The Skill of Spotting
If I had to pick one skill that I’d say helps me out in science and mathematics the most, it would be the skill of “spotting”. Simply put, it’s how good one is at figuring out the essence of a question. Personally, it’s a skill that I cherish, because it allows me to do so well during my exams. Rarely do I read a question and go blank. Instead, I’ll immediately get to work, going through the steps needed to solve the problem.
Of course, there are really two ways to solve a problem: the “make it up as you go along” strategy, and the “spotting” strategy. The former can work, but it’s likely a longer method and can result in a lot of dead ends or useless work. However, the “spotting” strategy allows one to know exactly what the steps are to solve the problem.
For example, if I’m given a problem on mathematical induction, I know the steps I need to do. First, I write the base case out to show that it is indeed true, and then I do the calculation with $k=1$ and $k=2$, just to show the pattern seems to hold. Next, I write down the equation with k, and then I try to solve it by induction using k+1 in conjunction with my base case and assumed truth of the statement with k.
This is my “format” for solving induction. What you can notice is that there isn’t any numbers or specific examples in the above case. It’s just a template for solving problems involving mathematical induction. By “spotting” the problem, I can just apply this template and be confident that I will get the correct answer.
This is why the “spotting” strategy is so good. It takes the thinking out of the present moment by referencing a template for a specific kind of problem.
So how do you cultivate this skill? The best answer is that you have to do a lot of problems. By practicing over and over, you will begin to sort out problems into various categories. You’ll start recognizing exactly what you have to do when you get a problem with acceleration, velocity, and position, or when trying to find a tangent plane to a surface. The values and functions might be different, but the approach is the same. Slowly, you will amass an archive of examples that you can reference in your mind when faced with a new problem.
When I enter a test now, I always try to spot. If I’ve prepared well for the exam, this shouldn’t be a problem. After all, the content of the exam is stuff I’ve seen, so there’s no reason I shouldn’t recognize it. That’s not to say that a certain question won’t be difficult, but the odds are with me that I’ll be capable of spotting a problem.
This calms me down immeasurably during a test. Since I’m hyper-focused on getting a great grade, it’s a relief to me when I know exactly what I have to do to solve a question, and all that’s left is for me to go through the motions. Basically, I practice a lot so that I can offload the work on the test to my vast archive of previous examples in order to solve the question.
My advice to you is this: if you want to have an easier time during tests, learn to spot similar questions. It will save you the mental energy of always figuring out from scratch what you should do. It’s like using formulas. After you’ve been exposed to the proof, there’s no need to prove the formula you use on every question you answer. You just use it. Likewise, don’t waste time reformulating the same strategy over and over again to solve a question. Use the one that worked, and just apply it.
It will save you a lot of time and make tests go that much more smoothly.