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

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

• Chris Rielly
• Department of Chemical Engineering

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Acknowledgements

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

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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.

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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

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Widening access to Chem Eng
offer
other qualifications
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This years 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

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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

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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

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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

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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

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Worksheet examples
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Worksheet examples
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Worksheet examples
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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

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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

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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