Opening photo of co-author Owe’s colourful toenails – a different colour for each of the 10 Delta conferences!
Photo available here
Paper available here
Traditionally, engineers demand from mathematics fluent use of techniques.
With technology, is this as important as conceptual insight?
Procedural (mechanical) knowledge in mathematics, e.g. ‘For this function, what is the equation of the tangent line at this point?’
Conceptual knowledge link relationships between verbal, visual, symbolic representations. E.g. Match graph of derivative to a written description.
SA – Sweden project.
Quantitative analysis: Junior students in 3rd semester; senior students in 7th semester.
Qualitative analysis: interviews with Swedish and SA engineers.
Swedish engineer
- Procedural maths needed as a basis for mathematics (concerns that he understood procedural knowledge as basic maths background for applications, equivalent to learning the language of maths).
- Conceptual understanding = engineering judgement, broader than maths.
- New engineers should be able to be independent, deal with a whole problem, be self-confident.
SA engineer
- Has used very little of school maths
- Doesn’t value procedural fluency
- His university courses were very procedural
- Values conceptual knowledge
- Test of materials: plot results, extrapolate. He sees fitting the graph as conceptual work.
- Procedural work seen as technician’s work, not engineer’s.
- Distinguishes between brilliant (can do procedural) and bright guys (understand conceptual). He prefers the bright guys.
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