Mathematicians tell you not to do a lot of things which are very useful for non mathematicians who are using math. The practices of applying math to your problem is worlds apart from that of operating on the body of mathematical knowledge.
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@Kamuela and@StephenJMaguire Mostly it's me expressing frustration on pedagogy. I've been revisiting how I was taught and comparing it to how I would teach now, knowing what I know already. I think even in math-y fields, there is too much *early* emphasis on formality.1 reply 0 retweets 1 likeShow this thread -
One example, the assumptions on a linear regression are basically always violated. But, as a tool, it's remarkably robust. When I was trained, we spent a lot of time on the why formally. It does impart some intuition and serve as a guide.
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But, the way most people use linear regressions, I think it would have made more sense *at that point* showing examples of what egregious violations look like, in practice. That gives practical intuition. Then, given accumulated experience, revisiting it pays off big time.
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Like, Anscombe's quartet conveys some really good practical advice in an incredibly effective way. Knowing how most people use statistics, it gives much better bang for your buck!pic.twitter.com/DKHsfMSw3f
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Another example would be how much effort is spent on explaining that manipulating differentials so you can cancel things or rearrange is a bit "hand wavy." Okay, sure -- but most of the time it works very well.
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Unless you're going to show egregious cases of "why", it's misspent time. Again, this is all an itch and and intuition. Maybe you can't really revisit, "I wish I could have done this knowing what I know now."
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But, I really don't think enough training is contextualized enough. As in, "okay, this is your field, lets teach you to be effective in it first. Then, the intuitive stuff will be intuitive and practical, and therefore retained."
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