Education, from N&A

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Education, from N&A

Postby Zamfir » Mon Jan 16, 2017 9:21 am UTC

http://echochamber.me/viewtopic.php?f=9&t=3126&start=80#p4133614
Continuation of above education discussion from N&A. Topics were, amongst others, class size, elasto's experience with Chinese primary schools, and the importance of calculus in high school.

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Re: Education, from N&A

Postby Zamfir » Mon Jan 16, 2017 10:30 am UTC

I'll start.
elasto wrote:I agree we should give a basic education in a variety of subjects. Just apparently we disagree about the definition of 'basic'.

I think school should be less about cramming in facts and obscure skills, and more about learning how to learn.

Also, I agree that 14yo is too young for people know what they want to do, but I disagree that the answer therefore is to teach them everything. I think a much better answer is lifelong free academic education - people should be allowed to learn anything at any time.

We all live 11 lives

Trouble is, serious career switches are expensive, even apart from the cost of education. It's easily a few years of foregone income, followed by some years of entry-level income while you're building a new resume.

My wife made such a switch in the last years. It went very smooth and mostly risk-free, plus we had a small inheritance to carry the costs. It was still stressful, though worth it because she's much happier in this new job. At one point, I was considering a similar (but smaller) switch, more on "why not" grounds than on dissatisfaction. I am so glad I didn't do it. It would have cost me about a third of income at first, plus some years of nightly cramming to fix holes in my knowledge. It would not have been worth it, and that's in the relatively good case where I could start directly in a serious job, just at a junior level. Instead I spent an extra month looking for a job that matched my experience, and that was wise. Spending many such months would probably have been wise as well.

So, I am a tad skeptical about "life long learning", let alone SMBC's proposal to start over every 7 years... it's possible, and people should keep it mind as an option. But realistically, young people get one shot to start a career smoothly - later changes tend to be hard and much more constrained, or the result of arbitrary events (good or bad) outside of your control.

I see the same in economic policy discussions. People talks about life long learning as a fix for job insecurity, but often it's a very limited fix, especially for older people.

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Re: Education, from N&A

Postby elasto » Mon Jan 16, 2017 10:56 am UTC

Unfortunately, my ideas are holistic in nature. I advocate a citizen's wage alongside free lifelong learning, so career changes are not so risky/painful.

It's hard to implement any one of my ideas in isolation because many of them depend on each other to be practical :(

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Re: Education, from N&A

Postby CorruptUser » Mon Jan 16, 2017 2:24 pm UTC

Here's the problem about teaching "concepts" in History class; everyone will fight you tooth and nail on what those concepts should be. The reason for the "facts and dates" is because the teachers threw up their hands rather than deal with every nutjob, because actually consider WHO shows up at those PTA meetings...

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Re: Education, from N&A

Postby LaserGuy » Mon Jan 16, 2017 7:13 pm UTC

Picking up a few things from that discussion:

Zamfir wrote:
The discussion is getting out of the topic ("News in brief"), but it would be awfully late to get started on calculus for the first time not until you are a freshman in uni.


I that really true though, or more true than for other topics? Calculus seems to have a fairly unique position among high school subjects.
- Quite a lot of time and effort is spent on it, especially in higher tracks
- It's a useful tool, more than general knowledge. The existence and the very basics of calculus might be considered general knowledge, but there's a lot of math that seems just as relevant in that regard
- It's very specific. If you don't move on to certain careers, you'll never use the tool
- the above holds across a surprisingly wide range of countries and education systems


How much calculus do you get taught in high school where you're from? Here in Canada, there's usually one senior level math course where it's covered, but it isn't required for graduation from high school or entrance to university, even in majors where you'll need to use it (eg. math/physics).

The answer is that they had to keep working at the material after school, and all weekend if need be. Failure was just not an option.

The normal school day ran from 8am to 5pm. The poorer kids would then go do homework at home assisted by family. The better off kids would go to homework clubs which might have 10-20 in a class, and the teacher there would help with homework questions, re-explaining things if need be.

If my kid understood the day's material, they might finish their homework in an hour or two. If they didn't, they might not finish homework club until well after 9pm. They might not be in bed before 10pm. And they had to be up before 7am the next morning to get ready for school of course.

And this is all at 6 years old...

Oh, and there is huge pressure on parents from the school. My wife would get regular calls from the teachers that might last 30 mins, berating her if my kids' standards dropped at all.

