Play-Based Mathematical Learning for Young Children

In a previous post, I discussed the Finnish approach to mathematics in the early years,  

It really isn’t rocket science – Finnish teachers “expand children’s understanding of mathematics” naturally, using  include “play, stories, songs, physical exercise, small tasks, discussions and games and ample use of illustrative examples”. That’s not something that’s very difficult to do or costs a lot.

In this post, I will be discussing a few ideas for play-based mathematical learning. Play is so broad and all-encompassing and I will only be able to scratch the surface. But I thought to throw up some ideas, and it would be lovely if you could share your own ideas and experiences too! Honestly, the best ideas are often the most most simple and practical!

First of all, play-based learning is simply the best kind of learning there is for young children  (and the grown-ups involved as well). Imagine if you wanted to plan an “lesson” that children would enjoy. It would usually take a lot of planning and involve painstakingly creating beautiful materials and making everything perfect. Then, when you implement it, children may or may not be receptive to it or even remotely interested in it. All that effort… I’m not saying that the effort isn’t worth it, it’s simply that play-based learning offers a great alternative with just as much, perhaps even more learning value (open-ended learning that encourages creativity and outside-the-box-thinking).

Play-based learning, in my opinion, is working with children and giving them opportunities to learn at their own pace. Children are notoriously independently minded. Instead of trying to fit them into the lessons that we plan, the success of which evades even the most experienced teachers,  play-based learning makes learning more natural and relaxed. It involves setting up activities, materials and environments that children enjoy and are keen to explore. Not all learning can be accomplished through play alone, but children’s understanding and concept development, a solid understanding and intellectual maturity, comes through play and taking the “slow road” rather than the fast track.

If you were to look up math activities for young children, you’ll come across something like this:

Strictly speaking, an activity like this isn’t exactly “play-based”. First of all, it takes a tremendous amount of effort to create these materials.  They are useful because they are hands-on, colourful and appealing to children. However, I would not call them play materials but teaching materials, and there is a big difference. Play is open-ended while many of these activities are close ended. There is only one right answer and there is only one way to do it. Children don’t get to explore and to create their own answers – they have to do something in a very specific way, and grown-ups are there to tell them if what they do is right or wrong. This isn’t play! This is fun and child-friendly formal or academic learning.

Many of these materials have their origin in the Montessori method. Montessori herself made a clear distinction between her pedagogical method and play. She described her didactic materials as a kind of “work” for children, that allowed them to apply themselves, solve problems and develop concentration and other attributes.

The reason that I’m saying this is because children still need authentic, genuine play.  It’s a fundamental part of childhood. Play helps them “play out” and cement concepts that they’re interested in and are learning about. It helps them build a strong foundation for life. When it’s a lesson, then the focus is on learning something and getting things right. When it’s play, the focus is on play itself and the process. Learning can “happen” organically and naturally, but there’s no pressure on the child to succeed, simply to be involved. It’s open-ended.


1) Hopscotch

Hopscotch involves hopping and counting. You can kill two birds with one stone and do both physical education and mathematics in one activity. All you need for this, at the its simplest, is a concrete ground and a piece of chalk, the way my granny taught us to play it.

You can draw the hopscotch “track” together with children or let them do it. You can change things around. But at its simplest, it involves jumping and counting from one to ten. You don’t even have to draw the numbers, maybe just jump and count. It’s infinitely flexible and expandable.


2) Water, Sand and Mud Play
A bucket “scale”

Mathematics isn’t just about numbers and arithmetic. Weight and volume are both mathematical measurements. Water and sand play can be enhanced with different “toys” such as measuring cups and spoons, inexpensive weighing scales, jugs, pitchers, and other. Just realising that the more sand you put in your bucket, for example, makes the bucket heavier to carry can be an epiphany. If you can’t get ahold of play sand, mud and water are basically inexpensive. A large plastic container can be placed on top of a low bench and filled with the play material. Or just dig a mud pit and let children wallow in it with different toys!

Water play at a Scottish school

3) Going Shopping – Pretend Play

Shopping is loads of fun. It’s especially lovely to see children being involved and learning about the process. Children often love to imitate grown-ups. Playing shopping can be loads of fun. Old milk cartons and cereal boxes can be re-purposed into props. Toy money is easy to get ahold of. If children are interested, you could provide them with paper to make grocery lists (pictorial or numerical) or old shopping catalogues to peruse. It can be very simple and inexpensive.


4) Baking and Cooking

These aren’t actually child-led “play” activities, but honestly, baking and cooking are amazing activities children can be a part of. They can learn while being with you in the kitchen and having fun exploring taste and texture. Letting the children “put one teaspoon of salt in the pot” is already a maths activity. So is setting the table, with one plate in each place, one place for each person and so forth – this develops the concept of one-to-one correspondence.

Simply saying, “Let’s cut the tomato in half” is already setting children up to learn fractions later on.  Children also can appreciate the relevance and applicability of maths. Its not just about counting for counting’s sake, but counting how many cups of flour we need to make cookies, counting how many onions are needed to make some yummy soup.

Check out this lovely article by Kidspot Australia

4. Music

Music is linked to mathematics. There’s a lot of rhythm and counting that goes on when exploring music. It doesn’t have to be anything fancy and you definitely don’t need an expensive class or programme. Just sitting down and singing with children is really enjoyable for them – I remember one child loving the song, “One, two, three, four, five; Once a caught a fish alive”. This lovely article discusses how music-inspired free play nurtures children’s creativity.

Image result for nursery rhyme youtube

That being said, I would caution that there are many low-quality music videos for children on Youtube. They are “mindlessly” repetitive, the animations are poorly done and the music and singing robotic. It would not be good for children to be exposed to those hour-long videos of the same thing playing over and over again, as that is similar to extensive television-watching (perhaps even worse, because there is no quality control). Of course, there’s no scholarly evidence at the moment what the long-term effects are of watching “Five Little Monkeys” for seventy whopping minutes, but from what I’ve observed in children it does not look positive. Human interaction can never be replaced by devices, especially for young children.

5. Block Play

Handling, manipulating and stacking geometric solids is excellent for children’s development of mathematical thinking. There are three-dimensional and two-dimensional shapes children can work with.

This image is from a blog called The Pinay Homeschooler. She uses the Montessori method and this is a picture of her son playing with “geometric solids”.

Friedrich Froebel, a 19th century German educator, is known as the father of kindergarten education. He invented educational toys for children known as Froebel’s gifts. Today they are sold as “spielgaben” and they include these shapes for children explore geometry and patterns with.


Math is all around us and is a huge part of our daily lives. We use clocks to plan schedules, we make purchases with money, we drive around in number-plated cars and observe speed limits. We count, add, subtract and divide and multiple all the time. In being a part of and imitating the world around them, children explore mathematics.

In all our busyness and rush to drill different skills into children from an early age, let’s not forget to simply savour childhood and let children play.




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