> For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment.
Good grief. No, it's just the pandemic. The kids whose middle school years got disrupted are behind on skills taught in middle school.
Can you squint and blame other things? Sure. But experimental education policies are hardly new ideas, and none of the nonsense from previous decades has shown an effect like this. If you want to show up to the game with a claim that it's some other effect, I want to see a big exposition of why it's not the obvious hypothesis at work.
It's covid, folks. And over the next 3-4 years the scores will bounce back (to much crowing in the media from whichever faction wants to claim credit). Write it down.
It’s a shame other commenters are so busy waging culture war that this explanation is being minimized and dismissed. I’m married to a high school teacher, and not only is there a super obvious cohort that spent 8th-9th grade playing Fortnite instead of learning algebra, their successors are doing a lot better. Sure, the current cohort of college students needs remedial math. Let’s acknowledge the cause, offer them remedial math, and move forward. It’s not a sign that the sky is falling. The sky fell five years ago and we borrowed against the future to fix it. It’s the future now and the bill is due.
COVID was a problem, but other systemic problems allowed the lack of math skill to go unnoticed until the kids showed up to college. This article[1] discusses how high school teachers were subject to political pressure, forcing them to give A's to students in a Calculus class who barely knew fractions. Combine that with UCSD dropping SAT requirements, and you've got a horrible mess.
If the rest of the system was functioning properly, the COVID-related problems would have been caught early when those kids started failing their high school math classes-- which would have left them with plenty of time to go back and learn what they missed. And if UCSD still required the SAT, it would have been painfully obvious that they were admitting students who don't know basic math.
".....In 2020, system leaders voted to phase standardized-test scores out of admissions decisions. They argued that the tests worsened racial divides and unfairly privileged wealthy students. But SAT and ACT scores are the most reliable predictors of a student’s math ability, the report found...."
Standardized tests are reliable predictors of students' abilities to solve standardized tests, which is not necessarily a 1-1 correlation with aptitude in that field. It is much like how your ability to sort a binary tree in a development interview isn't a 1-1 correlation with your ability to effectively upgrade your production website's Angular to the latest version.
My wife works in private college admissions counseling, so I've been privy to a lot of conversations around these issues over the years.
The article is paywalled, but I feel that in this sentence the author is using all reasons used against standardized testing to criticize the elimination of standardized math testing.
The concerns around racial divides have been mainly in the non-math portion of the SAT's, where it's been found that students with a non-white background don't choose the "right" answer on ambiguous questions because they don't have the same shared experience that would make the "right" answer obvious to someone with a white background. Its inclusion here sounds like the author is trying to inject a little anti-woke hysteria into her argument.
Wealth leading to increased standardized test scores is a very real thing. Many of us have taken multiple choice tests where we've known that the best answer isn't necessarily the "right" answer, and that in order to pass the test we have to select the answer the test is looking for. The SAT and ACT are littered with these questions and there are test prep companies who have decades of industry knowledge that they provide their clients with to get a boost on their scores. No amount of non-profit or public school provided test prep can compete with that.
As someone else commented, someone with an 800 on their SAT math will get admitted 99 percent of the time. Colleges are always very open about their admissions criteria and students are always free to choose to apply or not based on those.
> “Who is going to trust somebody who got a degree in airline engineering who doesn’t know how to think through a problem without a computer telling them the answer?”
In the day job, how many people have to use maths skills beyond arithmetic?
What about trigonometry?
Differential equations?
Integration and calculus?
To be honest, if I am using Boolean Logic then that might as well be 'advanced mathematics', far beyond the comprehension of non-coders. Even simple trigonometry isn't so simple to most people.
Clearly we need some people on the planet able to do more than basic arithmetic, however, what is the point in trying to teach the whole population how to do differential equations given the lack of workplace opportunities to use such knowledge?
The why question isn't explained with maths beyond the theoretical 'yep, you will earn more'. Too many maths textbooks are utterly abstract, you might as well be learning cuneiform for the amount of practical use cases.
It seems to me that the policy makers and journalists that complain about the demise of maths skills aren't doing a lot of maths themselves yet they want to force maths on the masses, as if it was good for you in a 'eat your greens' type of way.
Maths is hard and it really does not suit a lot of people. Fluency in maths is only attainable by a few, the majority that can do maths need a lot of armbands, whether that be calculators, text books or internet crib sheets. Then there is everyone else, not even floundering, just giving it a miss.
