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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

#241

Post by darkerside »

username90 wrote: post #151
darkerside wrote: post #144

Earlier quoted context omitted.

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.

I'm well out of my wheelhouse, so anyone else chiming in would be appreciated. I'm not sure what you mean by "looks like", but I would imagine other "nonstandard" measures of deviation would also result in a consistent model.

My larger point is that, something can be arbitrary and still be meaningful. If people agree on a common meaning, it formalizes a communication protocol that allows for much better information sharing.

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

#242

Post by username90 »

barry-cotter wrote: post #224
username90 wrote: post #216

Earlier quoted context omitted.

Yes the seasons are due to earths tilt, but the tilt still doesn't change between seasons as his wife thought, only earths position compared to the sun does.

The tilt of the earth relative to the sun does in fact change. That’s what the seasons are. If the earth was tilted but the tilt didn’t change over the course of the year the areas that had longer days due to being tilted towards the sun would be permanently hotter than the areas tilted away. There would be a permanent summer and winter, rather as at the equator it’s always summer. The changing tilt of the earth rela…

I'm not sure what you are trying to say, you probably misunderstood what elcheif said. Earth is tilted towards the sun in the summer and away from the sun in the winter due to its tilt changing, not due to its position changing. That is what you are saying, what I am saying and what elcheif was saying. What elchaif's ex thought was that earths tilt actually changed over the course of the year instead of earth just moving to the other side of the sun. There is no energy which could alter earths tilt like that, instead the tilt was set in motion a very long time ago and has been basically fixed ever since.

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

#243

Post by LegitGandalf »

wnoise wrote: post #88
LegitGandalf wrote: post #49

Earlier quoted context omitted.

University of Chicago study for you to peruse https://news.uchicago.edu/story/female-teachers-can-transfer...

Even assuming the study holds up, that doesn't mean that only the girls picked up the fear. It means only the girls were affected by the fear, by overly generalizing from this one example.

Yeah it could be that the boys noticed and ignored the fear. The impact on the girls is troubling though.

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

#244

Post by dclowd9901 »

seppel wrote: post #213
chrisseaton wrote: post #138

Earlier quoted context omitted.

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…

> Why are we doing things in decimal? I think this is maybe the crucial part that you might be missing. All this long division (and long multiplication) stuff works on base-n represenations of numbers. I.e. if you have an number like 3376, it is actually a short hand for 3*10^3 + 3*10^2 + 7*10^1 + 6*10^0. And if want to divide it 4 and, suppose, you cannot do it in your head, you do it step by step, by clever regroup…

Hell yes! You finally made this clear for me why we can go through the dividend number by number (or power of 10 by power of 10) to apply the divisor. Thank you so much!

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

#245

Post by chongli »

all2 wrote: post #222
hervature wrote: post #215

Earlier quoted context omitted.

How do you compute square roots by hand? Isn't it just a rudimentary root finding algorithm?

The only by-hand method for finding roots I know is "Newton's Method". I think I learned this in pure calculus? https://en.m.wikipedia.org/wiki/Newton's_method

The older method is attributed to Hero of Alexandria [1].

[1] https://en.m.wikipedia.org/wiki/Hero%27s_method

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

#246

Post by krilly »

geomark wrote: post #8
_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…

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.

I was never told this, and I'm sure the reason why is because my teacher didn't have a clue either

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

#247

Post by username90 »

darkerside wrote: post #241
username90 wrote: post #151

Earlier quoted context omitted.

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.

I'm well out of my wheelhouse, so anyone else chiming in would be appreciated. I'm not sure what you mean by "looks like", but I would imagine other "nonstandard" measures of deviation would also result in a consistent model. My larger point is that, something can be arbitrary and still be meaningful. If people agree on a common meaning, it formalizes a communication protocol that allows for much better information s…

"Looks like" as in the difference approaches zero as the number of times approaches infinity.

This means that any distribution with standard deviation of X will behave as a normal distribution with standard deviation X when you have enough of them. Or in other words, any distribution with standard deviation of X will behave like any other distribution with standard deviation of X when you have enough of them. There is no other measure like this as there is no other equivalent to the central limit theorem. Therefore it makes sense to have this as a universal measure of random processes.

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

#248

Post by gshubert17 »

hervature wrote: post #215
billfruit wrote: post #178

Earlier quoted context omitted.

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?

The calculation of the square root, relies on this result from squaring a number N = 10d + e (that is, single digits d and e, but d is in the 10s place):

NN = (10d + e)(10d + e) = 100dd + 20de + ee

Group the digits of the square by two, and add extra values to the "divisor" so that the extraction of the square root in effect undoes the squaring above.

See, for example, https://sciencing.com/calculate-square-root-hand-5081134.htm...

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

#249

Post by dclowd9901 »

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…

Maybe we ought to meet people where they are. What if math class was a series of practical problems that the students had to figure out together and make proofs for and the teacher has the classes compete with one another for progress through the lessons? You could make sure no one gets left behind by having a test with a minimum threshold of passing scores. Gets those less motivated, yet competitive kids behind it, even if they couldn’t give a hoot about math. Plus it’ll make nerds heroes!

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

#250

Post by _bxg1 »

kasey_junk wrote: post #162
_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…

I was taught math via spatial properties and it wasn’t until I came back to it from a logical perspective that I was able to understand it. Just another anecdotal data point but my experience was completely opposite yours.

True; part of the problem is that everyone is different.
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