Ramblings on Math and Testing

I was teaching math to one of my cousins who's about to get certified as a 10th grade pass out. I now figure pass out rhymes with drop out :-).

Math is an interesting subject. You have hundreds of theorems and corollaries, millions of formulae and lots of problems that appear like "Life and Death" problems to some of us at. I was looking into arithmetic progression in particular. There have been many theories based on which there is a formula that looks something like this :

Tn = a +(n-1)*d

In straight forward problems, students are asked to find one of the above parameters while giving away the rest. For e.g. Find Tn given a and d. What some students don't realize is that n is present in Tn itself. They go looking for n, get lost and leave the problem unsolved.

I was trying to simplify this for my cousin. First, I made her write down all given parameters, followed by some parameters known to her. I asked her to list out what her end goal (Tn) is. I asked her what more she needed to calculate Tn. And she did.

Trap Gods must be happy
Trap Gods are happy whether they trap you or lead you towards traps. One striking thing about my cousin was this. The moment I dictated one problem, she pounced upon the problem like a tigress on its prey. That is how some of us feel when we are working on math problems ;-). She didn't notice what's in the question, what is she supposed to find and how to proceed. All she did was to listen to one key term (Tn, in this case) and go looking for it. In short, she heard what she wanted to hear. Rest escaped into wilderness.

Why math class on a testing blog?
As I was helping her with her problems on problems , I figured how similar it is to testing.

• We are given some problem to test(product).
• We may know a few things about the product.
• We may not know many things about the product.
• Based on what we know, we go scouting for new things.
• If we don't know anything about the product, we still need to figure out how to know (learn) the product.
• Once we think we know at least a decent part of the product, we go figure new stuff again and again and again.
• Every observation made, every direction taken leads to different paths which become solutions.
• There is no one right answer, there could be a second right answer and even more.
• There is no one time permanent solution unlike in math.
• Every time, there is a new solution, there is a new breakthrough.

Heraclitus, a Greek philosopher once said, "Expect the unexpected or you won't find it". Unless we look for the unexpected, we won't find it. If we do, we may not recognize it. It's good to calm down, relax and look for the unexpected. Often, we lose out on sometimes obvious things either because we are looking for something else or we don't recognize what we see.

 [ PS : I have been struggling to write this post. I wanted to write this because I am thrilled for some weird reason. At the same time, I am not too thrilled with the way I am struggling to think and write. Need to be writing more often. Until then, have a good time reading this post. Who knows, a few years down the lane, I may look at this post and proudly say, "Oh! My writing used to be so damn bad :D" ]

Update: My friend Dhanasekar asks, "Expect the Unexpected, how is this possible? You are expecting so it can no more be called unexpected". Me : Go read some of Heraclitus's writings.
Expect the Unexpected,
Regards,
Parimala