AUSTIN, Texas (AP) — The Texas Board of Education gave preliminary approval Thursday to dropping algebra II as a requirement for high school graduation.
Seems like they’re going the wrong direction of what Paul Lokhart wrote should be done in A Mathematician’s Lament.
I loved reading then when I found it awhile back!
[Trigger warning: Opinion below:]
On one hand, I think that standardized testing should be severely limited like it is in Sweden (hell, let me just suggest most of their system should be put into place here), and that will help a huge amount (not just in math)!
However, should I never have gotten it in school, I never would have discovered it myself. I think that he’s claiming that higher-level mathematics should never be included in the curriculum by default, since no human being is going to get by without arithmetic, some basic logic, and some problem solving that comes with Algebra I and II.
Honestly, I’d be completely okay with removing trig (and most geometry) from the curriculum entirely since they’re rather archaic, and replacing with stats, matrices, discrete math, etc.
The distrust of mathematics has more to do with how it’s taught than anything else. What’s taught is almost exclusive from how math actually is — it’s not about arbitrarily finding x and whatnot. There’s usually no (relateable) context. As such, students get the idea that mathematics is all about arithmetic and pointless trigs proofs. Lord knows I did.
As such, in the vein of art, teach math as guided self-discovery. Once students have the basics down (basic operations, finding x in a linear equation, etc), give them topics to work on rather independently. But, I haven’t given this too much thought, so, take it with a grain of salt.
[Large opinionated “rant” following]
Yes, testing and the huge focus on getting the next grade is a problem with the way kids learn in general, and not just math.
I agree about removing trigonometry - today it’s more about almost mindless manipulation of a few memorized identities than anything else. Geometry I’m not so sure about - it seems like the beauty is almost reachable, with some change in methodology of teaching, to remove it completely.
I think one area that would do a great job in teaching kids how interesting math really is (and how non-repetitive it is) is combinatorics. With simple and elegant arguments without fussing about notation at first that it has, students can have a chance to actually explore for once and see the beauty of simple thinking. Combinatorics (and discrete math in general) is something that is practically never touched upon in school.
At higher levels stats and matrices (in context, not just doing Gaussian elimination and finding determinants for no apparent reason, as it is done here in India) would be wonderful. Thanks to the handling of statistics in the textbooks here, I was convinced statistics was essentially data accountancy for years till a course in college.
Yes, and there’s direct evidence for this being the source of distrust in the countless internet memes and images poking fun at the artificial “word problems” found in textbooks.
While I’m not sure if I entirely agree with Lockhart’s description of math as an art in the same vein as music, painting, and the other traditional art forms, I do like his point that the whole problem is that people view mathematics as being “useful” in a practical sense. Viewing it primarily as an intellectual or artistic activity with some nice side-benefits would in itself help fix the mindset of teaching mathematics.
Self-guided discovery is a great description. But yeah, it’s not clear how one might implement it practically in such a wide variety of classroom settings. I certainly can’t imagine any of my teachers following such an approach, as much as I would love too.
That became longer than I expected.
No, it’s quite alright! I agree with pretty much everything you said. I know I did some very very basic combinatorics when I was in high school, and even those problems were at a middle school level (I even took some problems out of Alan Tucker’s “Applied Combinatorics”, and once I pointed out that “There are 5 possible choices for the first slot, how many for the next slot?” etc., I got a couple of 8th graders to do combinatorics for extra credit. I’m thinking it could be even better than that, since it was all done over the course of about 20 minutes.