Getting anything less than 100% on any work was regarded as a failure by all involved.


I'm honestly not sure that this really supports the notion that class sizes don't make any difference (likewise in the original study that prompted this discussion where they compare to Korea and Japan). What you're really saying here is that the students in China are spending nearly twice as much time on academics as their counterparts in the United States and elsewhere. That alone can should be able to explain the bulk of the achievement gap. In fact, I would tend to argue that these systems are actually really inefficient in terms of achievement per hour of class time--look at Finland, where students start school later (age 7), have quite short school days (4-5 hours of instructional time per day), and basically no homework, and their students are consistently top-ranked in educational achievement. A Finnish student may well be getting a third as much instructional time as the students in China you're talking about, yet is still outperforming them.

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Re: Education, from N&A

Postby eran_rathan » Mon Jan 16, 2017 7:44 pm UTC

LaserGuy wrote:Picking up a few things from that discussion:

Zamfir wrote:
The discussion is getting out of the topic ("News in brief"), but it would be awfully late to get started on calculus for the first time not until you are a freshman in uni.


I that really true though, or more true than for other topics? Calculus seems to have a fairly unique position among high school subjects.
- Quite a lot of time and effort is spent on it, especially in higher tracks
- It's a useful tool, more than general knowledge. The existence and the very basics of calculus might be considered general knowledge, but there's a lot of math that seems just as relevant in that regard
- It's very specific. If you don't move on to certain careers, you'll never use the tool
- the above holds across a surprisingly wide range of countries and education systems


How much calculus do you get taught in high school where you're from? Here in Canada, there's usually one senior level math course where it's covered, but it isn't required for graduation from high school or entrance to university, even in majors where you'll need to use it (eg. math/physics).


largely depends on two things, the type/wealth of school and what track you are on. My high school had three 'tracks', General, College Prep and Honours. If you chose the Honours track, like I did, you could take one year of Geometry/Geometric Algebra, one year of Pre-Calc, and 2 years of Calculus.

I should state that I went to a semi-private academy, but from what my friends who went to public high schools said, it was much the same there.

The answer is that they had to keep working at the material after school, and all weekend if need be. Failure was just not an option.

The normal school day ran from 8am to 5pm. The poorer kids would then go do homework at home assisted by family. The better off kids would go to homework clubs which might have 10-20 in a class, and the teacher there would help with homework questions, re-explaining things if need be.

If my kid understood the day's material, they might finish their homework in an hour or two. If they didn't, they might not finish homework club until well after 9pm. They might not be in bed before 10pm. And they had to be up before 7am the next morning to get ready for school of course.

And this is all at 6 years old...

Oh, and there is huge pressure on parents from the school. My wife would get regular calls from the teachers that might last 30 mins, berating her if my kids' standards dropped at all.

Getting anything less than 100% on any work was regarded as a failure by all involved.


I'm honestly not sure that this really supports the notion that class sizes don't make any difference (likewise in the original study that prompted this discussion where they compare to Korea and Japan). What you're really saying here is that the students in China are spending nearly twice as much time on academics as their counterparts in the United States and elsewhere. That alone can should be able to explain the bulk of the achievement gap. In fact, I would tend to argue that these systems are actually really inefficient in terms of achievement per hour of class time--look at Finland, where students start school later (age 7), have quite short school days (4-5 hours of instructional time per day), and basically no homework, and their students are consistently top-ranked in educational achievement. A Finnish student may well be getting a third as much instructional time as the students in China you're talking about, yet is still outperforming them.


Also, as a parent of children school age, I really wonder how much actual 'educational achievement' is going on at 5 or 6 years old. I mean, letter and number recognition, simple spelling/reading, basic addition and maths skills, etc sure, but the over-emphasis on testing in the US is mindbogglingly overwhelming. My 10 year old had 3 solid weeks of testing this year, and in each case that whole week and the week before was dedicated to teaching the tests. I understand that they need the data to coordinate learning and all the other statistical analysis they do, but that seems really excessive.
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Re: Education, from N&A

Postby Chen » Mon Jan 16, 2017 8:52 pm UTC

LaserGuy wrote:How much calculus do you get taught in high school where you're from? Here in Canada, there's usually one senior level math course where it's covered, but it isn't required for graduation from high school or entrance to university, even in majors where you'll need to use it (eg. math/physics).


