Learning in the early years
The first few years of a child’s life are especially important for mathematics development, says the National Center for Excellence in the Teaching of Mathematics.
Research shows that early mathematical knowledge predicts later reading ability and general education and social progress.
As young as eight months old, children are developing an awareness of number names, and include these in their speech, as soon as they begin to talk. As children listen to the talk around them, they are introduced to numbers through opportunities that occur in everyday life, and experience a variety of number rhymes. This supports their growing knowledge of number names.
According to the NCETM, there are:
- Cardinality and counting
- Shape and Space
Looking briefly at each in turn:
Cardinality and counting
When children understand the cardinality of numbers, they know what the numbers mean in terms of knowing how many things they refer to.
Comparing numbers involves knowing which numbers are worth more or less than each other.
Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding.
Developing an awareness of pattern helps young children to notice and understand mathematical relationships.
Shape and space
Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes
Measuring in mathematics is based on the idea of using numbers of units in order to compare attributes, such as length or capacity.
Learning to count in the early years is a fundamental skill and key to mastering mathematical concepts in the future, but there’s more to it than you might think, says Sabrina Pinnock, a primary school teacher in Yorkshire.
According to researchers Rochel Gelman and C.R. Gallistel, these are the steps needed to successfully count:
- The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted
- The stable order principle: children must know how to count in the right order
- The cardinal principle: children need to understand the last number in the set is the total amount
- Counting anything: children need to realise that anything can be counted, not just objects that can be touched, but also things like claps and jumps
- Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount
Assessing children to find out which step they are struggling with is key to helping them overcome difficulties and become confident counters.
How do children develop counting skills?
Very young children start to count spontaneously and later begin to refine their skills by pointing their finger at the objects they are counting.
They will often try to get all the names of the numbers they know into their count as they pass their finger along the objects. They also reuse numbers. If they have not finished and they have used up all their known numbers, they will begin using the same numbers again. For example, a child might decide to count eight shells she collects at the beach. She might line them up carefully, tag numbers to them by pointing as she slides her finger along the shells, quickly counting out loud, “one, two, three, four, five, one, two, three, four, five, one, two, three.”
In their drive to make meaning, children are eager to experiment as they acquire new small bits of mathematical knowledge. It is extremely important to respect their developing understanding and not expect “perfect” counting sequences.
By valuing children’s partial understanding, children will develop enthusiasm for numbers and become confident mathematicians.
Activities to boost number sense in Reception Year
Children need lots of opportunities to develop number sense and deepen their conceptual understanding. Here are some simple activities to get your Reception Year learners counting:
Display the number of children allowed in each area using pictorial representations of cubes on a 10 frame. Once the children begin to realise how many are allowed in the area, they start to discuss the meaning of more and less. For example, “no more children are allowed in,” or “you can come in because one more than three is four.”
Encourage children to show numbers using their fingers above their head. “Bunny ears six” means they place their fingers above their head to show six. They may decide to use three fingers on each hand. As they become more confident, you could introduce swapping, where they show the same number but with a different configuration of fingers, in this case two and four, or five and one.
Each morning, drop different amounts of art straws all over the carpet. Say something like, “oh no class, I can’t believe it. I’ve dropped all my straws again. They were all in 10s. Can you help me?” This activity helps children consolidate counting objects and gets them to think about stopping after they have made 10. Providing elastic bands helps them to keep track of their groups of 10.
Fastest 10 frames
This game can help distinguish between those who have developed a good understanding of number sense and those who need further support. Give each child their own frame and cubes. Tell them a number and observe how they place the cubes on the frame. If the children are working with the number eight, do they say each number name as they place the cube on the frame, or do they realise eight is two less than 10? If so, they should be able to place the cubes down faster than other children.
What do they do when you say the next number? For example, for the number five, do they automatically remove three cubes, or do they remove all of the cubes and start over counting from one to five?
Everyday questions to develop number sense
These questions for children aged five to six help develop their number sense and let them practice using mathematical terms.
When prepping lunch or a snack, count out the different types of food with your child, and as you lay the table, count out the different items. Ask your child questions like:
- How many grapes are there?
- How many tomatoes are there?
- How many plates are there?
Practice using the terms more than, fewer than and as many as by asking:
- Are there more grapes than tomatoes?
- Are there fewer tomatoes than grapes?
- Are there as many plates as people eating?
Remember to practice each sentence:
- There are more grapes than tomatoes
- There are fewer tomatoes than grapes
- There are as many plates as family members eating
When counting, make sure that you count one number for one item to strengthen your child’s sense of one-to-one correspondence.
