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I think for three years I watched Robby Suave at The Hill tee off on the Teacher's Union for fighting against phonics based teaching, despite all the science and decades of outcomes showing that whole language teaching is a miserable failure. But teachers hate it, because it's rote and boring, and they insist on narcissistically avoiding all unpleasant aspects of their job. Despite being responsible for the education of our next generation. So their union fights phonics based teacher curriculums tooth and nail.
At least that's what Robby's reporting showed consistently over the years. It was a bit of a hobby horse for him, and an area where his libertarian brain really found a nit to pick with the "trust the science" blue team.
The point I'm drifting towards is that this is really a proxy battle against teachers. The profession is overrun with activist LARPing as educators, their union is controlled by a lesbian activist, and to whatever degree education is occurring, it's haphazard and inertial based on decades of diminishing institutional knowledge. It's a low pay, highly political profession, and increasingly only true believers are attracted and willing to stay in the profession. The ones that treat the trials and tribulations of the profession as a test of faith for their activism are the only ones that thrive.
Luckily I went to school before the "whole reading" thing kicked off (indeed, I was able to read before I started school) but I was there for when the New Maths kicked in, and oh brother.
I think they did to English what they did to Maths: don't teach it the old boring rote way, be the guide helping children discover for themselves, draw out of them what is naturally there.
That's fine for people who have talent for maths and can figure out on their own from first principles. For the likes of me, it meant I understood nothing of what was being taught and scraped along with barely passing. The old "rote learning" would have worked a whole lot better for me, rather than "now we'll just write this on the blackboard and you can all figure it out for yourselves". Even the teachers were stuck at times! They couldn't follow the methods in the new textbooks and were reduced to "just look up the right answer in the back".
For kids who got thrown in at the deep end with "just look at the shape of the entire word and take clues from the context and then you'll figure it out", that must have been a nightmare if your parents weren't teaching you how to read at home.
I'm so sorry. I truly don't understand how anyone can have a functional use of math if they didn't at least learn basic arithmetic by rote. These alternate ways I see of doing addition, subtraction, division and multiplication out of common core are bonkers to me, because of how intensive they are in terms of the number of steps they require, or how much scratch paper you'd need for all the intermediate parts. They look more like academic proofs of how basic arithmetic works than how a person should be expected to functionally work with numbers in the spur of the moment.
I mean shit, just yesterday I was playing a game, figuring off the top of my head what the odds of a single 5 or 6 were off rolling a pair of dice. Came up with 20/36 in fairly short order. Although I will be marginally embarrassed if my off the top of the head work turns out to be wrong after all that.
I'm so bad at memorization that I never learned the multiplication table by heart. If someone asks me what 7 x 8 is, my mental process goes: Okay, I have no idea what 7 x 8 is, but that's the same as 14 x 4 (multiply the 7 by 2 and divide the 8 by 2). Then I can just:
Which only takes me a few seconds, even in my head.
Likewise, I never memorized most of the trigonometric identities. Instead, I memorized cos x + isin x = e^ix and rederive them at need. When I took the ABCTE math exam, I even practiced using Feynman's notation to make this faster. And the only reason I know the common derivatives is because of this song.
The one math quiz I totally bombed in high school was when our teacher gave us a list of squares and cubes to memorize and then deliberately did not give us enough time to calculate them, to check if we had indeed memorized them.
See, that's the kind of 'innate understanding from first principles' that my brain just does not have for numbers. I learned my times tables and I'd be lost without them.
I look at that and go "but why pick 2? Why not multiply the 7 by 3 and divide the 8 by 4 if you're doing it that way?" Not getting the underlying patterns means I'm blind as to why "this number rather than that number, this of course is the quadrant of the circle for cos" etc. It's like trying to explain to someone tone-deaf that of course this note from hitting this key on the piano is not the same as this note hitting that key. (I'm bad at that as well, I love music but in music classes at school when we had to identify 'what note was that?' I bombed).
You have to pick the same number for the multiplication and division, but other than that 2 is picked just because it's a small, easy number to do division and multiplication with. (You could think of it as "taking" the number out of the one you're dividing and then "putting it back in" to the one you're multiplying, so the whole problem has the same numbers in total, just moved around.) Since 8 isn't divisible by 3, 3 isn't very useful - unless you really like fraction mathematics, I guess - but 4 works equally well:
Or, for the way I would do that last line in my head:
that still requires you to know that 4 x 7 = 28 and to me it's just as fast to learn all the times tables in that case.
I was just using it because you'd brought up "why not pick 4" - and, as demonstrated it's perfectly valid to pick 4! It would work fine. It's just that multiplying and dividing by 2 is usually easier for people, so that's what erwgv used.
Thank you for the explanation. It still seems a longer way round than just remembering the times tables, but if it works for people to understand the principles, I suppose that's the main point.
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