The reading scores look good, stable with pre-covid and ranked 9th in the world. This might be a curriculum related issue. I've heard from friends that they have to send their kids outside of school tutoring in math now because their local public schools decided to keep everyone at the same math level and their children are bored out of their minds.
> local public schools decided to keep everyone at the same math level
That was a thing when I went to public school in the late 80s-90s. Easier for schools to manage assembly line thinkers. This is 100% intentional government policy. The kids who don’t fit in the system are “troublemakers”.
My family is full of PhDs and tutored me. Teachers tried telling my parents otherwise but the fam laughed in their face and pulled the “free speech” card.
Look at the ages of politicians, the material comfort they have, then question with a straight face why our society is ossified and half asleep.
I am not sure why so many people are against mathematics in school. Cambridge is full of harvard, mit, bio and tech employees. I would think they would realize the importance of math.
This trend is really upsetting. My daughter is a baby but i am already looking into math circles and alternative mathematics curriculums since us math education was bad before this trend of gutting mathematics education.
> their local public schools decided to keep everyone at the same math level and their children are bored out of their minds.
What is the thinking behind this? Is this similar to what was happening in the Bay Area where people took issue with some racial group not being perfectly represented in advanced classes so they scrapped them altogether?
I think there's several things at play. Disclaimer: I'm not endorsing any of these arguments, just restating them.
There's resistance towards "creaming" elite students out of classrooms, as it can increase a teacher's workload: all the students who require zero assistance and could possibly assist their peers are now removed from class, and replaced with different students who will require more of the teacher's attention, reducing individual attention on students who need help.
There's also some equity concerns, where there's reluctance to invest additional personnel and administrative overhead on students who are "going to be fine no matter what" and would rather see those additional resources towards students who are struggling - lots of this is based on the belief that low-SES students are less likely to be part of any gifted/honors program compared to high-SES students.
Edit: And finally, there's the cynical data-driven reason that underscores this, where if you need to maximize the number of students who demonstrate reading/math proficiency, you need to pull as many students as possible over the line - once they're over the line you can "ignore" them and focus on getting others over the line. Schools unfortunately aren't measured by how they serve their most dedicated students.
In short.... The math curriculum my kids have experienced in California and Colorado is village idiot stupid.
Math course need to be based upon well written books... student need print copies of the book. The books need to have well written and designed lessons with numerous fully worked out examples, and need to use good print quality with an appropriate amount of limited color to the engage the reader. Books do not need to change every 2 years at the K-12 level... the books i used back in the late 80's, early 90's were fine... the math literally hasn't changed at all since then.
Students need to be encouraged to take written notes during class.
Students need a lot of consistent homework practice with gradual increase in concept complexity/difficulty (ranging from "plug & chug" to challenging word problems and physics/engineering/real-world examples) and proper spaced repetition.
A "proper" rate of increase in difficulty and the amount of spaced repetition is critical to optimize kids confidence in their mathematical capability and their enjoyment of the topic... if they think/realize they are actually good at math, the may enjoy and appreciate it more.
In both CA and CO the math classes:
- have no book, or an e-book which is dog shit bad.
- my kids were encourage just to listen and pay attention but not take notes.
- only had like 2-5 homework problems every other night.
- lesson plans seemed to make many illogical leaps in topics and subject matter and material difficulty... I'm especially looking at you, California.
Literally copying the Kumon math curriculum would be better.
I'm begin to believe that the degradation of US math education is a "long-game" plan of "nefarious actors" to rot the US's long term technical capability from within. Also considering how little teachers are paid, etc.
I’ve seen several articles now about an increase in private and home schooling after the pandemic. I don’t recall the numbers quoted, but my local district’s budget shows a significant drop in enrollment in a lot of its schools in 2021, which it has not yet recovered from… I wanna say it’s over 30% at some elementaries, even though the city population has grown, and school boundaries have remained similar.
Taking out a significant chunk of the better-off kids (who tend to score higher in the first place) seems like it’d contribute to a drop in average scores.
I might be wrong, but based on my understanding is that PISA also covers private schools, although that may only apply outside the US perhaps? I say this because many studies that compare US public vs private education student populations will sometimes cite differences in PISA scores.
