I am immediately reminded of the opening of Lockhart's essay "A Mathematician's Lament"[0]:
> A musician wakes from a terrible nightmare. In his dream he finds himself in a society where
music education has been made mandatory. “We are helping our students become more
competitive in an increasingly sound-filled world.” Educators, school systems, and the state are
put in charge of this vital project. Studies are commissioned, committees are formed, and
decisions are made— all without the advice or participation of a single working musician or
composer.
> Since musicians are known to set down their ideas in the form of sheet music, these curious
black dots and lines must constitute the “language of music.” It is imperative that students
become fluent in this language if they are to attain any degree of musical competence; indeed, it
would be ludicrous to expect a child to sing a song or play an instrument without having a
thorough grounding in music notation and theory. Playing and listening to music, let alone
composing an original piece, are considered very advanced topics and are generally put off until
college, and more often graduate school...
I think the analogy here is that after graduation, the kids are going to be asked to play a song from sheet music, but the school doesn't want them to be forced to (or feel bad if they have trouble to) learn the terribly constraining rigors of musical notation. Or worse, the teachers don't really understand how to teach the notation themselves.
Instead, we want them to invent how to write music "using the innate and self-discovered techniques for music notation that make sense to them as whole individuals".
You'd be surprised - for a number of musicians it's not about sight reading notation and playing fom there, it's about developing musical talent and variations and adding in formal notation reading | writing later.
I've known a family of three siblings who all played in the state orchestra in their teens and only one was a fluent reader, the other two were extremely good musicians that practised hard and either very slow worked through written music note by note, or, once familiar with a piece looked at a page of music with a helicopter view, not reading" individual notes, but tracking off entire blocks .. like seeing a page of text w/out wearing glasses.
From the same music roots, some years later, Tim Minchin- admittedly more an Entertainer than a pure Musician - but none the less someone that made their name and living from performing original and relatively complex music on stage playing piano and singing - also doesn't read music:
I used to play in a couple of competitive bands, I always ended up in 1st / 2nd chair, but I always started in lower chairs because I can’t sight read music and would botch my auditions.
Once we were in the room and playing, and I got to hear the music, I was good and the notes on paper made sense- but out of context the notes didn’t do it for me.
Doesn't read | write sheet music (see youtube interview linked in GP comment)
Oxford English Dictionary:
musician - A professional performer of music, esp. of instrumental music.
Wikipedia:
Timothy David Minchin is a British-born Australian comedian, actor, writer, musician, poet, composer, and songwriter.
Also - pretty much the entirety of Indonesian traditional ensemble musicians (Gamelan and other) going back to the bronze age - no sheet music so no reading writing music - they train like Homer delivered poetry and use non Western scales - their music is available in notation, but notation created by westerners.
Here's a bit about Western students learning to learn music w/out using sheet music ...
Many of the greatest jazz musicians of the 20th century didn't know how to read music, and jazz is rather famously considered overly complex and obtuse for the typical listener. Notation is useful, but it is not music.
The volume of fairly famous or otherwise well-established musicians in rock, funk, and even jazz with a poor or non-existent ability to read or write music notation is not insignificant.
Then there are all the non-western scale musicians who learn other systems, or use some variation of solfège to explain musical ideas.
I'd say Michael Jackson was a musician given I'd never seen his videos but loved his music as a kid and still do. Dude did his own compositions & simply sang the parts to other musicians.
The analogy is quite on-point. In the 18th-century conservatories that trained scores of outstanding composers[0] the "cornerstone of music pedagogy" in the early years was singing, making up little embellishments or variations on existing melodies (these were called passaggi or diminutions) and using solfège (or rather an early variety thereof, based on the hexachord) to reverse the process and discover the deeper, simpler melodic structures underlying existing pieces. In later years the best students would be sat at the keyboard and taught to improvise entire pieces from a bassline. Paper was very expensive, so sheet music was little used: wax tablets would be used as a scratchpad when needed. Merely playing written-out pieces was seen as sub-par, something for those who couldn't attain the more highly valued skill of actual improvisation.
That whole skillset is all but lost now, long supplanted by a hyper-competitive culture of supposedly 'virtuoso' performance. It survives to some extent in organ playing, and the jazz tradition as a whole may or may not be an offshoot of some popularized ("folk") variety of it.
[0] See Robert O. Gjerdingen Child Composers in the Old Conservatories: How Orphans Became Elite Musicians. (2020) Oxford University Press.
I've no idea why your comment was flagged and moved to [dead] - it seems fine as a comment to me.
That said:
> you're still talking about performing existing pieces from a very well-defined canon
My first comment in this thread could not have been "still talking" - and I contrasted two things, - reproductive orchestra performances by people trained in composition and improvisation two of whom considered themselves unable to read music (responding to the person above me) and
an "entertainer" considered by many to be a real musician (that's a whole thing in itself, isn't it) who also can't read, composes his own music, and improvises around his own work during nearly every performance.
I'm actually siding with yourself, the formalities in both mathematics and music are important and useful but they aren't fundemental for a great many with talent in those fields - they can intuit they way through to a large degree and teaching based on intuitve methods can make great inroads when introducing new students to these subjects.
Formalities can come later (or drilled in parallel), they have their place - but having a 'feel' for these subjects carries a great deal of weight, if not more.
I disagree with what you say about 'formalities' in math, since they're practically the whole subject. It's a question of how they're taught, not whether to teach them. Not teaching the formal part and leaving it all to 'intuition' amounts to letting misconceptions fester with no feasible way to correct them. Even in music, a successful composer or improviser needs to know a lot about viable patterns and rules of thumb, and this knowledge would've been conveyed explicitly as well as by example. (These are not really 'formalities' in a strict sense but they're the closest thing in that domain.)
You might be imagining you think I said about formalities in mathematics, they're more or less essential in making something rigorous and passing it on to others but you'll find that many prolific mathematics start with intuitions, invent their own informal notations, and move toward a formal expression only when some new direction or concept is almost complete.
Maths proceeds faster with those who have been passed good intuitions about lengths, symmetries, and other concepts - these are the fundemental groundings. The formal notations follow to add rigor and to assist in the reasoning and formal proof.
