MASTER EDUCATION PRIMARY/HIGH SCHOOL MATHEMATICSChapter 2
Mathematics in the Primary Classes
We saw in the last chapter, how implicit measurements happen via comparing, classifying, counting, sorting and ordering.
All these happen naturally by the senses of sight, hearing, touch, taste and smell, via the Child's sensitive and discriminatory mind.
This could be called implicit mathematics or the Pre Mathematical level concepts or abilities.
Mathematics is also a subject and a powerful one. The interesting thing about mathematical concepts is that they simply make conscious and precise, the pre-mathematical concepts, and these concepts too have to be learned by linking with real life. These concepts are NOT abstract things detached from real life.
Let us look at the basic concepts of maths that we need to learn in the primary level.
The first concept of mathematics is obviously the NUMBER concept, but we must really recall here that the child already has a concept of number in a certain sense.
A child knows that there is ONE table or ONE apple or ONE book or ONE samosa or ONE person.
He knows this concept of 1 implicitly because if you bring in one more, let's say you have one ball and you bring another ball, the child will know, via his senses that it is not one now, but TWO books, thus he does have a concept of two books, two balls, two samosas, two people, etc.
Also, it's a well known fact that human beings can directly sense without counting, one, two, three, four and five. This is called subtitation After five, it becomes many, even here, if a child is shown, let's say 12 pencils, he can break it into three fours and thus grasp the concept of 12. Also, if there are three pencils and one more is added, the child can directly perceive that it has become four now, if one more is added it has become 5. So clearly there is an Ordered numbering concept, already present in a child!
In school that implicit order 1, 2, 3 is made conscious, so this become the conscious concept of one, two, three, four, five, six, seven, eight, and nine, after which we create a concept, the PLACE VALUE system.
We create 10, meaning 1 tens and 0 ones.
11 is one ten and 1 ones
12 is one tens and 2 ones
And so on with
100, 1000 etc
We created so that we can have larger numbers. Now, let's say we take 16, 16 is perceived by the child as one tens and 6 ones, only by lots of linking to real life and via games.
This is where we should be very careful, not to detach the concept of number from real life. It is very easy to detach the concept of number, let’s say a higher number, 25 from real life, and that is, what is happening in most schools.
They take the concept of 25 and directly teach 25 as an abstract number, and then they start playing games with that number, in a detachment way, with mechanical rules of addition, subtraction, multiplication tables, multiplication and division..
They forget that 25 is actually two tens and five ones and that this concept must be highly concretized directly through real life activities in real life games.
If that is not done, the concept of 25, 35, 55, 53, 54 remains abstract in his mind and most people have such abstract concepts of numbers in their mind. They can't see 55, they can’t see 67, they can't see 535, but a good student, who directly relates mathematics to real life is able to see 535 clearly as 5 hundreds, 3 tens and 5 ones. An image is formed in the mind.
Thus it is very needless to detach the concept of number, including the place value concept from real life.
How do we directly connect numbers including higher numbers to real life?
here are two ways to connect to real life: One is directly to connect to the actual things happening or seen in the world, and the other is to play creative games, so that the students can reinforce these concepts directly and feeling them and seeing them as REAL LIFE numbers of things.
We can teach the place value system too by connecting it to real life. So we MUST NOT teach the place value system as an abstract thing, we directly use activities.
Also we teach all basic operations addition, subtraction multiplication and division via many activities and play repeatedly done.
Here we must use real life situations.
We have seen from our experiences that there are great possibilities of creating real life situations and games, and that the possibilities are actually endless and this requires only a proper creativity from the part of the teachers.
We also have lots of mathematics directly that we can use from real life, like supermarket with lots of goods with prices on them,
we can use weights and heights of students in class and the weights and heights of family members,
We can use expenditure at home, we can use length and breadth and height of the room, of the Board, of the Corridor and all the measurements of areas of the ground and you can get a sense of the numbers.
We can also have ads, we can also observe whether there are numbers in it with discounts,
We can have railway time tables, we can have all time measurements or daily time management, weekly time managements, monthly time measurements and yearly dimensions,
We can have ages and differences of ages between people, we can have scoring in games where numbers are added, so addition, subtraction, multiplication and division can be taken from these real life situations and activities.
The next major concept we have in primary classes is the concept of fraction. A fraction is wherever there is one unit which has been divided to many parts and you consider the parts that's when the fractions come in. So fractions come in many real life situations and here we use the real life games.
Illustrative activities and games to teach concept and operations in fractions.
While teaching fractions, the concept of LCM, equivalent fractions, multiplication of fractions and division of fractions should not be made mechanical. Like, for example, we say that 1/2 divided by 2/3 is 1/2 multiplied by 3/2 where 2/3 is reversed.
It cannot be felt if one merely gives the rule.
As can be seen from the
Steps of the ladder….given below…
Each concept or operation is felt and understood naturally.
Let us look at each of these from an educational point of view.
1, 2….9 – operations of addition, subtraction, multiplication and division
1 to 100 - operations of addition, subtraction, multiplication and division
Big numbers - operations of addition, subtraction, multiplication and division
Fractions - operations of addition, subtraction, multiplication and division
Decimals - operations of addition, subtraction, multiplication and division
Factors Each of these must be connected to reality and the operations must be learnt with that feel, of it being, natural and simple. That is the litmus test. This can only be achieved by researching on countless activities vailable. The simple point is that every student must GET the result. He must grasp the concept fully and feel comfortable fully in the operations of it.