Students who are home schooled are excluded, but that population (even in the US) is far too small to move the average (It peaked at 5.22% during the pandemic I believe)
"31 countries and economies maintained or improved upon their 2018 math scores, including Switzerland and Japan. Countries that did so shared some common characteristics, including shorter school closures during the pandemic and fewer impediments to remote learning, per the report."
Who could have predicted that lockdowns and Zoom class would have a negative impact on education? I'm shocked.
The Economist did an article about this as well and pointed out that math scores were already sliding downward in the US prior to 2019. They argued that COVID is only partly to blame for the decrease.
Anecdotal side story: I grew up in Asia (30 years ago) and went through primary school there before moving to the US. The country I was raised in had and has some of the highest international math scores in the world. But I always wondered why that mattered at all.
Every weeknight after school, I was forced to attend something called "Kumon", which is a Japanese torture method that puts kids in dank basements for multiple hours a day, doing hundreds of rote math problems in harsh florescent light. https://www.kumon.com/how-kumon-works
I did that for several years in lieu of having any after school social life or what the West would consider a "childhood". Eventually I just couldn't take it anymore and started getting all wrong answers on purpose, then tearing out random pages, then throwing entire booklets out the window, much to my proctors' and parents' chagrin. Eventually I just refused to do any more, period, and would rip up every booklet and break every pencil they gave me.
All that really taught me was to absolutely hate math and question authority. It contributed to significant depression and I dropped out of high school as a suicidal teenager.
Eventually I moved to America and got a GED (high school equivalency diploma). I finished the test in a third of the time and scored the highest math scores that exam center had ever seen (they told me), ending in the national 99th percentile. I shrugged. What the US considered high school equivalent I had learned in elementary and middle school. I wasn't proud of it, far from it... it all seemed like a pointless dog and pony show.
I never really used math again after that, even after 20 years of programming. Maybe some arithmetic here and there for bills and to split a Venmo dinner. That's about it.
Why was there such a high focus on such a pointless yet painful skill? I know one statistician in my life, but nobody else I know uses anything past basic algebra in adult life. Most never even use arithmetic.
Meanwhile, traditionally underappreciated humanities like English reading and writing have profoundly shaped who I am as a person, in terms of developing perspective, ethics, and empathy. Being able to write fluently in English -- better than some native speakers -- has led to more job and career and romantic opportunities than math ever did.
Maybe it's not a bad thing we're falling behind in math. The US still has one of the biggest economies (the wealth gap is different), and maybe that is in part because of our cultural focus on individual differentiation and a diverse curriculum, not a tunnel vision focus on rote STEM problems?
Maybe kids shouldn't waste time on esoteric math that they'll likely never use in adult life anyway. It's like cursive, some aristocratic holdover from a time before everyone had smartphones, Google Sheets, etc.
Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming. It's not that arithmetic is the only thing that could be taught. I could think of many formal systems we could start with like lambda calculus.
However arithmetic has the advantage of being immediately obviously useful, and also helps build intuition for other things.
Also, the question is... Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture
> Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming.
I know this is the conventional wisdom, that math is the underlying foundation for programming, etc. And I think that's true in the strictest sense: there is certainly a lot of math underlying all our software and hardware.
But for learning basic programming? Honestly, I don't think it matters at all.
I was first exposed to programming via Logo (as in the turtle mover), and while there's math there, I never really got beyond "bigger numbers move the turtle further / rotate it more".
What really taught me logic & programming was the visual Warcraft 3 map editor, basically an early version of Scratch where you would compose logic out of nodes and make things happen in the game. Having that instant visual feedback of seeing units follow your automated commands was much more effective than sitting in a classroom doing math problems. These days there are a bunch more games like that (shameless plug: https://github.com/arcataroger/awesome-engineering-games)
> Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture
Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? I bet kids would be much happier, and learn a lot more, if they could swap out math hours for time in the woodshop, on the potter's wheel, or making maps for Roblox or Fortnite or whatever -- none of which require a heavy investment in math at first. (Reminds me of this place: https://www.blueoxmill.com/blue-ox-school.htm, a continuation school for high schoolers who don't do well in the classroom. Instead, they learn woodworking, smithing, print-setting, etc. alongside the basic curricula).
Then you could ease them into the math by showing them how can it help them make different shapes, then show them how real-world CAD and Unity/Unreal work, etc. Work backwards from instant gratification to ancient theory, and only cover the details if they really care. But otherwise just let them know that somebody else did the hard work (much appreciated) so they can move shapes around on a screen. It's not that different from graphics designers making art without ever having to know how a Bezier curve is calculated.