> Even in music, a successful composer or improviser needs to know a lot about viable patterns and rules of thumb, and this knowledge would've been conveyed explicitly as well as by example.
There are entire schools of music that are conveyed entirely by example with no formal music theory whatsoever.
No it's not!!! For starters look at the Suzuki method! Also life stories of many great musicians tells us they learnt by listening and playing along, a lot.
We live in that world: copyright, as it has become, is fundamentally incompatible with music as a field. To say nothing of the issues it creates for covering, sampling, remixing, and setting new words to existing tunes (a time-honored musical tradition), there are increasing numbers of law suits over things that basically boil down to existing in the same genre or using the same fundamental musical laws.
Even if the suits don't go unfavorably, simply publishing an original song opens one up to a major risk.
It's been interesting to watch Adam Neely, a music theory YouTuber and practicing musician, become increasingly disillusioned with copyright after analyzing a handful of high profile music lawsuits...all of which were as ridiculous as Oracle v Google.
Kids who have wealthy/involved parents that push them will always outperform kids who don't. The government can do whatever they want to try to equalize that (except encouraging parents to do better), I just hope they waste as little money as possible and don't interfere with gifted kids.
FWIW my 14 year old is doing pre-algebra now, she struggles with math and the way they are teaching it seems insane. Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing. That probably results in relatively equal outcomes but she has no clue how to do things that fall outside of the frameworks they established.
Someday a “reality check” situation happens. Might be writing a cover letter for their first job. Or trying to pass college-level calculus. But eventually, if someone doesn’t actually know how to read, write, or think logically it comes to a breaking point.
It doesn’t matter if a high school gave someone all As and a college gave out a degree in Community Building. The market judges everyone’s skills, and barring nepotism, the market will pay everyone what they are worth, which is sadly not much for a lot of people.
After all, if you had to hire someone, are you going to offer a job to someone who writes in broken emoji-gibberish and can’t multiply?
One time I got a resume from someone at a fairly well-regarded college for an internship, and the cover letter was a single run-on sentence without any capitalization. How could this person possibly succeed? How much money did they spend getting to this point of obvious failure? Very sad
Sure, you're utterly incompetent but you have the Approved Believes, support the Approved Causes in the Approved Way, and you ticked the right superficial Identity+ checkboxes we needed.
The really sad thing is that the once the markets stop rewarding woke-ism, all these people will be out of a job AND lack the skills to make it in the real world, because these companies have coddled them their entire working lives and stifled any growth opportunities to defend a "safe space".
If you're a straight white male, have you tried identifying as LGBT for oppression ladder points? If I was an American in need of a job I'd do it for sure.
That "reality check" will never come for some people because they will get government jobs where the hiring process depends more on ideology than competence. For example, do you believe that working in the San Francisco Department of Homelessness and Supportive Housing requires thinking logically?
Do you believe that so many government jobs that would completely ignore results exist that will absorb our entire society’s yearly group of young adults entering the job market or do you maybe think that’s an extremely niche situation even if we accept at face value that they target ideology over all results?
> The market judges everyone’s skills, and barring nepotism, the market will pay everyone what they are worth, which is sadly not much for a lot of people.
false in the general case, you're basically invoking a just world hypothesis without actual proof for it.
For a counter example, please see slavery - slaves were not paid anything, despite obviously producing something of worth. Furthermore, there was no difference in the salaries between slaves, despite there presumably being differences in output.
For another counter example, you can look into the variation in programmer salaries based on country, or more generally location. The same job will pay anywhere from $180k in SF to $8k in India, due to differences in cost of living, which have a priori zero effect on programmer 'worth', which I presume would be how good the programmer is at writing code and delivering business value.
It is true that at a certain point, 'real skills' matter - eventually, if you're working as a software engineer, you need to write code. However, it is false to assume there is anything besides a maybe a very mild correlation, if any, in the salaries of software engineers and their ability. You can have a Polish dev with 15 years of experience making less than a new grad in California, and that has nothing to do with skill, but everything to do with regional differences in salary.
everything you have used as an example is not a free market, it is government interference.
1) slavery was enforced by the government who had use of force to compel. There was no voluntary two party agreements.
2) countries are governmental constructs with barriers enforced by use of force. A polish programmer cant work in the US due to governmental interference.
Now that the borders are wide open expect to see programmers exploiting the work loopholes to get work visas that allow them to work at market wages.
there is no perfect information and there will always be mismatches. But in a free market those mismatches are temporary. Also the market may be valuing things other than technical prowess (e.g. english proficiency, understanding of cultural norms etc)
Voluntary two party agreements work because they are enforced by a government.
Markets only exist in the presence of government. Read David Graeber's Debt if you want a history of how markets and money work - generally speaking, they are things created by governments, to ease the work of figuring out taxation. Those quarters and nickels and dimes only have value because you know that come tax season, Uncle Sam will knock on your door and ask you for some, and if you don't give them to him, he'll toss you in jail. This creates a demand for those coins, and therefore a market for them, so now Uncle Sam can pay his soldiers in coin, the soldiers trade it with civilians for food and lodging and boom, it's a market!
You seem to be doing that thing where you want to believe the world is fair, so you invent this magical free market to be able to pretend that life is fair.
To paraphrase Dan Luu: markets are people, all the way down.
You're missing the point. OP is generally right. It's a hard world out there, and you have to be educated to succeed at anything more than a trade or service industry job.
The market pays what their skills are worth given the demand for their skills in that location. That's all. If someone is in India they will not be paid a SF salary for many reasons. But the market sorts all of it into a quantifiable price for labor. If you want to voluntarily pay more than what the market demands, that's more akin to charity.
this may be a difference in definition of worth that we have.
You seem to equate "worth" with "market price"/"business value".
I equate "worth" with "how much money they make the business".
So in my defintion/worldview, an programmer in India that increases the click through rate on $AD_TECH_GIANT's ads by 1%, raising the ARR from $1 billion to $1 billion, $10 million dollars is worth $10 million, and a programmer in San Fransisco who accomplishes the same is worth the same.
In your worldview, how much value they bring to the organisation is irrelevant, and they are worth what the market pays them... which honestly doesn't strike me as a particularly useful mental model if you're trying to get rich, but if it works for you, keep using it.
To quote Warren Buffet:
"price is what you pay, value is what you get."
