The most common question that I get from my students: “Cher, how do I stop making careless mistakes during math exams?”

The most common reason I get from my students when they didn’t do well : “Cher, I made a lot of careless errors sia!”

Careless mistakes are also known as “dumb mistakes”, “autistic errors”, “retarded errors”, “stupid mistakes” and the list goes on. But attributing this type of error to one’s intelligence seems to be ironic because this error are often made by people who are smart, competent and over-confident.

So the million-dollar question is “how do we avoid making careless mistakes during mathematics exams?”

Find your careless mistakes yourself during practice!

When you get an answer wrong during practice, DO NOT simply strike off your working and re-attempt the question. If we shun our mistakes, erase them and get embarrassed by them, we will never learn from our mistakes! Instead, take the time and look through your working to search for the mistake(s) (it could even be more than one!). Do not move on until you have successfully identified the mistake and corrected it. This itself is a valuable opportunity to practice checking your work. Also, math tutors, teachers and parents SHOULD NOT deprive the student of the learning opportunity by helping them find the careless mistakes.

Some “Careless Mistakes” are not Careless Mistakes! Identify and Fix the Correct Problem!

One of the key causes of so called “careless mistake” is actually due to a shaky foundation. Often, students, teachers and tutors WRONGLY CLASSIFY a maths foundation mistake as a careless mistake. If you notice yourself making the same type of “careless error” several times in a single session, then it is likely due to a lack of understanding of a prior chapter instead of a careless error. For example, I once had a secondary 4 student (learning calculus) who kept making the error that x^(-2) = -x^2. This is due to a weak foundation in secondary 3 “indices” chapter. Instead of attributing it to careless because “he is supposed to know that already”, it would be more beneficial that we pause the calculus practice and revisit the secondary 3 “indices” chapter.

Practice the same Questions again!

You overcome careless not by doing tougher and more challenging questions. Instead, you practice the simple ones and the ones that you have done before. We usually make careless mistakes when facing questions that we are familiar and are confident of. For students preparing for O-levels, try doing your ten-year series (TYS) a second or third time. Yes, you will find it easy. And it is precisely because you find it easy, that’s why you make the careless mistake.

Practice the Fundamentals perfectly!

Michael Jordan, one of the greatest basket ball players of our time, was asked why he shoots a thousand hoops daily even though he is already so good at it. He answered “So that when it is time to take the shot that matters, I am able to do so perfectly.” It is the same when mastering math. We practice the basic math questions repetitively such that we perfect them and have a crystal-clear understanding of each concept. It is only after doing so, that we start working on the more challenging ones. That way, our chances of making careless mistakes will be significantly reduced.

Practice checking you work EVERY SINGLE TIME!

Check your work not by checking the answers at the back immediately. Check your work by using your own abilities first. Depending on the kinds of question, there are many ways to check the validity of your answer after you have obtained it!

- For an algebra question, you can often substitute the final answer back to the original equation to check that the equation holds true.

- For geometry questions finding lengths and angles, one can do a visual estimate to ensure their final answer makes sense and fall within the ball-park figure (For example, you know you are wrong if your calculations show that one of the angles in a triangle is 200 degrees!).

- For real life questions, consider whether your answer makes physical sense. If your answer shows that a boy takes 10 seconds to run a 3km route and did not mention that his name is Flash or Quicksilver, then you better start checking your work line by line for mathematical error!

- If the particular question has more than one way of solving it, you use the other method to confirm your answer.

While you learn and practice new topics, continually develop a greater armory of ways to catch mistakes before they propagate!

Refer to this article for 24 ways to avoid making careless mistakes during math exams!

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

Mr Ausome