In Quebec we have 2 years of CEGEP between Grade 11 (last year high school) and University. I took no calculus in high school and took 3 courses over the 2 years in CEGEP. The last course (creatively named Calculus III), was the equivalent to intermediate calculus in university and I was able to get credit for having done it at the CEGEP level.

Note that students who came to Quebec universities from other provinces generally had to pass through the year 0 requirements (at least in engineering) which contained Introductory Calculus. This was basically a combination of CEGEP calculus I and calculus II which introduced differentiation and integration, respectively. I presume there might have been some other provinces' high schools where an exemption from Introductory Calculus could be obtained if they took the optonal calculus courses.

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Re: Education, from N&A

Postby morriswalters » Mon Jan 16, 2017 11:42 pm UTC

A Finnish student may well be getting a third as much instructional time as the students in China you're talking about, yet is still outperforming them.
That depends on the student not the school day. All kids aren't created equal for conditions not related to genetics. If the teacher doesn't have the number of instructional minutes that each student needs, then class size becomes irrelevant. So your point says more about the student population. Finland is relatively homogeneous, small, and with a good social welfare system. It's possible to do the same thing in the US, and it is done in private schools. But the US public schools are in a realm of their own in respect to preparedness of some students entering school. I don't know much about the Chinese. But as described it seems to be a machine. Forced involvement of the parents, long school days and pushing. Pick someone in the pack intelligence wise, and teach to him. But if you do it right then you graduate students at high rates. Like my DE class. It turns out that the Chinese are filtering as well.
Critics of PISA counter that in Shanghai and other Chinese cities, most children of migrant workers can only attend city schools up to the ninth grade, and must return to their parents' hometowns for high school due to hukou restrictions, thus skewing the composition of the city's high school students in favor of wealthier local families.

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Re: Education, from N&A

Postby Vahir » Tue Jan 17, 2017 3:49 am UTC

A bit late but

elasto wrote:
CorruptUser wrote:Depends what you get a job in. If it's a STEM or Finance field, you damn well will see algebra constantly. It will even make its way to some of the Humanities, especially Music.

I'm talking about knowledge like being able to integrate/differentiate an equation by hand. To me these seem like archaic skills akin to knowing how to use a log table.

Remember, my kids are still in primary school. The job market is going to be vastly different by the time they graduate university, and the stuff you talk about seems just the sort of thing AI will be much better at than people by that time.


As an engineering student I can say that being able to integrate and differentiate by hand is extreeeeeeeemely important. If you can't integrate when learning, say, fluid mechanics, you aren't going to be able to follow the matter. And you get PDEs that are downright impossible to solve with conventional integrating calculators.

This stuff NEEDS to be taught for students to comprehend STEM fields, and universities already have too much matter to go over to teach basic algebra.

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Re: Education, from N&A

Postby sardia » Tue Jan 17, 2017 5:03 am UTC

http://www.npr.org/sections/ed/2017/01/ ... -dont-work
We keep talking about such a vague measure like class size and usefulness of calculus, when the reality is the world isn't made up of homogeneous teachers. Anyone noticed how everyone touts school choice, but we can't pick our teachers?
Many education reformers tout school choice as a tool for parent empowerment and school improvement through competitive pressure. But Hattie says his research shows that once the economic background of students is accounted for, private schools offer no significant advantages over public schools, on average. The same goes for charter schools.

But there is one kind of choice that Hattie does believe makes a difference: teacher choice. Being able to select the best teacher for your child, Hattie suggests, could be truly empowering for parents — albeit a challenging strategy for a school to adopt.

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Re: Education, from N&A

Postby morriswalters » Tue Jan 17, 2017 4:33 pm UTC

sardia wrote:We keep talking about such a vague measure like class size and usefulness of calculus, when the reality is the world isn't made up of homogeneous teachers. Anyone noticed how everyone touts school choice, but we can't pick our teachers?
Obviously you weren't paying attention in college. Part of what you buy at Harvard is the best and brightest in terms of instruction. The same for lesser schools, they are just less bright(or at least less well published). They are priced accordingly. They can also be selective.

Elementary and secondary schools in the US have a different problem. Public schools, at least, can't be selective. And you can't have better teachers everywhere. There isn't enough money or teachers. And unless you see something I don't, you aren't ever going to have them. What you can do is make the best of what you have.

Consider that point in respect to China. I Assume they have to have big classes if you assume the same funding limitations as the US. Larger class sizes helps reduce the number of teachers required, but rigid adherence to a schedule and rigid control over content might allow the Chinese to reduce the impact of teacher quality. You do it by rote. Read, write, recite, and reinforce.