I try to find things with a good value/price ratio. Using your model, the value of a thing is it's price, so... not really sure how you can make purchase decisions thinking like that, honestly.
By that definition, a business has to always pay someone less than what they're worth in order for hiring them to be a value proposition.
If I'm paid what I'm "worth" why would a business spend any time/effort interviewing and hiring me -- the best that can happen is they will break even through the deal.
It would be like buying a stock you know will flatline at the purchase price for the next 20 years. No monetary loss, but no gain either -- that's almost the definition of opportunity cost.
Getting a first job is very helpful with nepotism. But to sustain being a negative employee - one that brings no value if not hurts the organization - I have only seen with the children / relatives of executives, and in the government.
I am sitting here thinking exactly the same thing. The wealthier (and even middle class) kids with parents who understand will learn the material as always, and the rest of the kids without this stewardship will be even more disadvantaged than before.
Every culture values different things. I'm Asian and grew up bottom middle class.. I'd say 80% of our Asian parents pushed us hard to succeed. I have friends who aren't Asian and well.. I recall their parents were happy their kid got a C ("oh well at least you tried") at best or in general just didn't care.
It’s hard for me to be unhappy when I check my bank account and future prospects when it comes to jobs. My upbringing definitely didn’t make me happy at the time. But as an adult I see why my parents pushed me. They had absolutely nothing then they scraped together something all for me to do better than them.
If entrepreneurship doesn’t work out worst case I’ll be making 250k plus somewhere, or 400k plus at big tech.
And if I don’t want to do that I could just learn something new since I learned how to learn. Yo dawg.. jk but seriously I can’t complain. Given our socioeconomic circumstances (dad was making like 30-40k and once my mom was able to get work authorization she could only find temp or part time jobs) I couldn’t have asked for a better set of parenting and parents.
I can imagine an objection being "happiness is not just about money" - and that's true!
But it seems to me that if one (subconsciously, maybe) worries about money, one will be better off psychologically, compared to someone who has so little to worry about that they start to worry about things that they can't control.
The only people who say that are either well off, or have no chance at ever getting out of poverty (any one of the billions of people who aren't in 1st world or in major tech hubs in 3rd world, who we won't see except on documentaries about how f'd up situation is in xyz country).
Money means you can eat and have a roof over your head. More money means you can do more after those needs are met.
that's interesting, because for the small amount of exposure I have had to common core math that has been pushed federally was actually the opposite. it seems to eschew the simpler methods to "just get the right answer" in favor of more long-hand methods that help with understanding of the concepts.
This is not the same as common core. Common core for the most part was pretty well designed AFAICT and was grounded in real pedagogy.
Like you point out, common core was focused more on understanding concepts as opposed to reaching answers.
What the California standard appears to be doing (full disclosure, I’m basing this on second hand accounts all of which have been negative) is simply eliminating certain fundamental math altogether.
common core is not methods at all. Common core is only standards. Like be able to solve 3 digit addition. Or be able to estimate the the product of 3 digit numbers
The methods themselves can be any methods. I agree that the methods Ive seen associated with common core are designed to help people understand how the math works. Like why when you add fractions do you not just also add the denominator. However it is a tough balance between just memorizing how to do the problem and understanding why you do it a certain way.
The big push I see is word problems in lieu of worksheets. The huge issue is word problems take a long time and kids havent done enough worksheets to become fluent in the techniques. Teachers call worksheets drill and kill and want to "teach to the whole child".
The big problem is that people in education are simply not very smart. The education researchers are also not very smart. Ive seen data that shows that stem teachers are ok, but I dont think those are the majority of education academics.
The way math education has evolved is the same way software development has evolved. Infinite naïve abstraction and checklist-ification that obscures the necessarily complexly defined cognitive work essential to real improvement. I think it would improve in either case that more time was dedicated for respectively teachers and engineers to set their own agendas rather than such being under control by managers/institutional hires.
> Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing.
Maybe this raises the floor of math education? The majority of US high school graduates are not rated as proficient in math and a small minority are actually ready for college level math. That's been true for a very long time now.
It appears that there's a belief among educators (or whoever comes up with the curriculum decisions), that it's better for society to raise the floor than the ceiling on math. Given how poorly math education outcomes have been for a long time now, I'm all for them trying something new (it would be insane to continue to do what clearly hasn't been working for a long time now). That said, I'm pretty conflicted on it meaning that more gifted students lose out on access to learning anything more than the floor level. I don't understand why they need to make that tradeoff at the expense of those who have above average mathematical aptitudes during their school years.
Suppose a team was given a goal of reducing variance in latency on an API.
Getting to the root causes of variance and fixing them is hard.
Injecting extra latency on the fast queries is easy. Even if the query returns in 80ms, we just wait until 800ms have passed before returning the result.
These are the same incentives given to administrators tasked with improving equity.
I think this model is wrong. The so-called understanding is a realized pattern matching that comes from deep memory of many things. I have a very good memory (I recall my car's VIN) and it mostly comes from practice at reading large volumes of material.
Understanding came rapidly for me as I grew up - arising primarily from seeing repeated patterns. Isomorphisms are natural to pick up once sufficient data is shoved into the mind.
I will try the same with my children. The real lack in the US is that most children here consume small quantities of information. The few who are pushed or permitted to push themselves succeed greatly.
pretty much this. My 15 year old is in precalc and everything is memorization of steps. So I explain everything to her so she doesnt have to memorize how to solve the problems.
For example in trig they define quadrant I, II, III, IV and whether sin, cos, tan, sec, csc, cot are positive or negative. Im sure they briefly taught why, but for the problems it is just memorization. Most in the class dont understand the relationship between sin/cos and X and Y coords in the unit circle.
I told her it can be faster to memorize, but understand it so you can double check to make sure things are right.
There is no way a poor student can get through precalc unless they are way above the average because their parents likely cant help them at all.
Kids that have only 1 or no parents in the home are at a significant disadvantage compared to kids that have 2 parents. Spending per pupil, income level, education level of teachers, teachers per pupil - all that is in the noise compared to this one factor.
> Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing. That probably results in relatively equal outcomes but she has no clue how to do things that fall outside of the frameworks they established.
Do you have some examples of these frameworks that eschew understanding?
