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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

#201

Post by war1025 »

rocqua wrote: post #187
zamfi wrote: post #85

Earlier quoted context omitted.

> Imagine if teaching paid as well as software development. I’d love this personally. But the organizations that employ teachers do not make the same amount of money, per employee, as organizations that employ software engineers. Depending on your state, your property taxes would need to double or triple to make the math work out. To be clear: I’m not making a comparison of the value provided, just the accounted-for…

Its weird that education is payed for completely by property taxes in the US. The benefits of education go to more than just the (parents of) the recipients of that education. You also get weird incentives for people to reduce these taxes if they send their children to private schools.

I believe the idea of schools being funded by property taxes is that you then spread the cost load out over people of all age groups, in a way to acknowledge that having educated children is a benefit to the community.

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

#202

Post by barry-cotter »

rocqua wrote: post #187
zamfi wrote: post #85

Earlier quoted context omitted.

> Imagine if teaching paid as well as software development. I’d love this personally. But the organizations that employ teachers do not make the same amount of money, per employee, as organizations that employ software engineers. Depending on your state, your property taxes would need to double or triple to make the math work out. To be clear: I’m not making a comparison of the value provided, just the accounted-for…

Its weird that education is payed for completely by property taxes in the US. The benefits of education go to more than just the (parents of) the recipients of that education. You also get weird incentives for people to reduce these taxes if they send their children to private schools.

> Its weird that education is payed for completely by property taxes in the US.

This isn’t true.

From the CPC Popular Front funded Brookings Institution.

https://www.brookings.edu/research/how-progressive-is-school...

> School funding systems vary by state, but in the typical state, the financing of K-12 education is shared roughly equally by the state and local governments (with the federal government covering less than 10 percent of the cost). Most states have provisions designed to target additional funding to districts attended by low-income students, with the goal of making up for these districts’ limited capacity to raise revenue through property taxes and other local sources.

> Nationwide, per-student K-12 education funding from all sources (local, state, and federal) is similar, on average, at the districts attended by poor students ($12,961) and non-poor students ($12,640), a difference of 2.5 percent in favor of poor students.

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

#203

Post by pbhjpbhj »

symplee wrote: post #37

A couple examples from the article: >> A colleague told me of vainly trying to persuade a college student that .015 was less than .05; the student insisted “but 15 is more than five.” >> To [students], [the equals sign] doesn’t signify equality, but instead means “put the answer here.” Imagine their confusion when, in algebra, they first encounter problems with numbers on both sides of the equal sign.

Sounds like you can just say (as happens) we have to get the answer we're looking for on the "put the answer here" side.

7 + x = 12

"The 'x' represents the answer, so we have to get it on the 'put the answer here side'; lets write 12 = x + 7 ; now we just need to take 7 from the 'put the answer here side' and we're done. But whatever we do on one side we have to do on the other. Take 7 off. 12 - 7 = x + 7 - 7 => 5 = x ... bingo".

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

#204

Post by theli0nheart »

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?

Shift the decimal point of the operand right by N places (where N is how many decimal places of precision you want), do the long division, then shift the decimal point of the result left by N places, and you have your answer.

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

#205

Post by smabie »

chrisseaton wrote: post #120
smabie wrote: post #97

Earlier quoted context omitted.

Because the derivative at 0 of abs is undefined.

Why do I care about that though?

Taylor series, calculating maxima/minima, etc. also standard deviations compose in a very nice way. All throughout math, we use squared terms instead of absolute value all the time because it’s convenient.

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

#206

Post by barry-cotter »

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

Your ex was correct.

https://spaceplace.nasa.gov/seasons/en/

What Causes the Seasons? The Short Answer: Earth’s tilted axis causes the seasons. Throughout the year, different parts of Earth receive the Sun’s most direct rays. So, when the North Pole tilts toward the Sun, it’s summer in the Northern Hemisphere. And when the South Pole tilts toward the Sun, it’s winter in the Northern Hemisphere. It's all about Earth's tilt!

Many people believe that Earth is closer to the sun in the summer and that is why it is hotter. And, likewise, they think Earth is farthest from the sun in the winter.

Although this idea makes sense, it is incorrect.

It is true that Earth’s orbit is not a perfect circle. It is a bit lop-sided. During part of the year, Earth is closer to the sun than at other times. However, in the Northern Hemisphere, we are having winter when Earth is closest to the sun and summer when it is farthest away! Compared with how far away the sun is, this change in Earth's distance throughout the year does not make much difference to our weather.

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

#207

Post by jampekka »

username90 wrote: post #130
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?

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

Normal distribution can be parameterized with almost any measures of location and dispersion. The reason why standard deviation (which is just variance in hiding) is used is because it makes the equations (that non-statisticians practically never need to look at) a bit nicer given the other (mostly arbitrary) conventions used in the maths.

Put simply, standard deviation is arbitrary for most people.

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

#208

Post by adwn »

chrisseaton wrote: post #172
username90 wrote: post #170

Earlier quoted context omitted.

Right, that is how statistics usually is done. Note however that you don't need IDD, independence is enough. So you assume independence, from that CLT follows which means that standard deviation is all that matters. Then the real world deviates from this based on how much your distributions fails to be independent. I'd assume that computer benchmarks have very low correlation between runs, unless you leak ram or your…

I can't understand this. Surely either samples are independent, or they are not? And they are not in a computer program. The state of, to just give one example, the processor cache depends on what happened in the previous run. We have all this rigour in how statistical techniques are applied, and we make black or white decisions based on the numbers that come out of them, but at their very foundation we're saying 'wh…

Statistical techniques are a model of reality: Reality is not rigorous, but when our models are rigorous, imprecision enters the computation at one place only. If our models aren't rigorous, imprecision occurs at more places, blurring the answer even more.

"All models are wrong, but some models are useful." Just remember that there's some imprecision in the answer a model gives you, and keep that fact in mind when applying that answer to make real-world decisions.

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

#209

Post by galangalalgol »

dannypgh wrote: post #180
spodek wrote: post #174

Or: why do so few people who understand math teach elementary school? Once someone learns math, what incentives do they have to choose teaching elementary school over alternatives? I could imagine that the skills to learn math don't overlap with the skills to teach elementary school and that time spent one detracts from the other. If mastery in each takes a decade or so and few people dedicate themselves to double ti…

I would love to teach math to elementary students but I make a base-10 order of magnitude more as a software engineer for a FAANG. I'd take a pay cut of a factor of 4 or 5 to do it in a heartbeat... but having to go back to school to get a teacher's certificate (and likely a master's degree) to get paid 1/10th as much is challenging. I may end up doing it in a couple of years when I'm even more solidly financially in…

Also consider FAANG pay 2-3 times more than other software development jobs. When the next bust comes some of these problems will be alleviated.

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

#210

Post by brianwawok »

dannypgh wrote: post #177
_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 still don't know why long-division works I was taught long division in the 4th grade (age 9) but wasn't taught a proof of why it works until a college algebra course (age 19). For whatever it's worth a different type of long division is taught now under common core. The common core math stuff that I've seen is impressive - there is more focus on teaching things in a way where comprehension of deeper concepts shou…

Yes I love the Facebook memes by parents talking about how math is so complicated now. Most American adults struggle to solve a basic algebraic equation, because it’s not used in day to day life. If a new teaching style gives us a better way to teach concepts, seems worth a try..
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