Rather than forcing the entire population to be maths geniuses, which will never happen, maths needs to be a specialist subject chosen by those that know what it can be used for, and with ambitions to take a career path where maths happens.
1. A lot of math crops up in unexpected ways in everyday life. Trig in construction & wood working, calculus & integration when doing finance, &c.
2. It's not about teaching how to crunch numbers, it's also teaching general problem solving, and using tools to break down complex problems using your various tools to solve it. This translates directly to everyday life.
As a programmer we use calculus and integration all the time in performance testing and stats when we aggregate the data and pull insights. I have started getting into making canopies for events and I have todo a lot of trig to calculate the dimensions of the shapes before I send them to the printer. Hell I even use lots of my high school physics when I go to calculate the load to choose to right type of rope or metal wire and to determine if anchoring points are safe or not. We also use a lot math when calculating generator loads and building power grids for raves & festivals. I also do aerial circus and we use lots of physics when setting up rigging points and determining safety margins. Hell just having a basic physics understanding is really important to figure out if the carabiner you're using is going to kill you or not.
So yea math is really fucking important, and you do use it everyday even if it's just the problem solving it teaches.
From what I understand, 'rave' was a late 1980s to early 1990s phenomenon. It was a time when everyone had an excellent time, high on drugs. Nobody was 'calculating generator loads and building power grids' even if you had 14kW of sound system to plug in, monitor speakers and some lights obtained for the weekend from the local theatre.
Electrical items would be plugged in with a slight risk of electrocution or fire, possibly in a pig's shed, in the pouring rain and in the dark. But this was not a worry since the show had to go on and there was the danger of the police turning up in force, with the legal right to steal the whole sound system, which could be big enough to require a semi truck to get it places.
Either the setup worked or it didn't. There was nobody doing advanced maths to get it working, and yes, there would always be a setup problem or two, which happens with kit that is made to work hard. The far more useful skills were the soft skills, so teamwork and coordination, not maths.
In time the rave scene was commercialised to the festival nonsense we have today. A proper rave was a full-on temporary autonomous zone where you could have small children trying to sell you acid tabs or ecstacy. Everything about it was illegal and nobody was sober.
Moving on to festivals and organised mandatory fun events, you have to have an entrance fee, the guys providing the music have to be paid, there has to be a small army of people in high visibility 'security' jackets and you certainly don't have small children trying to sell anyone any drugs.
In this secondary 'professional' context, where the goal is to make money not give people the best party they have ever been to, you really do have to 'calculate generator loads and build power grids' or else you won't get the venue, insurance or the event happening.
Clearly the free party scene is not what it was. Kids today have their five hundred social media friends so they don't need to socialise in real life. However, there was a time, not so long ago, when it all came together wonderfully, with the rave scene, and, part and parcel of that was the complete lack of professionalism. There was fun in taking your life into your own hands.
The aerial circus sounds fun (as does the canopy making). However, across all of the extreme sports where some acrobatics is needed, nobody is doing maths. Engineers behind the scenes, maybe, but the performers? It is all about dedication and practice. To take a relatively modern 'sport', parkour. That dangerous jump from building A to building B, that is done by eye, gut feeling and intuition, after lots of experience doing other jumps. No parkour person is going to whip out the old slide rule to work out the parameters of such a jump.
You mention the carabiner, which is a mountaineering gadget. Again, nobody doing mountaineering is doing fancy maths to select the right carabiner for the job. It comes down to intuition again, and what you and your climbing partner have fielded for the day.
Regarding finance, maths is allegedly useful, but how many bookkeepers are doing any maths beyond addition, subtraction and calculating percentages, mostly for tax paying purposes? In America, where everything is financially engineered and the economy is all about debt payments, maybe more maths is needed for the average citizen, but those hundreds of millions struggling to make their car payments just need a living wage, not added maths skills.
I will stop shouting at the clouds now, however, have you done any of your canopy designs in Blender with the cardboard box plugin that enables you to unwrap a 3D shape into 2D flat surfaces? If that is a no, then give it a go and see if it works for your projects. Note that it enables you to do a render that the client can approve before printing happens.