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Re: Education, from N&A

Postby sardia » Tue Jan 17, 2017 5:08 pm UTC

Wait why are you comparing teacher choice from a secondary vs primary education?
Also, with some rule changes, you could do something like have the best teacher get a big class, and the crappy teacher gets a tiny class. That way, the families can choose their teacher. Post some (non) controversial metrics and have parents choose.

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Re: Education, from N&A

Postby Chen » Tue Jan 17, 2017 5:26 pm UTC

I'm not really sure what metrics you'd use to determine what teacher to pick. If there was a standard set of metrics, wouldn't everyone gravitate towards the same teachers?

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Re: Education, from N&A

Postby freezeblade » Tue Jan 17, 2017 6:01 pm UTC

LaserGuy wrote:How much calculus do you get taught in high school where you're from? Here in Canada, there's usually one senior level math course where it's covered, but it isn't required for graduation from high school or entrance to university, even in majors where you'll need to use it (eg. math/physics).


For reference, I went to Public High School in California, graduating class of 2004 (first year to have the exit exam implemented), and there was no required Calc in the curriculum, or at least, nothing called calc. You were required to take math for 3 of your 4 years of High School (9-12), with the minimum required level of Trigonometry achieved. The "standard" math track was as follows, beginning with Algebra as the standard, below if you tested poorly:
Remedial Math > Algebra > Geometry > Trigonometry > Precalculus > Calculus
You could take Statistics instead of Precalc if you wished, to have them work as an additional math elective. Calc itself was probably taken by 15 or so kids in each year.

If you decided to go to the community college after high school (as I did to transfer), you had to take a proficiency exam for placement in math. Most kids tested into Precalc, and of the few that tested into Calc, most chose to take precalc anyway, as the Calc class was notoriously difficult. Pass/Fail rate for calc at my community college was under 50%
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Re: Education, from N&A

Postby morriswalters » Tue Jan 17, 2017 6:29 pm UTC

LaserGuy wrote:How much calculus do you get taught in high school where you're from?
In 1978 or thereabouts two students from the Catholic High School System entered my DE class straight out of high school. I believe that is still possible today.
sardia wrote:Wait why are you comparing teacher choice from a secondary vs primary education?
Also, with some rule changes, you could do something like have the best teacher get a big class, and the crappy teacher gets a tiny class. That way, the families can choose their teacher. Post some (non) controversial metrics and have parents choose.
I didn't. I lumped them together. I compared them to post secondary education.

Remember what you are there to do. My son has an IQ of less than 60. No teacher, no matter how good their skills will ever get him to the point where he can read the Iliad. So it isn't all about how good the teacher is. If you have a class where the students have IQ's of around 120 and you might teach a lot of kids at once. Make the range between 75 to 120 and the picture changes. If you have 4 hours a day and 5 days a week with a student, you have 20 hours a week direct classroom time for whatever number of students. If some of your students need more of your time than others then someone will suffer. At best, assuming that range, the better students will suffer because you have to slow down and spend more instructional minutes on the ones who can't go as quick.

And they are currently doing as you suggest. In my locale they are called magnet schools. Parents spend a lot of time getting their kids in those schools. The seats are limited and the getting in requires work. Nobody calls it that, but they are filtering. Parents do it all the time by choosing where they live and what schools they send their kids to. Within the county I live in is a system called the Anchorage School System. It is among the richest zip codes in the state and in the country. They have their own school system. 380 students, 38 teachers. Ranked fourth in the state. But the most telling statistic is that no one is on subsidized meals.

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Re: Education, from N&A

Postby ahammel » Tue Jan 17, 2017 6:34 pm UTC

Calculus:
Spoiler:
Where I went to university (in Canada) there were two entry level calc classes: one for those who took calculus in high school and one for those who did not. Students in the latter (including myself) went to the same lectures as those who had done calculus in HS, but we had to attend a supplementary lab session taught by a grad student.
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Re: Education, from N&A

Postby sardia » Tue Jan 17, 2017 7:34 pm UTC

Morris, you need to differentiate school choice from teacher choice. Once you controlled for wealth, all those fancy schools don't beat out equivalent public schools. No school in the country does teacher choice. You're also denigrating real statically significant findings by demanding it meet outliers.

