With changing perspectives of Mathematics teaching-Learning, we find that nowadays the focus is shifted on ‘CONSTRUCTION OF KNOWLEDGE’. Though it is difficult to construct knowledge in Mathematics, still some efforts can be made to motivate students to construct the basic mathematical rules, and formulas themselves.

One example of Constructive Approach of Mathematics Teaching-Learning is:

‘Rule formation for Addition of Integers’. For this we require Integer Tiles or colored buttons (in two colors) as improvised apparatus. Assume one color will represent positive (+ve) integer and another color will represent negative (–ve) integer. The group of equal no. of both color tiles will represent zero (0).


(Note: Here we have associated the abstract concept of positive and negative integer with specific color to concretize it.)


Case I: When both Integers are negative

To add above integers, we will take three red tiles/red buttons in first row to represent (-3).

Similarly, to represent (-4) we will take four red tiles/red buttons in the second row.


As the colour of tiles is same in both rows and there is forming no group of different colors so the total tiles we get are 7 in number and red in color. The resultant/answer will be -7.

Applying Inductive Method (i.e. taking similar type of problems and solving them with the help of Integer Tiles) and using probing skill, at the end we can conclude and generalize that if negative integers are added then the resultant will be the addition of abstract value of all integers and be negative.

Similarly, we can also generalize rules for other cases of Addition of Integers.

This is only one example of how students can construct knowledge (generalized rule or formula) themselves by providing hands-on experiences to them.

In the same way, we can also construct other mathematical formulae and rules (e.g. formula of Area of Rectangle, Addition of Algebraic Expressions and formula of Total Surface Area of Cuboid etc.)