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It’s certainly true that an adult would tend to have more additional knowledge and be better able to understand a lot of writing, but if you avoid exposing kids
by thfuran 1mo ago
It’s certainly true that an adult would tend to have more additional knowledge and be better able to understand a lot of writing, but if you avoid exposing kids to anything they don’t have total understanding of the context of, you won’t really be able to teach them anything. Discussing books can help provide some of that context they’re missing. It’s probably fine to teach arithmetic before algebraic number theory too.
- fluoridation 1mo agoI'm honestly of the opinion that teaching children arithmetic (as in, having them perform arithmetic algorithms) is not just a complete waste of time, but actually detrimental as it sours them to the idea of anything labeled "mathematics".
- deleted 1mo ago[deleted]
- kccqzy 1mo agoAt their young age, it typically takes children the ritual of performing arithmetic algorithms at least several dozens of times if not a hundred times to get them to understand and internalize the algorithm itself. You can't actually teach the algorithm itself because they haven't studied basic algebra yet, so the only approximation is using the algorithm on multiple numbers. Then afterwards just give them a calculator. In contrast, in high school, when a student has sufficient mental maturity to understand algorithms abstractly, it suffices to have the student do a few integrations by hand (say using the integration by parts technique) and then hand them a computer algebra system.
- fluoridation 1mo ago>Then afterwards just give them a calculator. If problems were properly designed the students shouldn't even need calculators. In math the specific numerical value of a result is far less important than how it relates to the inputs. Raw calculation doesn't develop the intuition of when one operation is more appropriate than another.
- kccqzy 1mo agoAbsolutely not. Properly designed problems involve numbers that simulate the real world (Benford’s law). Specifically choosing numbers that are easier to compute mentally or by hand would lead students to doubt themselves whenever they encounter something difficult to compute, so you can consider that either cheating or giving them undue psychological stress.
- fluoridation 1mo agoIn math they shouldn't be computing at all, they should just be performing symbolic manipulations.
- thfuran 1mo agoYou’re saying people shouldn’t be taught how to add and subtract?
- fluoridation 1mo agoI'm saying young children shouldn't be led to believe that that's what math is. People should probably learn how to do basic operations, but it should have much, much less emphasis than it does now, and it would be much more useful to teach intuitions regarding how to stop when you've made an error, how to estimate, which operations useful when, etc. As an example of what I mean, my mom is an accountant and I've caught her on at least one occasion multiplying a monthly interest rate by 12. That's an OK method to estimate, but it's pointless when you're doing it on a calculator anyway.
- watwut 1mo ago> but actually detrimental as it sours them to the idea of anything labeled "mathematics". Except it does not. Or, maybe some kids do build up lifetime hatred of math due to arithmetic. But it is not what happened with my kids, their friends, me myself back then or my friends. The thing that pushes people to dislike math is when abstract concepts are taught too soon, before the brain develops the abstract thinking. Or too fast, or in a bad way. But where I have seen dislike of math. it was not arithmetic part of it. It was seemingly magic incomprehensible concepts later on.