Children start developing their mathematical skills while they are still babies exploring their environment and continue into their preschool years.
By the time they are learning formal mathematical concepts in the first grade, the foundation for success is already set.
Here are some tips for how to teach maths to preschoolers at school or at home by using hands-on activities and following a concrete-pictorial-abstract approach.
What are Early Maths Skills?
Early maths refers to the mathematical concepts and skills a child builds informally during the first few years. These are also called pre-maths skills or early numeracy skills.
It is essential to first develop these before trying to introduce concepts that are too advanced.
When wanting to introduce your child to maths, you may immediately think of numbers and try to teach your preschooler how to count, recognize the numbers and add or subtract them, but these are really some of the more advanced early mathematical skills.
It’s important to first understand how children learn mathematical concepts.
How Children Learn Maths: The Concrete Pictorial Abstract Approach
The three stages of learning any mathematical concept are concrete, pictorial and abstract.
The Concrete Stage
In the concrete stage, children need to physically experience a concept. They need to develop an understanding of one item by holding one block.
By playing with concrete objects, children form the concept that there can be one object, multiple objects, less objects, more objects, etc.
Many mathematical processes are going on while a child is building a tower of blocks next to his friend. Concepts such as more, less, one more, not enough, how many, plenty, fewer, take away and add on are picked up.
Children compare objects and learn that a value can be attached to objects.
The Pictorial Stage
In the pictorial stage, which follows the concrete stage, children are able to see a picture of objects and understand that it represents real objects.
For example, a child can look at a picture and understand that the 4 leaves represent 4 actual leaves.
Later on, a child can see a dice with 4 dots on it and assign the value 4, knowing that the dots could hypothetically represent any object.
They would then be able to add the 4 dots on one dice to the 3 dots on another and say there are 7 dots altogether.
The Abstract Stage
This is the final stage of understanding a mathematical concept. It means that a child can look at a sum, e.g. 4 + 3, written in number symbols, and add them without concrete objects or pictures.
The child has matured enough to understand that the symbols 4 and 3 represent a number of objects to be added.
This post contains affiliate links for educational products that I personally recommend. If you purchase through one of them, I earn a commission at no extra cost to you. Read the disclosure for more details.
Are Preschoolers In the Concrete, Pictorial or Abstract Stage?
Preschoolers are mostly in the concrete stage.
In fact, up until the third or fourth grade, any teacher worth their salt will still introduce a new concept in a concrete way before moving onto books or worksheets with examples to solve.
When children understand a concept concretely, it is then much easier to solve abstract problems.
This means that in the preschool years, trying to push a child to count pictures of objects or understand the value of the number symbols is premature and will cause frustration.
You may want to expose your child to numbers (e.g. playing with wooden numbers like these or magnetic number tiles) or rhymes that teach counting, but do not expect your child to understand the value of these numbers yet.
Here is a summary of this approach to learning:
How to Teach Maths to Your Preschooler: 15 Simple Activities
The best way to teach preschoolers mathematical skills is through their main medium of learning – play!
This means that during these early years children don’t need formal lessons, activity sheets and workbooks, or anything that looks more like “real work.”
Here is a list of just a few basic everyday opportunities that double up as the perfect preschool maths activities.
1. Play With Shapes
Playing with foam or wooden shapes familiarises your child with basic geometric shapes, as well as their properties. It teaches shape recognition.
2. Make Shape Pictures
Cut basic shapes out of colored paper and make a picture out of them. Children learn to join 2D shapes together to make different forms.
Tangrams (like these) are great for making pictures with shapes.
3. Build Puzzles
Puzzles are excellent for developing visual perception and will build a child’s understanding of geometry.
Choose good quality wooden puzzles with a wooden tray.
4. Play With Pegboards
Pegboards are another great activity for building mathematical skills. They develop number concept and geometrical knowledge.
5. Build Forts
This may not seem like a math activity, but building forts and other structures and climbing inside them is the first step in a child learning about space and shape. These early play sessions are a must!
6. Use Manipulatives
There are so many benefits of playing with blocks and that children should have opportunities to play with manipulatives daily. Also offer beads, counters or other construction toys. (read about the benefits of Lego too).
Playing with blocks is the first step in building a number concept and every child should have a good set of wooden blocks at home. This set is perfect for the classroom or home.
7. Make Mud Pies
When children play in the sandpit and make mud pies and other structures, they begin to use terms such as “I need to make another one,” “There are 3 cakes” or “I made one for each of us.”
8. Learn Counting Songs
Counting songs are a fun way for a young child to learn to count forwards and backwards. This is known as rote counting. They also learn about increasing and decreasing quantity in songs such as “5 Green Bottles.”
9. Play With Numbers
Let your child play with foam, rubber, wooden or plastic numbers in the bath or on a magnetic board. Because they are physical objects, your child can touch them and feel their shapes.
This is far more meaningful to a young child than looking at numbers on an activity page. With time, they will naturally learn to recognize them and know how they are formed.
10. Make Playdough Numbers
Playdough is one of the best substances out there, with some amazing benefits. Take the previous activity a step further and mould the numbers out of playdough. This sensory activity will imprint the numbers in your child’s mind far quicker than trying to write the numbers on paper.
11. Play With Containers
Provide containers of different sizes and shapes and let your child discover the basics of capacity while having fun in the bath or sandpit.
Baking is a great mathematical experience. Let your child be involved in measuring the ingredients to introduce them to units of measurements and quantities.
12. Measure Objects
Ask your child to measure certain objects – such as a book, table or room – using body parts such as hands or feet, and later objects, such as a block or book. Children must first learn to measure length using non-standard items before they can be introduced to standard measurements.
13. Talk About Time
Find opportunities daily to talk about time. Use the daily routine as a starting point. Discuss concepts such as the time of day (morning, afternoon) as well as clock time (“I’ll pick you up at 12 ‘o clock when the school bell goes”).
14. Play With Objects
Give your child different objects and ask him to feel which are heavy or light and to compare the weight of different objects. Use a balancing scale (or make one) and place various household items on it.
15. Problem Solve
Problem solving can be the most, um… problematic, of all the maths tasks! Children in the grades often struggle to visualize problems and what they actually mean.
They often resort to guessing operations (e.g. it says more so I should add) without having any idea what the problem is actually about and how, when visualized, the solution is usually so logical.
The best way to prepare your child for problem solving is to give non-stop opportunities to actually solve real problems!
You need to train your child to develop their critical thinking skills.
You don’t necessarily need to be giving mathematical problems, just general problems that require training the brain to think, and think outside the box!
Allow many opportunities to:
- Build puzzles
- Solve brainteasers such as tangram puzzles
- Solve riddles
- Play games that require thinking
- Play with construction toys (e.g. figuring out how to make a bridge that doesn’t fall)
- Discuss problems and solutions during storytime
- Ask your child for solutions to everyday problems
As you can see, most play experiences have hidden opportunities for learning maths.
Learn to recognize them and use them to consciously teach certain skills. Remember to introduce new vocabulary and ask questions constantly during play.
Introduce words such as: heavier, lighter, longer, shorter, earlier, later, more, less, more than, less than, fewer, extra, not enough, altogether, left, another, full, empty, matching, same, different.
I hope you’ve enjoyed reading this article and have some new ideas to try!
Would you like a year of done-for-you, ten-minute activities to teach your 3-5-year-old through play? Get your copy of the Learning Through Play Activity Pack for only $27.