Every student who has sat for mathematics exams understands the feeling of knowing how to do a question, but getting marks unnecessarily deducted due to careless errors.
Mistakes can also be a frustrating phenomenon during regular revision. How many times have you been bogged down trying to get the correct numerical answer to a question, and having to recheck your work repeatedly and even entertain serious doubts as to whether your conceptual approach to the problem is valid, only to find some obscure careless mistake buried deep within your tedious algebra?
Both math students and math tutors need a clear cut approach to minimizing careless mistakes and making math a more enjoyable experience.
(a) Constant practice
The first pointer is pretty much common sense. Practice makes perfect, and this is especially true in mathematics as well as the mathematical sciences. Constant practice improves your ability to handle complex algebraic expressions, perform numerical computations seamlessly, and in general, dot your i’s and cross your t’s correctly the first time round. That does not mean mistakes won’t happen if you practice enough. It means their occurrence is reduced, and when they do occur, you will be able to find them more rapidly.
(b) Develop a keen sense as to what numerical answers seem reasonable
If you are obtaining the weight of a man to be 200kg, something might be incorrect. Teachers usually set questions in which the final answer is reasonable from a physical perspective, so as to avoid confusing the student. Constant practice again comes into the picture. After you have been exposed to a wide variety of questions, you would know generally the range in which numerical answers should lie. Certain values are mathematically impossible. For instance, if you are asked to compute the value of the sine of an angle, and you obtain an answer that is less than negative 1 or greater than positive 1, you know for sure you have gotten it wrong.
(c) Develop the habit of checking your work
Under math exam conditions, the temptation is to go through all the questions as quickly as possible. Unless you are extremely pressed for time, constantly glance back at what you have written in the last few minutes to see if there are any obvious mistakes. Also, remember to check that you have answered all parts of the question after you have completed it. Start developing the habit of constant checking during your regular revision and you will find that the process should not consume an onerous amount of time under exam conditions. Do not just speed through without constantly looking back.
(d) Be enthusiastic and pay close attention to what you are doing
This might sound too philosophical, but it is true, and I can attest from personal experience, that being motivated and enthusiastic about what you are doing reduces the chance of making glaring errors. Pay close attention to the math problem at hand, develop the habit of staying mindful and alert under revision as well as exam conditions, and you will find that mistakes are spotted much more quickly and make far less often.
(e) Master the concepts and formulae well
Again, this is a common-sensical piece of advice. If you understand the subject matter perfectly and have the formulae at the tip of your fingers, you should find yourself less prone to careless mistakes.