Common Core math teaches how things work, it's just different, so people think it's wrong. But when you actually pay attention and learn it, it helps explain things better at a more fundamental level.
However, parents didn't learn this way, so it's bad.
It can, and it should. However, that doesn't mean that the books are doing it successfully, and the teachers understand the underlying principles.
Too many years ago, I was pleasantly shocked at looking at what was being covered in elementary education by tutoring a friend. They were teaching discrete mathematics, different numbering systems ... forcing the teachers to learn how think in a different system. It was inspired (and harder then I would have expected). However, the book author's did not seem to realize what they were doing or why. They were meeting the requirements without understanding why they were requirements. It unfortunately seemed far too appropriate for what would be happening in many grade schools.
There is a widespread misconception, especially amongst its critics, that Common Core prescribes how to teach. It generally just sets goals.
There are dozens of Common Core compliant math curriculums that teach in all sorts of ways, some are more "how" some are more "drill". The more trendy curriculums make a false promise of a painless "How" that ends up with kids neither learning How it Works, or How to get the right answer.
Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing.
Isn’t this how pre-undergraduate math education has been for the entire history of mass education?
How else would you describe everything from how to multiply two numbers to simplifying fractions to the chain rule?
Well you kind of have to take addition on faith, but everything else is pretty built up - subtraction is adding negatives, multiplication is repeated addition, division is repeated subtraction, fractions are division, decimals are fractions, and so on and so forth. Maybe some explanations were a little more handwavy than others, and certainly some algorithms could be better explained (took me quite some time to grok long division), but I can't think of anything that was just "trust me it works."
No you don't, addition is taught by making kids count up sums, not by giving them magic rules to follow. Addition has by far the strongest connection to reality and that connection gets hammered into every child. Basically everyone knows how to add by counting on fingers.
You can see that it works, but only because you have defined it to work that way. There is no explanation of why it works based on more fundamental principles. With a much more advanced math education you can derive addition from more fundamental axioms, but that is way beyond what a child should ever be required to learn.
I can think of a couple. limits at infinity are thoroughly hand wavy, at least at the level they're introduced in high school or lower division college calculus. And I would say this even projects backwards into geometry, and even the Blurred overloaded operations of rational numbers and simple fractions. the notion of being able to add up an infinity of nothing and get a quantifiable something is just sort of taken for granted without elaboration.
The equality operator ( = ) is also presented as an implicit expression of truth when introduced, when it clearly admits to shades of true at best. 1*1 = 1 = 1^1 = 1^2 is one kind of true and a bunch of kinds of false. and although at a young age kids may not be sensitive to this, letting it go without explanation or curious challenge can be the source of inarticulate senses of doubt about what's really going on when they get introduced to higher levels of math.
The point is that math is not typically taught as just memorizing the schoolboy multiplication algorithm without being given an understanding that addition is commutative and what commutative means.
Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing.
This is exactly what happens with multiplication (and simplify fractions and taking derivatives). That’s been exactly my claim all along.
Virtually no 16 year olds know why the procedure they were taught to multiply 123 x 456 produces the correct answer. Not today, not 20 years ago, not 50 years ago. They know how to execute the algorithm. That’s it.
"This argument is ridiculous" only because you keep shifting goalposts and refusing to actually back up anything you're saying while just repeating your personal belief that mathematics has always been rote memorization of algorithms.
If it was that way, there would not be so much variation between performance in math around the world, as they'd all just be having kids memorize the same stuff.
An ex-girlfriend passed her Occupational Therapy degree with flying colours, despite her extreme dyslexia. She had scribes and all sorts of help to get her through it.
Day One of her cool new job in the UK NHS she was handed a stack of paperwork that she had to fill in. Needless to say she did badly; it took her forever and everything was misspelled. She lasted a month before they let her go, and she was glad to go. Her degree was very vocational - there aren't many opportunities for qualified OTs outside the health industry - and every single OT needs to deal with stacks of paperwork every day. [0]
There's no point getting people qualified in an area they can't actually deal with. Making people who don't get on with maths work in an area that requires a decent understanding of maths is just going to make everyone unhappy.
I understand the need to even out results and provide opportunity for people who are less STEM-oriented. But (as with the ex-gf) it doesn't work like this. If she had had less help in her degree, she would have wasted less time trying to get into an industry she was fundamentally unsuited for and everyone would have been better off, including her. Providing her with all the help was well-intentioned but ultimately hurt everyone.
Except the university, of course. By providing assistance to an extremely dyslexic student they got another win on the board. Another "disadvantaged" student passed. Social goals met, etc. Everyone else suffered, but the uni got a win. Which was the point of the policy.
I suspect the same is true here - the change in maths teaching is about making it easier for the schools to claim their wins, not about making it easier for students, or providing a better education. It's all about education metrics, not actual education.
[0] Just to close out the story: she ended up getting another degree in Fashion and Textiles which was her real passion and what she was really good at. The OT thing was about making her mum happy; she came from a long line of nurses.
> Day One of her cool new job in the UK NHS she was handed a stack of paperwork that she had to fill in. Needless to say she did badly; it took her forever and everything was misspelled. She lasted a month before they let her go, and she was glad to go. Her degree was very vocational - there aren't many opportunities for qualified OTs outside the health industry - and every single OT needs to deal with stacks of paperwork every day. [0]
I'm sorry to hear your ex-girlfriend's employer failed in their legal duty to provide reasonable adjustments under the Equality Act.
If it was a trust in England I'd be happy to push through complaints for her.
Yeah I was interested in this, too. It was a major hospital in Cardiff in 1998. She wasn't keen on pursuing them because the entire culture of the place was hostile, and she was pretty broken by the experience. She did go on to work briefly as an OT for a care home in England, but found a lot of the same problems with paperwork even though they tried to accommodate her. The basic problem remained; this is a paperwork-intensive job, and she sucked at paperwork because of her dyslexia.
What are the options, and what are the legal responsibilities for the employer here?
Basically taking dictation and/or editing her written work for clarity. She couldn't write legible English, all her spelling was a complete mess, but she could speak it fine. Dyslexia is strange.
The article offers two examples from "Not California" and neither of them are too scary sounding to me.
Is there any real danger that this "is about to go national"?
