Common errors in maths exams and how to avoid them

Explore the PSLE Companion microsite for more insights and tips.

SINGAPORE – Careless mistakes are a common reason marks are lost during an examination, but they can be prevented, say educators.

Some parents may think their child is lazy when they are prone to such errors, but carelessness could be because of factors such as a lack of exam stamina, anxiety or a shaky foundation, says Zhou Shicai. The founder of NickleBee Tutors coaches pupils in PSLE and Olympiad mathematics programmes.

Zhou adds: “Accuracy is a skill, not an accident, so losing marks to careless errors is most definitely a fixable problem.”

He says carelessness in the PSLE mathematics context usually boils down to hidden gaps, which could include a lack of focus, jumping to conclusions or simply not having a proper checking system.

“It’s not something we can ignore and hope will magically disappear,” he says, adding that there are strategies pupils can pick up to reduce the chances of these errors.

Primary 6 pupil Lucas Yee, 12, is strong in maths, but tends to be careless when doing problem sums.

Lucas’ mother Jessy Liu, 45, says he once lost more than 10 marks in a test because of careless mistakes.

“He tends to do his work fast, so he may skip certain words or not read the question carefully. Or there are times he thinks of one number, but writes another,” says the mum of three, who is a founder of a tuition centre focusing on languages.

She has tried sitting beside him to remind him to slow down when reading a question, and to do it one step at a time. “Once he understands why he must do that, hopefully he can replicate that during the exam,” she says.

Why do pupils make careless mistakes?

There are different reasons for careless mistakes in maths, one of which is pupils rushing to complete the questions owing to time pressure, says Cheryl Ang, head of the mathematics department at Pei Hwa Presbyterian Primary School.

For example, pupils may read a question and immediately recall another question they had practised previously. They then solve it using a similar method, rather than reading carefully to understand what is being asked.

“Our brains naturally look for familiar patterns, but it is important for students to understand the problem and apply the appropriate method to solve it,” she says.

Another reason could be messy handwriting or unclear presentation of working.

Also, some pupils may view a problem to be harder than it is and end up spending too much time on it. “Students need to learn when to move on to the next question. This way, they will have enough time to complete the paper and check their work,” says Ang, who has 20 years of teaching experience.

Zhou says that to avoid running out of time after spending too long on challenging problems, he teaches his pupils a time management rule of thumb: They should be spending about one minute a mark. 

So, pupils should spend about two minutes on a two-mark question and five to six minutes for a five-mark question.

“This will give students plenty of time to check their work or buffer for any unforeseen circumstances,” he says.

5 common errors and how to prevent them

1. Transfer errors: These occur when pupils misplace decimals or transfer figures wrongly.

They can be avoided by having pupils point their non-writing finger at the original figure until it is copied over, says Zhou.

2. Calculation mistakes: They can happen when pupils are anxious or rushing through their work.

This can be avoided by writing down every intermediate working step, avoiding mental calculations and using a calculator or a separate working to double-check simple steps.

3. Misinterpretation of questions: This can be avoided by underlining, circling or highlighting key details that a question is asking for, for example, “unshaded area”.

4. Unit conversion errors: This happens when pupils forget to convert between different units of measurement.

These errors can be avoided by marking out the different units and converting them to the same unit of measurement, usually the smaller one to prevent awkward decimals, before starting calculations.

They can also happen when pupils confuse the units of measurement, for example, converting 1kg to 100g instead of 1,000g, says Ang.

5. Applying the wrong concept: Avoid this by building strong conceptual foundations rather than rote-learning questions, so that pupils can apply what they know to unfamiliar problems.

Strategies to minimise careless mistakes

Ang uses two acronyms to help her pupils solve maths problems. STAR is a problem-solving approach.

S – Study the problem: What is the key information in the problem? What concept is the question testing? What am I asked to find?

T – Think of a plan: Which strategy will work? Have I solved a similar question before?

A – Act on the plan: Write down each step clearly and check the steps and calculations along the way.

R – Reflect: Review the answer using the next acronym, NTUC:

N – Number: Is my final answer reasonable? For example, is my answer more than the numbers given for a question that requires summing up all the numbers?

T – Transfer: Did I transfer the numbers correctly?

U – Units: Did I leave the final answer in the correct units?

C – Calculations: Did I calculate correctly at each operation? Did I key the numbers into the calculator correctly?

Ang says introducing these strategies early will give pupils time to practise so that the habits will be ingrained when it comes to exams.

For pupils who get overwhelmed by long questions, Ang encourages them to break them down into parts.

This helps to reduce anxiety as pupils learn that they do not always need to solve the entire question to earn marks. This encourages students to attempt the question instead of leaving it blank, she says.

“Even if they cannot obtain the final answer, they may still be awarded method marks for showing correct working or applying an appropriate strategy,” she says.

When students are unsure how to proceed with a task, one way is to draw a model or use pictorial representations to better understand the question.

After pupils complete the paper, Zhou reminds them to do a quick assessment to check if the final answer makes sense. “For example, did you get the age of the girl to be 250 years old? Or the number of boys in the class to be 5.76?”

Another way to check is to work backwards instead of rereading the steps written.

“Approach the problem from the opposite direction to force your brain to process the data afresh. So, if you did addition, check by subtraction; if you did multiplication, check by division,” he suggests.

Another method is to substitute the final answer back into the original question to ensure it fits.

“Always remember that the PSLE examiners are trying their best to award you every single mark that you deserve, so don’t give them an opportunity to take those marks away,” he says.

If pupils lose focus or panic during the exam, he advises them to take a few slow, deep breaths, to calm themselves down and reset their mental state before reading the question again with a fresh eye.