Pāngarau
Mathematics
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.
Learner focus
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
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.
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Useful resources
The Best Evidence Synthesis Effective Pedagogy in Mathematics Pāngarau
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.
Kei Tua o Te Pae – Book 18: Mathematics
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
Key points
- Giving mathematics visibility in the community
- Capitalising on activities enjoyed by families
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.
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Transcript
Jasmine Heads: Bluff is a small fishing community. The kindergarten is situated in the middle of our community in close proximity to both schools. Seventy-five percent of our whānau are Māori that attend our service.
At the beginning of this project I was not confident with mathematics. I purely thought of mathematics as being number. So I didn't really see where we fitted into the picture of things. One of the biggest outcomes for the team was to raise the awareness of mathematics and mathematical concepts within their environment at home, within the community – producing a resource that was available to families that was free and that they could utilise that was easy.
We wanted whānau to recognise the mathematical concepts within everyday experiences with their children – whether it be at home, in the supermarket, going to their local marae. Looking at all the different shapes, patterns, and number because number is important but it's not the only mathematical concept that they can see.
We created an adventure pack for the children to take away from the kindergarten. We designed the pack with mathematics in mind of course. Every activity has a mathematical concept behind it. One of the main concepts was our community I spy which was a collection of photo cards that we took of different landmarks/aspects around our community where children were asked to find them. Behind each photo there is a question to ask like where the photo is located. So we asked the children to tell us where they located the picture. We also asked the children a question it could be; was there pattern around this area, was there shape, was there number? All different mathematical concepts to look for. We also found that with our activity pack it crossed over into literacy. So we have also provided an assortment of books that go with the pack as well.
The other thing that we also added to the pack was information about the community. Walks that are made available for our families, free activities around our community that a lot of whānau didn’t actually even know about. Historical aspects to our community that children could also look at that were outside of the actual activity itself. That was information which we want to build on.
The other thing that we added to it was a guide to their hīkoi or driving. We produced two packs. One was a driving pack for whānau that had access to a car and then we also had another two packs that were made available to whānau that didn't have access to a car but either families could try them. Then we also added a scrapbook which is the tamariki documenting their journey. We called it Tamariki Kōrero which is the child's voice and it was a way for them to revisit as well.
Also within the packs we have provided the whānau with cameras to video or take photos of their journey. This has been really popular as the children have been allowed to take over and do all the filming and things themselves. So it's really nice when the backpacks come back to the office that we can actually look through that footage and we have a bit of a laugh and it's lovely.
We want to have a whānau evening at the end of this project. We thought that maybe we would put it into a wee movie for families to see like with captions of all the families' journeys all put together in a wee movie. We thought that would be kind of nice and to give it to the families that participated.
I think a lot of the time like our parents thought it was going to be number. A lot of them knew shape and colour come into it but locating, distance, all the measurements, and just lots of different things that they've used in the everyday experiences but they didn't realise that there was a mathematical education for their children behind it.
One of the best parts of the feedback was hearing from family and whānau that they had fun and that they were spending quality time with their tamariki. Mathematics was fun. It wasn't actually all hard work.
Helen Jackson: Our vision was that we wanted whānau to participate, have fun doing it, and just have a great time with their tamariki. The outcomes we wanted was to have whānau feeling confident that they could be teachers at home or away or at kindergarten. But just that they had confidence about maths and that they were able to bring something with their children as well.
To get our whānau and community involved we started off having an activity night where we invited whānau to come at night with their tamariki and we had a PowerPoint presentation. It was just a wee short thing about our objectives of what we were doing so they could come on board with what we were doing and support us, as well as us supporting them. Then the next thing we did is we got them to move around the kindergarten to different station points and work with their children doing mathematical things that they would actually find at home. We tried to use resources that they had at home so they could take what they learnt that night and take it back home and maybe have a go with it at home. That it doesn't have to cost them money. I think some of our whānau were thinking I have to buy them maths books to take our children to a different level. They don't need to do that now. They can see that they can do it themselves which is really exciting for us.
Some the feedback that we got from the activity night was that it was interactive – that they could participate. Whānau before thought that it was written format as maths but actually being involved and being interactive with their children was a better way to teach their children mathematics.
One of the most exciting things about these adventure packs is that whānau are coming to us and having huge kōrero with us about what's the next thing, which is really exciting for us because we didn't even know if they would take this concept on at all. But they are asking what's the next bag going to be? What else can we do? So it's really exciting that they came on our journey with us and actually now they are wanting to lead it a bit more.
Perry Savage: It was great to see with the kids and that then all the different aspects of maths. Stuff that you never knew that was like that – especially with fishing and all the different mathematics we use for navigation and stuff. Then go down the street and there's mathematics everywhere. One of the biggest things is maths is more than just numbers for the kids.
Roxanne Frahm: From the maths backpacks my family learnt that maths is really happening out in the world, in the real world that we live in – here in Bluff. That being able to see what numbers are different, and see shapes and count how many there are was actually useful and relevant. It was really exciting and great fun.
The maths backpacks are really constructive. I was just blown away by what a cool experience it was for my son to go out there and use his maths skills and see that they were useful. When we buy petrol reading numbers was actually a really useful thing to be able to do. Because those numbers told us how much the petrol cost. It was a useful thing that he could tell that it was a nine. He was really proud of himself.
The other thing we really loved about the maths backpack was taking Grandad around Bluff and introducing him to lots of local landmarks. It gave us an activity to do with a visiting family member and that was really exciting. I was just like we need more of these. I want to do this in the future.