1. Just because a few commercial American events masquerade as raves or fedtivals, doesn't mean all events are like this. You just don't hear about the good events. We have to calculate generator loads because we're running 500-1000 person festivals with permits &c, but it's still an underground party operating by rave rules. No high vis security or police around. Also we're not doing this in the US, please don't project your shitty culture onto the whole world.
2. Aerial circus it's extremely important to inspect the rigging points and the hardware being used due to the sheer amount of force being generated by drops. You absolutely need to know the load of carabiniers, regular rock climbing ones are often not sufficient.
3. Blender could be a fun idea but you often are limited by the room and where the rigging points are, than what you can dream up.
You clearly are not a multi-drop delivery driver, a chef, a customer service advisor, a nurse, a sales assistant or a barman.
As it happens, I was working in production AND engineering AND finance all at the same time. I will leave you to guess what roles are in the middle of that Venn Diagram, however, that was a while ago when one of my clients was Lehman Brothers. I had deliberately tried to avoid working in the city, so I was reluctant to work with them, however, they hired my intern for mega bucks. That didn't last long though, as we all know! Ah, the shame...
It is precisely because I do the technical roles that others are scared of that I know most people don't need to know maths beyond basic arithmetic.
One huge advantage of this is that I never treat the maths illiterate with condescension. Unlike some I don't sneer at those that are just trying to get by in life or those that have found there is more to life than maths. Condescension is just plain ugly and there is no need for it.
> “Who is going to trust somebody who got a degree in airline engineering who doesn’t know how to think through a problem without a computer telling them the answer?”
Years ago when I was working in education (Canadian public schools) our school board had a conference ahead of the school year. The keynote was an inclusive-ed researcher / consultant / speaker who told an anecdote of how they had successfully lobbied for a student with a substantive intellectual disability to be registered for the high school physics courses.
Part of the anecdote was pushback from the physics head: "I've known Jake for years. Great kid. But what is he supposed to get out of physics class?"
The consultant's in-anecdote response: "what is anybody supposed to get out of physics class?"
Wild laughter and applause.
---
A surprising number of people in education seem to simply not know that there is substantive and consequential content in the curriculum.
Having never really learned math, they've never really used it. Having never used it, they don't recognize its utility.
They seem to earnestly believe that it isn't an actual tool but a gatekeeping mechanism devised by autistic persons to humiliate normies.
The anecdote I heard was a grade-school teacher admitting they had never used the Pythagorean formula IRL.
Well, no fucking shit, Sherlock! You aren't the sort of person to turn to math to solve problems. You're the sort of homesy chuckle-cluck who puts up inspirational posters on your bedroom wall.
OTOH, I've been on my back in an attic with a house builder, and calculated the 3-dimensional length of the bizarre edges of a skylight (where the ceiling opening was completely skew to the roof opening). We absolutely used math to solve the problem.
That grade school teacher? They wouldn't have been asked to check the calculations. The carpenter? Used math IRL.
Having learned math a lot in university, it is mostly useless knowledge outside of academia. Some basic calculus and logic is useful for sure, but overall, 98% of the math is needed just to be able to learn other math topics later.
As someone who loves math, I do think math education would benefit from making the primary focus be probability and statistics for high school. In addition, financial math instead of algebra. I would replace trigonometry and geometry with discrete math as electives. And have calculus as another elective but taught without a focus on calculation.
As someone who went to economics school and had roundabout the math curriculum you suggested, I think it was a terrible idea. It leaves one with the wrong idea that math is mostly about handling money. Only later, when I got to study math for the computer science degree, I realized that financial math is only a small part of this marvelous huge pie of knowledge.
Thanks for sharing your experience. I do think it’s more important for most students to understand money than most of what is currently taught with algebra, geometry, trigonometry, and calculus. My main point though was to focus on probability and statistics. Right now, most students barely understand and remember what is currently taught and also lack knowledge to understand important matters that directly affect them.
Alternative anecdote. I was a students physics TA which involved lecturing and labs and lots of homeworks and in class work. I had a student who really never seemed to understand algebra and he came and said he couldn't really understand how to do the physics problems very well. I said well its going to be hard without really getting your algebra issues figured out and so he just went and did that. I think having a solid understanding of where it is deeply useful (and math and physics have evolved together forever) can be the spark that lights the fire to build the missing understanding. I can say math was very rote for me until I got into physics and I would never have gotten into hairy math without a physics motivation.
