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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

#101

Post by DanBC »

_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…

> They really should try to come up with algorithms that are more intuitively linked to a spatial comprehension of the numbers.

Have you heard of "chunking"?

This video shows old style long division (and you're right, the method is confusing). It also shows an easier method that is based on understanding numbers rather than just applying an algorithm by rote. https://www.youtube.com/watch?v=K2rBaSj2L74

Here's another explanation: https://www.theschoolrun.com/what-is-chunking

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

#102

Post by pas »

_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.

https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3

For anyone interested in going down the rabbit hole of those infinite levels.

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

#103

Post by Tomte »

abakker wrote: post #90
mavhc wrote: post #81

Earlier quoted context omitted.

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?

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

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

#104

Post by cjfd »

chrisseaton wrote: post #61
dboreham wrote: post #46

Earlier quoted context omitted.

Try this? https://web.stanford.edu/class/ee486/doc/chap5.pdf Edit: standard deviation is just a fancy name for root mean squared over the sample offsets. The square is there to deal with the fact that there are positive and negative offsets. The mean is the whole point of the exercise, and the root is to negate the fact that we squared earlier.

But why not use the abs function or operator rather than squaring and rooting? This is 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.

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 pairs of equal value and in the second case there is only one pair that is of equal value. The squaring and rooting does this for you. Of course, other functions could do a similar thing for you. The squaring and rooting has nice mathematical properties especially if you consider the variance, i.e., omitting the square root. That is much more differentiable than an absolute value.

Also, consider that the correlation coefficient consists of similar formulas. They all look like the theorem of pythagoras. This ties in nicely with the fact that observables can be seen as having angles in between them where the correlation coefficient is the cosine of these angles.

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

#105

Post by OscarCunningham »

chrisseaton wrote: post #61
dboreham wrote: post #46

Earlier quoted context omitted.

Try this? https://web.stanford.edu/class/ee486/doc/chap5.pdf Edit: standard deviation is just a fancy name for root mean squared over the sample offsets. The square is there to deal with the fact that there are positive and negative offsets. The mean is the whole point of the exercise, and the root is to negate the fact that we squared earlier.

But why not use the abs function or operator rather than squaring and rooting? This is 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.

> 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.

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

#106

Post by cjfd »

_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…

Not really something to be proud of. You basically have just admitted on a forum for programmers that you don't have very much insight in algorithms.

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

#107

Post by layoutIfNeeded »

_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…

Long division is just polynomial division with x = 10.

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

#108

Post by jimhefferon »

I am a math professor. I teach in a SLAC, St Michael's College in VT. In our state education majors must also major in another subject (on an approved list). Every year we graduate one or two future Elementary Educators who are math majors. They take the same courses as any other math majors, and do just as well.

One thing it helps is that they are quite employable since their resume stands out.

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

#109

Post by TeMPOraL »

OscarCunningham wrote: post #105
chrisseaton wrote: post #61

Earlier quoted context omitted.

But why not use the abs function or operator rather than squaring and rooting? This is 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.

> 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 if someone told me that a) deviation with ABS instead of root-square is also a thing, and b) we use the root-square one because it amplifies offsets from the mean.

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

#110

Post by watwut »

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.

I don't know in your school, but in our people would complain and complain and complain about even theoretically having humanistic course compulsory. And those courses were designed to be free grade and any expectation on student to actually put effort into it caused complains. I did not wanted them either, it is not like I would just complain about other people.

Nobody expected tech students to read Shakespear much less analyse it.

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