I'm out here in middle America with an 8th grader taking geometry and a 6th grader taking pre-algebra. And I certainly haven't heard anything about reducing math opportunities. Quite the opposite, really - they're talking about expanding a program where the school system will pay half the tuition for advanced math classes at the local community college if you end up beyond what they teach at the high school.
The top comment there is somewhat vacuous? Rephrased, "if we want the absolute best education, we will either pay for after school efforts, move to a wealthier place, or send to an expensive private school." That... is the same as it has been for a long long time.
Would we like better? I mean... yeah. Hard to say no to that one. What is "better," though? So much of education discussion is dominated by talk of things that "used to work," only, they probably didn't actually work that well.
> That... is the same as it has been for a long long time.
It really was not, at least in Seattle. Seattle had a pretty good gifted program for a very long time. If you got into that - you can get a very good education in a public school. They gutted it in last few years under the banner of equity.
It still exists in the suburbs like e.g. Bellevue or Redmond, but even there it is being watered down. I have 2 kids in various stages of gifted education and follow various covnersations about it and it definitely goes downhill.
This depends heavily on what part of Seattle you mean. I just moved out of Queen Anne, and it is still quite nice school wise compared to where I grew up.
That said, main city of Seattle used to be basically the industrial zone. Bellevue and Redmond had the better schools even a decade ago. Such that I have a hard time following that. Happy to see hard data showing a decline.
Even still, I meant my point to be what it has been like for most of the nation for a long time.
Again, happy to see hard data showing Seattle proper has had a decline in school quality. Most anecdotes I've heard don't really support that.
“ The document cited research that hadn’t been peer-reviewed; justified sweeping generalizations by referencing small, tightly focused studies or even unrelated research; and described some papers as reaching nearly the opposite conclusions from what they actually say.”
>Sometimes, as I pored over the CMF, I could scarcely believe what I was reading. The document cited research that hadn’t been peer-reviewed; justified sweeping generalizations by referencing small, tightly focused studies or even unrelated research; and described some papers as reaching nearly the opposite conclusions from what they actually say.
>The document tried hard to convince readers that it was based on a serious reading of neuroscience research. The first chapter, for example, cited two articles to claim that “the highest achieving people have more interconnected brains,” implying that this has something to do with learning math. But neither paper says anything about math education.
Obviously anecdotal, but I feel that my success in fields of programming and computer science are precisely because I had _more_ access to advanced math courses, not _less_. I started doing symbolic algebra in 4th grade, and by the end of high school I was doing multivariable calculus, which continues to be applicable in my field.
It's way, way more than just a tool that improves thought. It's a necessary tool to organize your life. How can you even budget or use a credit card responsibly if you don't know algebra? You need algebra to know how long a paycheck can last you.
My dad didn't graduate high school and even he knew enough algebra to work out how much money he needed a month for cigarettes (until he eventually quit once he really thought about the numbers).
That's a good question. Historic human societies without algebra somehow had working bean counting.
Using a credit card isn't very abstract.
You only have to use the concrete specific values in your situation, and not solve some generality.
Moreover, I don't think I had to ever square anything, let alone, cube, when reckoning over credit card transactions. Or find the roots of a polynomial, or do anything with polynomials.
I'm not saying that the intuitions gained from algebra are not relevant, mind you.
To use a credit card responsibly you need to understand the concept of exponential growth, or you might accidentally turn a manageable $500 debt into a burdensome $5000 debt. Same goes for understanding good debt (mortgages) vs bad debt.
It might not be solving a polynomial per se, but I don't see how you get to understanding exponential equations without at least understanding algebra.
There is understanding the concept of exponential growth, and there is being able to manage it. They are two skills. Where management is helped more by having resources than it is by understanding it.
>Where management is helped more by having resources than it is by understanding it.
There are many examples of lottery winners, athletes, and celebrities who came across considerable resources yet still went broke because they didn't understand how to manage it or the concept of exponential growth.
A fool and his money are easily parted, as the saying goes. People who don't have financial literacy will lose their money over and over again regardless of how much you give them.
There are, but there are also plenty of examples of lottery winners, athletes, and celebrities that came across considerable resources and then lived quite well on said resources. Probably more of those, but the stories are far less dramatic.
You are also picking a category of people that come across enough resources that make them a target to plenty of others. Such that it is almost an adversarial game, at that point.
>Probably more of those, but the stories are far less dramatic.
Evidence shows that having an excess of resources actually leads to more financial irresponsibly, not less. Or as the Illustrious Notorious B.I.G. eloquently put it: "mo money, mo problems":
"The CFP Board of Standards says nearly one-third of lottery winners eventually declare bankruptcy, and lottery winners are more likely to declare bankruptcy within three to five years than the average American."
I love that that evidence actually supports both of us. My claim was that more people that win the lottery do fine than otherwise. Your own evidence is that 2/3rds of them do so. You are focusing on that fact that 1/3rd of them declare bankruptcy, which is higher than the general populace.
That is to say, yes, you have to rack up some bad debts in order to declare bankruptcy. The kind of debts that just aren't possible for most people.
And this is ignoring the selection bias that almost certainly exists here. Buying a lottery ticket is, basically by definition, not a savvy financial move. That it basically works out for 2/3rds of the people that do it speaks to the power of additional resources. :D
The vast majority of lottery winners are not of the instant robber baron generational wealth level. "1/3 of lottery winners" has to be qualified with what the minimum payout was that we're talking about here because obviously a lot of lottery winners are exactly the sort of people who are going to be living paycheck to paycheck, or even in such dire circumstances that they are likely close to bankruptcy anyway. A 50000 or 100000 or even 500,000 dollar/euro lotto windfall is likely to exacerbate their fundamental problems rather than solve them.
I'd argue that you're not really using the credit on your credit card as a credit card. You're using it as a charge card.
Exponential growth is a fundamental concept of financial literacy. If you want to invest in the stock market or plan your 401k it helps to understand exponential growth. The reason why it's impossible to get rich off a wage is because of the difference between exponential vs linear growth.
>I don't spend money I don't have.
You've never taken out a mortgage or opened a margin account? Plenty of responsible people make money by spending money they don't have every day.
Sorry, yes. I do spend money I don't have, just not in the context of credit cards, as they have terrible interest rates. I go to the banker to get a loan.