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Re: Education, from N&A

Postby Chen » Tue Jan 17, 2017 8:38 pm UTC

sardia wrote:Morris, you need to differentiate school choice from teacher choice. Once you controlled for wealth, all those fancy schools don't beat out equivalent public schools. No school in the country does teacher choice. You're also denigrating real statically significant findings by demanding it meet outliers.


I ask again, how would teacher choice work? How would you objectively rate teachers? You'd seem to run into the same "Achievement standards" problem (item 1 from the article you presented) if you base it off student results in specific teachers' classes. Even if you did find a good metric, wouldn't everyone just end up gravitating towards the "best" teacher anyways?

If you're choosing schools and somehow not basing that choice on teacher quality (in at least some way) then frankly I think you're doing it wrong. In which case, if you give those same people a choice of teachers, I see no good reason why they'd suddenly make better choices.

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Re: Education, from N&A

Postby morriswalters » Tue Jan 17, 2017 8:59 pm UTC

sardia wrote:Morris, you need to differentiate school choice from teacher choice. Once you controlled for wealth, all those fancy schools don't beat out equivalent public schools. No school in the country does teacher choice. You're also denigrating real statically significant findings by demanding it meet outliers.
No, I don't think so. The teachers would be overwhelmed. Who wants second class teachers? Do you? School is 12 years long. Are you going to move every year? What if your favorite English teacher teaches somewhere other than where the Math teacher teaches at? You have what I would call a sparse resource and high demand.

And you miss the point on the Anchorage Schools. They attract good teachers by offering ideal students. What math teachers wants to teach arithmetic when you can do advanced placement with bright kids and motivated parents? The system is a marker for good teachers. And it's why they rank schools. If a school get good ratings, it's an acceptable marker for representing teachers.

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Re: Education, from N&A

Postby sardia » Wed Jan 18, 2017 12:52 pm UTC

Chen wrote:I ask again, how would teacher choice work? How would you objectively rate teachers? You'd seem to run into the same "Achievement standards" problem (item 1 from the article you presented) if you base it off student results in specific teachers' classes. Even if you did find a good metric, wouldn't everyone just end up gravitating towards the "best" teacher anyways?

If you're choosing schools and somehow not basing that choice on teacher quality (in at least some way) then frankly I think you're doing it wrong. In which case, if you give those same people a choice of teachers, I see no good reason why they'd suddenly make better choices.
your under the mistaken assumption that choosing which school to go to is a good thing, choosing is defined by allowing parents to send their kids to private or religious schools ALONG WITH THE Tax MONEY.
We are about to find out what choosing schools actually does. The Republicans are in charge and the education secretary is pushing school choice.

All the examples you and morris are using are either top foreign schools or high end white people schools. Trying to find the best teachers is a challenge, but at least it's a metric that has statistically significant effect sizes.

What problem is school choice trying to solve? Not enough money? Too far away? Segregation? Bad regulations? Unions? Bad lesson plans? What data do you have that choosing a private school solves any of that with meaningful results?

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Re: Education, from N&A

Postby Chen » Wed Jan 18, 2017 1:06 pm UTC

sardia wrote:your under the mistaken assumption that choosing which school to go to is a good thing, choosing is defined by allowing parents to send their kids to private or religious schools ALONG WITH THE Tax MONEY.
We are about to find out what choosing schools actually does. The Republicans are in charge and the education secretary is pushing school choice.

All the examples you and morris are using are either top foreign schools or high end white people schools. Trying to find the best teachers is a challenge, but at least it's a metric that has statistically significant effect sizes.

What problem is school choice trying to solve? Not enough money? Too far away? Segregation? Bad regulations? Unions? Bad lesson plans? What data do you have that choosing a private school solves any of that with meaningful results?


Im not making any assertion as to whether or not school choice is a good thing. The article you quoted said its bad, and proffered teacher choice instead. I'm trying to figure out how that makes any lick of sense, especially if you go with the premise that school choice is bad. If school choice was fixed and you could somehow choose teachers within the schools, wouldn't it just become a microcosm similar to the current private/public system? The best teachers with the best classes, would likely be the ones who got the best materials, more access to field trips etc. Or those that did get the better materials or did more extra-curricular stuff or whatnot, would be the ones considered the "best" and thus they'd have more students flocking to them.

