Each year the International Mathematical Modeling Challenge (IMMC) gives students an opportunity to team up with up to three other students in their school to work collaboratively on a complex modelling task which connects the mathematical learning they're experiencing in class with a real-world situation. Once they receive the task, teams have just five days to write and submit a report.

This year's problem, The Best Hospital, asked students to consider the factors that contribute to variation in hospital quality and devise a decision-making model that would help a prospective patient to choose a hospital under circumstances other than an emergency situation.

For the 2018 IMMC, 75 teams from across Australia submitted a final report. That's up from 45 in 2017.

Teams were expected to prepare a written report up to 20 pages long, plus a one-page summary, and a user-friendly memo (of up to two pages long) that would help a non-expert use the team's results to make a decision about which hospital to choose. The IMMC website provides useful instructions, rules and advice about preparing a team report and some additional recommendations on how to submit the best possible report.

The Best Hospital was a particularly challenging problem given the complexity of the context, the range of different variables that might be relevant, and the difficulty of obtaining data to analyse the possibilities. Successfully devising and testing a decision-making model and evaluating the stability and usefulness of this model were also challenging aspects.

Observations from the Australian judging panel

The fundamental approach to the problem:

• Many teams mixed emergency care into their considerations even though the problem statement directs attention to non-emergency situations.
• The 2018 problem assumed the patient's condition was known. Therefore, factors such as timeliness or accuracy of diagnosis and time needed to rush a patient to hospital by ambulance weren't relevant.

The need to devise a model to compare hospitals, not seek factors that might reduce avoidable deaths:

• Many teams did interesting work to identify factors that affect mortality rates, and other desirable features in a treatment environment. The better team reports went on to apply the results to inform comparisons among hospitals.

The extent to which team reports provided a two-page memo that would help a non-expert choose a hospital:

• Better team reports presented a memo giving a very clear guide to choosing, based on a model that they thoroughly understood and therefore could properly communicate.

Definitions, and the testing and evaluation of models:

• The use of real data is usually preferred (when it is available). The better reports looked for a way to obtain data for this purpose, or at least simulated data that could be used.
• Important terms and concepts were defined and treated consistently throughout the investigation.

How the judging panel used the assessment criteria based on the IMMC Checklist:

The five areas of the panel's special interest in evaluating the 2018 modelling efforts.

Benefits for students

Team advisors, generally a teacher, responding to a survey following the completion of IMMC 2018 pointed to many benefits to the students coming directly from their participation: building higher-order thinking skills, creative and critical thinking, exposure to real-world maths applications, using team work and drawing on experiences and strengths of other team members, planning and time management, sharing responsibilities, learning to communicate mathematical ideas in a meaningful way, growth in confidence, greater engagement with mathematics and increased enthusiasm.

We think that opportunities for those experiences and to develop those kinds of skills are worthwhile, in spite of the challenges involved.

The international judging panel named Australia's Radford College from Canberra as the team who submitted the best report. The Radford students, along with other international finalists, will be attending an award ceremony in Melbourne this week.