When it comes to spending money on credit, you need an intuition for running sums. This lets you maintain an estimate in your head tracking how much you charged on the card.
People without that intuition are surprised at how fast the little charges added up to an unexpectedly large sum.
But I only spent a hundred here or there; how did it blow past $4700?
And at the basic level, it almost isn't even mathematics. It's basically more applied logic. The whole "I'm bad at mathematics" schtick oft repeated at the high school level and below can be translated into "I'm bad at basic logic and reasoning", which makes the gap much more real and apparent.
Mathematics is not some magical piece of knowledge that needs all sorts machinations to teach. Like any subject, it should be moved away from rote teaching and into projects and applications rather than mindnumbing exercises.
It's only because of the mindnumbing exercises that you can sit down with a pen and paper, and use algebra to solve something, when you're 45 years old. :)
You mean if there's no internet connection for wolframalpha? I half-kid, obviously if you don't understand what you're asking for the best software in the world won't give you the right answer, but I also don't find myself solving equations with a pen very often as an adult...
As someone with a background in mathematics that had to deal with lawyers, regarding something as mundane as buying a house, I would say that they indeed do not operate on logic and reasoning. I mean no personal offense, since you mention you attended law school. It was just very eye opening how much of a constructed language lawyers speak. In dealing with contracts, I found that the contract itself was effectively meaningless. The important part were its interpretations and what could be litigated or not, mainly set by precedent. It was such that no application of logic and reason could be applied to the contract. Not to mention, I had to correct several mistakes in the contract.
It’s ok; the only way to offend me is subject-verb disagreement. And anyway, I also have a degree in math, which is why I find the constant “I’m a lawyer it’s ok that I can barely count” particularly amusing.
Indeed, that's the second layer of meaning. Yet another meaning is that in eastern philosophy, mastering symbols is how one develops the higher abstract mind, so it can see truths directly, rather than relying on the rational mind that's called "the destroyer of reality" for its ability to bury truths under piles of thought models.
Actually,combinatorial thinking is more useful for understanding Algebra and not the other way around.Key word is understanding.No need for a beautiful formula you cannot understand.
I'm really glad our kids will have high esteem about their inability to do algebra when it comes time to try to re-onshore our semiconductor design and manufacturing capabilities.
Reminds me when, as I recall, Kansas was going to start teaching creationism/intelligent design as being on par with evolution in terms of credibility. Sure the driving ideologies are very different, but being ideologically driven is the same. At this point I've resigned myself to having to teach my kid (SFUSD) if he going to get any sort of decent education.
My daughter is 13 and has completed algebra one and is now taking geometry. She will have as much as a year of high school credits completed before she gets there. Covid was actually a tremendous academic breakthrough for her, as it gave her the chance to finally work at an independent pace. Before the teachers thought her disruptive, afterwards they realized it was because she needed more independence and challenge (which I'd been telling them since Kindergarten, but...).
I bring this up because that's what I want for every student. Why shouldn't each student receive a kind of individual plan where they can have lessons and classes tailored to their needs? That's the outcome our kids deserve, rather than some reduction to the mean where no one's needs are met.
> Why shouldn't each student receive a kind of individual plan where they can have lessons and classes tailored to their needs?
A nice idea that runs aground in reality, due to typical teenager personality characteristics and the teacher to student ratio that is required to educate a whole generation.
I certainly understand the reality on the ground, but I also think in many districts, especially with the number of electronic lessons (read: limited actual teacher planning or participation) that we are getting closer to this as a possibility.
Hilarious that the people that are the problem think they can solve the problems. But that is impossible since they don't realize they are the problem. Education can easily be fixed by giving students vouchers and let them decide where they get the best education,i.e, probably Khan Academy. The market knows best.
Isn't the California cost per student per year is like 20k or something ridiculous where each kid can get a private tutor?
This is nuts. You don’t “easily” fix education by telling over-burdened parents that now they have to both evaluate every school they can find, hope that the voucher covers the education and that the act of providing it doesn’t shut down every neighborhood school, figure out how they’re going to get their child to it, and require them to do that every single year for 14-17 years.
Especially given competing education standards, especially given the insanity of trying to find childcare at all.
And advocating online-only education is a great way to ensure another generation grows up incapable of interacting with anyone.
But this kind of thinking is what happens when we let people who know literally nothing whatsoever about education feel like their opinion matters as much as an expert’s.
Not all parents have to be unburdened enough to motivate public schools to improve.
Even if there's only a tiny minority of parents who are able to research and move their kids to a better school, their experience will motivate others, word will spread and the public schools will feel the pressure to improve their environment and outcomes. Even the threat of competition can be motivating.
I dare to believe that the majority of parents across the US do care about their kids and are willing to drive their kids to a different school if doing so means they'll achieve significantly better success in life.
But if I have no idea which school to pick, I’m left with the choice of either my now-failing public school, or a random pick of for-profit schools that may or may not educate my child.
You’re giving poor families appalling choices for no net benefit.
And again, you’re assuming all parents can drive their child across town to that one school that took them with no additional fees and had space leftover. That’s just not reality for a lot of people in this country who depend on the country at least trying to provide equitable education instead of finding new ways to lower the income burden on rich people.
When you can guarantee perfect access and perfect information, then sure, let’s talk about vouchers. Until then the only reason to advocate for them is to facilitate and speed up the creation of a permanent societal underclass.
You're asserting vouchers would bankrupt public schools. How do you figure that? Maybe you're assuming that parents will move their kids to a better school, resulting in dwindling enrollment? If so, good! A public school that's not doing a great job should lose students. Let them feel the pain until they work to do better.
> When you can guarantee perfect access and perfect information, let’s talk about vouchers.
Your goalposts are unreasonable. Of course access and information will never be perfect. But they don't need to be.
When I started school, my parents were very poor. When they went on a date, they split a Taco Bell bean burrito (seriously). They had to sell a lot of stuff on the front lawn one month to make ends meet. My dad had to ride the bus to work for a while, and had to borrow money from his brother. But they still somehow managed to send me to private school (probably with tuition assistance), because they believed doing so was the right thing.
I understand a lot has changed since then; minimum wage is not a living wage anymore; many parents depend on free meals from public schools to make ends meet. But that doesn't mean the availability of other options is a bad thing or would be harmful.
