“Success does not consist in never making mistakes but in never making the same one a second time.”
George Bernard Shaw
While preparing for the SAT math section, you must be solving many practice problems - either found in the official SAT guide or in any other book/s published by major SAT preparation companies.
Undeniably, even the most brilliant students get some of the answers wrong. It won't be fallacious to assume that you wouldn't be at a 100% accuracy level (well, at least initially and most likely until you reach the end stage of your preparation).
But the important thing to ponder over is - what do you do with the DATA you have about the mistakes you commit?
In my experience, most of the students brush aside these errors, typically accompanied by this self-assuring (but self-deceiving in reality) self-talk:
"Oh, this is because I misread the problem statement - of course, I will do it with utmost care in the actual test"
"Well, this one was out of my reach - maybe I will revisit the logic later"
"This was just a silly mistake - I am sure this is just an anomaly and won't repeat in the actual test".
Undoubtedly, it would help if you didn't allow such errors to cause deep despair, but at the same time, too much optimism about your future performance won't come without its perils.
Essentially, if you ignore your mistakes in the present, they will come back with a vengeance later. And since we are talking about math right now, it will only be appropriate to say that if you don't take action in time, then time will faithfully repay you with the power of 'compounding' (with all the negative connotations, of course!).
So what do we do here?
Well, the first cognitively sensible response is to - analyze for root causes. The first step is to organize the errors (or their root causes) into different categories. Some example categories will be:
- Silly mistakes caused due to negligence or undue hurry (e.g. instead of adding two numbers, you subtracted them).
- Inability to grasp the correct logic required to solve the problem (e.g. you read the problem many times but had no way to make any sense of it or chose to follow a logically incorrect pathway!).
- Solving the problem correctly and yet failing to answer the question (e.g. you solved for the variable x correctly and picked an answer option based on this, but the problem statement wanted you to find the value of x + 1).
You can add more categories to this depending upon your preferred style/logic of classification. But the fundamental goal of this exercise is to segregate the most common mistakes you commit to addressing them with more precision systematically.
So you have your mistakes neatly categorized now. But what comes next?
Well, we spoke of systematic and precise redressal. So now is the time to get to the level of brass tacks.
But first, we need to perform some elementary numerical/visual analysis of the distribution of the different types of mistakes.
To do this, we must first find out the percentage contribution of each type of mistake. In general, you can expect to find that one or two classes will be more dominant than the others.
Also, it is essential to consider the effort required to remedy each type of mistake.
For example, you may find that a significant percentage of mistakes happen due to your inability to comprehend and apply correct logic. However, this type of mistake is not that easy to remedy.
At the same time, you may find that the other significant contributor is - silly mistakes. As you can imagine, this is something easier to address. The following 2 x 2 matrix depicts this visually:
In the figure above, along the horizontal axis, you have the dimension of effort involved going from low to high (from left to right). You have the percentage share of the error category (or frequency, if you like) going from low to high (from bottom to top).
As you can infer from the figure, it is wiser to embrace the following approach:
- First, focus on eliminating silly mistakes (high percentage-low effort).
- Next, focus on devising strategies for developing correct logic in those areas that require this type of attention (high percentage-high effort).
- Finally, you can work on being more careful each time you read a problem statement (low percentage-moderate effort).
At a broad level, your next step must be to devise effective strategies for each error class. And I need not tell you that the overarching goal is to do something to minimize the likelihood of you making an error.
Let's get more specific here and work by way of examples.
First, let's see what we can do about silly mistakes. Research evidence suggests that we make stupid mistakes when our brain's processing power is overwhelmed by the amount of information that we need to hold in a short period.
For us, what it means is that if we try to do too many calculations in our mind (and in succession), then there are enough chances that somewhere, a slip will happen.
Essentially, the lesson is that if you find yourself committing too many silly mistakes in the math section, then it's time to consider adopting a new habit - of doing calculations in writing in a clear, step-by-step manner.
I know that this advice sounds egregiously pedantic. Still, with time you will gain mastery over simple measures, and perhaps one day, you may get rid of this brutal torment in its entirety.
