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So much dialogue is around how to pace and sequence the traditional math curriculum (geometry, trig, precalc, calc). Are those still the most important things t
by abeppu 5y ago
So much dialogue is around how to pace and sequence the traditional math curriculum (geometry, trig, precalc, calc). Are those still the most important things to teach? And do they need to be taught and tested through working through the same calculations framed in the same narrow scenarios? When's the last time you solved a quadratic equation or did integration by parts in the real world? The concepts may be important, but is chugging through trigonometric identities really helping kids?
I use the concept of a derivative often, and I'm glad it enriches my understanding of the world even if I calculate derivatives almost never. But there are so many other useful math concepts which might be better to communicate than just doing exercises around techniques (e.g. can you apply the quotient rule correctly).
Concepts I wish we emphasized instead:
- stats: uncertainty, confidence intervals. (In)dependence of variables. Correlation.
- discrete math: enough to communicate the concept of structure being preserved. Enough combinatorics to understand why some families of structures might be huge. Basic concepts around graphs.
These ideas don't necessarily need to be sequenced. You can deal with plenty of integrals while learning stats, but you don't have to.
What if our concept of woke math involved introducing posets and relations and cases where comparison isn't possible? What if we stopped talking about high school math as a single ladder and consider it more as a landscape to explore? By desequentualizing topics, maybe upper class hs students can actually catch up by taking more than one math class at a time?
- legerdemain 5y agoShow me an American university that doesn't spend the first two years of a STEM major's life on the three-semester calculus sequence, linear algebra, and ordinary differential equations, and I will then come up with a secondary school math curriculum targeting admission to such a program.
- abeppu 5y agoActually, the "S" is pretty broad and I'm guessing there are multiple majors at reputable universities that don't require all that.
- legerdemain 5y agoSure, if your S is sociology, your math requirements will be 0-2 units of calculus and a statistical methods course taught in the department. The secondary school preparation for such a program is called "stop taking math in 11th grade."
- abeppu 5y agoYou're being snide and not actually constructive. E.g. here are requirements for molecular and cellular bio at UC Berkeley, which requires a 1 year sequence covering calculus, stats and combinatorics. Linear algebra and differential equations are not requirements. http://mcb.berkeley.edu/undergrad/major/major-requirements/requirements http://mcb.berkeley.edu/undergrad/major/major-requirements/r...
- legerdemain 5y agoThat sounds like it requires a high-school math sequence that prepares students for college calculus, doesn't it? Edit: You hardly contradicted me. My claim was that the math requirements of non-engineering science majors were 0-2 semesters of calculus and a course on statistical methods. You added combinatorics, which I usually just see taught as part of that applied methods course, rather than a stand-alone semester of mathematical combinatorics (I welcome correction). This is exactly what the current secondary math curriculum leads up to: calculus.
- diffeomorphism 5y agoThat completely contradicts your point. > my claim was.. No, it wasn't, but nice try.
- legerdemain 5y agoYou can literally read what I claimed, verbatim, a couple messages above. Please do!
- hintymad 5y agoCan you really learn stats without calculus first? How would you explain continuous probability to students? If you're talking about descriptive stats and the parts that do not require calculus, then high school will teach them. As for geometry, isn't it the only course that teaches kids rigorous proof? It helps students build math maturity and is a segway into other type of proofs used in discrete maths.
- zbobet2012 5y agoI'll echo this. Everyone says "learn stats not calculus", but... statistics is based in calculus. Even discrete probability relies on a lot of infinite series. I mean we should definitely teach basic probability and combinatorics early on, but my recollection was that is the case.
- koheripbal 5y agoYou don't need much calculus to teach probabilities. So little that you could cover what you need in the first day/week.
- threatofrain 5y agoThe central point of contention is not whether the Common Core, which already emphasizes depth over rote learning, ought go even deeper. The contention is also not over whether we ought have more combinatorics or Linear Algebra in the curriculum, and nor whether schools ought be able to pursue CS or Statistics programs — they are already free to do so, although schools across the entire nation have largely failed to persuade universities as to the reliability of their programs, and thus they rarely count for credits earned or requirements met. Instead, the central question is whether all students ought be in the same class up until the senior year, regardless of their individual ambitions or abilities in math. For context, Californian math classrooms may have ratios of 1 teacher to 40 students, and classroom sizes are not penalized past middle school. This is the context under which teachers must somehow address cohort variability, the same context under which we might somehow expect an Algebra teacher have units planned for those who are ready for Geometry. This is not a realistic assumption of teacher competency. Equitable Math would be a huge win for private schools and after-school programs such as RSM.