Whether or not private schools should be getting government money or not is not immediately obvious. Yes, that takes money away from public schools. But it also takes STUDENTS away from public schools. The government pays less to the private schools per student than public (well at least here in Canada). So you'd need to weigh how many private school students would move to public schools, if the subsidies were removed and the private school cost went up accordingly. In the extreme cases we can clearly see that if all private students moved public, we'd actually make the money/student situation much worse. If none move private to public it would be great since the public system would recover a whole bunch of "free" money. Reality would be somewhere in between so depending on the details of the changes, it could be a benefit or detriment to the public system.

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Re: Education, from N&A

Postby morriswalters » Wed Jan 18, 2017 5:56 pm UTC

sardia wrote:What problem is school choice trying to solve? Not enough money? Too far away? Segregation? Bad regulations? Unions? Bad lesson plans? What data do you have that choosing a private school solves any of that with meaningful results?
It isn't trying to solve any problem. It is a natural consequence of the process which requires physical locations to teach in. Teachers teach, somewhere. Because schools are where people are.

School choice leads to segregation. White flight from the city center created all white schools in the suburbs and all black schools in the city center. This was litigated before I got into school in Brown v. The Board Of Education. Busing tries to fix that but has unintended consequences.

The Republican version of free choice seeks to take the money spent on public education and move those dollars to schools which reflect their desires through vouchers or subsidies. In other words they wish to return to separate but equal schools. The idea that schools funded equally can be fundamentally fair. But this takes money away from public schools while also siphoning away the better students. Would you disagree with that characterization? How I feel about this is complex given that I would send any minor children that I might be responsible for to private schools. And I would want a voucher if a voucher were available. But I wonder how fair that is.

Just out of curiosity how would teacher choice work given fixed locations for schools?

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Re: Education, from N&A

Postby Qaanol » Sat Jan 21, 2017 6:54 pm UTC

Calculus should be taught in middle school.

If elementary school is not teaching students sufficient geometry and arithmetic-with-letters to tackle the calculus of one variable by age 12, then that elementary school curriculum is a mathematical failure.

Obviously some students are slower learners and won’t progress at the same pace as everyone else, but the vast majority of kids should master basic arithmetic by age 8 or 9, become proficient in arithmetic-with-letters and the geometry of triangles by 10 or 11, and thus be ready for calculus.

Middle-schoolers should also learn about linear algebra. High school math would then include probability & statistics, differential equations, complex analysis, and abstract algebra.
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Re: Education, from N&A

Postby Zamfir » Sat Jan 21, 2017 8:15 pm UTC

Why?

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Re: Education, from N&A

Postby morriswalters » Sun Jan 22, 2017 3:02 am UTC

I can see how that could help a framing carpenter. Probably plumbers too.

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Re: Education, from N&A

Postby Thesh » Sun Jan 22, 2017 3:22 am UTC

I think we're at the point where, no matter what we teach in high school, a four year general liberal arts degree might be a good idea to start providing for free to anyone who wants it in the very near future if we want to make sure people are as prepared as possible to adapt to any new technologies and opportunities in a market with rapidly advancing technology.
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Re: Education, from N&A

Postby Mambrino » Sun Jan 22, 2017 4:38 am UTC

Qaanol wrote:Differential equations, complex analysis, and abstract algebra.


...why? Okay, i can see differential equations as a motivation for calculus (we even had a couple of very simple one-dimensional examples in our calculus books in high school: "this stuff does have applications! see, dynamic models! physics!"). And an introductory course in abstract algebra might be a nice elective that showcases what the theoretical mathematics at university level is like, for those students with such interests.

But complex analysis? Complex numbers are fun and very useful for widening your thinking ... but c'mon, any serious course in Complex Analysis is a graduate level course. Recommended after approx. two years of proof-based undergraduate maths. And a watered-down complex analysis class would nigh useless. (TBH I consider that complex analysis course quite useless myself, even though it was fun.) What the hell your regular high schooler is going to do with Cauchy integration theorem or conformal mappings (or appreciate them)?

In the ideal world, I would double down on probability and statistics. Maybe introduce a separate subject of "statistics" in addition to mathematics. And get more serious on computer science, both theoretic CS and practical programming.

But we are not in an ideal world. I suspect you have not seen, or do not remember what your regular student is like and is capable of.

