An effective mathematics curriculum begins with the premise that all children are powerful mathematics learners irrespective of age and ability. However, it is when children have numerous opportunities to see themselves as powerful and competent mathematical learners that the curriculum can justly be called effective.
Early years education plays a crucial role in the development of infants’, toddlers’, 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.
Mathematics helps children to think logically, strategically, creatively, and critically – skills and knowledge which are particularly valuable in today’s information and digital age.
Te Whāriki positions mathematics as one of the many forms of expression that children need in order to communicate successfully and widely. This view of mathematics as a language is embedded in the learning outcome, he kōrero pāngarau: recognising mathematical symbols and concepts and using them with enjoyment, meaning, and purpose.
Infants, toddlers, and young children become powerful and competent learners in the language and expression of mathematical ideas when:
- mathematical learning is grounded in their interests, abilities, purposes, and cultural understandings
- they are exposed to a diverse range of mathematical concepts, not just numeracy (Te Kākano 1 outlines six strands – pattern, measuring, sorting, locating, counting and grouping, and shape)
- learning to think mathematically is the aim of the curriculum, for example, through estimating, connecting, speculating, ruminating, problem solving, and playing with possibilities.
Early mathematical learning is a gradual process of moving from concrete to abstract understandings. To grasp the abstract conventions such as number and measurement, children first need frequent and equal opportunities to:
- manipulate objects and make sense of the relationships between these
- hear mathematical concepts and vocabulary from kaiako and others around them.
Kaiako who understand the progression from concrete to abstract also know that mathematical experiences are as relevant in an infant curriculum as they are for older children. Likewise, paying attention to mathematics is a vital part of an inclusive curriculum.
1Te Kākano first appeared in Kei Tua o te Pae Assessment for Learning: Early Childhood Exemplars Book 18, Mathematics. It was also the subject of a CD publication, Te Aho Tukutuku/Early Mathematics (no longer in print). Some of the content on this web page summarises key ideas in this publication.
Te Kākano is a framework developed for early learning services in Aotearoa New Zealand to support the teaching and learning of mathematical ideas.
Te Kākano is based on the metaphor of a seed, embedded in a cultural context. The metaphor of a seed acknowledges that children do not arrive in ECE as empty vessels; they bring knowledge and understanding with them. It also recognises that learning and development, in this case mathematical learning and development, is influenced and nurtured by the “food” or “soil” (context) in which te kākano is embedded.
The framework Te Kākano 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.
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.
Te Aho Tukutuku | Early mathematics diagram
The role of kaiako in mathematics learning
Kaiako responses shape the development of mathematics 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. On the other hand, very structured, teacher-directed practices 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.
Kaiako who facilitate positive knowledge and attitudes to mathematics do so by:
- linking mathematics to children’s lived experience, cultural practices, and general interests – kaiako make a point of finding out what these are
- highlighting the purpose and usefulness of mathematics in daily life
- capitalising on this potential through mathematically-oriented actions and interactions while not “hijacking” the situation (for example, interrupting a child’s exploration of a complex science topic with an irrelevant “how many… ?” question)
- appreciating that mathematics is more than just numeracy, by referring to wider frameworks (as in Te Kākano)
- putting the fun in mathematics through games, waiata, stories, and physical activities
- being interested and curious about children’s mathematical thinking
- examining, and if need be working on, their own attitudes towards mathematics knowing that these "rub off" on the children they teach.
Taking mathematics into the community – one service’s solution
When Maketu Educare and the junior class teacher at a local school wanted to strengthen mathematics in their curricula, they looked for innovative ways to bring the whānau on board. The teachers felt that simply giving parents information would not be enough – they needed to also show what a rich source of mathematical learning their community offers by providing hands-on experiences beyond the classroom.
“Maths in Maketu” has become the catchline for activities that whānau can do with their tamariki around the town. These have included:
- putting a height measurement chart and book to record heights in the local fish and chip shop – a place where tamariki and whānau go together and have time while they wait for their order
- developing picture cards of local landmarks and flora with accompanying mathematical questions that tamariki and whānau can play together
- mathematics walks up the local mountain Pukemaire.
These activities are helping to build a community-wide understanding that mathematics learning can happen anywhere and does not need costly resources.
This publication summarises research evidence on mathematics teaching and learning from early childhood through to secondary school. Chapter 3 provides a useful synthesis of pedagogical practices (with examples) related to successful mathematics learning in early childhood.
This resource provides further detail on Te Kākano and also provides assessment narratives that illustrate the different strands.
This is a useful foundation for considering and discussing a Te Ao Māori worldview in relation to mathematics in early learning services. It also contains examples of practice, some of which link well to promoting mathematical thinking and learning.
Mathematics through Manaakitanga
Bluff kindergarten was involved in Ministry of Education-funded professional development. In this video kaiako and whānau from the kindergarten share their story about a mathematical resource they developed and the outcomes for their community engaging with this resource.