1) Silly mistakes are not silly! Take it seriously!

The fact that you are reading this article means that you are taking this issue seriously. Please do not ever sweep it away as “just another silly mistake”. Instead, do your corrections, beat yourself up a little as the discomfort will train yourself to watch out for it.

2) Check your work by substituting final answers back into original equation.

For any problem that involves solving equations (be it algebraic, simultaneous, modulus, logarithm or trigonometric equations), always substitute the final answer back to the original equation and verify its accuracy using a calculator. This is the fastest way to know whether you are right.

3) Estimate the accuracy of your final answer!

One of the first chapters you learn when you enter secondary 1 is estimation and approximation. These estimation skills are going to be useful even when you are in sec 4 or higher! If the length and breadth of a rectangle is 2.13cm and 49.1cm, you would expect the area to be around 100cm^2.

4) Checking that your final answer makes physical sense.

If your answer shows that a boy runs 2.4km in 2mins or the price of a pencil is $2000 or the bank interest rate is 80% etc, you should guess that something is off. Time to check your work again!

5) Always make sure you copied the question correctly!

Copying the question wrongly is the most painful careless error possible. You will not get half a working mark even if you had done the rest of the question diligently and properly.

6) Always Check that you have attempted every question and every part on every page.

I have had students who missed the last page of their mathematics exam simply because they “did not know there was a last page”. Also had students who skipped parts of questions along the way and “forgot” to return to attempt them when they had the time!

7) Play Chess (International or Chinese) and strictly disallow undoing of moves

When playing chess, if we make a stupid move, we feel the pain of losing an important piece. Hence it trains us to check and re-check several times before making any moves. This is an excellent way to train ourselves to avoid careless mistakes.

8) Write neatly

You should know why. I don’t think I need to elaborate this.

When doing algebra, students often make a careless mistake because their written Z looks like a 2. So, start writing “Z” with a strike through instead!

10) Strengthen your mental calculation through training.

You should be able to at least do basic addition, subtraction, multiplication and division mentally. The more you strengthen this aspect, the stronger will be your number sense. A good number sense is like Spiderman’s “Spider sense”, it alerts you when a mistake is nearby.

11) Practice lots!

Make the mistakes before the exam and be sure to learn from them. The more you do, the sharper your skills will be.

12) Practice Checking!

Aside from practicing lots of math questions, it is important to practice checking as well. Checking to spot error is a different skill itself. Each topic or type of question has its own way of checking effectively.

13) Insist on finding the careless error yourself!

If you are studying with a friend or tutor or parent and they manage to spot your careless error, warn them not to tell you the error. This would deprive you the opportunity to practice spotting careless mistakes. Only allow them to help you if the mistake is a conceptual one and not a careless one.

14) Ensure you are in top condition when taking any math exams.

Math is a subject where you need razor sharp focus to excel. You want to reduce any discomfort as they could distract you during exams. Make sure you have enough rest the night before and you are well hydrated before the exam. If the exam hall is cold, make sure you have a jacket/sweater.

15) Always check your units!

There are tricky exam questions that traps you into making errors. One such way is to vary the units. It is possible for the dimensions of a rectangle to be labelled 3m by 20cm. Some students will neglect the units and end up finding the area as 3 x 20 = 60m^2.

16) Be confident, but not overconfident!

Lack of confidence and overconfidence are both causes of careless. To build confidence, do varied practices such that you are exposed to various kinds of questions. However, always stay humble because the moment you look down on a question, you are doomed to make careless mistakes. During practices, whenever a student says “this question is chicken feet”, I would instinctively tell them to check their work. From experience, they are likely to have made a careless already.

17) Don’t Skip too many steps!

If you do so, you will make careless. Period.

18) Don’t Mix up power and multiplication!

It just so happens that 2^2 is 4. But 2^3 is not 6!! And 3^3 is not 9!! Yet I have seen these kinds of errors so often! And even secondary 4 students make them!

19) Place more focus when checking the beginning of your working!

When the top is wrong, the rest are wrong. If it is an O-level Additional Math question, you get 0 marks since there is no error carry forward. If the bottom is wrong, at least you still get some marks at the top. However, because of our eagerness to jump into a new question, the top part of every question is often the most vulnerable to careless. So please spend more effort checking the top part of every working.

20) Focus whenever you are doing math.

Be it practice or exams, always get into the good habit of staying focussed. If your mind get distracted by other things like “what to eat for lunch” or “should I pon cca later”, you have a higher probability of making careless. This is true even for teachers! So, stay focussed!

21) Always assume you are wrong until you have checked.

Yes, checking your work often feels like a pain in the butt but…Just do it. It is the best method to reduce careless. Tick the question number once you have checked, certified and “confirm plus chop” you are correct. Then continue the checking process for those without a tick yet.

22) Don’t stop checking until the very last minute.

Yup, don’t stop. But avoid making changes in the last 2-3mins because any changes made in a haste often ends up being worse off.

23) Compile your math careless mistakes during practice.

Make a habit to compile all the types of careless mistakes that you making during math practice. You can compile it on the front of your math notes or on a separate notebook. Keep track of the kinds of dumb mistakes that you make and watch out for them during exams!

24) Time Management.

Put some time pressure on yourself when doing the exam. This is such that you have some time to check your work at the end.

To get professional help (Math tuition) on secondary school mathematics in Singapore, click here.

Mr Ausome