How Problem Solving Makes You An Active Learner

Newton was right, as I know it from experience.

A few incidents have changed my mindset radically. One of them happened in BDPhO 2016 Dhaka regional. 

I found interest in math and physics since my secondary school days. Actually, may be I was fond of these subjects because it took a lot less effort to score good in them. And, maybe because once any topic was understood, I didn't forget it.

But, there was one problem. I was a passive learner. I only wandered in a limited region of the vast sea of knowledge. If I could understand a certain portion of the theory, it was OK for me.

I never wanted to find out what's beyond the horizon of my comfort zone. I considered the ability of developing a scientific thought as a divine skill, then.

Most of secondary school days were in a small town high school. So, there was no sign of math or physics Olympiad anywhere around. So, I was a frog living in a well, delighted under the illusion that I had good cover over physics or math.

So, with this outlook for learning, I passed secondary school. Then, I came to my country's capital, Dhaka, for higher secondary education. 

And a few incidents happened which made me learn how much I don't know. One of them I would like to share.

In December 2016, I registered for BDPhO Dhaka regional round, . Few days before the event, I started checking the solution book of Irodov's Problems in General Physics. I was still passive about learning back then. So, it seemed the only way to 'prepare' for physics Olympiad, which you all know was a foolish thing to do.

The day of the event came. And I was at the event venue. The exam started. I got the question paper. And I looked it for a while, scrimmaged through the pages. I was terrified as I couldn't solve any of the problems.

My heart started beating faster. My self-image as good learner was broken to pieces. And then I was depressed. And it made me more depressed that some of the people in the room were writing with fast pace. I started thinking what did I lack.

When the time was over, I submitted an empty paper.

Exam was over. I was depressed but watched the prize giving ceremony for some time. Then, I left before the result of my group was to be announced; as I knew I had no luck.

I was back at my home. Depressed as ever and wondering what was wrong with my learning process that I couldn't solve a single problem in PhO. Slowly, I started to realize I have a passive attitude towards learning physics. I didn't solve problems, I just learned the theory and try to be contented with it. Surely, this was my problem.

I realized I needed to change. So, I started studying Resnick-Halliday-Walker. At first it was tough to solve problems on my own and letting go off that passive outlook of looking at a problem and getting the solution instantly. But, I realized I am a person with no special talent. I needed to put effort and time into learning the craft of problem solving, the truest way to learn any scientific subject.

I started from solving the easiest ones. After solving them, I attempted the tougher ones. At first it took much time to see the connection between different parts of the problem. Also, it was hard to figure out how to even approach the problem.

But, that's the way it is. Everything worthy that you want to achive will require a long, ardous process. In the first stages of it, you will probably have no idea how you will go ahead. Blunders will be there. You will become depressed as the expectation will hardly match the reality. And you will want to give up many times. 

All of these things happened to me. But I didn't give up. Maybe because if I could even solve a single problem, even after hours of attempt, there was a blissful feeling in my mind. And I liked it very much.

So, I continued.

And to my surprise I completed the electricity and magnetism part of that book in about one or two months, with almost all the problems solved. I also completed the theory of the modern physics part.

This event started changing my outlook about learning physics. I was still very passive, there was subtle, innate fear in me about facing tough problems. I used to skip problem solving section as much as possible for a year so after that. But slowly I lifted myself from that passive state.

Now, after almost two years of that incident, I am here. I realize now that there is no alternative of solving lots of challenging problems to master a theory. I have divided equal half of time for learning the theory and solving problems. It works great for me. You see you can never realize the subtleties of a theory by only learning how the proof is done. You have to apply the theory to various physical systems or phenomenas to get a feeling of its strengths and weaknesses.

Moreover, problem solving develops an active learning mindset. I am sorry to say but the stories of getting scientific ideas out of the blue are not true. You only get what's going on after great efforts and lots of failures. Problem solving will make you habituated with this process.

Connecting the dots between different concepts is also very important. And I think the best way to do it is to solve a lot of problems.

For example, I was solving a problem which required me to proof the diffeomorphism of tangent function from the interval (-pi/2, pi/2) to the real number line. It required me to proof that inverse tangent functions is infinitely differentiable. But, obviously I couldn't differentiate infinite times. So, I differentiated once and got 1/(1+x^2). And then I realized there is a polynomial Maclaurin expansion of this. And polynomials are always infinitely differentiable.  

The thing is you get better and better with practicing. Your reasoning will become better, it will take less time to learn something. You will make less errors while advancing on the logical process of getting a result. I know all of these positive effects from direct experience.

So, people, what more reasons do you need to spend long hours solving problems? Go and get down to it.