“Natural Maths” for 3-5 Year Old Children

Can mathematics be taught at an early age? Is it beneficial to do so? What sort of mathematics can be taught in the 3-5 year old age group?

In this blog post we will answer these questions (and, as a sneak peak, here are the short answers: Yes, Yes, and Pretty Advanced Stuff, as it turns out!)

Mathematics can indeed be taught at an early age and it is beneficial to do so for at least two reasons: first, it helps put in place the fundamental mathematical concepts, which will carry a child’s understanding of the subject through primary school and beyond; and second, it introduces the topic without cumbersome tasks that tend to tire children and possibly dissuade them from taking up mathematics later on.

The prevailing wisdom among parents and early years professionals is that early math should begin with numbers and counting, starting with small numbers up to 5 and slowly introducing bigger numbers, before moving on to addition and eventually subtraction (in primary school). Multiplication and division are more advanced operations that are taught only in primary school. All through this linear progression from one task to the next, there is a strong focus on calculation. As a result, central concepts of mathematics, such as functions and variables, limits and symmetry, are typically introduced in high school. However, these very concepts are the ones that mathematicians identify as their true “tools of the trade”. The ability to memorize a multiplication table, by comparison, is only marginally useful.

Children nowadays have access to a wide range of computing devices – an entry level tablet or laptop has enormous computing power and can perform multiplication and division, exponentiation and logarithmic calculations, at the press of a button. The difficult part, it seems, is how to get children to understand fundamental concepts, the underlying logic of calculations, and how all this can be used to solve real-world problems. Another key challenge is how to teach children mathematics without tiring them and, for some children at least, turning them off the subject for good.

At Alphablocks Nursery School & Pre-Prep, Hadley Wood, we follow a hybrid early mathematics approach, which complements the traditional early math curriculum with more innovative approaches, such as the one that is known as Natural Math.

We believe that the traditional approach, which starts by introducing small numbers, performing matching and classification tasks, has several benefits – least of all the fact that it is straightforward to assess and helps prepare our children for the challenges of primary school, which precisely follows this curriculum – and we therefore rely on it. On the other hand, we cannot ignore more recent advances in academic research, which have shown that fundamental mathematical concepts lie outside the scope of this curriculum, and that these concepts are both naturally comprehensible by preschoolers and possibly very beneficial for their understanding of mathematics.

Practically, the main point of this recent research has been to question the effectiveness of  promoting hard tasks with simple underlying mathematical concepts at the expense of complex mathematical concepts demonstrated through simple tasks. For example, learning to count all the way to one hundred, or learning a multiplication table by heart, are tasks with increasing “hardness” and yet their underlying mathematical ideas are rudimentary. On the other hand, devising an interesting game that demonstrates what a mathematical function does is very simple, and children find it easy to grasp, while the underlying mathematical ideas are complex and carry through to the most advanced areas of calculus (cf. the table below and references at the end of the post).


Early Mathematics Quadrant: the complexity of a mathematical idea and the difficulty of a task associated with its teaching to 3-5 year old children are independent dimensions. At Alphablocks Nursery School & Pre-Prep, Hadley Wood, we focus on the lower right quadrant – relatively easy tasks, such as ‘function box’ play schemes, which help teach complex ideas at the heart of advanced math.

Example: a “function box” game

The references and resources section below includes various teaching tools for a complete early mathematics curriculum, using both the traditional and the “natural math” approaches.

For now, as an illustration of the “natural math” approach, we provide here a very simple example of how to familiarize children, through play, one of the most fundamental concepts of calculus, which is also prevalent in modern computer programming, namely, a mathematical function. There are many variations one could think of for this game, but we just pick one of them, which can be changed in practice according to the situation.

  • The task can be introduced as part of an arts and crafts project, for instance, which includes strips of paper or cloth.
  • Take strips of various lengths, from (say) 10cm to 100cm long.
  • Introduce a “function box”, of particular colour (say, white), which turns a strip into two halves of the same material. Here’s how it can work:
    • We put the box on the floor or on a table and, outside of it, on its left side we lay all the strips of material that we want to half in two (e.g., in a tray)
    • We take each strip, in turn, and put it in the box – once the strip is in the box we cut it in half – and the two halves are placed on the right, outside the box (in, e.g., another tray).
  • The purpose is to give children an appreciation of the function of halving (in this case): that this white box takes in strips of material of any length, and gives out two strips of half the length.
  • Another box, say blue colour, could be used to cut the strip into three pieces of equal length (approximately).
  • So each box turns a single strip of material into either two (white box) or three pieces (blue box) of equal length.
  • Variations of this can be built up over time, with boxes which do different things to strips of material, or other shapes or objects, and the person (child or adult) who does the cutting or gluing, etc., can be assigned a special role of carrying out the “halving” operation (or whatever else it might be), as part of the overall project.
  • Adult-led prompts could include questions like, “What does this box do?” or “What will happen if we take the new strips and put them through the box again?”

We will be updating this post with more resources, natural math games and ideas, etc., so bookmark this page! Outdoor environments also offer great opportunities for natural maths, so more on this as well in future.

References & Resources

Alphablocks Nursery School & Pre-Prep in Hadley Wood, between Enfield and Barnet, is a boutique nursery with specialist teachers, focusing on outstanding early education practices, delivered through personalized learning. To find out more, visit our Frequently Asked Questions page.