- #1
member 392791
Out of curiosity, is it the case that math is taught in the typical sequence in the order for which it was discovered?
Is math taught in the order in which it was discovered?
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Discussion Overview
The discussion centers around whether mathematics is taught in the same sequence as it was historically discovered. Participants explore the implications of teaching order on understanding mathematical concepts, referencing historical developments in arithmetic, algebra, geometry, and calculus.
Discussion Character
- Debate/contested
- Conceptual clarification
Main Points Raised
- Some participants assert that math is not taught in the order of discovery, noting that while arithmetic is foundational, the overall sequence diverges significantly from historical development.
- One participant highlights the early teaching of counting, emphasizing that the concept of zero is relatively recent compared to the practice of counting itself.
- Another participant mentions that the teaching of calculus does not reflect its historical discovery, pointing out that modern approaches incorporate concepts like vectors that are much newer.
- A participant argues for a return to teaching geometry in a manner similar to Euclid's original approach, suggesting that this could enhance understanding of real numbers and their historical context.
- There is a mention of personal teaching experiences, with one participant indicating that they taught counting starting from zero, contrasting with the common practice of starting from one.
Areas of Agreement / Disagreement
Participants generally disagree on the teaching order of mathematics, with multiple competing views on how historical context should influence educational practices. No consensus is reached regarding the best approach to teaching mathematics.
Contextual Notes
Participants express varying opinions on the importance of historical context in mathematics education, with some suggesting that understanding the historical order could enhance comprehension, while others argue that the current teaching methods are more effective despite not following historical sequences.
- #2
Vargo
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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
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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.Woopydalan said:
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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Not a big matter but people are typically taught to count starting with "1", NOT "0"!D H said:
- #5
NemoReally
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HallsofIvy said:
That's not how I typically taught my children. They learned to count to the Apollo launch sequences and worked towards zero!
- #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...
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...