Early Days of Math in School

The first few months in school are very crucial in setting the correct stage for math learning.

Children Come With Some Prior Math Knowledge

Children do not come to schools as "blank slates" on which the teachers have to help them to "write"! It would help if teachers get an idea of what they have learnt at home. They can build on what children already know and also use teaching/ learning methods which are in tune with children's previous experiences. Here are a few guidelines which may help.

1. Children come with Math ideas from home

   1. Teachers should realise that the children already come with a lot of math related ideas gathered from their home experiences.

   2. These are ideas about smaller numbers, usually from One to Five. Ideas of comparison like more, less, longer, shorter etc

   3. The extent of their vocabulary in respect of the above ideas.

   4. Teachers should observe the children and judge for themselves, the level of their understanding of the various ideas and vocabulary

2. Learn through Activities & Without Pressure

   1. The best way children learn is through play and direct experiences.

   2. Teachers should design activities for understanding the extent of their knowledge & vocabulary related to math

   3. Learning through activities also requires a lot of order, planning & self-discipline on the part of both teachers and children. They need to learn them through repeated practice.

3. Understanding Small Numbers Visually

   1. Humans have five fingers in each of our hands. Children are looking at them 24X7X365!

   2. By this continuous experience, over 3 to 4 years, children develop the ability to see numbers from one to five as patterns

   3. This ability is called Subitizing, the ability to "perceive" a quantity without the need to count!

   4. Numbers one to five are also called Perceptual numbers.

   5. All the math children learn in school is built on the foundation of perceptual numbers.

   6. We will look at Perceptual Numbers in detail in the next chapter.

Learning at School Vs Learning at Home

If what children experience in school is completely different to their home experiences, then they will take a long time to get adjusted to school. No wonder they cry in the first few days of school. It would be strange if any child does not cry on its first few days in school. But it would be a tragedy if, because of early experiences, some of them may end up not liking schools and, what is worse, learning itself.

Mode of Learning

Young children’s paper-and-pencil skills generally lag behind their thinking skills, so worksheets often are not the best way for them to explore new ideas deeply or to show what they know and understand.

Preschool Math Curriculum

The pre-primary math curriculum is far more than just writing & reciting numbers.

We will describe in brief the various topics which need to be learnt at the pre-primary stage. Each of these will be dealt in detail in the subsequent chapters.

1. Pre-Number Concepts

   1. Number is a very abstract concept.

   2. There are a whole range of activities & language that children need to master in order to be ready for learning numbers in a formal way. These are called pre-number activities. We have seen that they have already learnt some of them at home.

   3. Teachers should use a lot of activities in the class, both to check the level of understanding and to learn or strengthen their knowledge.

2. Strengthening Perceptual Numbers

   1. The ability to perceive smaller numbers, usually 1 to 5, by sight is an important skill for learning math.

   2. We have seen that it is the foundation on which math learning is built.

   3. Hence the teacher should have a lot of learning activities for strengthening Perceptual Numbers

3. Single Digit Numbers

   1. The numbers from 6 to 9 should be introduced as an extension of the ideas & vocabulary learnt through perceptual numbers & pre-number concepts.

   2. They should be introduced using the "one more" principle

4. Counting Vs Reciting

   1. Many teachers mistake mere "reciting" of numbers as "counting". A subsequent chapter (5.6) will clarify the difference.

   2. Counting is a complex skill which children should learn through practice

5. Properties of Numbers

   1. Many properties of numbers can be learnt through activities with tokens including making different patterns.

6. Role Modelling Simple Math Stories

   1. Children do not have to wait for formal school to do "word problems". They can role model simple math situations & stories with the activity materials they have in class.

   2. Math word problems can be called math stories; stories which use numbers

   3. Ability to make such stories and understand stories of others improves math competency.

   4. All these activities should be done only orally & by discussions.

7. Number Sense

   1. Number Sense is considered one of the most important foundations of math competency.

   2. In simple language, it is the ability to think flexibly with numbers and partition, combine & recombine them in various ways.

   3. Strengthening of number sense should be an on-going activity at every class level.

8. Number Talks

   1. All the above ideas could be conveyed through "Number Talks" with children.

   2. Number Talks are nothing but informal conversations & discussions conducted and encouraged by the teacher to use numbers & number-related ideas in daily conversations.