Why You Should Make Mistakes When Practicing for Math Contests
One of the major problems in test taking is making mistakes. Countless times I heard students saying “I made a silly mistake”. You were probably warned many times to avoid mistakes in your training and heard, read, or thought of strategies on how to avoid mistakes. In this article, we will see a different approach: Making more mistakes during practice and understanding our mistakes to help us avoid them during contests.
If you are confused with this approach, don’t worry, you are not alone. As a defensive mechanism, to avoid a bad outcome, we try to do what we can to prevent it from happening. To avoid mistakes in an upcoming Math contest, like MathCounts, AMC 8/10, AIME, etc. our natural instinct is to avoid making mistakes while we train for them, too. To see why a different approach might be more beneficial, let’s look at two real-life examples.
By now, you might have heard an infinite number of times the importance of washing hands, social distancing, and using masks to minimize the risk of catching and spreading COVID-19. These are all important and useful preventative measures. Vaccination on the other hand is the best measure against the disease, but it works quite differently. On first sight it is a crazy idea: It actually exposes you to a weakened version (or some knowledge) of the virus. Your immune system then learns from the experience, and recognizes/defeats it in the future when you catch the virus itself. Making mistakes while practicing is injecting yourself with the knowledge and experience that can help you prevent making similar mistakes in actual contests.
In a circus, when you see a funambulist walk on a tightrope, you see perfection: no falling, no mistakes. What you don’t see is the countless number of falls during practices, learning from them, and each time getting closer and closer to that perfection. Indeed, perfection only follows a lot of hard work and many many mistakes on the road.
I have seen thousands of gifted students over the past two decades but I am yet to see one who has never made a single mistake in solving math problems. Everyone is bound to make mistakes and it is better to make and learn from them while practicing, rather than during the actual contest.
Making more mistakes while training gives us the best chance to understand what kind of mistakes we are prone to make and why. Then and only then we can come up with strategies that work best for us to minimize the risk of making such mistakes.
Ok, suppose we are now cool with this crazy sounding idea of making more mistakes in training. But how do we achieve that? For many students, this is not an issue, as they are already making a lot of mistakes. If you are not so fortunate to be one of them, you can try giving yourself more pressure to increase the likelihood of making mistakes, for example, by trying harder problems, giving yourself less time in a practice test, or trying to solve lots of easy problems very fast in a row, like countdown style, etc. Remember, we want to make mistakes that we are likely to make in an official test, so no faking them, for instance by intentionally making a calculation error or circling a wrong choice. If none of the methods are helping, and you are still making no real mistakes, try the next best thing: imaginary mistakes. While solving problems, think about the instances where you might possibly make mistakes, for example, if you might confuse the diameter with radius, forget to divide by two when finding the triangle’s area, a carry over mistake in a multiplication, etc.
Once you are successful in making a (real or imaginary) mistake, the second and probably the most important step is going over your mistake slowly and carefully. Instead of categorizing it as a “silly mistake”, treat it with utmost respect. There is a reason for its existence. Ask questions like
- Why did I make this mistake?
- Do I remember making similar mistakes in the past?
- What makes me vulnerable to this type of mistake?
- What could/can I do differently to avoid this type of mistake?
For example, if the problem asked you the diameter of a circle but you found the answer based on the radius instead, perhaps you can underline some words in the future which might lead to similar mistakes, or you can start your work by clearly writing what they are asking for “DIAMETER=?”
Continue your practice journey with this awareness and any new mistake-avoiding habits you equip, focusing more on the types of mistakes that you are making repeatedly. You can also have your own mistakes journal to list your mistakes and see your progress. Even if you don’t come up with any good strategies to avoid these mistakes, there is a good chance that the sole awareness of it will help you recognize them and alert you when you are about to make the same type of mistakes in the future.
Now, go and practice with making (and correcting) mistakes to your heart’s content.
Somewhat related Quotes:
“An expert is a man who has made all the mistakes that can be made in a very narrow field.” – Niels Bohr
“A man who has committed a mistake and doesn’t correct it is committing another mistake.” – Confucius
“He who never made a mistake never made a discovery.” – Samuel Smiles
“Keep your friends close, your enemies closer” – Michael Corleone in Godfather-II
“Oops!…I Did It Again” – Britney Spears in the song Oops!…I Did it Again.
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