Math Prior to Schooling

Many of us "theoretically" know that children have already learnt many things at home, before even coming to school. But this information has not "sunk in" and become part of our understanding. The fact that children pick up language at home is not surprising to us. But most people would be surprised that they also pick up a lot of math at home!

Incidental Learning

Children learn at home, by a process that is quite different from the "formal" way schools teach them. It can be called "incidental learning". This happens through extended experiences over a period of time. We often observe new things out in the real world without a goal of learning about them. Simply being exposed to experiences makes an impression in our mind and leads us to be ready to learn about them later.

This kind of "incidental learning" occurs throughout our lives.

Babies, as small as 6 months, develop a sense for numbers. They can even do elementary addition and subtraction. If a toy is added to a box with one toy, they seem to expect two toys! The rate of growth of the brain is fastest in this stage. The rate of learning of children is far faster than that of adults.

Children are constantly learning to make sense of the world around them. Breaking, tearing, exploring and playing are part of their process of learning. Researchers estimate that almost 90% of brain growth happens before the child is 5.

This does not mean that they already "know" 90% of what an adult knows. It means that their "capacity & capability to learn" is much higher. It means that processes & structures for observing, understanding, thinking, relating & remembering have developed. The child also intuitively practices life skills which are important for its wellbeing & survival. The child learns to cry for attention and also to avoid obvious dangers. In computer terminology we can say that the child comes with the DOS (Disk Operating System) on which any other software can be built.

Evolution has provided them with the motivation for learning. Hence they do this without any formal instruction from parents & other members of the family. No one is consciously "making them learn". They do this by seeing, hearing and interacting with what happens around them.

Effectiveness of Home Learning Math

A report in the SCIENCE magazine dated 9 Oct 2015 (Vol 350, Issue 6257, pp. 196-198, DOI: 10.1126/science.aac7427) reports about a study which seems to prove that children who have had some "math opportunities" at home.

The authors report that "Children's emerging language skills are supported when their caregivers read to them at home. Math skills, however, are often relegated to the schools. Improved math skills were apparent within months for elementary school students. Improvements were most dramatic in families where the caregivers reported themselves to be anxious about math."

Understanding Concepts

Their mental powers, however, are not strong enough for learning abstract ideas. They need many repeated experiences for this. They learn sophisticated skills & concepts by experiencing them over a long period of time.

They will not be able to easily understand concepts like country, beauty or even number. For example, they form their own ideas about a family, which is actually a very sophisticated concept which even adults cannot explain in simple terms!

They pick up many abstract social & science concepts because they occur in the context of their life and they observe them over a long period of time.

Learn Happily Without Pressure

At home, parents "compel" children in only a few basic things like eating, personal safety & toilet training. Otherwise, children are "left to themselves", learning at their own pace and mostly without any compulsion. Hence, they are mostly "happy" and "learning".

Whenever they are unhappy either due to hunger or any physical discomfort, they cry and ensure that help arrives from others. This is one of the earliest lessons on "how to get attention?" which children learn.

Learning Math Ideas

The math they learn intuitively at home can be classified into 5 kinds - magnitudes, numbers, transactions involving quantities, spatial relations and patterns.

Magnitudes

They understand magnitudes of different kinds - weight, size, length, height, time intervals - by experiencing them. They also pick up the related vocabulary to a certain extent.

They learn to visually compare quantities. They can differentiate a larger portion of a sweet dish from a smaller one. If a child likes toffees, and is offered 2 packets of toffees, then most likely it would pick up the packet which has a larger number of toffees.

Transactions

They pick up many transaction related concepts like Give/ Take One, Share, One Each and One/ Many etc.

Spatial Understanding

Through movement & exploration they pick up a lot of spatial understanding & vocabulary like above, below, next, behind etc.

Patterns

By playing with & handling things of different shapes, they develop a feel for patterns. They build structures with blocks and try to put together broken or separated parts of toys!

Pre-Number Concepts & Numbers

All the above ideas are learnt mostly in "spoken/ oral" form. They form part of what are called "pre-number" concepts. They are preparatory activities which would help children understand an abstract concept like numbers.

Numbers are very abstract concepts.

But children learn the meaning of numbers, over a long period of time, by listening to instructions and conversations using numbers and relating them to the actual context. They constantly hear small numbers (1, 2, 3 etc) being used frequently in relation to plates, spoons, cups etc. They also learnt to relate their body parts with numbers - two eyes, five fingers etc.

We have talked earlier about number sense developing very early in children. Research has proved that most children can recognize quantities of objects up to five because of regular practice. Hence numbers from 1 to 5 have been called Perceptual Numbers meaning numbers which can be "perceived" by sight, without counting. This is the math equivalent of the language idea of "sight words". We will see more about this in the next chapter.

Role of Parents

But we have seen that the sense of numbers takes more maturity & experience to develop as compared to the sense of magnitude.

Research is proving that "number talks" at home, before children attend school is very beneficial for learning math at pre-school. Research also is proving that parents underestimate the ability of their children to learn math even in pre-school. Hence It would be good if parents explicitly use a lot of math & number related language at home while talking to their children, before they start school and even when they are in pre-school.

Schools need to educate their preschool parents to realise that their children can pick up ideas about numbers from home also.

Parents can talk, with their children, about the math in daily life situations. Let children participate in activities like preparing food, laying the table and arranging clothes. Join them in playing with toys. Take them along for shopping and ask them about shapes, sizes, colours and quantities. Ask questions like how are two things similar & how are they different. Ask children questions related to space and orientation. Have conversations.