Effective mathematical teaching and learning begins with the premise that all children are capable of being competent mathematics learners. Early years education plays a crucial role in the development of infants’ and young children’s mathematical proficiency because it is the time when attitudes towards mathematics are formed.
Positive attitudes are more likely when children’s mathematical learning begins as informal and intuitive learning, influenced by the culture and experiences they are growing up in.
Te Kākano is a framework developed as a tool for ECE services to support the teaching and learning of mathematical ideas. It is aimed to spark mathematical discussions and understandings. All services should have a CD called Te Aho Tukutuku, which contains Te Kākano framework. Additional CD copies can be ordered from the Ministry of Education resource catalogue website Down the back of the chair.
Te Kākano framework recognises the range of mathematical ideas (cultural tools for mathematical thinking) within a setting. The strands in the diagram represent these ideas. Depending on how the seed is nurtured these strands may be numerous and strong, or, in a less nourishing setting, they may be limited because only some strands are supported, or the strands may be weak.
People, places, and things provide the food or soil that surrounds the seed. These include kaiako pedagogy, kaiako content knowledge, family/whānau knowledge, and resources. These interact with the children’s interests to foster particular mathematical learning.
Pedagogy has been defined as the techniques and strategies that enable learning to take place and that provide “opportunities for the development of knowledge, skills, attitudes and dispositions” (Siraj-Blachford, 2010, p. 150). Kaiako pedagogy shapes the development of Te Kākano in particular ways.
Laissez faire approaches and fond notions that “maths is everywhere” and therefore does not require kaiako planning or involvement, may limit development. At the same time, as with learning to read, there is a danger that inappropriate practice might raise the achievement of particular skills in the short term, but lead to negative attitudes that are detrimental to enjoyment and progress in the long term (see Carr & Peters, 2008), thus stunting Te Kākano’s growth over time.
How can we ensure that mathematics learning is a satisfying, interesting and meaningful experience? The Best Evidence Synthesis Effective Pedagogy in Mathematics Pāngarau (Anthony & Walshaw, 2007, p. 24) provides a useful synthesis of pedagogical practices related to mathematics learning in ECE. A number of these (for example, shared purposes and interests) connect with the findings of longitudinal studies that show that children who attend ECE centres with high quality adult-child interactions have higher scores in mathematics and literacy at school (Sylva et al., 2004; Wylie & Thompson, 1998).
Ideally, pedagogy will focus on strengthening dispositions and encourage an orientation towards learning goals where children persist with difficulty and strive to understand or master something new. This contrasts with performance goals, where children strive to gain favourable judgments or avoid negative judgments (Smiley & Dweck, 1994). If we want children to develop learning goals then it is counterproductive to have an emphasis on performance goals when it comes to mathematics.
Children can be supported to explore further mathematical ideas, contexts or concepts. However, it is important to remember that sometimes the mathematical element in a situation is secondary to another purpose and it is appropriate to respond to the main purpose rather than “hijack” the situation (for example, not interrupting a child’s exploration of a complex science topic with an irrelevant “how many… ?” question). At other times it may be appropriate to provide the space for children to consolidate something they are exploring (for example, counting or sorting small collections of objects) without always pushing for a “next step”.
Assessment for learning: Kei Tua o te Pae
Kei Tua o Te Pae provides some excellent resources to support the teaching and learning of mathematics in an early childhood programme.
Mathematics is the exploration and use of patterns and relationships in quantities, space, and time. Statistics is the exploration and use of patterns and relationships in data. These two disciplines are related but different ways of thinking and of solving problems. Both equip students with effective means for investigating, interpreting, explaining, and making sense of the world in which they live.
Mathematics through Manaakitanga
A guide to children’s early mathematics – Education Review Office
This mathematics resource developed by ERO focuses the “balance between spontaneous child-initiated play and planned mathematical learning.” It outlines strategies for teaching, as well as examples of what mathematics learning can look like across a range of early childhood services.