Mathematical Modelling and Problem Solving

1. Project Aims and Rationale

This HE STEM project "Mathematical Modelling & Problem Solving" aims to equip first year STEM undergraduates with a high level, transferable skill – “the ability to solve problems in science and engineering by setting up mathematical models and using mathematics”

Such skills are highly valued by both employers and researchers:

Thirteen Project Partners in 8 Universities

There are currently 13 HE STEM Departments (Physics, Mathematics and Engineering spread across 8 universities who fully recognise the importance of modelling and problem solving skills for STEM undergraduates and are now actively engaged in introducing such skills into their curriculum in ways that are most suitable for their needs. This approach has enabled the 13 departments to implement tailored approaches based on agreed concepts.

There are, in fact, several ways of introducing modelling that are particularly appropriate for engineering, applied mathematics and physics students, of which Newtonian mechanics is just one.

2. Mathematical Modelling

What is a model?   What is Modelling?   What has modelling got to do with problem solving?

The concept of a “model”

This London tube map generally comes in useful for visitors who need to get around the capital.

The map is in fact a model in the sense of an approximation to reality; one which has the essentials that the traveller needs to know – tube lines, tube stations, main line stations...

So a model is an approximation or representation of reality which is useful for the task or problem in hand i.e. “how to plan a route?”

Modelling is a process that begins once a problem has been formulated

In the following example; the aim is to move (pull) a heavy object across rough ground with the least effort!

One interesting question/problem would be:   What is the best pulling angle?

The next step is to 'set up a model'!

There are 2 distinct modelling skills:

Setting Up a Model

The idea of “setting up a model” is to convert a real problem into a mathematical problem

Setting up a model involves:

• Making assumptions
• Drawing a diagram
• Introducing variables
• Applying a law or principle

Multi-Stage Modelling

Starting with a real problem, multi-stage modelling involves the execution of a full modelling investigation by following the stages of a multi-stage modelling cycle

• Setting up a model is the first stage of the modelling cycle.
• The second stage is to solve the mathematical problem and
• The third is to interpret/validate the solution
• Having gone around the cycle once, it is often necessary to seek an “improved solution” by refining the model and repeating the process again – and perhaps yet again!

3. Project Partners

4. Project Reports

5. Evaluation

6. Examples of students

7. Bank of Modelling Problems

8. Videos

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