Solving real-life problems with maths

NJC students (from left) Liu Zimu, K. Mutthu Lakshmi, Megan Wee Rui En and Shi Lecheng collected data in an attempt to construct a relationship between the diameter of the base of a tree and its height. Such activities push students to go beyond the
Students from Raffles Girls’ School used various techniques to create bubbles. They also collected and analysed data from the activity as a way of applying mathematical concepts in real life. Mrs Caroline Tng, assistant head of the school’s maths department, pointed out the other skills they learn in the process, such as logical reasoning, communicating ideas and investigating. ST PHOTO: NG SOR LUAN
NJC students (from left) Liu Zimu, K. Mutthu Lakshmi, Megan Wee Rui En and Shi Lecheng collected data in an attempt to construct a relationship between the diameter of the base of a tree and its height. Such activities push students to go beyond the
National Institute of Education’s Associate Professor Ang Keng Cheng (front row, right) has been working with teachers, including NJC staff (back row, from left) Ling Hwee Cheng, Chung Yeong Hui, Tjhin Ke Ming, Jason Lee Jian Hao, Muran Wang and Mr Kester Wong Yew Chong (front row). ST PHOTO: JONATHAN CHOO
National Institute of Education's Associate Professor Ang Keng Cheng (front row, right) has been working with teachers, including NJC staff (back row, from left) Ling Hwee Cheng, Chung Yeong Hui, Tjhin Ke Ming, Jason Lee Jian Hao, Muran Wang and Mr K
NJC students (from left) Liu Zimu, K. Mutthu Lakshmi, Megan Wee Rui En and Shi Lecheng collected data in an attempt to construct a relationship between the diameter of the base of a tree and its height. Such activities push students to go beyond the traditional syllabus. ST PHOTO: JONATHAN CHOO

Building maths models from data is helping students think outside the box

Last month, Raffles Girls' School (RGS) student Marsha Shahrin and some friends played around with dishwashing liquid and water to create bubbles. "Our aim was to create the most number of bubbles with the least number of tries," said the 16-year-old.

The activity was part of a series of year-end modules that the school introduced to Secondary 4 students four years ago. Students learn how to collect empirical data for analysis using data loggers - devices that record data - and use software to create virtual models, for instance.

Some schools are adopting such methods - known as mathematical modelling - in efforts to help students see the power of maths in solving real-life problems.

This includes deciding how to maximise one's wealth with a $300,000 prize or coming up with the best location on an island for a ferry terminal for tourists.

A new online resource - www.mathmodelling.sg - launched in September by a National Institute of Education (NIE) professor will give teachers greater support in teaching and learning resources.

Associate Professor Ang Keng Cheng, from NIE's mathematics and mathematics education academic group, who along with two other researchers came up with the website, said schools are recognising the value of maths modelling.

Unlike typical maths questions that have one right answer, maths modelling begins with a real-world situation or problem, he said.

HANDLING UNCERTAINTY

Very often in our maths classes we have only one answer. But in real life your answer depends on a lot of factors. We want students to learn that and to deal with uncertainty.

MS LING HWEE CHENG, mathematics head of department, National Junior College.

These scenario-based tasks are more open-ended, and train students to think more critically, said Prof Ang, who has been working with teachers over the last decade to use maths modelling.

These schools include National Junior College (NJC), RGS, Assumption English School, Ngee Ann Secondary, Dunman High School and Jurong Junior College. Some integrate maths modelling as part of lessons, projects or enrichment activities, while others have organised competitions where students from various schools are given tasks to solve.

Schools in places like China, Australia and Germany have also used maths modelling, which tends to be taught at the university level.

The maths modelling process, said Prof Ang, develops skills such as analysing data, coming up with equations to represent the relationships between variables and using software to run simulations.

"These are skills that we need moving forward in the information technology age," he said.

Prof Ang, who holds a PhD in applied mathematics from the University of Adelaide, said: "I remember during one of my university courses on advanced hydrodynamics, the lecturer asked us how a jumbo jet can stay in the air when it's so heavy.

"It's something we don't even think about. Maths is actually very powerful. It involves concepts like vortex, thrust and having a streamlined body."

NJC, which uses maths modelling as part of its assessment, encourages students to think beyond the traditional syllabus.

Said Ms Ling Hwee Cheng, NJC's head of department for mathematics: "Very often in maths classes, we have only one answer. But in real life, your answer depends on a lot of factors. We want students to learn that and to deal with uncertainty."

Students agreed that maths modelling exercises were more complex than pen-and-paper questions.

NJC student Megan Wee, 16, who did a research project on the spread of forest fires with her classmate, K. Mutthu Lakshmi, said: "In the process, we ran several hundred simulations over six months. We divided land on a map into grids and calculated the possibility of fire spreading to the next grid. There were so many factors such as wind direction and type of vegetation."

Said Marsha: "Maths modelling goes beyond the basics. It's an accurate test of our mathematical knowledge. It's not something you can study for or keep practising."

Mrs Caroline Tng, assistant head of RGS' maths department, said: "The focus is on the thinking behind maths concepts - formulating problems, making assumptions, interpreting maths solutions in the real-world context.

" The skills they learn - logical reasoning, communicating ideas, investigating - are also more related to what the girls will do in the future."

Said Prof Ang: "Besides maths skills, students learn perseverance through trying again and again. These tasks are so open you don't even know if there's an answer."

A version of this article appeared in the print edition of The Straits Times on November 13, 2017, with the headline 'Solving real-life problems with maths'. Print Edition | Subscribe