My underlying assumption here is that public schools fail to educate kids primarily because they never feel the consequences of failure. If a private school fails, its attendance dwindles, funding drops, heads roll, and it closes if the problem isn't fixed. Not so for public schools -- the money just keeps on rolling in.
so your explanation for why schools in wealthy suburbs always do well and schools in poor urban areas do poorly is simply because somehow, suburbanites are holding their schools accountable while the urbanites are somehow not?
Really, the explanation is that suburban schools generally have a greater proportion of students from the socioeconomic and demographic groups that do better no matter where they are; typical metrics of school quality don't measure the effect of the school, but what the school is working with.
Yes, exactly. Suburbanites generally have more ability to move their kids to private schools if they want to. So the public schools have a higher bar to clear to keep attendance high.
That's very likely not true in the slightest. Only a very small percentage of suburbanites are close to a private school. And of that small percentage, most aren't close to being able to afford private school.
> Only a very small percentage of suburbanites are close to a private school.
I just used Esri geoenrichment tools to create maps of private schools (based on SIC code lookup) in the LA area, central Michigan, and Pennsylvania. Your assertion doesn't hold. There are multiple private schools in every local suburban area I've looked into. Or did you have a particular area in mind? (or maybe you meant to say "rural"?)
Southern California alone (south of San Luis Obispo) has 962 religious private elementary schools, and that's not counting the nonreligious, Montessori, preparatory schools, etc. Even charter schools in California (not counted either) often present excellent competition to traditional public schools, primarily because through them parents have greater choice (and no tuition!).
The assumption that public schools fail to educate kids is already erroneous and baseless.
That a public good, meant to ensure an equitable start for all children, regardless of their or their parents’ circumstance, is being treated like a free market asset is a bizarre failure to understand the fundamental difference between, say, Apple and your local elementary that must be prepared to educate kids ranging from G&T to barely able to read, and must often take the place of parents who are either incapable or unable to be present and continue the kids’ education outside school.
Your comments are case in point why people who don’t know anything about education shouldn’t have any input into how it’s delivered. I can’t tell if it’s Dunning-Kruger, or just an assumption that educators are idiots, but I can assure you the latter isn’t true.
Public school teachers certainly aren't idiots. I've personally known several as friends and acquaintances, for whom I'd vouch for their character and integrity.
Public school administration, public policy, and the content of education degrees is where I'd place the blame (and some curriculum publishers) -- the sort of people who write and listen to the kind of drivel TA is talking about.
This drive towards "equity" is creating even more disparate outcomes; and the notion being taught in some education degrees that a teacher's primary job is to make activists out of kids is hurtful to the kids, and to society.
Again, what is your expertise in education? Why do you think “equity” is driving disparate outcomes, let alone more disparate outcomes?
Do you actually think that any teachers are being taught that their primary job is to create activists (and do you have a source), or are you just repeating X memes because being angry feels good? What, specifically, do you think an education degree consists of, and what is your personal experience with that curriculum?
I can’t imagine you’re continuing to make sweeping pronouncements about something I’ve already asked you if you have any experience with.
Expertise in a subject is not required to think rationally about it. Do you require those who agree with you to have expertise in order to form a rational opinion?
> Why do you think “equity” is driving disparate outcomes, let alone more disparate outcomes?
Because according to hard data, it is. For example, delaying Algebra 1 and the other "equity" programs in the San Francisco school system did not improve outcomes or even manage to bring down top performers. Everyone did worse except those with means to be tutored outside of the classroom -- that's a more disparate outcome.
> Do you actually think that any teachers are being taught that their primary job is to create activists?
Yes, I do.
> (and do you have a source?)
Many. Here are a few I just cribbed from Google. These demonstrate the ideas that are going around in modern liberal education:
> What, specifically, do you think an education degree consists of, and what is your personal experience with that curriculum?
Again, why is this relevant to the discussion? I have heard multiple sources I trust from multiple angles emphasize that today's educators must make activists out of the next generation.
I've also read that today's graduating seniors feel a massive emotional burden because of the beliefs that their education has (probably unwittingly) instilled in them -- namely, that it's up to them to fix society's problems through activism.
Internet comments and most public discussion doesn't have to be held to the same standards that academic papers do... I hope you don't require people you talk with in person to have expertise in order to have a rational opinion on a subject.
I've posited a reasonable mechanism that explains a phenomenon. We know stores fail if they don't provide competitive service - which means those that survive do a good enough job to survive... why shouldn't schools function similarly? No one (including school administrators) really tries hard to succeed if failure isn't a possibility.
If you have an alternate explanation, I'm all ears.
> A public school that's not doing a great job should lose students. Let them feel the pain until they work to do better.
This is such a lazy, uninformed take. Someone's sad? Keep physically abusing them until they're less sad. Public schools do a bad job because they are under-funded, and have to use the limited funding they do have just trying to get their standardized test scores up so they don't lose even more funding. Punishing under-funded schools by giving them less funding is exactly the bad-faith strategy of people who are trying to destroy public schools so they can rake in money with their private schools. Private prisons going well? Private healthcare? Private unregulated utilities? Why would private schools be any better? The obvious answer is to actually invest in under-funded public schools, not punish them for being bad by making them even worse.
Not every problem can be solved by throwing money at it.
The US spends more per student than essentially every other country in the world (besides the few statistical anomalies like Luxembourg), and most of the areas with poor-performing schools are funded at an equivalent level to nearby schools that are high-performing, thanks to large state and Federal subsidies to make up for lower local taxes.
What, specifically, are you counting in “education funding”? At least in my state, the vast majority of a given school’s money comes from a local mill levy, creating significant disparity from neighborhood to neighborhood, in day-to-day dollars. Facilities, on the other hand, receive most funding at the state level.
In neither case are we adequately paying teachers, which is generally the “funding” issue - if you want the best people to teach, you need to pay them like they have value. Currently, we pay them like 7-11 employees, make them buy their own supplies, and arm them with books chosen by lunatics in TX (if we’re not still recycling 30-year old books), and then wonder why they aren’t constantly turning children whose parents work three jobs into Rhodes Scholars.
