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Is math taught in the order in which it was discovered?

  • Thread starter Woopydalan
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  • #1
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Out of curiosity, is it the case that math is taught in the typical sequence in the order for which it was discovered?
 

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  • #2
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No, it is definitely not taught in the order of discovery. Though in some sense, students must follow the historical pattern VERY roughly, since you basically need to learn arithmetic before anything else. And there are other issues in math where prerequisite knowledge coincides with the order of historical discovery/invention. However, in general the answer is definitely not.
 
  • #3
D H
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Out of curiosity, is it the case that math is taught in the typical sequence in the order for which it was discovered?
Of course not. Just look at how you are taught to count very early on: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... What's that "0" thingy? The basic concept of counting is very, very old, most likely predating writing. The concept of zero as both a number and as a placeholder is only 1400 years old or so. Next you are taught bits of algebra (1000 years old), then geometry (2300 years old), then more algebra, then calculus (400 years old). Note that the way you are taught calculus is not the way it was originally discovered. Somewhere along the way you are taught to use vectors, which is only 100 years old.

Teaching any of the sciences or technology in the order in which they were discovered just doesn't make sense.
 
  • #4
HallsofIvy
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Of course not. Just look at how you are taught to count very early on: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... What's that "0" thingy? The basic concept of counting is very, very old, most likely predating writing. The concept of zero as both a number and as a placeholder is only 1400 years old or so. Next you are taught bits of algebra (1000 years old), then geometry (2300 years old), then more algebra, then calculus (400 years old). Note that the way you are taught calculus is not the way it was originally discovered. Somewhere along the way you are taught to use vectors, which is only 100 years old.

Teaching any of the sciences or technology in the order in which they were discovered just doesn't make sense.
Not a big matter but people are typically taught to count starting with "1", NOT "0"!
 
  • #5
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Not a big matter but people are typically taught to count starting with "1", NOT "0"!
That's not how I typically taught my children. They learned to count to the Apollo launch sequences and worked towards zero! :cool:
 
  • #6
mathwonk
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One case where math instruction does not follow history is in modern geometry courses, which follow Birkohff and base geometry on the real numbers. Historically, Euclid treated geometry first without real numbers (in Books 1-4), and real numbers (as approximations by sequences of rationals), followed (in books 5-6).

This is in my opinion the correct way to do things, as it allows motivation for real numbers, and I try to advocate for a return to this approach when i can. In general although math is often not taught according to the order in which it was discovered, in my opinion much is lost when it is not. The learner sees more clearly where the ideas came from when the historical order, or an approximation to it, is followed.

I.e. the best order to learn in is not always the historical one, but one which might ideally have been the historical order, as Spivak says in his introduction to his Differential Geometry. But many times I myself have understood some concept only after going back and reading the original treatment by the discoverer or the best early expositor, whether it is Euclid, Archimedes, Zariski, Mumford, Kempf, Euler, Lagrange, Poincare, Riemann, Gauss, Goursat, Serre, Grothendieck, or someone else......
 

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