Plato said, “The highest form of pure thought is in mathematics.” If education is the progression towards pure thought, mathematics – with its emphasis on exactness, order and relationships – will play a huge role in refining the thought processes. An early introduction to the basic concepts of mathematics will go a long way in priming a child’s thought process and leveraging it towards higher order thinking.
Introduction to mathematics can be started around the age of 3 – 3.5 years when the child’s mind is ready to explore the world of mathematics in its earliest forms. It is when the child starts asking questions like “how much”, “how much more” etc, that it is deemed to be ready to appreciate the elements of mathematics because it has started showing signs of recognizing comparisons, relational differences and quantitative variables.
It is best to introduce mathematics to the child by moving from the concrete to the abstract. The concrete experience enables a child to visualize the quantity that the symbol suggests; without the concrete experience the operations in mathematics will not make much meaning to the child. Thus, numbers, quantity, shape, space, measurements, relationships, properties of quantities etc – all of which are basic concepts in mathematics – should be introduced to the child in the concrete form first, in a sequence, that will help the child progressively climb the ladder of expertise in mathematics.
Introduction to mathematics is a three-step system:
Step 1: Allowing the child to understand mathematical units such as size, dimension, weight, distance etc in isolation through sensorial materials i.e. introducing them in the concrete form.
Step 2: Provoking name associations with each of the units, so the child becomes familiar with language of mathematics
Step 3: Initiating the child into mathematical operations through experiential means, so the child relates to these operations through visual and experiential means.
Establishing the concept of a Unit
The first element of mathematics that should be introduced to the child is the concept of the unit. Every material that is given to the child is a mathematical concept that is fed through the senses. Weight, space, dimensions etc – each of which forms a part of the sensorial material, indirectly prepares the child to assimilate the higher aspects of mathematics later on. The activities with the materials should be repeated till the child is able to grasp the central concept. These activities help create an image in the child’s mind about the nature of the concept. Besides this the sensorial activities should also arranged in a certain sequence, so that the child gets into the habit of forming a work sequence.
Establish the association between names and the quantities they denote, names and symbols they denote
The second element of arithmetic that needs to be introduced to the child is the nomenclature of the units. At around the age of 4, when the child starts to show interest in naming, nomenclature should be introduced. Association of the name with the activity should be encouraged. This is to enable the child to grasp the language of mathematics.
Establish the relationship between names and symbols; between quantities and symbols via names
Once the child is able to name quantities such as numbers and name symbols, the next step should be to help the child form a relationship between the two. The child should be introduced to mathematical operations through a series of experiments designed to help the child experience these. Once simple mathematical operations become familiar to the child, the child should be progressed to higher order mathematical operations.