Let's be clear though, there's quite a difference in doing problems related to working memory, mental computation, etc. under time constraints - usually what you get when taking standardized tests, aptitude tests, IQ tests, etc. - and solving "actual" real world math problems, like mathematical modelling, numerical methods, and what have you.
I'm sure if I walk around in the office and ask people a problem like "Car A starts driving south at time zero, with speed 30km/h. Car B is located 10 km down south and starts driving north 5 minutes later, at speed 45 km/h, at what time do they meet? You have 1 minute. Go." a bunch of them will start to sweat, and many will likely fail - even though they have graduate STEM degrees.
Maybe there are too many colleges if there's not enough qualified students. Perhaps save taxpayer money and downsize UCSD. Better have fewer, but qualified, students than load it up with people who shouldn't be there.
What if USA would stop treating education like a business - customer paid for degree, customer gets the degree no matter if customer has essential knowledge for the degree?
I never understood why math is such a divisive topic and gets certain people all defensive. Why is the reaction so different from literacy? For example, I have never heard anyone say "I am not a reading person; I don't like to read." but I have head the "I am not a math person" so many times (I'd estimate 30%+ of population around me).
I think bad math teachers (educated in the education department) and bad textbooks are to blame for this collective trauma inflicted on the general populaiton... grown up adults swerving away aggressively at first mention of an formula or algebraic equation.
Chill, y'all. Some of this stuff[1] was know thousands of years ago... it would take you a few months to (re)learn all of high school math and solve all your math phobia issues. You're an adult now, you can totally handle that shit.
Math is the most abstract logical way of human thinking. On the other side pure art is totally on the other side. If you are an artist or similar, you don't need math. If you are a STEM professional, definitely. In between (eg health care, management, politics) it is desirable but not necessary. That simple.
It seems we have entered the Find Out phase of FAFO; which FA began with a lack of preparation in US educators in the 1960's for "New Math" which focused on conceptual understanding and abstractions, such as set theory and differential number bases. This lack of preparation, especially among primary educators (who had not themselves encountered mathematical theory in their own education) led to a regression; "Back to Basics" in the mid 1970's. Those missteps; both in educator preparedness, and in systemic regression to a rote memorization approach were substantially aggravated by reduced standards testing in the 1980's to hide the resulting weaknesses resulting from this regression.
First hand experience as a student through these epochs from the late 70's through the 80's and 90's in US academia led to thinking I was 'not good at mathematics.'
For me the 'breaking point' of this pattern was the discovery that even with an undergraduate STEM degree from a PAC10 university, including 'advanced' math courses available therein, I was not sufficiently mathematically educated to qualify for enrollment in a post-graduate physics program at a leading scientific institute or to participate in advanced mathematics discourse at an international mathematics symposium.
During COVID lock-down I attempted graduate level bio-molecular studies from several tier-one US and UK online university programs and ran into proctored coursework where the educators opined that "some problems are simply intractable due to scope or complexity" and I was unwilling or unable to accept that there was no approach to solutions for these systems.
The ensuing self-directed relearning from international curricula and classical resources has remedied my misconception of inability; extended my approaches to include concepts such as p-adic bases and complex topological approaches. and shows that current cohorts of US students will need to become self empowered to learn conceptual math beyond what their educators believe achievable.
Those who do not grok math will always be in the position of being taken advantage of by those who do.
40 comments
[ 3.3 ms ] story [ 71.8 ms ] thread> For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment.
Good grief. No, it's just the pandemic. The kids whose middle school years got disrupted are behind on skills taught in middle school.
Can you squint and blame other things? Sure. But experimental education policies are hardly new ideas, and none of the nonsense from previous decades has shown an effect like this. If you want to show up to the game with a claim that it's some other effect, I want to see a big exposition of why it's not the obvious hypothesis at work.
It's covid, folks. And over the next 3-4 years the scores will bounce back (to much crowing in the media from whichever faction wants to claim credit). Write it down.
If the rest of the system was functioning properly, the COVID-related problems would have been caught early when those kids started failing their high school math classes-- which would have left them with plenty of time to go back and learn what they missed. And if UCSD still required the SAT, it would have been painfully obvious that they were admitting students who don't know basic math.
[1] https://www.theargumentmag.com/p/when-grades-stop-meaning-an...
My wife works in private college admissions counseling, so I've been privy to a lot of conversations around these issues over the years.