Of my elementary school class of 25 students (Medium sized town, the classroom was quite nice intersection of the whole community, from children of janitors to the children of doctors), around half considered percentages a challenging topic. After 6 years of basic arithmetic and advancing to middle school level, ~3 were transferred to "special learning needs" class, we the rest were introduced to "maths with letters" and spent 3 years with very basic algebra and geometry, and in the end I suspect maybe a half actually got that stuff. Probably less. After the middle school level, most of them already had had enough of theoretical learning, including maths, and opted for vocational school instead of high school. Yet the first maths module in the high school advanced maths program was mostly concerned with remedial review of basic algebra (and after which several students then dropped out of the advanced maths class anyway for the short course in maths, with less of "hard stuff" like calculus). Not all the advanced course students who remained and passed, did pass with a good command of calculus.

I'm not the kind who goes to the school reunions and such (and I haven't been invited), but as far as I know I'm the only who got into studying maths in the uni and probably the only one who took a class in complex analysis. (Rest of the ones with good maths grades wanted to get started on more profitable careers.) And I'm quite mediocre student in my maths program.

And this was in the wonderland of Finland.

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sardia
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Re: Education, from N&A

Postby sardia » Mon Jan 23, 2017 2:23 am UTC

Zamfir wrote:Why?

The only thing I can think of is to earn college credits early, thus saving money at accredited universities. That was a big thing in high school, take hard classes now, and save money in college later. You could get most of your gen ed requirements out of the way, at least a decent chunk of them with AP calc, physics, chemistry, english, and history. If you took them all, you just cut the cost of college by 12.5%, and you get out into the work force faster. That is the goal right? To educate students to increase GDP growth/go up the value chain of economic goods.

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freezeblade
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Re: Education, from N&A

Postby freezeblade » Mon Jan 23, 2017 4:13 pm UTC

I took a few Community College classes in late High School, for the reason listed above (save money for transfer), as well as each class taken at a college was worth double credit, as well as an extra gradepoint in my GPA (One semester of CC class counted as two semesters of AP class as far as my high school was concerned). Not only that, but they were free to me (minus the health fee of $17/unit) to use as a high schooler. I really think that more would take the option, if they knew it existed. One of the classes I took was a Trig class.
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eran_rathan
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Re: Education, from N&A

Postby eran_rathan » Mon Jan 23, 2017 8:33 pm UTC

Mambrino wrote:
Qaanol wrote:Differential equations, complex analysis, and abstract algebra.


...why? Okay, i can see differential equations as a motivation for calculus (we even had a couple of very simple one-dimensional examples in our calculus books in high school: "this stuff does have applications! see, dynamic models! physics!"). And an introductory course in abstract algebra might be a nice elective that showcases what the theoretical mathematics at university level is like, for those students with such interests.

(snip)

In the ideal world, I would double down on probability and statistics. Maybe introduce a separate subject of "statistics" in addition to mathematics. And get more serious on computer science, both theoretic CS and practical programming.



Honestly, if one were teaching, i suspect it would be much easier to introduce and teach the more complex concepts of calculus and linear equations specifically by showing the actual usage, instead of merely the equations.

Heck, I've taught my 10 year old basic trigonometry and algebra, by focusing it on actual uses (I'm a surveyor, its what I do (shrug)).


But remember, in 5th grade, just before they hit middle school, you've got kids who are still working on their multiplication tables, never mind complex analysis or other BS like that.
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CorruptUser
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Re: Education, from N&A

Postby CorruptUser » Mon Jan 23, 2017 9:04 pm UTC

Since when do you even see complex analysis prior to college? I mean sure, imaginary and complex numbers and their relative distance to 0, but nothing more, errm, complex than that.

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eran_rathan
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Re: Education, from N&A

Postby eran_rathan » Mon Jan 23, 2017 9:31 pm UTC

CorruptUser wrote:Since when do you even see complex analysis prior to college? I mean sure, imaginary and complex numbers and their relative distance to 0, but nothing more, errm, complex than that.


Circuits/electrical engineering. We did some (albeit very little) in physics class in high school.
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Ixtellor
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Re: Education, from N&A

Postby Ixtellor » Mon Jan 23, 2017 9:32 pm UTC

As a 12 year vet teacher and a wife who is a 'big wig' in a large school system, I thought I would add some points.
(I have taught at the poorest school in my State and I have taught at a 'rich white' school, I have taught the lowest performing students as well as the highest)
1) How do you measure if a teacher is good or not? Before you answer, I'm just going to tell you that there is no metric that can actually tell you, but at the same time, after a while everyone knows who the good and bad teachers are. The closest I have ever come to a metric is just student input, but that has its obvious problems. (Coaches who show Youtube video's can get high ratings from unmotivated students).

