Except the quadratic formula, just as an example, has a lot of positive qualities when taught to children: * The longform is fairly complex, so it is non-trivi

Except the quadratic formula, just as an example, has a lot of positive qualities when taught to children: * The longform is fairly complex, so it is non-trivial to remember or recount. You can't just guess it (at least without knowledge well beyond it). So it looks like "magic". * It is a great introduction to what formulas are. They are non-trivial proofs of concepts that took research and logic to conclude. Learning logic and learning patterns, especially the non-obvious ones like the qf, are what promote analytical thinking. We need more of that, not less. Maybe the problem is more that kids are shown a magic formula and made to mechanically repeat it on a couple dozen data sets than to actually learn how to reach conclusions like the qf. Making kids proof it would probably be more valuable than making them repeatedly use it beyond a few times to assure them it is valid magic math.