> This isn't really the place to have a lengthy debate To the contrary, this is Hacker News! Unfortunately, the situation that I'm referring to with children

> This isn't really the place to have a lengthy debate To the contrary, this is Hacker News! Unfortunately, the situation that I'm referring to with children inventing their own long-multiplication algorithm was presented at a talk, so I can't point to the specific results, if they're even published yet, but my contention is based on an academic research study. The punchline of the experiment was that a full class of approximately-average grade-schoolers were taught math in a novel method, and developed their own multiplication algorithms, and went on to have above-average improvements in math test scores. The development of those algorithms were probably guided to a certain extent, but they looked to me like someone who was working the problem out from the first principles based on the concept of place value. That said, I'm definitely willing to accept the evidence you claim to have (especially since it leaves open the meaning of "correct"). I definitely agree that education should be based on science and not on dogma. Just because we think something ought to work doesn't mean that it works (it usually doesn't), and education is something you don't want to fuck up because the stakes are high and you only get one chance. But, I'm not sure we're even at the point where we can do research yet. Before you can measure results, you need to decide what results you're looking for and how you're measuring them. I'm a mathematician, and I'll be the first to admit that being able to perform long-multiplication isn't actually that useful of a skill, and yet that's mostly what we measure on standardized tests. Understanding what multiplication means and being generally numerate is far more useful and not measured very often (the best we have is word problems). The more desirable side-effects, such as the ability to abstract concepts, to generalize processes, and to apply knowledge from one domain to another, aren't being measured at all, and those are really the only things from my math education that I use in my day-to-day life. Similar things happen across other subjects--knowing what year the War of 1812 happened in isn't useful, while understanding the social, economic, and political conditions that led to that war is useful for the average citizen in a democracy (but doesn't fit well in a scantron). I think we as a society need to first have a big sit-down and figure out what the point of education is. We know it's important, but we've never coherently stated particularly why, and that lack of explicit direction is what lets politics, dogma, and fads more easily take control of the process. Once we've done that, we can let science guide the structure of education. Or rather, we should. There's a bit of a chicken-and-egg problem that without solid backgrounds in quantitative and logical thinking, most people have difficulty making data-driven decisions, and people in general won't get better at that until the education system improves.