Sharing an e surprise with kids after a question from Sam Shah and a comment from Steven Strogatz yesterday: https://mikesmathpage.wordpress.com/2019/03/02/sharing-an-e-surprise-with-kids/ … #math #mathchat cc: @samjshah @stevenstrogatz
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Replying to @mikeandallie @samjshah
I'm open to being persuaded, as I always am! If e emerges naturally in an activity and is well motivated, I have no objection to showing it before calculus. My complaint is that it too often seems to come from nowhere. Since e always involves limits, IMO it belongs in calculus
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Arguing against myself, my reasoning above would suggest that, by the same token, pi does not belong in geometry since it too relies on limits and hence on calculus. Yet we all include pi in geometry class. So maybe I'm going too far by banishing e from Alg 2?
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Replying to @stevenstrogatz @samjshah
At least part of why I'm happy to share more advanced math ideas (however defined) with algebra 2 kids is that algebra 2 has reputation for being dull and soul crushing that taking a risk here and there with something advanced even if it isn't fully motivated seems ok.
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Surely nothing *should* be less dull and less soul-crushing than a second course in algebra, for algebra is vast and marvelous. I can't help thinking that the right approach, especially with young kids, is to exhibit the marvels in countless concrete examples, and stand back.
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Replying to @MathPrinceps @mikeandallie and
One phenomenon of extraordinary depth and power with which a second course in algebra ought to deal is the intimate analogy between polynomials and integers (and between rational functions and fractions.) How about Bezout's theorem for polynomials? How about Pade approximants?
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So many wonders to choose from! And, again, one has the great past masters to look to -- both for broad-strokes direction, and for tactical brilliancies in pedagogical execution. Read Euler, read Euler, he is the master of us all!
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