Earlier quoted context omitted.
Just a reference frame change right?
In the same way that "the earth doesn't orbit the sun" is true, yeah it's just a reference frame change.
Invariant under Lorentz transform.
Many elementary teachers don’t understand math, and it makes them anxious
341–350 of 356 posts
Re: Many elementary teachers don’t understand math, and it makes them anxious
#342Earlier quoted context omitted.
> But why not use the abs function or operator rather than squaring and rooting? You can. It's called the mean absolute deviation. Which one you use depends on your application. If you just want to give a summary of how spread out the data is then either would work. Lots of people say that we should use the mean absolute deviation as the default rather than the standard deviation.
And suddenly another small subarea of maths starts to make sense for me. Thank you, and thanks to everyone commenting in this subthread. I too have a problem with math tools passed down without any surrounding context - without telling why are we using this formula, instead of any other variant from the family of formulas that would satisfy the same goals. I'd have much easier time dealing with statistics in school i…
>I too have a problem with math tools passed down without any surrounding context
Also one of my peeves. However over the years I've come to realize that in addition to teachers who omit the context, there is also a class of student that actively doesn't want to hear the context. I'm not sure exactly why this is, but I see it in my immediate family quite a bit. A sort of kind of thing perhaps due to difficulty taking on too much information?
Re: Many elementary teachers don’t understand math, and it makes them anxious
#343Earlier quoted context omitted.
The standard deviation is not arbitrary, it tells us what the final normal distribution would look like if you averaged a lot of independent distributions. You can read up on the central limit theorem if you want to understand more. https://en.wikipedia.org/wiki/Central_limit_theorem
I don't want to keep going on because it sounds like I'm trolling, but when you tell me 'it tells us what the final normal distribution would look like if you averaged a lot of independent distributions' I just want to say 'why do I care about that? where did that requirement come from?'
I think it begins with binomial expansion and coin tossing.
e.g. https://socratic.org/questions/what-is-the-difference-betwee...
Re: Many elementary teachers don’t understand math, and it makes them anxious
#344Earlier quoted context omitted.
Okay, we have deviations from the mean. They are (0.1, 0.1, -0.1, -0.1). Or we have deviations from the mean (0.2, 0, 0, -0.2). I think is is pretty intuitive that in the second case the deviation is larger. In the first case there are only two differing values that are 0.2 apart. In the second case there are three differing values and some are 0.2 apart and others are 0.4 apart. Also, in the first case there are two…
I still don’t understand why we pick a metric because it’s easy to work with. Isn’t it either the right metric or not?
>Isn’t it either the right metric or not?
To illustrate, perhaps an example closer to home:
If someone asked you to tell them "how many lines of code in this project?" you'd start wondering things like "do I count comments?", "do I count dependent libraries?", "perhaps some metric that is equivalent of a statement count but not strictly counting lines?" and on and on.
Statistical measures are like that. Someone with a decent knowledge of the problem space came up with the best stab at how to characterize the data.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#345Earlier quoted context omitted.
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
Interesting, I'll start using that short version now. I always hated the long version because it took up a ton of vertical space and I didn't need the extra verbosity. In fact, I'll probably teach me kid that method when he gets to division in school.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#346Earlier quoted context omitted.
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.
It’s notation only. I “invented” it as a kid to save space on division problems and reduce the chance of copying errors. It’s the same method as long division (and TIL it already existed!)
It definitely looks nice, and I'll probably start using it. If something is too inconvenient to use short division for (e.g. large divisors), I'll probably just use a calculator.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#347Earlier quoted context omitted.
I'm missing the context here. The only arrows I'm familiar with are vector notation and ion spin notation.
I think they're talking about this, which appeared in a front-page HN post from yesterday: https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
Not that story in particular, it's a perennial story on HN - I first learnt about that notation through the "largest number you can write on a postit note" challenge.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#348Earlier quoted context omitted.
> But why? Why are we doing things in decimal? We’re subtracting off multiples of 10^N because that’s easy when you write your numbers in base 10. Try subtracting off multiples of 9^N, or multiples of N!, or some other choice, and you’ll see why.
Ok, but do you see what I mean about how that part was just sitting there without any explanation? That's why I find it hard.
Is the question really why we train children on basic arithmetics in base 10?
That could be meant shallow or deep. The shallow answer is because that's all you need to do to function in society (and conversely, while arguing with a police officer about the presumed base on speed limit signs may be fun, it is also pointless).
The other answer probably needs to explore the question a bit further. Perhaps a good starting point is the fact that we almost universally share the physical characteristics of having ten fingers.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#349Earlier quoted context omitted.
Yeah, when we were taught short and long division I had the same question and it was not until quite late in high school we got the explanation. I went to school in Sweden where we do teach all this things, but in a strange order.
Went to school in Sweden too in the 90-00s. I wasn't taught long division until I had to divide polynomials in my last year of high school, and that course was an elective.
Apart from the long division method pointing out that division is just repeated subtraction, that's the only reason to use it.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#350Earlier quoted context omitted.
Which is all well and good... Until you need a half of a quarter (which I'd use tablespoons for as there are 16 tablespoons in a cup), a half of a third of a cup, or need to add 1/3 and 3/4 together. Which isn't so bad for a recipe because most things aren't that precise in cooking - but not so easy for all students to work out, especially without having a tablespoon to use. This is even so when you have tablespoons:…
> Those 1/3 cups don't divide neatly into tablespoons. But they do into teaspoons.
Sure, but if you actually count out 16 teaspoons, you are likely to lose count :)