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So much of the discussion is around how to pace/sequence the same traditional list of topics (geometry, trig, precalc, calc) but maybe we should be considering

by abeppu 5y ago

So much of the discussion is around how to pace/sequence the same traditional list of topics (geometry, trig, precalc, calc) but maybe we should be considering that these might not be the most important concepts anymore? More people should know stats, and this doesn't need to be strictly sequenced with those other concepts. Yes, integrals show up with continuous distributions, but we don't need to really care that much. But if we had a population that understood confidence intervals, (in)dependence, correlation etc at a conceptual level, would we fall for fewer dubious claims? Discrete math, like enough combinatorics to understand why some families of things that sound simple are huge? Or enough to communicate the idea of a homomorphism? What if our concept of "woke" math introduced posets, and the idea that things can be literally incomparable?

Der_Einzige 5y ago
Not sure why you're being downvotes. Stats and discrete math are sorely underrepresented in high school math education. The harm of this continuing will be extremely high going forward.
YeBanKo 5y ago
Statistics is based on probability and probability is based on set theory and a concept of measure. Discrete probability may do away without calculus. But it needs some basic understanding of algebra. Concept of probability, imo, is very hard to understand. And then you have conditional probability, which fooled even high ranking mathematicians. Allegedly Paul Erdos didn’t get it until a computer simulation was presented to him [0]. I think venturing into statistics may be left for later. I would agree though that combinatorics can be taught earlier and give a good understanding or discrete probability. I don’t see thought how it can be successfully without algebra and calculus. [0] https://www.wired.com/2014/11/monty-hall-erdos-limited-minds/ https://www.wired.com/2014/11/monty-hall-erdos-limited-minds...

by abeppu 5y ago

Der_Einzige 5y ago

Not sure why you're being downvotes. Stats and discrete math are sorely underrepresented in high school math education. The harm of this continuing will be extremely high going forward.

YeBanKo 5y ago

Statistics is based on probability and probability is based on set theory and a concept of measure. Discrete probability may do away without calculus. But it needs some basic understanding of algebra. Concept of probability, imo, is very hard to understand. And then you have conditional probability, which fooled even high ranking mathematicians. Allegedly Paul Erdos didn’t get it until a computer simulation was presented to him [0]. I think venturing into statistics may be left for later. I would agree though that combinatorics can be taught earlier and give a good understanding or discrete probability. I don’t see thought how it can be successfully without algebra and calculus. [0] https://www.wired.com/2014/11/monty-hall-erdos-limited-minds/ https://www.wired.com/2014/11/monty-hall-erdos-limited-minds...