alt Hacker News> No learning linear systems without learning how to do linear approximation of systems in a mostly non-linear world.
That's why Common Core trains kids on estimation from Grade 2. Instead of adding 12 + 23 = 35, you add 10 + 20 = 30 to get a number close to the right answer.
This plants the idea "I can simplified numbers to get the answer if I don't need the last digit, which lets me solve problems faster". Which gets generalized as "I can use the simplified Ideal Gas Law to model a complex system if I don't own a supercomputer".
Even in university I had this: my physics course heavily emphasized properties of linear systems to demonstrate why I'd want to use one and we ran linear regressions in other courses if we didn't "know" the true equations.
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It annoys me, though, that there's a prescribed method of estimation, which is hard to remember. I always used to get the "wrong" answer because I picked easier-to-add approximations, even though my estimates were generally both faster and closer. (To use your example, I'd have estimated 35 or 36: the sum of two small numbers, like 2 and 3, is normally about 5; and this sum is a little bit less than (1 + 2)×12 = 3×12.)
Nod. A random TIL from Friday, courtesy to qwen.ai: In contrast to USA educational estimation, which emphasizes point estimates, China reportedly emphasizes directional estimation to establish an envelope, upper and lower (strict) bounds - Da Gu and Xiao Gu.
I've long though we'd be better off doing incremental bounding, hard and soft, in part because the group discourse dynamics are so much better. "Ok, who can suggest another bound, upper or lower, hard or soft?" vs "Your step 2 is too big. Well, your step 4 is too small!".
Which raises a question - might this diversity be leveraged? Science education content improvement is often bottlenecked on regional conditions. As when a high-stakes exam doesn't cover topic X, so there's regionally less interest/opportunity to explore better teaching of X, or using X to better teach other things. This especially bites when you wish to explore mashups, X+Y+Z with each taught well, but they're every one both in poor shape and bottlenecked.
Both countries largely fail to create a physical intuition, a feel for reasonable values - in the US because it's a secondary priority, and in China reportedly because estimation has become nationally high stakes, so memorization gets emphasized over feel.
Can we leverage that regional difference? For a strawman, might one develop content with improved bounding facilitating a rough quantitative feel for reasonable values, in China where it's sort of aligned with the flow, even if off to the side, rather than in the US, where the aligned energy is much less. And then, having developed that content in China, bring it back to the US, where again off to the side, there's perhaps the flexibility and inquiry perspective for the material to appeal in its developed form? And WeChat Groups seem potentially a way to get heterogenous ad hoc communities around content development, for which I don't know a US equivalent.
For analogy, I'm told the US advanced placement exam for French, is both hard, and narrowly focused on a style of conversational French. So people teach to the test, and all else that is "French", is deemphasized. But let's say you have a VR app which develops both that conversational, but also cultural and business and travel. You might develop it the US, leveraging the conversational incentive. And release elsewhere, where there's interest and room for the other bits, even if there wasn't sufficient incentive elsewhere to build the app in the first place. Maybe?