The article is paywalled, but I feel that in this sentence the author is using all reasons used against standardized testing to criticize the elimination of standardized math testing.
The concerns around racial divides have been mainly in the non-math portion of the SAT's, where it's been found that students with a non-white background don't choose the "right" answer on ambiguous questions because they don't have the same shared experience that would make the "right" answer obvious to someone with a white background. Its inclusion here sounds like the author is trying to inject a little anti-woke hysteria into her argument.
Wealth leading to increased standardized test scores is a very real thing. Many of us have taken multiple choice tests where we've known that the best answer isn't necessarily the "right" answer, and that in order to pass the test we have to select the answer the test is looking for. The SAT and ACT are littered with these questions and there are test prep companies who have decades of industry knowledge that they provide their clients with to get a boost on their scores. No amount of non-profit or public school provided test prep can compete with that.
As someone else commented, someone with an 800 on their SAT math will get admitted 99 percent of the time. Colleges are always very open about their admissions criteria and students are always free to choose to apply or not based on those.
I think the answer is Boeing
In the day job, how many people have to use maths skills beyond arithmetic?
What about trigonometry?
Differential equations?
Integration and calculus?
To be honest, if I am using Boolean Logic then that might as well be 'advanced mathematics', far beyond the comprehension of non-coders. Even simple trigonometry isn't so simple to most people.
Clearly we need some people on the planet able to do more than basic arithmetic, however, what is the point in trying to teach the whole population how to do differential equations given the lack of workplace opportunities to use such knowledge?
The why question isn't explained with maths beyond the theoretical 'yep, you will earn more'. Too many maths textbooks are utterly abstract, you might as well be learning cuneiform for the amount of practical use cases.
It seems to me that the policy makers and journalists that complain about the demise of maths skills aren't doing a lot of maths themselves yet they want to force maths on the masses, as if it was good for you in a 'eat your greens' type of way.
Maths is hard and it really does not suit a lot of people. Fluency in maths is only attainable by a few, the majority that can do maths need a lot of armbands, whether that be calculators, text books or internet crib sheets. Then there is everyone else, not even floundering, just giving it a miss.
Rather than forcing the entire population to be maths geniuses, which will never happen, maths needs to be a specialist subject chosen by those that know what it can be used for, and with ambitions to take a career path where maths happens.
2. It's not about teaching how to crunch numbers, it's also teaching general problem solving, and using tools to break down complex problems using your various tools to solve it. This translates directly to everyday life.
As a programmer we use calculus and integration all the time in performance testing and stats when we aggregate the data and pull insights. I have started getting into making canopies for events and I have todo a lot of trig to calculate the dimensions of the shapes before I send them to the printer. Hell I even use lots of my high school physics when I go to calculate the load to choose to right type of rope or metal wire and to determine if anchoring points are safe or not. We also use a lot math when calculating generator loads and building power grids for raves & festivals. I also do aerial circus and we use lots of physics when setting up rigging points and determining safety margins. Hell just having a basic physics understanding is really important to figure out if the carabiner you're using is going to kill you or not.
So yea math is really fucking important, and you do use it everyday even if it's just the problem solving it teaches.
Electrical items would be plugged in with a slight risk of electrocution or fire, possibly in a pig's shed, in the pouring rain and in the dark. But this was not a worry since the show had to go on and there was the danger of the police turning up in force, with the legal right to steal the whole sound system, which could be big enough to require a semi truck to get it places.
Either the setup worked or it didn't. There was nobody doing advanced maths to get it working, and yes, there would always be a setup problem or two, which happens with kit that is made to work hard. The far more useful skills were the soft skills, so teamwork and coordination, not maths.
In time the rave scene was commercialised to the festival nonsense we have today. A proper rave was a full-on temporary autonomous zone where you could have small children trying to sell you acid tabs or ecstacy. Everything about it was illegal and nobody was sober.
Moving on to festivals and organised mandatory fun events, you have to have an entrance fee, the guys providing the music have to be paid, there has to be a small army of people in high visibility 'security' jackets and you certainly don't have small children trying to sell anyone any drugs.
In this secondary 'professional' context, where the goal is to make money not give people the best party they have ever been to, you really do have to 'calculate generator loads and build power grids' or else you won't get the venue, insurance or the event happening.