> I never really used math again after that, even after 20 years of programming. Maybe some arithmetic here and there for bills and to split a Venmo dinner. That's about it.
Really, this sounds believable. How often does the average programmer use anything beyond arithmetic? I'm only a few years out of school, but I'm re-learning calculus since I haven't touched it once since college.
I'm not saying that no programmers use math, but I don't -- as a run-of-the-mill frontend web dev, it's just not something I regularly encounter. The overwhelming majority of my work is composing JSX components out of other people's JSX components, spending some time in Figma or Illustrator, and then going back to the JSX to tweak some pixels. In an average month (hell, average year), the most math I do is increment some versions in package.json. Maybe the occasional CSS calc().
I'm sure if you're doing games or algorithms or data science, it'd be different, but there are many programmers who work in boring business logic, APIs, databases, etc. Relationships and concurrency and graphs, yes, but not at the lowest levels where the math is actually implemented, unless you're the person writing those libraries/frameworks (in which case, thank you!). And most people don't become any kind of programmer.
I think the most advanced math I ever did was figuring out how to rotate a polygon in place, but even then we used a library and I just copied and pasted a Stack answer (https://longviewcoder.com/2020/12/15/konva-rotate-a-shape-ar...). That was before GPT. I don't remember how to do that now, or how a sin is different from a tan, except one you confess for and the other gives you cancer.
Another example was a line graph where we had to comb through several tens of thousands of data points in Javascript. Our initial implementation was terribly slow and I was tasked with improving it. I started reading about binary trees and b-trees and O(n) notation, but I had no idea what any of that meant -- I couldn't even understand the first paragraph on Wikipedia (https://en.wikipedia.org/wiki/Big_O_notation). I ended just copying some example from Stack, the search became much faster, and that was that. I never understood the math (nor do I really care to, if I'm being honest).
And get this: Among the frontend devs I've worked with (again, just in regular small/med companies, not FAANG or any glorious science work), I actually had the strongest math background among them. That's only because I was an environmental science undergrad, and some of the introductory stats stuff transferred over into analytics (which, again, is something I just copy and paste from Stack or Lynda or whatever without ever actually understanding how a Pearson's correlation is different from any other correlation). To me and the people I've worked with, math was just a problem to be outsourced to someone else's implementation, same as any other NPM package or Stackoverflow answer. We worked in abstractions on top of abstractions in service to mid-managers and business needs, not in pursuit of algorithmic elegance.
In my mind, that's another reason why web dev is often considered the low-hanging fruit/bastard child of "programming", still more akin to lightweight scripting and Dreamweaver/Frontpage than any real comp sci. There's a reason why 6 months of bootcamp used to be enough to do the job.
------
Just to support your point though, I once interviewed for a Canvas-based web app (as in the HTML element that lets you draw pixels), a mapping system similar to Google Maps. Their interview coding test was to make an analog clock with animated hands. I completely failed the test and was not hired. Maybe if I knew more math and algorithms :) Alas.
But in the rest of my career, math was not important at all.
Readit News
That was a thing when I went to public school in the late 80s-90s. Easier for schools to manage assembly line thinkers. This is 100% intentional government policy. The kids who don’t fit in the system are “troublemakers”.
My family is full of PhDs and tutored me. Teachers tried telling my parents otherwise but the fam laughed in their face and pulled the “free speech” card.
Look at the ages of politicians, the material comfort they have, then question with a straight face why our society is ossified and half asleep.
https://www.boston.com/news/the-boston-globe/2023/07/18/camb...
This trend is really upsetting. My daughter is a baby but i am already looking into math circles and alternative mathematics curriculums since us math education was bad before this trend of gutting mathematics education.
What is the thinking behind this? Is this similar to what was happening in the Bay Area where people took issue with some racial group not being perfectly represented in advanced classes so they scrapped them altogether?
There's resistance towards "creaming" elite students out of classrooms, as it can increase a teacher's workload: all the students who require zero assistance and could possibly assist their peers are now removed from class, and replaced with different students who will require more of the teacher's attention, reducing individual attention on students who need help.