Carefully select number rhymes to include those that children are familiar with from home. Make sure the rhymes include:
- Counting back and counting forward
- “No” or “none” (Five little ducks went swimming one day)
- Counting in pairs (two, four, six, eight, Mary at the cottage gate)
- Counting to five, 10 and beyond
Problem solving, reasoning and numeracy
The EYFS requires children to be supported in developing their understanding of problem solving, reasoning and numeracy in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. They must be provided with opportunities to practise these skills and gain confidence.
Young children learn best through play. For their learning to be effective, they need sensitive and informed support from adults.
All children can be successful with mathematics, provided they have opportunities to explore ideas in ways that make personal sense to them and opportunities to develop concepts and understanding. Children need to know that practitioners are interested in their thinking and respect their ideas.
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Research from Carruthers and Worthington into children’s mathematical graphics reveals young children use their own marks and representations to explore and communicate their mathematical thinking. These graphics include:
- Tally-type marks
- Invented and standard symbols including numerals
Young children’s graphical exploration “builds on what they already know about marks and symbols and lays the foundations for understanding mathematical symbols and later use of standard forms of written mathematics,” the researchers said.
In a 2009 publication, the UK Department for Children, Schools and Families, says practitioners should: “Value children’s own graphic and practical explorations of problem solving” and observe “the context in which young children use their own graphics.”
Developing understanding with careful questioning
When children play and interact with other children, there are always opportunities for maths talk to help them develop a deep understanding, says Sabinra Pinnock.
- I have made a pattern. What’s your pattern?
- How many blocks taller is my model compared to yours?
- How do we know this area is full?
- I have three cars, how many do you have?
- Do you have more?
- How do you know?
Give learners long enough to think about their answer and give their response, but not so long that it disrupts the flow of play.
Adding maths talk activities to your daily routine
Developing maths talk in your daily routine gives learners a chance to understand concepts while using real-life concepts. It also means that children can consolidate what they have learned.
The following activities can get you started:
How many children are at school?
Get your class to work out how many children are at school by placing a picture of themselves or a counter representation on large 10 frames. Ask them questions like:
- How do we know this 10 frame is full?
- How many children are absent?
- How do you know?
- What can you tell me about number seven?
Sorting and grouping objects as a class
Sorting and grouping objects as a class helps children learn to reason and look for patterns. Give them a variety of buttons each day and ask open-ended questions like, “how can we sort the buttons?” They can use critical-thinking skills to come up with a range of ideas like sorting by size, colour, pattern, and shape.
Vote for a story
First, ask a child to pick two books. Everyone in the class gets to vote (using a piece of lego, for instance) on which of the books should be read. Tally the votes at the end of the day to determine the winner. This can lead to questions such as:
- How do you know?
- How many more votes did one book have than the other?
The key to introducing mastery in the early years is to keep activities fun and part of your daily routine. The more learners explore maths through play, the more engaged they become.
Dr. Sue Gifford, emeritus fellow at University of Roehampton, says recent research shows a child’s ability to spot mathematical patterns can predict later mathematical achievement, more so than other abilities such as counting. It also shows pattern awareness can vary a great deal between individuals.
Australian researchers, Papic, Mulligan and Mitchelmore have found pattern awareness can be taught effectively to preschoolers, with positive effects on their later number understanding.
Explicitly teaching pattern awareness links to encouraging “pattern sniffing” with older children in order to develop mathematical understanding and thinking.
What is mathematical pattern awareness?
Patterns are basically relationships with some kind of regularity between the elements. In the early years, Papic et al suggest there are three main kinds:
- Shapes with regular features, such as a square or triangles with equal sides and angles, and shapes made with some equally spaced dots
- A repeated sequence: the most common examples are AB sequences, like a red, blue, red blue pattern with cubes. More challenging are ABC or ABB patterns with repeating units like red, green, blue or red, blue, blue
- a growing pattern, such as a staircase with equal steps
Children who are highly pattern aware can spot this kind of regularity: they can reproduce patterns and predict how they will continue.
Why is pattern awareness important?
Spotting underlying patterns is important for identifying many different kinds of mathematical relationships. It underpins memorization of the counting sequence and understanding number operations, for instance recognizing that if you add numbers in a different order their total stays the same.
Pattern awareness has been described as early algebraic thinking, which involves:
- Noticing mathematical features
- Identifying the relationship between elements
- Observing regularities
The activity Pattern Making focuses on repeating patterns and suggests some engaging ways of developing pattern awareness, with prompts for considering children’s responses. Children can make trains with assorted toys, make patterns with twigs and leaves outside or create printing and sticking patterns in design activities.
It is important to introduce children to a variety of repeating patterns, progressing from ABC and ABB to ABBC.
Focusing on alternating AB patterns can result in some young children thinking that ‘blue, red, red’ can’t make a pattern. They say things like, “That’s not a pattern, because you can’t have two of the same colour next to each other.”