Teaching of Engineering Mathematics

The application of computer algebra software in the teaching of engineering mathematics : 

The application of computer algebra software in the teaching of engineering mathematics Chris Rielly Department of Chemical Engineering Engineering Mathematics Examples and Case Studies Swap-Shop Thursday 29 January 2004, LTSN Engineering, Loughborough University

Acknowledgements : 

Acknowledgements LSTN mini-project:July 2003 - July 2004 Sarah Williamson Rawson Pilon & Greg Ihnatenko(final year students) Engineering Education Centre - Loughborough University Dr. Marie Bassford

First Year Engineering Maths : 

First Year Engineering Maths What we need to achieve revise / re-learn A-level maths topics knowledge gaps increasingly with algebra and calculus practice on a variety of examples introduce some complexity and numbers build maths models for engineering problems real world applications related to Chem Eng sort out algebraic misconceptions assumed linearity, e.g.

First Year Engineering Maths : 

First Year Engineering Maths Problems we face vast range of abilities Straight ‘A’ grade  a few GCSE maths students Semester 1 revision largely comprises definitions boredom / complacency for the bright students too fast for the weak students difficulties with “hard” GCSE material experienced by the whole class algebra arithmetic vs algebra : numbers vs symbols

Widening access to Chem Eng : 

Widening access to Chem Eng other qualifications offer

This year’s experiment : 

This year’s experiment New format 1 lecture + 1 examples class + 1 computing class Lectures using printed notes lists of definitions + workspace for examples concentrate on working examples Conventional / paper based examples classes give practice in algebra by solving problems hand written solutions methods staff support + personal tutorials Computer algebra software (CAS) supervised sessions: prepared worksheets develop maths skills using Maple

White box, not black box : 

White box, not black box Aims of using CAS remove algebraic tedium and concentrate on developing higher-order maths skills solve basic problems, divided into maths steps same methods as handwritten solutions develop understanding / selection of rules develop their maths vocabulary solve more realistic / interesting problems engineering applications interface with numerical methods

Integrated Maple worksheets : 

Integrated Maple worksheets Interactive notes Introduction to the background maths line-by-line analysis of a worked problem graded examples to be solved by the student using line-by-line working and / or short-cuts Supervised computer lab sessions sheets delivered via the Learn Server students work at their own pace staff + PG help available for 2 h per week no assessment (this year) but can use Maple to solve other maths coursework assignments

Why use Maple? : 

Why use Maple? quick-start fairly user-friendly / interactive no programming skills required widely available across the campus lots of material available via www.maplesoft.com and many other sites BUT, much is designed for pure maths students Student packages built-in, for example: rule-based differentiation methods rule-based integration methods ODE solution methods

Semester 1 worksheets : 

Semester 1 worksheets So far … Numbers, variables and algebra Single variable functions Differentiation Integration Emphasis on doing, not simply reading read text and execute Maple commands follow through the worked examples write your own Maple commands to solve some new problems

Worksheet examples : 

Worksheet examples

Worksheet examples : 

Worksheet examples

Worksheet examples : 

Worksheet examples

Semester 1 experience : 

Semester 1 experience User-friendliness many students find that the Maple syntax is cumbersome requires attention to detail (brackets, arguments etc) animations and graphs well-liked templated solutions are OK for some Dyslexic students problems viewing one screen at a time printed versions now available

Improvements required : 

Improvements required Navigation shorter worksheets, but more of them aim to complete ~ one per week (~8 per semester) more hyperlinks between theory, worked examples and problems Maths examples better engineering examples, particularly in algebra, use of units, use of functions effective means for students to check answers assessment and integration with other modules

Conclusions … so far : 

Conclusions … so far Student benefits fun and stimulates an interest in maths improved confidence in applying maths removed algebraic distractions cooperative working Attendance: excellent, even with no assessment Negatives requires a certain level of maths understanding limited benefit to weakest students quicker done by hand (in some cases) not available in Halls / personal use does not save staff time + –