Our webinar with early childhood researcher Dr Erica Zippert explored the foundational maths skills that teachers may see children exploring in play, which include numeracy, patterns, and spatial understandings. It also provided examples of ways to support and develop these skills in the early childhood curriculum.
Non-symbolic numerical knowledge is a foundation for early numeracy
Children enter early childhood settings already holding non-symbolic numerical knowledge (understandings about quantities without the use of symbols such as number names). Research shows that infants, as well as some non-human animals such as primates, are sensitive to quantities, and are able to estimate the magnitudes of different quantities. Infants are also very sensitive to what happens when quantities are modified. For example, when they are shown a group of objects, which is then hidden and modified by adding or subtracting items, infants are highly sensitive to the change.
Children then go on to develop knowledge of the different symbolic representations used to quantify non-symbolic groups of objects, such as number words and the order of them in the count string. They may have rote knowledge of the count string at first, without understanding the significance of that order (in other words, without understanding that numbers are organised in order of magnitude). Children also need to learn to recognise written numerals, and, when they have enough fine motor control, to write numbers or to represent quantities in forms such as tallies.
Children need to acquire number and counting skills to support their developing mathematical understanding
These skills include:
- Learning to count by connecting symbolic representations of number to non-symbolic quantities. This involves applying number words to objects in sets, matching every number name said with an object. For example, the first object they count is assigned the number one, the second number two, and so on. Be aware that children do not need to always count correctly to demonstrate that they understand that symbolic representations of quantity connect to non-symbolic (actual) quantities.
- Understanding one-to-one correspondence (in other words, knowing that one number name corresponds to one object).
- Understanding the principle of cardinality (that the last number said is the size of the set).
- Learning to apply numerals to represent quantities, such as connecting the numeral 4 with a set of four objects.
- Becoming more flexible in quantifying objects and different ways to do so, such as counting right to left as well as left to right, or skip counting.
- Understanding symbolic relations and combinations – in other words, comparing the magnitude of different quantities (saying which is bigger or smaller) and arithmetic (adding and subtracting quantities).
Spatial skills are important for later skills in mathematics, including numeracy
Spatial skills involve visual-spatial working memory for remembering and mentally manipulating spatial information, which is important for later mathematical skills such as visualising arithmetic problems. Spatial skills also involve skills such as:
- mental rotation, which involves mentally working out how to rotate a shape for a given purpose (such as to fit a puzzle or in a game of Tetris)
- shape knowledge, which is linked to early geometry knowledge, and starts with recognising shapes and distinguishing them from less familiar versions of the same shapes and from different shapes
- patterning skills, which help children with understanding predictable sequences of objects. In early childhood, patterns with a repeating unit (blue, red, or triangle, square) are most appropriate, and can be made more complex when they involve a greater number of elements in the repeating unit and greater variety in the elements (blue circle, red triangle, green square). Children can progress from copying or duplicating patterns to extending a pattern (working out what comes next) and abstracting a pattern (duplicating a pattern rule, such as two of one thing and one of another, or 2:1) with different objects.
Everyday materials can spark interest in and exploration of maths concepts
Teachers can help children to focus on and discuss mathematical features in their play. Useful materials are:
- coloured objects, used with a balance scale, to learn about non-symbolic quantities, or to practise sorting, counting, and comparing.
- cash registers and play money can support children to learn about symbols used for quantities in a culturally relevant way.
- story books, number blocks, and playing cards also offer children exposure to numerals. These resources can support children to talk about symbolic representations, non-symbolic quantities, and the relationship between them.
- building activities, which are good for spatial skills, especially when children are given a picture or model or imagine what they will build first, as this involves more visual-spatial working memory and skills such as mental rotation.
- Tangram blocks and MagnatilesTM are good resources but, when using commercially available shape sets, be aware that these sets feature typical shapes and not irregular shapes like obtuse or isosceles triangles. Teachers may need to create some of their own shapes to ensure the full spectrum of shapes is included.
- beading activities and UnifixTM cubes are great resources for working on patterns, especially when children are offered different opportunities to copy, extend, or abstract a pattern.
While children do benefit from opportunities for independent exploration, teachers can build on children’s play to develop skills in an explicit but playful way
Rather than a didactic approach, in which teachers present information to children in a formal manner, the aim is for a guided play experience in which the teacher is sensitive to the child’s interests, engages in back-and-forth dialogue, and makes it fun! Research has shown that card games such as War, in which players place one card out at a time and figure out who has the higher card (magnitude comparison) do improve children’s numerical knowledge. Other good games include Go Fish, in which players request specific number cards from each other to make pairs, and Memory, in which players turn over cards to match numerals or non-symbolic quantities. Board games like Snakes and Ladders help children connect symbolic numerals to non-symbolic quantities (the number on the dice is converted to the number of spaces to move) as well as practising counting with one-to-one correspondence.
Providing mathematical language to children in guided play is very helpful
Research demonstrates that parents’ spatial talk, for example, predicts children’s spatial skills.Teachers can use spatial language when children are doing puzzles, using language such as ‘corner’, ‘edge’, ‘top’, and ‘bottom’, and teach children to think about the rotation of pieces. As children build, teachers can comment on the different shapes used and the rotation of blocks, the relationship between blocks, and how they relate to the picture or model that the child might be following. Teachers can also use specific ways to talk about pattern, such as the ‘repeating unit’ or the ‘secret code’ of the pattern. They might name the shapes or count the different elements, and talk with children about whether their strategies are working or not.