An international mathematical modelling competition is helping to produce students who can not only solve problems set by others, but are able to identify and address problems themselves.
One of the reasons so many people feel negative about their school mathematics experience, and perhaps about their mathematical knowledge and abilities more generally, is that opportunities to see how maths can be used in the lives of ordinary people are often not pursued with much vigour and rigour in school. Without that connection, it is hard to see the relevance of mathematics.
The International Mathematical Modeling Challenge (IM2C) has been established to encourage a far greater awareness of, and willingness to explore, possible connections between challenges that people confront, and the mathematics they know or could learn.
Coordinated in Australia by the Australian Council for Educational Research (ACER), the IM2C is a competition for teams of up to four students from secondary schools around the world that sees students use their research, mathematical and creative abilities to develop a mathematical model to address a real world problem.
Experiencing mathematics as a mental discipline, with its set of tools and techniques that can be used to explore something that may not be well defined, is a novel experience for many students. They may start out thinking there must be a single correct answer (something their previous maths experience may have led them to expect) but quickly realise that the real world is often much more messy than that.
Consider these real-world problems:
- What is the best location to hold a three-day international meeting of participants travelling from different parts of the world in order to minimise the jet lag and maximise the productivity of participants at the meeting?
- Which hospital would be the best choice for non-emergency medical treatment based on doctors’ experience levels, mortality and other factors?
- How can the organisers of an athletics competition minimise their financial risk as they consider offering incentive payments to attract top-level competitors?
- What might be a sustainable population for the Earth under current conditions? How would that differ based on projected changes to policy and environment?
This last problem, from the 2019 IM2C, was far more open-ended than those of previous years, seeking analysis and investigation to understand different relevant factors and how they might interact to affect the solution.
Beyond mathematical learning
Difficult problems in society are almost always tackled by groups of people with different areas of expertise. By mobilising students in teams, the IM²C replicates real-world conditions; requiring collaboration and contribution from different skill sets, perspectives and methods to achieve overall success.
When students work together in a task-focussed team, the possibility exists for a different kind of educational experience. Students encourage and learn from each other. Roles and responsibilities can be shared, so that individuals who might otherwise tend to sit back and observe may be taking a much more active role for the first time. The opportunity to think hard about how a real-world context can connect to mathematical ideas and techniques is often very challenging and stimulating.
Students must work together to connect the problem with the mathematics they know, or learn new mathematics that could be relevant to investigating the problem. They need to define which parts of the situation they will focus on. They need to identify relevant variables and make some assumptions – perhaps in order to simplify an initial approach before later refining and expanding their direction. This is closer to the way mathematicians actually work, and is a long way from the atmosphere and expectations often established in school mathematics. And finally, their communication skills come in to play – they need to talk, to read, to write, to cooperate in the preparation of a report, and sometimes to present their report and work to others.
As 2019 winning team advisor Bhavya Bhalla tells it, the IM2C shows students that mathematics is more than algebra and numbers: it shows that maths can be used to find the answers to problems in real life.
‘My students now see themselves as mathematicians, not just as students who do mathematics,’ Ms Bhalla said. ‘They were able to build on their knowledge and skills, and now identify themselves as successful mathematical thinkers.’
Through participating in the IM2C, Ms Bhalla reported that her students learnt how to communicate their ideas and developed their critical and creative skills, analytical skills and group working skills.
‘It was amazing to see how the groups worked as a team, learning from each other and supporting each other, and finally successfully completing the challenge as a team,’ Ms Bhalla said.
In providing an opportunity for peer-based learning, the IM²C also helps to incorporate and reinforce the Australian Curriculum proficiency strands – understanding, fluency, problem-solving and reasoning – as students work together, communicate with one another and employ creativity, reason and logic to successfully solve the defined problem.
How IM2C works
The IM2C has been held annually since 2015 and now involves more than 50 countries. It is overseen by an international organising committee, which includes an ACER Principal Research Fellow.
