When we walk we take one step at a time. When we run we still take one step at a time! And when we jump the situation does not change. One jump at a time! Till the time we don’t experience a firewall, we shall continue with the assumption that mathematics is all about counting-measuring, weighing and finding rates being the other forms of counting. Counting

Result: + lane= +1+1+1+1= +4

Result: – lane= -1-1-1-1-1-1=-6

As is clear the symbols + & – do not tell us about the direction in which the athletes are running. Both are moving in the same forward direction much like the time which moves linearly into the future. Both athletes count their progress and when the coach looks at the result he declares the negative lane runner the winner because 6 is numerically bigger than 4. The second next thing he does is by how many numbers (or by how much) does the winner take the cake! He again counts forward from 4 to 6 to arrive at the quantified value of the win. -6+4 =-2 tells us the person in the second lane is the winner!

It is very clear that addition has to happen in a lane of linear expansion. As is won’t in languages, the symbol 1 (one) apart from being a shape has a name or carries a sound as well. Teaching means establishing a reflex response in a student. We make a sound say nine the student writes 9. The visualisation part of learning if possible, makes it easy for the students learn faster. So the math student is learning counting. He is in lane one (+ lane) and the number 1 is moving, gaining 1 at each step. Next he visualises two lanes, +ive and –ive, where counting is in process. The idea, once again I will stress, is that before he is conscious of the difficulty of juggling with the symbol minus or subtraction, he should be familiar with it. He immediately learns that identical specie of numbers add or a linear progression is happening. Birds of the same flock fly on their designated route!

The most confusing application in mathematics which the students face is the operation of subtraction. This operation has become the bane of the students. So I suggest that the term subtraction should be excommunicated from the math lexicon. It should be replaced with the term, comparative linear counting. Similarly addition should be termed as linear progressive counting. The idea is that a visual image should go with each concept.

53 46 69

+43 +68 -31

Now this is a wrong way of placing the numbers sans their identity cards. The correct version should be:

+53 +46 +69 -83

+43 +68 -31 +31