131–140 of 356 posts
Some people might not have made the connection, but by and large programming languages make this mistake too. All the major ones are using the = glyph for assignment.
I still don't know why long-division works. I don't think I even remember how to do it as an adult. I've always had a very intuitive grasp of math, which meant I excelled at solving things in my head but struggled with (and resented) having to show my work in the arbitrary algorithms we were taught. I understand division despite my education. They really should try to come up with algorithms that are more intuitively…
I don't understand why long division would be a mystery. It's just repeated subtraction - you are finding how many times you can subtract the divisor from the dividend, in a systematic way.
Afaikr it's just division, how man X are in y.
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> how I always find maths and particularly statistics - I always just want to answer ‘but why’ and then people lose interest in explaining after a while. Unless you try to solve more problems yourself, you won't understand the advantages or disadvantages of some methods in solving the problems. So the real answer is: construct the examples, compute and compare, don't approach it "philosophically." All the methods use…
I think you just described the common core method. The main problem is teachers don't understand all the methods they are teaching and kids pick up on this. Then the parents don't understand all the methods and the few intellectually curios help their kids figure it out; but he vast majority of people just tell their kids it's stupid.
"I have a PhD in computer science but I cannot understand long division"
For that, personal experience in devising the examples, evaluating them and comparing the results is the only way to get the understanding. One can't complain that one doesn't understand Greek texts if one personally never tried to learn the Greek letters. One could have learned "about" Greek but at the end one hasn't done the inevitably necessary preconditions to actually read Greek texts.
The error in thinking is believing that because one already learned about something else somewhere else he should somehow "understand" something without doing the necessary work on that something. The solution is "make your own homework" to fill the gaps.
The topic of what, how and why children learn in schools is much more complex.
Edit: Also, now reading the Wikipedia article: https://en.wikipedia.org/wiki/Long_division I do understand why people don't understand it: the taught notation for the process, used in many countries, is utterly confusing to me, so my reason for confusion when looking at various notations is not that I don't understand the nature of the method but that I haven't spent time analyzing what was built on top of the basically simple idea -- I can also "understand" all the notations but I'd also need more time for that. Still, having enough experience, I can claim that I understand the idea and the process even if I never learn all the notations and conventions in different countries (which part of the process you write where, what you write and what you don't when etc). The idea is simple, the conventions enforced don't have to be. Those who only learned the conventions maybe never invested any time to figure out what's behind the conventions: what is actually being done.
I have a hard time explaining to my children how addition of fractions work. Not how to do that, but how to feel the intuitive way. And percentages, to some extend. The sad part is that I have a PhD in physics and an engineering degree in CS. I used to teach physics at the uni and loved it. My children like me to explain them physics because I love it so much and they appreciate the analogies, their limits etc. It is…
The benefit of this approach is you can easily go to 1/8 and 1/16 and do addition and subtraction. Even multiplication and division. Get two pizzas to show 8/4 and 16/8 etc.
And you can eat the whole thing afterwards. Fractions are delicious.
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Sure you can! Just look at a typical fifth- or sixth-grade classroom. Most of them can perform long division, briefly, before the test. They may even remember it for several days after the test.
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
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Sure you can! Just look at a typical fifth- or sixth-grade classroom. Most of them can perform long division, briefly, before the test. They may even remember it for several days after the test.
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 went to school in Sweden where we do teach all this things, but in a strange order.
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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
What is short division? I only remember being taught long division and having a calculator. Is there another method?
Edit: although if someone else can explain it better I'd really like to know.
From what I have searched,(quickly mind you), it seems to be a mind set.
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No I have genuinely tried to learn it and I have no understanding why I am doing any of the steps in the algorithm.
Try again? Long division, dividing A by B, is a for loop that maintains the invariant A = QB + R, where Q is the number written on top (initially 0) and R is the number written on the bottom (initially A), by subtracting values of the form B(C)(10^N) from R and adding values (C)(10^N) to Q to compensate. func Longdiv(A, B) { // Assume A > 0, B > 0. N = floor(log10(A)) Q = 0 R = A while (N >= 0) { // Invariant: A = B…
I mean your very first line has a logarithmic operation that was not mentioned anywhere in your text or your comment! Just pops in there out of nowhere. I guess it's about the number of decimal digits? But why? Why are we doing things in decimal?
A dense ten-line algorithm like this seems far more complicated than other algorithms we try to get school children to memorise.
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Sure you can! Just look at a typical fifth- or sixth-grade classroom. Most of them can perform long division, briefly, before the test. They may even remember it for several days after the test.
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
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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
Thanks! What you said, except my own point d) that Swedish Wikipedia tells that apparently short division is also used in Swedish elementary schools now.