Additive Thinking

Additive Thinking is the identification of real life situations, where 2 changing parameters are of the following kind.

1. Constant Sum

2. Constant Difference

Constant Sum

Imagine that a child has many toys. While it is playing with them, some of them may be inside a box (and not visible) and some may be spread on the floor and hence visible. In another situation, at the start of play all the toys are piled in one place. After playing for some time the toys get spread out in the room.

Development psychologists say that until a certain age (or stage of development), children may think that the toys that are not visible “do not exist anymore” or have “vanished”. They may also think that in a spread situation, there are more toys than there are when they are piled together. It is only after certain cognitive development that they realize that “quantity” is conserved. That the total number of toys remains same. This is the concept of “constant sum”. This is one of the basic ideas for developing the idea of a number as a quantity.

At later stages, this thinking helps children to compose & decompose numbers and shift numbers flexibly. It helps in building number sense.

1. 5 + 3 = 3 + 5

2. 5 + 3 = 5 + 2 + 1 = 2 + 5 + 1

3. 18 + 25 = 18 + 2 + 23 = 20 + 23 = 43

Constant Difference

Ram is 8 when his sister is 5. Hence when his sister would become 8, Ram would be 11. The difference between their ages would be the same, whatever be their ages.

The concept of constant difference is more difficult than constant sum. It comes from the experience of understanding the progress of time and age.

This thinking also helps a student to compose & decompose numbers and shift numbers flexibly.

1. 18 – 9 = 19 – 10 = 9. Adding the same number to both the numbers does not alter their difference. Taking away 10 from another number is very easy.

2. If 7 – 3 =4 then 8 – 4 = 9 – 5 = 10 – 6 =……….. There are infinite ways of rewriting the problem to get the same difference!

Addition & Subtraction are related

Additive thinking also helps a student to realize that addition & subtraction are just different ways to depicting a relationship.

If 4 + 7 = 11, then 7 + 4 = 11 and 11 – 4 = 7 and 11 -7 =4

If 7 – 4 = 3 then 7 – 3 = 4 and 3 + 4 = 7

An addition situation can be represented as a subtraction situation and vice versa. They are just different perspectives of the situation.

Addition & Subtraction can be also seen as the “reverse” of each other.

Imagine Ram had 4 toffees and his sister had 7 toffees and she gave 3 toffees to him. For his sister it is a “subtraction” situation”. Now she has 7-3 ie 4 toffees. For Ram it is an “addition” situation. Now he has 4 + 3 i.e 7 toffees. But the total number of toffees which both have has not changed.