Oh, and all of this while we yell back and forth about CRT and whether it’s ok for gay people to exist in schools and do nothing to address school violence.
No wonder people think our schools are failing - they’ve created a self-fulfilling prophecy.
Regardless of what one considers 'adequate' pay for teachers, the aggregate statistics show that many -- most -- other developed countries achieve far better results with less spending per student.
At least in my state and area, I've read through the budgets, and the typical canard of 'administration' making up the bulk of the spending also doesn't hold water. Around 70-75% of the spending was directly on teachers salary/benefits, and only 10-15% for administration, and 10-15% on facilities. That certainly seems like a reasonable allocation to me, and I'm not sure how one could adjust it further without creating a new obstacle.
What do other countries pay teachers? What benefits are included?
What does your district pay teachers? What benefits are included?
Is part of what you’re counting as teacher pay something that’s taken care of via other taxes elsewhere (pension, healthcare)? I feel like this isn’t at all apples to apples.
In general, when a teacher can make $50k/year, and someone with a 6 month boot camp can double that, you’re going to lose a lot of potential teachers to other jobs, regardless of what other countries pay their teachers and their software engineers. The US, frankly, isn’t Sweden (or wherever). Pretending that what works in one should work in the other is confounding a lot of things - do other countries force disruptive students to stay in the classroom? What measures are being used to indicate quality? Do other countries have similar numbers of parents unable to work with their children at home? Do other countries base funding on neighborhood taxes, and if not, how are you normalizing costs between them?
I tend to think any comparative analysis is going to be extremely lacking, if it’s not done hand-in-hand with people who actually understand educational challenges in each environment. Certainly, reading a budget is insufficient.
I agree with your point in this thread. Teachers in Finland, for example, are highly respected (like doctors in the US). They're highly trained, highly paid, highly trusted, and they really do a great job.
I wish that were the case in the US -- but we'd be talking about overhauling an entire profession, not merely increasing wages. I do think increased wages would be a great idea, but I think it would take more than that to achieve what Finland has achieved.
Of course private schools spend less per student - they can selectively refuse to admit or kick out anyone they like, which eliminates all of the most expensive students.
Quite a lot of parents have to choose between driving their kids to school every day and working to keep their kids fed and sheltered. There's a real problem there, but it's not that they don't care about their kids.
one reason supermarkets keep their prices low is because of a motivated 8-10% that are avid coupon and price sensitive shoppers. They keep the supermarkets honest for the rest of us.
A 8-10% swing in topline revenue for the supermarket is a lot. Supermarkets can't afford to scare away those shoppers. We all benefit from that positive externality
Supermarkets aren’t judged on their ability to sell meat that has expired, or stale bread, or other suboptimal products. Public schools are required to educate everyone.
This is a bad comparison and another example of why “free market education” is nonsense.
If you give parents vouchers then all schools are just going to turn into IMG Academy because American parents only care about things like football. Inner city parents, football. Suburban parents, football. Its the only thing that unites the country actually; the farfetched notion that their kids will be pro football players.
This is just complete nonsense, "American" parents care about a lot of things clearly. Why are so many students enrolled in Kumon and whatever after-school prep is popular these days? Are kids just shuttling themselves to all sorts of activities just because they want to?
Sure some parents care about sports too. Maybe because their kid is athletically gifted. Not every kid needs to go into STEM. Why shouldn't they be able to enroll in a school that focuses on sports?
The CMF was designed by people who don't like math and prioritize the "human experience" over physical reality. When you read through the CMF, you begin to see all sorts of hints that their ideology is inspired by Continental philosophies such as Marxism, Existentialism, and all of the other ways of thinking that find "facts" and "reality" offensive. For example, I lost count of how many times they mentioned the word "authenticity" in the CMF.
To sum up the whole CMF in my words, it's Critical Theory applied without critical thinking used. Proponents saw that minorities were struggling in math class, so they proposed a solution to handicap math classes. That's literally what CMF is. Proponents would rather see everyone fail than some people succeed. Especially if those some successful people are not minorities.
Why we should learn math from people who clearly have no respect for facts and reality in the first place is beyond me. Bertrand Russell, one of the founders of set theory, would have outright rejected most of the philosophy that inspired the CMF.
Existentialism is hardly anti-reality, and for that matter, neither is Marxism. It kinda sounds like you're just repeating things you've heard without reading the sources.
I'm uncertain about the matters pertaining to this article.
As a reference, since the late 70's, California has a history of adopting unproven and untried pedagogical fads for the entire state. California's abandonment of phonics (reading) was the impetus for the creation of the private schools by the name of Challenger. A commercial productization of this superior method had an annoying TV ad that morphed into a meme.
I cant be the only one who thinks it sad that in the US that it takes six school years (K-5) to teach basic atrithmetic, fractions, decimals, and simple 2D geometry. Parents run, dont walk, to Kumon or AOPS or something similar. Our children got 5 on AP Calc in 9th grade. Note dont share with the school you are supplementing, most, not all, teachers resent it and your child will become the teachers assistant.
Math has always been taught badly.
Kids ought to have been exposed to Calculus concepts by middle school. Anything short of that is a coin-toss anyway.
How communism supposed to work: if we take away the wealth from rich people and spread it evenly, then everyone is equally rich.
How it worked in history: if we take away the wealth from rich people and spread it within the ruling classes, then every peasants are equally rich, or poor.
If we take the opportunity of education away from every students, then they are equally dumb, which means they are equally smart now!
I’ve only seen articles about the idiot bougie hippy math-hating socialistas and their conspiracy to stop children from learning how to do long division. Does anybody have any links to descriptions of the policies and their aims from the people that proposed/implemented them that doesn’t read like a post-apocalyptic retrospective written by the few remaining survivors of San Francisco Politics?
Thanks! That’s a lot of docx files, are there any regular people in the blogosphere that have took it upon themselves to explain or justify their support of this policy?
If on balance the only stuff to read on the internet is “the official proposal on ca.gov” and “a library of folks describing The Grapes of Wrath But It’s Math In California” that would be fascinating.
The main proponent of California's framework is (a) not a mathematician and (b) likely committing fraud [1]. (When the author of a standard is billing low-income school districts $50k to explain to them her new framework over eight hours, it looks more like corruption than clownishness.)