I know teachers at exclusive private schools and any success they experience in the classroom can just as easily be from good students with strong parental support as it is from good teaching. I have had students I could have given coloring assignments to all year and they still would score a 5 on the AP calculus b/c test.

2) Chinese numbers on education... take it with a grain of salt. First there are vast cultural differences. I have met a lot of students who don't give a lick about 'dishonoring' their parents. Also, Chinese numbers are from the eastern free economic zones from the emerging middle class. Go into Western China and look at how their kids perform... if they aren't working in the fields with their hands. (Those kids don't get counted in their National scores)

3) Finland --- it was already addressed. Small, homogeneous, and lack of poverty.

4) Public schools v Private schools. Private schools pick and choose their 'clients'. In public schools we teach everyone. Hate school, tell teachers to 'fuck off' to their face with Parents who respond "yea, fuck off!". Refugees, low IQ, zero family income, abusive parents --- we teach them all and their results on national and State tests are tallied.
In my State, there are 18 year old high school students who have been in America for 2 years, barely speak English and fled a wore torn nation (Syria/Napal) who are expected (BY LAW) to take the same State exams (in English) as everyone else.

Lastly, A private school teacher who teaches the most motivated students with vast economic resources or a public school teacher with all refugee kids who and a ZERO percent pass rating on State exams --- Whose the better teacher?

So I ask again, how do you measure if a teacher is good or not?

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Tyndmyr
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Re: Education, from N&A

Postby Tyndmyr » Tue Jan 24, 2017 5:12 pm UTC

elasto wrote:Unfortunately, my ideas are holistic in nature. I advocate a citizen's wage alongside free lifelong learning, so career changes are not so risky/painful.

It's hard to implement any one of my ideas in isolation because many of them depend on each other to be practical :(


If all your ideas depend on each other, that makes them extremely brittle. Anything not working out brings down the whole house of cards. This is a severe flaw. Economies invariably go awry at some point, and in ways we don't forsee. After all, if we all knew something was overvalued, we'd value it less.

Anyways, I think there's always a significant risk to career changes, even if the learning itself is cheaper or free. The newcomer to a field typically makes less than the guy with years of experience. Learning takes time. There are costs there, no matter how you try to disguise or offset them. Cheers for those people who wish to do this, but some people will not wish to. Time is a cost. Hell, learning time isn't equal for all people, even. So, a model in which people switch career fields frequently is not necessarily more egalitarian. Probably less so.

As for teacher selection, that would be amazing. College students sometimes rate teachers, because you may, through section selection, be able to pick or avoid certain teachers. It's far from perfect, but the difference between a good teacher and a shoddy one can be immense. In practice, however, it can be tough. If only section is offered for that class you need, actual choice isn't really there.

School choice may also have uses. Maybe it'll make it easier for a student to avoid a particular bad situation(particularly long bus rides, maybe) or something. But it *is* a very different level of selection, and can't really be treated as the same thing. Maybe if one has detailed knowledge of all the teachers at each school, it kind of puts some pressure on teachers, but it's way less direct, and the comparison problem is far harder.

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Re: Education, from N&A

Postby morriswalters » Thu Jan 26, 2017 1:28 pm UTC

Ixtellor wrote:So I ask again, how do you measure if a teacher is good or not?
You don't. What you can measure is the ability of a teacher to execute a lesson plan. But that isn't meaningful in any real sense. Given 30 students of varying backgrounds you can pick someone in the pack and teach to them. Slower students will have trouble and faster students will be bored. But if you stick to the plan and you have chosen your target student wisely, the class as a whole should be able to learn what it is that you have to teach. But never all of the class. And any comparison like that presumes that each teacher, teaches exactly the same thing, in the exactly the same way. Which is why learning by rote works.

I went to a boarding school for gifted but disadvantaged kids. Everyone had an IQ of at least 110. One would think that it would make for an exhilarating educational experience. Add to that young , committed teachers, and class sizes around 10 to 15. At least one third of the student body was gone by the end of the first year. Of those that remained some were in academic trouble, including me. The problems revolved around factors the school couldn't control. That would be the disadvantaged part.

On Trig. I never took it. And never needed it over and above what I could get out of whatever class I attended that needed it. On the other hand I took high school Geometry. And I would as soon pluck my eyes out if I had to go back and do it again.


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