The international organising committee sets the challenge problem and contest period, usually from mid-March to early May, and a competition centre is established within each participating country to coordinate the activities.
Teams of up to four students from a school, together with a team advisor, register online to enter the IM2C. Teams then choose a period of up to five consecutive days within the competition window in which they can work together on the centrally set problem. They then write and submit a report about their solution.
Each country selects two entries for international judging by an expert panel. Entries are designated as Outstanding, Meritorious, Honourable Mention and Successful Participant, with appropriate plaques and certificates given in the name of students, their advisor and their schools. Outstanding team members and their advisers are funded to attend an international awards ceremony that is held in a different country each year.
IM2C in Australia
Australia has participated in the IM2C every year since 2016, with ACER acting as the competition centre, guided by a national advisory group of experts in mathematics, modelling and education. The national competition phase is open to all schools and the competition window is shortened – it takes place within Term 1 in all states and territories so that the national judges have time to select the two entries for submission to the international judging panel. National awards are given in each of the same categories as the international judging (Outstanding, Meritorious, Honourable Mention and Successful Participant).
One of the most exciting features of the IM2C in Australia is the way students of all kinds have been able to take part. Almost the same number of girls and boys have participated each year, students have been involved from Year 7 to Year 12, teams have come from schools in all states and territories and all school sectors, and from schools in remote, rural, urban and metropolitan settings.
We would expect that older students with more mathematical knowledge at their disposal might tend to produce more thorough analysis and higher quality reports. However, a team of Year 9 girls from Lyneham High School in the ACT was among the national finalists in 2017, showing that the prizes here are not restricted to the senior year students.
The rapid growth of the IM2C in Australia suggests a widely perceived benefit of participation as schools seek to make their mathematics programs more effective. Once schools get involved they generally continue their involvement, and some schools are now seeking ways of building the opportunity to participate as a regular part of their school program. Others have made efforts to build mathematical modelling consciously into their maths programs
Table: Australian participation in IM2C
With four years of participation in the IM2C, we are seeing evidence that students and schools are learning about mathematical modelling and using their developing skills to great effect. A number of instances have now occurred where teams that participated in one year returned the following year and performed even more strongly. In 2019, both of the top teams contained team members who had participated in 2018. Experience with modelling makes a difference.
Australia’s top mathematical modellers
- Brisbane Boys College*, Toowong, QLD: James English, Ethan Waugh, Xavier Catford and Ometh Rajapakse, with team advisor Chicri Maksoud.
- Lyneham High School, Canberra, ACT: Khubaib Qureshi, Emily Brown, Sreeya Das and Junwi Bai, with team advisor Bhavya Bhalla.
*Brisbane Boys College went on to receive a ‘meritorious achievement’ award at international judging.
- Radford College*, Bruce, ACT: Ryan Stocks, Brianna Wiseman, Emily Li and Stone Sima, with team advisor Kym Palfreman.
- Baulkham Hills High School, Baulkham Hills, NSW: Clement Luong, Ezra Hui, Laeeque Jamdar and Alexander Tan, with team advisor Elizabeth Sree Kumar.
*Radford College went on to receive the only ‘outstanding’ designation among the 55 team entries at international judging.
- John Monash Science School, Clayton, VIC: Dylan Sanusi-Goh, Alex Socha, YiJie Neo and Paromita Mitchell, with team advisor Luke Bohni.
- Perth Modern School, Subiaco, WA: Indira Senthil Ajeetha, Yuqing (Sunny) Lu, Mehul Aggarwal and Kartikiya Bisht, with team advisor Glen McClelland.
- Trinity College, Perth, WA: Samuel Carbone, Kayvan Gharbi, Farruh Mavlonov and Trong Nguyen, with team advisor Ian Hailes.
- Perth Modern School, Subiaco, WA: Alan Cheng, Virinchi Rallabhandi, Alex Rohl and Daniel Ho, with team advisor Glen McClelland.
Visit the IM2C website to find out more and register your interest in the next challenge. https://www.immchallenge.org.au/