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".
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.
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.
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?
> 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.
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.
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.
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."
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 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.
Readit News
> 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...
[0] http://worrydream.com/refs/Lockhart-MathematiciansLament.pdf
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".
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.
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.
Copyrighting all the melodies to avoid accidental infringement | Damien Riehl | TEDxMinneapolis
https://www.youtube.com/watch?v=sJtm0MoOgiU
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.
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
That's when the the miseducated majority will find that the market is unjust. All goes according to plan.
And that's where Woke comes in.
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.
You're hired.
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.
this is a pretty big issue, though. even here on hn, many folks claim the best or only way to get a good job is by networking
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.
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.
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.
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.
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.
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.
Do you have some examples of these frameworks that eschew understanding?
However, parents didn't learn this way, so it's bad.
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?
Yes. Not sure why you're in the negative ATM.
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.
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.
What are the options, and what are the legal responsibilities for the employer here?
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.
Yikes. The great state of CA spreading hope.
>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.
Yikes.