There's also some equity concerns, where there's reluctance to invest additional personnel and administrative overhead on students who are "going to be fine no matter what" and would rather see those additional resources towards students who are struggling - lots of this is based on the belief that low-SES students are less likely to be part of any gifted/honors program compared to high-SES students.
Edit: And finally, there's the cynical data-driven reason that underscores this, where if you need to maximize the number of students who demonstrate reading/math proficiency, you need to pull as many students as possible over the line - once they're over the line you can "ignore" them and focus on getting others over the line. Schools unfortunately aren't measured by how they serve their most dedicated students.
In short.... The math curriculum my kids have experienced in California and Colorado is village idiot stupid.
Math course need to be based upon well written books... student need print copies of the book. The books need to have well written and designed lessons with numerous fully worked out examples, and need to use good print quality with an appropriate amount of limited color to the engage the reader. Books do not need to change every 2 years at the K-12 level... the books i used back in the late 80's, early 90's were fine... the math literally hasn't changed at all since then.
Students need to be encouraged to take written notes during class.
Students need a lot of consistent homework practice with gradual increase in concept complexity/difficulty (ranging from "plug & chug" to challenging word problems and physics/engineering/real-world examples) and proper spaced repetition.
A "proper" rate of increase in difficulty and the amount of spaced repetition is critical to optimize kids confidence in their mathematical capability and their enjoyment of the topic... if they think/realize they are actually good at math, the may enjoy and appreciate it more.
In both CA and CO the math classes: - have no book, or an e-book which is dog shit bad. - my kids were encourage just to listen and pay attention but not take notes. - only had like 2-5 homework problems every other night. - lesson plans seemed to make many illogical leaps in topics and subject matter and material difficulty... I'm especially looking at you, California.
Literally copying the Kumon math curriculum would be better.
I'm begin to believe that the degradation of US math education is a "long-game" plan of "nefarious actors" to rot the US's long term technical capability from within. Also considering how little teachers are paid, etc.
Taking out a significant chunk of the better-off kids (who tend to score higher in the first place) seems like it’d contribute to a drop in average scores.
Students who are home schooled are excluded, but that population (even in the US) is far too small to move the average (It peaked at 5.22% during the pandemic I believe)
Who could have predicted that lockdowns and Zoom class would have a negative impact on education? I'm shocked.
https://www.economist.com/international/2023/12/05/the-pande...
----
Anecdotal side story: I grew up in Asia (30 years ago) and went through primary school there before moving to the US. The country I was raised in had and has some of the highest international math scores in the world. But I always wondered why that mattered at all.
Every weeknight after school, I was forced to attend something called "Kumon", which is a Japanese torture method that puts kids in dank basements for multiple hours a day, doing hundreds of rote math problems in harsh florescent light. https://www.kumon.com/how-kumon-works
I did that for several years in lieu of having any after school social life or what the West would consider a "childhood". Eventually I just couldn't take it anymore and started getting all wrong answers on purpose, then tearing out random pages, then throwing entire booklets out the window, much to my proctors' and parents' chagrin. Eventually I just refused to do any more, period, and would rip up every booklet and break every pencil they gave me.
All that really taught me was to absolutely hate math and question authority. It contributed to significant depression and I dropped out of high school as a suicidal teenager.
Eventually I moved to America and got a GED (high school equivalency diploma). I finished the test in a third of the time and scored the highest math scores that exam center had ever seen (they told me), ending in the national 99th percentile. I shrugged. What the US considered high school equivalent I had learned in elementary and middle school. I wasn't proud of it, far from it... it all seemed like a pointless dog and pony show.
I never really used math again after that, even after 20 years of programming. Maybe some arithmetic here and there for bills and to split a Venmo dinner. That's about it.
Why was there such a high focus on such a pointless yet painful skill? I know one statistician in my life, but nobody else I know uses anything past basic algebra in adult life. Most never even use arithmetic.
Meanwhile, traditionally underappreciated humanities like English reading and writing have profoundly shaped who I am as a person, in terms of developing perspective, ethics, and empathy. Being able to write fluently in English -- better than some native speakers -- has led to more job and career and romantic opportunities than math ever did.
Maybe it's not a bad thing we're falling behind in math. The US still has one of the biggest economies (the wealth gap is different), and maybe that is in part because of our cultural focus on individual differentiation and a diverse curriculum, not a tunnel vision focus on rote STEM problems?
