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Many elementary teachers don’t understand math, and it makes them anxious

latimes.com

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Re: Many elementary teachers don’t understand math, and it makes them anxious

#151

Post by username90 »

darkerside wrote: post #144
chrisseaton wrote: post #119

Earlier quoted context omitted.

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?

I think you're right that there is an arbitrariness to this algorithm, and there are other ways of normalizing your data. And you could probably build entire new branches of statistics off of them (like non Euclidean geometry), and they'd probably even be better in some way. But, you'd be speaking a different language from everybody else. Speaking of language, have you ever thought about how all names and grammatical…

No, standard deviation is special. If you have a large enough amount of independent distributions which gets averaged or added in some way, then the only thing which matters are their standard deviations and average values for what the final distribution looks like.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#152

Post by jeltz »

nathanwh wrote: post #111
layoutIfNeeded wrote: post #107

Earlier quoted context omitted.

Long division is just polynomial division with x = 10.

This comment is hilariously on the nose for how a lot of math texts read (at least in my experience) $SIMPLE_CONCEPT that you’re trying your best to understand is easy if you think of it as a specific example of $MORE_COMPLICATED_CONCEPT that you surely can’t understand without understanding $SIMPLE_CONCEPT

That was quite an eye opener though when we were taught polynomial division in high school. Not necessarily for how long division works because I already understood that, but because it was an example where short division could not be used.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#153

Post by SamReidHughes »

chrisseaton wrote: post #138
SamReidHughes wrote: post #129

Earlier quoted context omitted.

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…

This is just re-stating the algorithm for the umpteenth time. I can read the algorithm. I just can't intuit why it works or why it has been designed this way. 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-li…

> 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.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#154

Post by username90 »

chrisseaton wrote: post #145
username90 wrote: post #130

Earlier 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?'

Economics of stocks is a good example, when you put a lot of stocks in one portfolio you can calculate its risk (standard deviation) and returns (average value), and see how much each piece of stock contributed to that. This is because the results of many variables looks like a normal distribution with the combined average and standard deviation. Now it gets a bit more complicated in the real world since stocks are not independent from each other, but it shouldn't be hard to understand why knowing the standard deviation of something is useful.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#155

Post by cptskippy »

_bxg1 wrote: post #2

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…

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 division and she still uses it to this day. It's simple and there is a history of work to easily identify errors.

The homework scene from The Incredibles 2 really hit home for me. I feel like book publishers development new methods or ways to teach the methods as a means to sell new editions of books, not because the new ways are better. This causes a rift in society because people no longer share a common understanding of a subject.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#156

Post by rocqua »

_bxg1 wrote: post #47
novok wrote: post #43

Earlier quoted context omitted.

I think it depends on how you were taught the concepts in elementary school. I think a lot of it is based on things like bar charts[0] and visual representations at first, so it's possible you were never taught how it was repeated subtraction and addition, how powers are repeated multiplication and so on. https://en.wikipedia.org/wiki/Singapore_math#Bar_modeling

Yep. I remember in college when I made that connection and realized you could create infinite "levels" of operation, with each repeating the previous one N times.

If you do this, 2 and 2 will always make 4, no matter what level you go to.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#157

Post by wrinklytidbits »

roenxi wrote: post #131

> But many elementary students don’t understand the meaning of the equal sign. 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.

Languages like J make this distinction: `=` is equals in the mathematical sense [1], while `=.` and `=:` are the assignment operators (the former being local and the latter global) [2].

Although the assignment operator and the equals operator are similar there is a preference to have the equals sign retain its original meaning.

1. https://www.jsoftware.com/help/dictionary/d000.htm 2. https://www.jsoftware.com/help/dictionary/d001.htm

Re: Many elementary teachers don’t understand math, and it makes them anxious

#158

Post by geomark »

novok wrote: post #43
_bxg1 wrote: post #17

Earlier quoted context omitted.

It wasn't until I learned about for-loops that I started thinking of multiplication as repeated addition and division as repeated subtraction. Before then I thought purely in terms of geometry.

I think it depends on how you were taught the concepts in elementary school. I think a lot of it is based on things like bar charts[0] and visual representations at first, so it's possible you were never taught how it was repeated subtraction and addition, how powers are repeated multiplication and so on. https://en.wikipedia.org/wiki/Singapore_math#Bar_modeling

At my kid's school they start teaching division as "sharing" - a kid has 10 pieces of candy he wants to share with 5 friends; how many pieces can he share with each friend. Later they describe it as repeated subtraction - how many times can his 5 friends take a piece of candy from the pile of 10 pieces.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#159

Post by chrisseaton »

username90 wrote: post #154
chrisseaton wrote: post #145

Earlier quoted context omitted.

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?'

Economics of stocks is a good example, when you put a lot of stocks in one portfolio you can calculate its risk (standard deviation) and returns (average value), and see how much each piece of stock contributed to that. This is because the results of many variables looks like a normal distribution with the combined average and standard deviation. Now it gets a bit more complicated in the real world since stocks are n…

> Now it gets a bit more complicated in the real world since stocks are not independent from each other

This is also where I get frustrated.

I'm taught about the CLT but every place I think I might use it, the samples aren't really IDD when you look hard enough, so it doesn't apply.

Computer benchmarking (which is where I'm usually trying to apply statistics) is the classic example. One iteration changes the state of the computer for the next iteration. They aren't remotely IDD, but people still try to claim the CLT. Seems like all their stats beyond that point is broken.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#160

Post by matwood »

Gunax wrote: post #67
alfiedotwtf wrote: post #3

On the flipside, I was in a Calculus lecture at uni and turned to the girl next to me who was crying. I asked her if she was ok, and she said she didn't understand why she had to sit in the lecture learning Laplace transforms when she "only wanted to be a primary school teacher". From the sounds of it, it was a prerequisite? Edit: Oh :) I just worked it out - I was taught to fold the subtraction and carry right in on…

There seems to be a culture of proud ignorance around math more-so than other subjects. While I am sure there is some engineering student out there griping about having to take a psychology course, they don't seem to complain as much as when non-mathy people have to study math. I think it is a mistake for our education system to treat math as something superfluous and abstract from daily life. While neither Laplace t…

> While I am sure there is some engineering student out there griping about having to take a psychology course, they don't seem to complain as much as when non-mathy people have to study math.

This is the underpinning of every conversation where engineers say college is a waste of money. If anything, I see engineers complaining more loudly about taking any course that isn't directly related to engineering. This not only includes the humanities, but also things like business.

> While neither Laplace transforms nor Shakespearen analysis are necessary to live, the former is probably more useful than the latter.

Learning Shakespeare is typically tied to learning how to communicate through reading, writing, and comprehension. IMO, that is much more generally useful than learning anything about a Laplace transform.

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