Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…
Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.
But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.
Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.
The non-statutory Development Matters Guidance, as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:
All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.
Maths problem-solving for young children involves them understanding and using two kinds of maths:
The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.
Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.
One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.
You can effectively support children’s developing maths problem-solving strategies through:
This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.
What you need to provide:
The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.
So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.
When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.
Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…
We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks, consider introducing maths problem-solving opportunities that extend this interest.
This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.
What you need to provide:
Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.
Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.
When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.
Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.
What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.
Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.
It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.
If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.
Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?
Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.
What you need to provide:
Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.
Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.
Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.
Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.
Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”
If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.
Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.
This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.
What you need to provide:
With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.
Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?
Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?
Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.
Extend children’s learning by modelling the language of weight:
Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of Foundations of Mathematics – An active approach to number, shape and measures in the Early Years.
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