In my experience, there's another factor that may be the root cause of silly mistakes for some of you. And that is - overconfidence. Typically, when we perceive a problem to be easy, we rush towards solving it instantly. And in this process, we tend to make false mental jumps and commit silly calculation mistakes.
And what's my proposed remedy for this?
I would recommend that for such problems, you make a conscious decision of slowing down a bit. You wouldn't lose more than 5 seconds for each of these types of issues in any case. And in the grander scheme of things, it's wise to be accurate at the expense of losing about 2 minutes.
You are welcome to do the actual cost-benefit analysis based on your mock test performances! But I will drop a hint - would you rather save 2 minutes of your time or lose 30 points on SAT and fail to get admission to your favorite college?
Ok, so the issue of silly mistakes was silly enough to be tackled first!
But how do we go about addressing the second type of mistake - arising out of a situation where we find ourselves to be utterly clueless?
I can tell you that two basic scenarios cover this - one, you haven't experienced the relevant concept in totality; second, you are familiar with the fundamental ideas about the problem at hand, but you are unable to navigate its logical maze.
The first scenario is relatively easy to handle. For example, you haven't seen enough trigonometry or complex numbers in school, and therefore, you can't do much about it in the test.
The remedy to this is as simple as it gets, and honestly, I don't even need to illustrate it here. In short, for these types of issues, you need to wait for the school to catch up. Else, if you are ardent about getting there faster, you can refer to online resources (videos, blog articles, websites) or consult a professional expert.
The second scenario is a bit daunting to disentangle.
But I will try to decipher it using simple examples. Whether we can solve a math problem quickly or not depends on our intrinsic mental models (ways of making sense of the given situation).
For example, I can confidently say that I can comprehend and solve calculus and algebra problems. Still, I can't make a similar claim about probability, combinatorics or maybe even geometry. What gives?
I believe that for calculus and algebra, I can use prior knowledge (which is there in my mind) to construct an accurate mathematical model based on the information given in the problem statement.
In other words, it's easy for me to access and manipulate the rules of algebra and make complete sense of what the problem is asking me to do and how to reach the final solution.
But for topics like probability, I struggle to leverage the existing conceptual knowledge and form a comprehensive and accurate mental picture that can describe the problem space and help me navigate my way to the solution.
While the actual causes of these topical deficiencies may be too hard to ascertain (prior exposure, natural inclinations, brain-wiring), it is nonetheless vital to overcoming these hurdles.
One way of achieving this is quite obvious, but it requires something special - keeping our ego aside. Essentially, to become a master in areas where we are struggling, we need to swallow our pride and pay close attention to the solutions provided by others (your peer, online resource, an expert tutor).
The key here is to analyse the problem-solving approaches microscopically and look for the 'deltas' - places where our reasoning broke down while others could make that jump with ease. After you have done enough of this exercise, it becomes easier to extract patterns of practical thinking and develop guiding principles thereon. Of course, the more you practice using these principles, the better you get at it.
Ok, so we seem to have covered lots of ground here, and now, we are poised to address the third type of error. I don't want to temper your enthusiasm, but this one is easy to handle once again.
Pardon me for being rude, but if you fail to read the problem statement correctly, you have not learned anything from repeated warnings! Time and again, almost everyone (your SAT tutors, SAT book authors, SAT blog writers) will caution you that in the math section, you will find that the test-maker decided to use some guile.
As an example, you will find problems where if you calculate the variable's value and choose an answer option accordingly, you will most probably be wrong. Instead, if you pay close attention to the problem statement, you will find that you have to use the variable's value and calculate the value of a different expression!
And how do you overcome this bad habit of not being careful while reading problem statements? A straightforward idea (and the best one, actually) is to underline the most relevant part of the problem statement (so you know what you need to find).
The Math and Coding experts at Cuemath firmly believe in this and design tailor-made courses to ensure that each child reaches his true potential. Cuemath conducts Live Online Math classes and Coding classes. Hopefully, you will find this information to be useful. Happy preparing!
-By Gaurav Pande