231–240 of 356 posts
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Up-arrow notation ftw.
I'm missing the context here. The only arrows I'm familiar with are vector notation and ion spin notation.
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What is short division? I only remember being taught long division and having a calculator. Is there another method?
Fascinating. I didn't know, either. After looking at the English Wikipedia I found that a) what I learned in school is long division b) the notation with the dividend and the divisor separated by a parenthesis and the result on top of a horizontal bar is totally alien to me c) I've never seen short division before d) the German Wikipedia doesn't even have an article about short division
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Shouldn’t that study focus on the distribution of types of master’s degrees, and a sub-population analysis showing which ones correlated most with teaching ability? I bet someone with a master’s in math would be better at teaching math than someone with a master’s in teaching theory. Ditto at the undergrad level.
I used to think subject matter expertise helped too. If you find any evidence it does email me, I haven’t found any research to that effect.
And yet, I cannot find anything on the subject. That is very suspicious. It’s like no one wants to look into it. Can anyone tell me what’s going on here? Did I miss something, or is it just common sense that the intelligence of your teacher doesn’t matter?
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What none of them can tell you is why they've been taught long division, when short division is faster. And it's because you need long division to do division in algebra
I've looked at both Wikipedia pages and still can't really understand the difference. Is it anything more than notational? Either way, you're calculating divisors for each component of the problem, and it only seems to matter whether you calculate it on paper or in your head.
The author of this article does not understand math :). Learning math is difficult. There're two things you need to learn: fundamental concepts and skills. These two things are related and commingled. Mastering both requires extraordinary effort. I come from a skill-focused math education. I was pretty good with skills. But I didn't understand fundamental concepts. I still remember my struggle with prime numbers. Tho…
Being able to mechanically perform an algorithm is the first step on the road to in some sense actually understanding it. If you think you understand the fundamental concept but you can’t solve a problem using the algorithm you probably don’t. > Young man, in mathematics you don't understand things. You just get used to them. - John von Neumann
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Well if long division is unintuitive, the procedure to compute square-roots by hand is even more mysterious, as if it has transcended dealing with numbers and instead become a symbolic manipulation. Thankfully it is something I never had to apply, even once in adult life till now.
How do you compute square roots by hand? Isn't it just a rudimentary root finding algorithm?
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Then you never knew it? Perhaps what you were taught wasn't long division. My kids were not taught the same math that I was taught in the 80s. My 17 year old was struggling with the division algorithm they were teaching in Elementary school at the time (late 2000s). I can't remember the details but it was something I had never seen before that was a step up from throwing poop at the wall. I showed her how to do long…
Conversely I have been immediately impressed with the way my first grader is being taught math. It’s completely different than the way I was taught so I have to invest in figuring it out but it’s led them extremely quickly through multiplication & division and into algebra. I’d characterize it as “multi-algorithmic”. They come at it from a variety of algorithms, assumedly so that each student can find one that works…
But in reality the common core way explained the actual algorithm and the reason it worked so much better, and further, the only reason it appeared more complicated was because the people who were targeted by the meme already knew long division. If you took someone completely new to both methods, they’d find the more “complicated” algorithm far easier, because a large part of its complexity was explaining why the division worked, whereas long division was about memorizing a process.
This is, of course, a well known and reliable way of solving fractional division problems, but it seems to be the _only_ way I’ve seen people solve fractional division problems (by using the reciprocal rule). What would be the approach that doesn’t involve using multiplication?
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Well if long division is unintuitive, the procedure to compute square-roots by hand is even more mysterious, as if it has transcended dealing with numbers and instead become a symbolic manipulation. Thankfully it is something I never had to apply, even once in adult life till now.
How do you compute square roots by hand? Isn't it just a rudimentary root finding algorithm?
https://www.solipsys.co.uk/new/SquareRootByLongDivision.html
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Then you never knew it? Perhaps what you were taught wasn't long division. My kids were not taught the same math that I was taught in the 80s. My 17 year old was struggling with the division algorithm they were teaching in Elementary school at the time (late 2000s). I can't remember the details but it was something I had never seen before that was a step up from throwing poop at the wall. I showed her how to do long…
Conversely I have been immediately impressed with the way my first grader is being taught math. It’s completely different than the way I was taught so I have to invest in figuring it out but it’s led them extremely quickly through multiplication & division and into algebra. I’d characterize it as “multi-algorithmic”. They come at it from a variety of algorithms, assumedly so that each student can find one that works…