SINGAPORE – A primary school mathematics question posted in the Reddit forum in May led to a discussion on whether a child’s written calculation or working that seemed to be correct was marked wrongly by his teacher.

The Primary 3 question was: Mrs Kim gave 5kg of rice to each family. She gave rice to eight families. How much rice did she give in total?

The child’s working of 5 x 8 was marked as incorrect, with the correct answer given as 8 x 5.

Netizens were divided over whether the child’s answer could be accepted.

Parents of pupils who will soon sit the Primary School Leaving Examination (PSLE) are concerned if their child will be penalised for not presenting their working in a certain order.

Mathematics experts and educators weigh in on the issue.

1. Will pupils lose marks in the PSLE maths paper if they do not present the working in a particular order – for example, 5 x 8 instead of 8 x 5?

Maths textbook author and former National Institute of Education lecturer Yeap Ban Har says both answers are acceptable because the working can be 8 x 5kg or 5kg x 8.

He explains that many teachers tend to write eight groups of five as 8 x 5.

“This is not unexpected because the symbolic expression is consistent with the verbal expression in the English language,” he adds.

He says it is more important to ask children what each number represents. “As long as they know the 8 represents the number of bags and the 5 the mass of the rice, their understanding is fine,” he adds.

“While we may have a preference for things to be done in a certain way, what’s important in this case is for pupils to know the meaning of each factor in the multiplication.

“So while some teachers may prefer pupils to write 8 x 5 for the scenario above, 5 x 8 is not wrong,” he notes.

Mr Al-Gene Tan, co-founder and chief education officer of Think Teach Academy, says: “In this question, the positions of the numbers do not matter. It can be marked wrong only if the pupil had written ‘5 x 8kg’ because this would mean the reasoning of the equation is wrong.”

A spokesman for the Ministry of Education (MOE) says the PSLE marking matrix allocates marks for both the working and final answer.

“Marks will be awarded for all mathematically correct workings that demonstrate the requisite knowledge and skills to solve a mathematical problem – regardless of whether the question is fully completed or whether the final answer is inaccurate,” she adds.

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2. How are open-ended questions for the PSLE Science Booklet B marked? Must the answer contain “keywords” for marks to be awarded? Can a child express the answer in his own words, as long as he gets the concept and application correct?

Marks will be awarded as long as “the ideas are expressed clearly, and are relevant and scientifically accurate to the given context”, says the MOE spokesman.

She adds that pupils are encouraged to demonstrate their understanding by using their own words when explaining scientific concepts.

For example, when asked to explain why water puddles on the road are not seen after a while, they can say that the water has “evaporated” or “turned into water vapour”.

“Both replies demonstrate an understanding that water has changed its state,” she says.

The focus of learning science is about developing the ability to inquire, understand and explain phenomena, and not on giving “standard answers” or “reproducing keywords”, she adds.

Mr Tan, from Think Teach Academy, says the crux of the issue is that a child who writes an answer in his own words might not fully or accurately answer the question and, as a result, marks are lost.

“Learning science is not just about understanding the topic. It starts by developing the skills to observe, investigate and explain. Learning to use the right words to describe and explain is part of it,” he adds.

Mr Jayce Or, founder of Germinate Learning, a science enrichment centre, says “keywords” simply refer to the scientific terms that the pupils have learnt in the syllabus.

They will often have to use these terms, for example, “photosynthesis, evaporation and condensation” to answer open-ended questions accurately.

They can use their own words, but will need to know how to describe the concept clearly, he adds.

Mr Or, who previously taught science in primary schools, says PSLE markers have a varied answer key to refer to for marks allocation.

The marking can accommodate a wide range of acceptable answers – from those containing keywords to those expressed in a pupil’s own words, as long as they are clear and accurate.

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3. Why are textbook questions so simple but exam questions so difficult?

The MOE spokesman says the questions in the PSLE are designed with a mix of basic, average and challenging questions to cater to a range of abilities, and gauge each pupil’s mastery.

The PSLE has been kept at a consistent standard of difficulty across the years, with a cap of 15 per cent of questions being classified as challenging, comprising about 15 marks, says the spokesman.

“The majority of questions are accessible to most pupils, with a small number of questions allowing stronger pupils to demonstrate their mastery of the subject,” she adds.

She says textbooks and workbooks also contain questions of varying difficulty, with a small proportion being challenging.

“The purpose of presenting a range of difficulty levels in teaching and learning materials is to assess the understanding of concepts and mastery of mathematical skills,” she adds.

Dr Yeap, the maths textbook author, says even if textbook questions seem basic, teachers will expose pupils to more challenging ones via additional worksheets.

“The best approach is to help students be better problem solvers as opposed to focusing on teaching them particular problem types,” he adds.

Mr Tan from Think Teach Academy says that while the regular primary school curriculum is designed for most pupils to be able to secure a pass grade, the difficult questions exist to differentiate between the AL 1 and AL 5 ones.

Each PSLE subject is scored using eight achievement levels, with AL 1 being the best.

“If PSLE questions are easy, then everyone will do well and it becomes tougher to identify the better pupils from the good ones,” he adds.

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