Senior Mathematics teacher Mrs Lily Tan introduces a decoding strategy to help her pupils with mathematical word problems.
When Mrs Lily Tan, a senior Mathematics teacher at Si Ling Primary School, noticed that many of her pupils had difficulty solving mathematical word problems, she observed that one reason for this was that the mathematical concepts tested were often embedded within a chunk of text. She decided that she would find ways to help her pupils in this area.
In the course of her research, Mrs Tan came across an article published in 2008 by American educator Ms JaLena Clement, "Does Decoding Increase Word Problem Solving Skills?" [PDF]. This paper was based on Ms Clement's action research study of her seventh grade mathematics class, and she proposed using decoding as a strategy to improve problem solving skills.
Mrs Tan tested this strategy with two Primary 3 classes last year and the classes' average mean score in Mathematics improved by 24 per cent. These results were promising enough that Si Ling Primary School decided to implement the decoding strategy to the rest of the school this year.
This is how decoding works when applied to mathematical word problems:
By decoding the vocabulary used in a mathematical word problem, pupils can more readily understand how to solve it.
Investigating mathematical problems
Mrs Tan divides her class into groups of four to solve the word problems together. Before giving them the problems, she goes through the key mathematics vocabulary related to the topic. For example, during a recent lesson with her Pri 6 class to revise the topic of percentage, the related vocabulary were words such as "discount", "cost price", "selling price" and "profit".
Each group of pupils is then given the mathematical problems and a basket of markers. Mrs Tan explains that her pupils are taught how to systematically solve a problem using the problem-solving model laid out by Hungarian mathematician George Pólya (as explained in his classic text
How to Solve It
- Do a first reading of the problem to get a general idea of the story.
- On the second reading, apply the decoding strategy:
- Red marker: underline the key operation words.
- Blue marker: circle the information.
- Green marker: underline the question deliverables.
- Optional: draw arrows to indicate connections between the highlighted words.
- What heuristics (problem-solving techniques) should be adopted to solve this problem?
- Does this answer make sense?
Mrs Ong found that using decoding helped her pupils to improve their mean Mathematics results.
Says Mrs Tan of this approach, "By taking things step by step and bringing decoding into the picture, we are making things more bite-sized for the pupils so that solving word problems becomes more manageable for them. This boosts their confidence in solving challenging questions. "
For Pri 6 pupil Toh You Chin, this decoding technique has helped to improve her mathematics score. "My Maths marks were around 50, but after learning decoding, I am scoring around 70 for this subject," she says with a smile.
Her classmate Dylan Goh eagerly waves his red marker. "I like to decode during Maths lessons. The colours make the questions look more fun, so I'm more motivated to try and solve the problems!" he admits.
In class, pupils work together in groups with coloured markers to improve their understanding of mathematics-related terms.
Another classmate Yeo Zhan Xiong adds that during timed assessments, he usually doesn't have the time to use the coloured markers. Instead, he would uses a pen or highlighter to underline the key terms. This helps him to decipher the word problems more quickly. "The decoding practice we do in class makes the key information 'pop out' during tests and exams," he explains. He and his schoolmates in Pri 6 describe decoding as their "secret strategy" to overcome the challenges of Math word problems.
Ms Jacqueline Oh, the school's head of department for Mathematics, observes that generally, pupils who have learned to 'decode' are making less careless mistakes in the subject. "It takes a while to see these improvements because the decoding process is very much a habit of the mind. But once pupils get the hang of it, many of them find this technique very useful," she says.
As Mathematical word problems make up 60 per cent of the overall Mathematics examination in the PSLE for merged stream pupils, pupils who are weaker in English often find such problems a challenge. To this, Ms Oh says that the teachers will constantly review the mathematics vocabulary with their pupils so they can apply the decoding strategy effectively. She adds, "If anything, it's a great technique for a pupil to use when he or she gets stuck on a word problem."