*A National HE STEM Project (with 13 Partners across 8 Universities)*

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:

“The ability to solve physical problems using mathematical modelling and mathematics are invaluable attributes for new undergraduates entering an engineering industry” | “A key attribute for engineering graduates is their ability to apply theoretical knowledge to a real problem to create a solution. Modelling skills are key to this process.” |

Dr Alan Stevens, Rolls Royce, Maths Modelling Group |
Professor Barry Clarke, President (elect), Institution of Civil Engineers |

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.

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

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?”

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'!

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

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!

Original Partners (2010) |
Leeds | Physics and Astronomy | Mike Savage |
---|---|---|---|

Manchester | Mathematics | Louise Walker | |

Keele | Mathematics | David Bedford/Martyn Parker | |

UWE | Engineering | Kevin Golden | |

2010/2011 | Leeds | Civil Engineering | Duncan Borman |

Leeds | Mechanical Engineering | Mark Wilson | |

Recent Partners (2011) |
Bradford | Mathematics | Jon Purdy |

Leeds | Chemistry | Annette Taylor | |

Leeds | Electrical Engineering | Bob Kelsall | |

Leeds | Applied Mathematics | Thomas Wagenknecht | |

Loughborough | Mathematical Eduacation | Paul Hernandez-Martinez | |

Portsmouth | Applied Phsyics | Chris Dewdney | |

Swansea | Mathematics | Andrew Neale |