetuated throughout school life:
In the early childhood years (0–8 years), Indigenous students are less likely to participate in pre-schooling that their non-Indigenous peers, they have higher rates of absenteeism beginning in primary school, and early indications show that, as a group, they perform at a lower level compared to their non-Indigenous peers (p. 1).
Findings in the 2011 census identified an increase in attendance at school with 56% of 3 to 5 year old Indigenous children attending pre-school or primary school. This rate is up from 53% in the 2006 census data (Australian Bureau of Statistics 2013).
Children learn most effectively when there is a partnership between parents and teachers, a sense of community between home and school and when they feel safe and valued (Dockett and Perry 2013). Studies (Woods 2004; Young-Loveridge 2011) have shown a positive relationship between parental involvement in their children’s schooling and numeracy achievement. Prior-to-school numeracy language and understandings need to develop as naturally as possible from children’s social contexts (Dockett and Perry 2013; Turunen and Dockett 2013).
Readiness to learn mathematics in the early years
Dockett and Perry (2013) found that children from disadvantaged backgrounds attended formal schooling with the same readiness to learn as compared with children from less disadvantaged backgrounds. The difference between both groups depended on their engagement with early number language and processes involving understanding number sequence, identifying ordinal positioning and simple word problems (Young-Loveridge 2011).
A study by Anthony and Walshaw (2009) discussed the importance of providing young children with the opportunity to learn mathematics at this early age. This research found that the development of mathematics begins at birth as babies are immersed in a world of mathematics and includes such things as problem-solving, measurement, and spatial skills. This study is supported by Warren et al. (2011) who state that young children are capable of engaging with mathematical concepts at an early age, one reason being because children enter different contexts with a substantive amount of intuitive mathematical knowledge which serves as a base for future learning. Further, additional studies have shown that having a sound understanding of mathematics at a young age makes for greater mathematical achievement in the future (Bottia et al. 2014).
Stephen (2010) explored the benefits of child-centred learning and examined how children learn. This research identified that utilising this strategy allows the child the opportunity to decide what to do and how to spend their time, with ‘play’ being the learning medium. Similarly, the research by Miller et al. (2012) examined how children learn. This study argued that understanding how children learn needs to be included in the curriculum in combination with subject knowledge. This was because the ages 3–7 constitute an important phase in a child’s development. However a research study conducted by Edwards and Cutter-MacKenzie (2011) revealed that in recent years the concept of child-centred play has been critiqued as an insufficient pedagogical approach for supporting children’s knowledge and development.
Child-centred play is criticised for having too much of a focus on activities and not on outcomes, skills and understanding. In addition, another study explored the need for children’s interests to be taken into account within the framework of early childhood education (Hedges et al. 2011). This research stated that universally, to date, there is little agreement to the nature of the early school years curricula; however there is much literature advocating that curricula for children, birth to five years should incorporate children’s interests. It has been identified that tailoring of curricula to a child’s needs has more substance as opposed to a traditionally child-centred play environment, and research identified argued that although they are only children, they are actually competent learners. Warren et al. (2011) reinforced that play based teaching provides many children with opportunities to developing their understanding of mathematics, which is vitally important for all in the early years.
Theoretical framework
A cognitive view of learning states that children are naturally curious and have an inherent drive to make sense of their environment, that is, they will naturally seek out patterns and relationships (Baroody and Ginsburg 1990). However, mathematics is also culturally-based (Saxe 1991) and represents the view of a particular class and background. Therefore, mathematics teaching is best seen as enculturation (Bishop 1988) which implies that Indigenous culture should have a powerful role in Indigenous mathematics learning. This view is in harmony with that of many researchers (Ewing et al. 2010; Ezeife 2002; Sarra et al. 2011) who argue that successful educational performance, motivation, and attendance are primarily linked to teaching that takes account of culture.
In the project a pedagogical model developed by researchers in the YuMi Deadly Centre (2012) was trialled because of its particular focus on teaching that was contextualised to students’ culture. The model was developed using a mathematical structure named RAMR which is an abbreviation for Reality, Abstraction, Mathematics and Reflection that contextualises the learning of mathematics to Aboriginal and Torres Strait Islander culture. The diagram in Figure 1 informed by the work of Ernest (1998) and Matthews (2008) encapsulates the framework by exploring the relationship and connection between culture and mathematics.
Mathematics starts from observations in a perceived reality. The observer chooses a particular part of the reality (represented by a grey circle), and then creates an abstract representation of the real-life situation using a range of mathematical symbols, which are put together to form a symbolic language we call mathematics. The observer uses the mathematics in its abstract form to explore particular attributes and behaviours of the real life situation and to communicate these ideas to others. From the mathematics, it is essential that the observer critically reflects on their mathematical representation to ensure that it fits with the observed reality. Consequently, the abstraction and critical reflection processes form an important cycle where mathematics and its knowledge are created, developed and refined (Matthews, p. 48).
Mathews identified three important features to the model in Figure 1 that needed to be emphasised when developing effective pedagogy in mathematics. First is creativity, which is particularly evident in the abstraction and critical reflection cycle. It is important to note that this cycle is similar to other artistic pursuits such as dance, music, painting and language as different forms of abstractions. Therefore, we can perceive mathematics as another art form and, in theory, relate it to these other forms of abstractions. In essence, it is possible to develop empowering pedagogy that allows students to be creative and express themselves in the mathematics classroom. This allows students to learn mathematics from their current knowledge (i.e., from the students’ social and cultural background), thereby providing agency through creativity and ownership over their learning. The abstraction process provides learning experiences using a variety of representations, actions and languages that enable meaning to be developed that carries mathematical ideas from reality to abstraction.
The second feature Matthews (2008) identifies is that as a product of the abstraction process, symbols and their meanings are important features of the model since they connect the abstract representation with reality. However, it is common that students do not make these connections easily and view mathematics as just sums with no real meaning. This is further exacerbated for students when they first learn algebra, and letters are suddenly introduced into mathematics without any obvious reason except that we are now learning algebra. Interestingly, focusing on creativity within mathematics, particularly with regard to the abstraction process, will naturally focus on symbols and meanings and assist in understanding the current mathematical symbols, and symbolic language, and their connection to the reality. This leads to the teaching and learning of the underlying structure of mathematics, providing students with a holistic view of mathematics.
The third important feature for developing pedagogy is to recognise cultural bias within mathematics. If we consider Figure 1, cultural bias exists in all aspects of the abstraction and critical reflection cycle. The observer expresses their cultural bias in the way they perceive reality and decide on which aspect of reality they wish to focus on. In the abstraction process, the form a symbol takes and the meanings that are attached to this symbol or group of symbols is biased by a cultural perspective.
Finally, the critical reflection processes are underpinned by the cultural bias within the abstraction process and the observer’s perception of reality. If we have an understanding and appreciation of the cultural bias within mathematics, new innovative pedagogy can be developed that moves beyond some cultural biases so that students can relate to mathematics and gain a deep understanding for the current form of mathematics and how mathematics is used.