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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

#91

Post by Tharkun »

BrandoElFollito wrote: post #79

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…

When I was first taught fractions in primary school, the teacher had a bunch of rods of equal length. Each rod was divided into segments of different colours. Each segment could be "fractured" off the rod because they were attached by magnets. I think they went from 1 to 10 or so segments.

This allowed for a great visual (and tactile) illustration of how fractions work. 1/2 + 1/4? No worries, just break off some pieces and add them together. Then you can compare the length to various other configurations, and you can viscerally experience that 3/4 really does equal 6/8.

I don't know whether this is a standard way of teaching fractions, or whether this teacher was particularly motivated or whatever. But it made a lasting impression on me. Thanks, miss Annie.

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

#92

Post by dragonwriter »

Broken_Hippo wrote: post #87
jfim wrote: post #83

Earlier quoted context omitted.

Just get a few measuring cups and some water. Half a cup and a quarter cup makes three quarter cups, because really, half a cup is two quarters of a cup.

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.

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

#93

Post by cultofmetatron »

elchief wrote: post #22

My ex taught grade 6 geography. Is a principal now. Thought the seasons were due to earth tilting back and forth. Didn't get that the tilt was the same, but the position around the sun was different

thats not incorrect though. The orbit of the earth is eliptical and during summer (for the northern hemisphere) the earth's tilts north end towards the sun. Fun fact, it is actually farther away from the sun as well during that time.

TLDR: the tilt does in fact affect the season

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

#94

Post by projektir »

Wonder why math is such a problem. Growing up in the Ukrainian school system I was doing very well in math for 3 years and was doing double exams in the span of one.

Moved to the US, math was easier and it kinda fell off. Was back to Ukraine for some time, but it was never the same afterwards, and now I have the same math anxiety many other people do.

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

#95

Post by CraneWorm »

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.

Oh, right! Easy!

Try it with 1/7?

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

#96

Post by BrandoElFollito »

ezequiel-garzon wrote: post #80
BrandoElFollito wrote: post #79

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…

To me what is utterly crucial is to use pie pictures to convince children (and adults...) that 1/2 + 1/3 cannot possibly equal 2/5. If they actually buy this that’s a pretty good inflection point in their education on fractions.

After going though the education of two children who like math very much I realize that fractions on their own are very natural.

It is their addition which is not, as it does not have any obvious counterpart in simple nature.

I had a math teacher at the university who told us once "there is a neat trick which is normally taught next year but is useless by then and super useful today. Just use it without too much thinking."

This is my reasoning too, I showed them the always working way to add fractions (cross multiplication) and hope that someday they will appreciate the beauty of the thing.

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

#97

Post by smabie »

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.

Because the derivative at 0 of abs is undefined.

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

#98

Post by fyp »

CraneWorm wrote: post #95
geomark wrote: post #8

Earlier quoted context omitted.

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.

Oh, right! Easy! Try it with 1/7?

School usually start with remainders instead of trying to teach repeating decimals at the same time. So here the answer is just 0 remain 1.

The same process still works if you want to calculate the decimals though. Just pretend you're doing (1000000/7) * (1/1000000) or however many digits you want.

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

#99

Post by xenihn »

elchief wrote: post #22

My ex taught grade 6 geography. Is a principal now. Thought the seasons were due to earth tilting back and forth. Didn't get that the tilt was the same, but the position around the sun was different

Are you saying that you believe that tilt is not a factor for seasons, and that it doesn't change between seasons...?

https://en.wikipedia.org/wiki/Season#Axial_tilt

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

#100

Post by chownie »

copperx wrote: post #77
_bxg1 wrote: post #64

Earlier quoted context omitted.

I didn't understand why it worked (a comment here pointed out that it's just division-by-repeated-subtraction which does make sense now). But I was still able to perform it, during the time when it was relevant to my life.

What's a red flag is being frustrated by long division and at the same time not being curious or resourceful enough to resolve your frustration. You blame your lack of understanding on other people. I can understand if most people shared your frustration, but not a PhD holder. Your degree basically says that you're capable of doing long, intensive research on arcane topics. What am I missing here?

From the other comments that user's posted I can kind of understand their sentiment, they've tried to form an understanding from others and then found the same roadblocks repeatedly.

I have impaired executive functioning and this is basically my experience in tying shoelaces, I struggled to accommodate the mental model of the process myself so I sought out others so manage it to try and learn from them.

What instead happened was exasperation on their part and frustration on mine, so after repeating that a few times a year until I was 22 I just stopped and bought shoes without laces.

When you go at it for long enough without succeeding it can make the experimentation not very fun or interesting.

I don't think I'd call it a red flag for a PhD to have fatigued themselves out of interest in a problem, it's something that happens to everyone at some point.

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