They know how to integrate these into their teaching practice. They share children's progress and learning with parents and whanau in wall displays and in assessment information such as portfolios. New Zealand and international research highlights the need for a balance between spontaneous child-initiated play and planned mathematical learning.
Epstein points out the need for both approaches. Similarly, children should be actively engaged and responsive during teacher-initiated and directed activities. Good teachers help support the child's learning in both types of activities. Esptein explains what intentional teaching is. Teachers must know when to use a given strategy to accommodate the different ways that individual children learn and the specific content they are learning.
There is now strong evidence that the most effective settings for young learners provide a balance between opportunities for children to benefit from teacher-initiated group work and freely chosen, yet potentially instructive, play activities. Teachers in early childhood settings need a sound understanding of mathematics to effectively capture the learning opportunities within the child's environment and make available a range of appropriate resources and purposeful and challenging activities.
Science and mathematics teaching through local games in preschools of Botswana
Using this knowledge, effective teachers provide scaffolding that extends the child's mathematical thinking while simultaneously valuing the child's contribution. Teachers' planning guides their deliberate use of teaching strategies as part of their broader curriculum. Teachers know how to provide a range of experiences for children to support and extend their learning.
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They can explain and discuss their pedagogy related to mathematics, how they integrate mathematics throughout the curriculum, and build on individual children's knowledge in both spontaneous and planned ways. Teaching of mathematics is intentional and embedded in a holistic curriculum. Leaders play a significant role in promoting deliberate teaching.
They access professional learning for themselves and teachers, encourage and lead reflective practice such as peer observations, videoed practice to review, and collaborative planning , professional reading, action research and internal evaluation self review. This leadership means teachers can keep up to date with current research and good practice and have the knowledge necessary to be innovative in their teaching of mathematics.
In services with a balance of deliberate teaching and spontaneous learning, children have access to high quality mathematics resources.
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Teachers are skilled at using interesting and challenging resources to scaffold children's learning and extend mathematical concepts. Teachers consider:. In the following example, ERO observed how a leader and teachers used their pedagogical and subject knowledge to deliberately plan for and extend children's mathematical learning. In this service, teachers empowered children to make choices about their learning. They also fostered children's exploration and experimentation by respecting and encouraging the children's thinking and ideas.
With this support, children in this service developed elaborate, imaginative and deep interests that extended well beyond their initial ideas. A four-year-old at this service had seen a YouTube video about constructing with plastic cups and he had shared his excitement about making some similar constructions with his teachers. A series of learning stories show the development of his ideas and the deliberate extension of his mathematical exploration by his teachers, which culminates in a long-term project not just for him but for many of the children in his group.
The learning stories in his portfolio showed him making complex and accurate 2D drawings of the 3D structures he wanted to create.
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Teachers placed these drawings on display for him to refer to as he began to construct in 3D. By this stage, other children in the group had caught his enthusiasm for designing and creating 3D structures from the plastic cups and had started building their own - with and without light. The teachers' planning shows a clear focus on supporting this mathematical learning.
They made sure that resources were available to prompt children's interests through construction sets, blocks of a variety of shapes, and a variety of games with a mathematical focus; and they intentionally used mathematical language with children. Children were urged to draw their ideas and then to transfer their 2D drawings into a 3D reality.
The following comments show the children's development of and reflection on their mathematical understanding - not only about shape, but also pattern, locating and counting. Remember the one where it went along the floor for a long way, and then went up the wall? I had to angle the cups to start going up the wall to make it balance. I had to use equal numbers of red and green cups to make the pattern.
The yellow ones are the contrast, but they are all the same size. The yellow ones just look bigger because they are nearer when you stand in front. Can you see how it alters the dimensions of my face when I stand behind the tower and you can see me in front? I had to work hard to get the balance right. Sometimes the cups are tricky, but I just had to concentrate to get it right.
First I just made a triangle shape, but now I'm making more linear shapes that can go across the floor. The children went on a trip to the local library, where the children's librarian explained how the Dewey Decimal System used numbers to categorise books so people could find books they were interested in. They went for a number hunt around the library, and found each of the big sorting numbers , , , , , , , , and His friend said he wanted to be The teacher noticed the conversation, and asked why the second child chose - he responded that it was because it was bigger than This was easily done, so the teacher suggested an even bigger number - The children did this, and then continued changing only the first digit, so they made all the hundreds up to The teacher guided him to name them correctly, and he quickly caught on, confidently counting in hundreds up to In another service, teachers supported new learning about measurement by planning to extend this learning in several different and meaningful contexts.
The children experimented with multiple ways of measuring things, such as how much water their gumboots could hold, how long they could hang off a beam, and how far playdough could bounce.
Help Your Child Develop Early Math Skills
Teachers extended this interest by showing them different ways the measurement information could be presented. They used the tape measure to measure each other's height and recorded these on a height chart. They counted how many segments were in their mandarins each day and recorded this data in a pictograph. Children at the centre had been exploring size. Teachers provided three rectangular mats, labelled big, medium and small; and a collection of objects, with a big, medium and small one for each object type.
The teacher demonstrated the activity, placing the biggest pompom on the mat labelled 'big', the next biggest pompom on the mat labelled 'medium', and the smallest pompom on the mat labelled 'small'. A child quickly picked up on the task, and placed the appropriate lock, bell, square etc.
This tied in to the language and comparative sizing used earlier in the Goldilocks and the Three Bears story. The teachers planned to extend that child's learning with activities that helped her to sort and classify based on more specific attributes, such as length, weight or height. An older child was comparing her shoe size to that of her teacher. The teacher suggested measuring their feet as a way of describing the length more accurately. They got a ruler and measured the teacher's foot, followed by the girl's foot.
They compared the numbers, and saw that the teacher had the bigger foot and the bigger number. The teacher then showed her how to measure the length of a line with her feet, carefully balancing and putting one foot exactly in front of the other. The teacher counted how many foot-lengths a line was, and then the girl counted how many of her foot-lengths the line was. The numbers were different, and the teacher asked why that might be.
The child replied that the teacher used fewer foot-lengths because his feet were bigger. The teacher planned to continue this child's interest in measuring by exploring other non-standard ways of measuring. When spontaneous learning is happening well, children experience a curriculum in which mathematics is included in meaningful contexts that recognise their strengths and interests and build on these.
Leaders and teachers understand how to integrate mathematics into the child's interests. Teachers may also integrate mathematics into their bicultural practice, for example, learning mathematics though waiata, creating and exploring kowhaiwhai patterns and Maori carvings, and using resources that reflect the cultures of children in the centre. Teachers in the service worked collegially to reflect on their practices, children's interests and new learning.
This collaboration meant that a child's success seen by one teacher was extended later by another teacher. The teacher noticed a child's interest in arranging blocks on a baseboard. After sitting together for a while making patterns, the teacher suggested she could try to cover the whole board with blocks.
This was a challenge, as there were a number of nodules on the board and the blocks were all different sizes. The child carefully started putting the blocks on from one side, making sure the blocks lined up. She then started adding more blocks from the opposite side of the board, and found herself stuck with a gap in the middle that was smaller than any of her blocks.
She asked her teacher if there were any smaller blocks to fill the gap, and was prompted to look for some other holes in her block arrangement. The teacher then helped her to count the number of nodules on the board in the space, and the number of nodules on her smallest block.
They compared the numbers, and realised that they were different. The teacher suggested making a bigger hole might help, so after considering for a while, the child moved the pieces across to fill one hole, and enlarge another.
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