Maybe kids shouldn't waste time on esoteric math that they'll likely never use in adult life anyway. It's like cursive, some aristocratic holdover from a time before everyone had smartphones, Google Sheets, etc.
Just my two trauma-informed cents.
However arithmetic has the advantage of being immediately obviously useful, and also helps build intuition for other things.
Also, the question is... Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture
I know this is the conventional wisdom, that math is the underlying foundation for programming, etc. And I think that's true in the strictest sense: there is certainly a lot of math underlying all our software and hardware.
But for learning basic programming? Honestly, I don't think it matters at all.
I was first exposed to programming via Logo (as in the turtle mover), and while there's math there, I never really got beyond "bigger numbers move the turtle further / rotate it more".
What really taught me logic & programming was the visual Warcraft 3 map editor, basically an early version of Scratch where you would compose logic out of nodes and make things happen in the game. Having that instant visual feedback of seeing units follow your automated commands was much more effective than sitting in a classroom doing math problems. These days there are a bunch more games like that (shameless plug: https://github.com/arcataroger/awesome-engineering-games)
> Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture
Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? I bet kids would be much happier, and learn a lot more, if they could swap out math hours for time in the woodshop, on the potter's wheel, or making maps for Roblox or Fortnite or whatever -- none of which require a heavy investment in math at first. (Reminds me of this place: https://www.blueoxmill.com/blue-ox-school.htm, a continuation school for high schoolers who don't do well in the classroom. Instead, they learn woodworking, smithing, print-setting, etc. alongside the basic curricula).
Then you could ease them into the math by showing them how can it help them make different shapes, then show them how real-world CAD and Unity/Unreal work, etc. Work backwards from instant gratification to ancient theory, and only cover the details if they really care. But otherwise just let them know that somebody else did the hard work (much appreciated) so they can move shapes around on a screen. It's not that different from graphics designers making art without ever having to know how a Bezier curve is calculated.
I don't believe this at all.
I'm sure if you're doing games or algorithms or data science, it'd be different, but there are many programmers who work in boring business logic, APIs, databases, etc. Relationships and concurrency and graphs, yes, but not at the lowest levels where the math is actually implemented, unless you're the person writing those libraries/frameworks (in which case, thank you!). And most people don't become any kind of programmer.
I think the most advanced math I ever did was figuring out how to rotate a polygon in place, but even then we used a library and I just copied and pasted a Stack answer (https://longviewcoder.com/2020/12/15/konva-rotate-a-shape-ar...). That was before GPT. I don't remember how to do that now, or how a sin is different from a tan, except one you confess for and the other gives you cancer.
Another example was a line graph where we had to comb through several tens of thousands of data points in Javascript. Our initial implementation was terribly slow and I was tasked with improving it. I started reading about binary trees and b-trees and O(n) notation, but I had no idea what any of that meant -- I couldn't even understand the first paragraph on Wikipedia (https://en.wikipedia.org/wiki/Big_O_notation). I ended just copying some example from Stack, the search became much faster, and that was that. I never understood the math (nor do I really care to, if I'm being honest).
And get this: Among the frontend devs I've worked with (again, just in regular small/med companies, not FAANG or any glorious science work), I actually had the strongest math background among them. That's only because I was an environmental science undergrad, and some of the introductory stats stuff transferred over into analytics (which, again, is something I just copy and paste from Stack or Lynda or whatever without ever actually understanding how a Pearson's correlation is different from any other correlation). To me and the people I've worked with, math was just a problem to be outsourced to someone else's implementation, same as any other NPM package or Stackoverflow answer. We worked in abstractions on top of abstractions in service to mid-managers and business needs, not in pursuit of algorithmic elegance.
In my mind, that's another reason why web dev is often considered the low-hanging fruit/bastard child of "programming", still more akin to lightweight scripting and Dreamweaver/Frontpage than any real comp sci. There's a reason why 6 months of bootcamp used to be enough to do the job.
------
Just to support your point though, I once interviewed for a Canvas-based web app (as in the HTML element that lets you draw pixels), a mapping system similar to Google Maps. Their interview coding test was to make an analog clock with animated hands. I completely failed the test and was not hired. Maybe if I knew more math and algorithms :) Alas.
But in the rest of my career, math was not important at all.