An engineer's approach to the quadratic formula

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Discussion Overview

The discussion centers around the understanding and application of the quadratic formula from an engineering perspective, contrasting memorization with deeper comprehension. It explores the implications of simplification and approximation in engineering practices, as well as the educational approaches to teaching these concepts.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant highlights the importance of understanding the quadratic formula beyond mere memorization, suggesting that true comprehension is essential in engineering.
  • Another participant notes that the original derivation of the quadratic formula may be more accessible and less mentally taxing for students, implying that educational methods could be improved.
  • There is a suggestion that simplification and practical forms of mathematical results are crucial for effective engineering design, which may not be adequately taught at the university level.
  • A claim is made that "Engineering is the art of approximation," advocating for the explicit teaching of approximation techniques in engineering education.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of current educational practices regarding the teaching of mathematical concepts in engineering. There is no consensus on the best approach to teaching the quadratic formula and its applications.

Contextual Notes

Limitations in the discussion include assumptions about prior knowledge of students, the effectiveness of traditional teaching methods, and the applicability of simplifications in various engineering contexts.

Who May Find This Useful

Readers interested in engineering education, mathematical applications in engineering, and the philosophy of teaching complex concepts may find this discussion relevant.

DaveE
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I stumbled across this article from decades past written by the best EE instructor I ever had. I thought it might be of some passing interest to others in highlighting the difference between memorizing a mathematical result vs. truly understanding it. The essence of engineering, in effect. We all know the quadratic formula, but do you ever really think about what it means, how it works in practice?

https://authors.library.caltech.edu/63245/1/00683365.pdf

BTW, this site has some really good papers, most of which you can read for free.
 
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Possibly because that 'original' version could be derived / solved without melting us hapless students' brains ?

Also, yes, it was expected you'd hand-calculate it, possibly with aid of slide-rule, four-figure logs, six if fussy.
"TEN significant figures ? You doing orbits, tide-charts or something ??"

Akin to way the generic 'Standard Deviation' formula does not suit use in a computer algorithm, requiring loops through stored data. Collecting the 'needful' as data entered is much faster and more accurate...
 
Nik_2213 said:
Possibly because that 'original' version could be derived / solved without melting us hapless students' brains ?
Yes, it's easy to remember a solution by 'completing the square'. His point is, both here and more generally in engineering, that you aren't done with your derivation until you get the result into a simple, practical, form. Simple forms increase understanding and allow you to make good decisions in design efforts. Things like simplification with good approximations for example. This isn't often taught to university level students they're stuck with their high school "hapless students' brain version".

He used to say "Engineering is the art of approximation", which I think is true. It should be explicitly taught, as he did at CalTech. He has several more complex versions like this in Analog EE analysis. I like this one because everyone uses the quadratic formula and everyone thinks they know all about it from high school.

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