Clearly the free party scene is not what it was. Kids today have their five hundred social media friends so they don't need to socialise in real life. However, there was a time, not so long ago, when it all came together wonderfully, with the rave scene, and, part and parcel of that was the complete lack of professionalism. There was fun in taking your life into your own hands.
The aerial circus sounds fun (as does the canopy making). However, across all of the extreme sports where some acrobatics is needed, nobody is doing maths. Engineers behind the scenes, maybe, but the performers? It is all about dedication and practice. To take a relatively modern 'sport', parkour. That dangerous jump from building A to building B, that is done by eye, gut feeling and intuition, after lots of experience doing other jumps. No parkour person is going to whip out the old slide rule to work out the parameters of such a jump.
You mention the carabiner, which is a mountaineering gadget. Again, nobody doing mountaineering is doing fancy maths to select the right carabiner for the job. It comes down to intuition again, and what you and your climbing partner have fielded for the day.
Regarding finance, maths is allegedly useful, but how many bookkeepers are doing any maths beyond addition, subtraction and calculating percentages, mostly for tax paying purposes? In America, where everything is financially engineered and the economy is all about debt payments, maybe more maths is needed for the average citizen, but those hundreds of millions struggling to make their car payments just need a living wage, not added maths skills.
I will stop shouting at the clouds now, however, have you done any of your canopy designs in Blender with the cardboard box plugin that enables you to unwrap a 3D shape into 2D flat surfaces? If that is a no, then give it a go and see if it works for your projects. Note that it enables you to do a render that the client can approve before printing happens.
As it happens, I was working in production AND engineering AND finance all at the same time. I will leave you to guess what roles are in the middle of that Venn Diagram, however, that was a while ago when one of my clients was Lehman Brothers. I had deliberately tried to avoid working in the city, so I was reluctant to work with them, however, they hired my intern for mega bucks. That didn't last long though, as we all know! Ah, the shame...
It is precisely because I do the technical roles that others are scared of that I know most people don't need to know maths beyond basic arithmetic.
One huge advantage of this is that I never treat the maths illiterate with condescension. Unlike some I don't sneer at those that are just trying to get by in life or those that have found there is more to life than maths. Condescension is just plain ugly and there is no need for it.
Years ago when I was working in education (Canadian public schools) our school board had a conference ahead of the school year. The keynote was an inclusive-ed researcher / consultant / speaker who told an anecdote of how they had successfully lobbied for a student with a substantive intellectual disability to be registered for the high school physics courses.
Part of the anecdote was pushback from the physics head: "I've known Jake for years. Great kid. But what is he supposed to get out of physics class?"
The consultant's in-anecdote response: "what is anybody supposed to get out of physics class?"
Wild laughter and applause.
---
A surprising number of people in education seem to simply not know that there is substantive and consequential content in the curriculum.
Having never really learned math, they've never really used it. Having never used it, they don't recognize its utility.
They seem to earnestly believe that it isn't an actual tool but a gatekeeping mechanism devised by autistic persons to humiliate normies.
Well, no fucking shit, Sherlock! You aren't the sort of person to turn to math to solve problems. You're the sort of homesy chuckle-cluck who puts up inspirational posters on your bedroom wall.
OTOH, I've been on my back in an attic with a house builder, and calculated the 3-dimensional length of the bizarre edges of a skylight (where the ceiling opening was completely skew to the roof opening). We absolutely used math to solve the problem.
That grade school teacher? They wouldn't have been asked to check the calculations. The carpenter? Used math IRL.
I'm sure if I walk around in the office and ask people a problem like "Car A starts driving south at time zero, with speed 30km/h. Car B is located 10 km down south and starts driving north 5 minutes later, at speed 45 km/h, at what time do they meet? You have 1 minute. Go." a bunch of them will start to sweat, and many will likely fail - even though they have graduate STEM degrees.
39% got this right:
34% got this right: 2% got this right: https://senate.ucsd.edu/media/740347/sawg-report-on-admissio... page 49That way, we can defend the study of mathematics as a form of discipline for the human mind that has benefits beyond the knowledge gained.
The meta-process for solving any mathematical problem is the same as any other form of project management.
Or maybe we should first try to teach kids the value of project management & then try to get them to apply those principles to math problems?
I think bad math teachers (educated in the education department) and bad textbooks are to blame for this collective trauma inflicted on the general populaiton... grown up adults swerving away aggressively at first mention of an formula or algebraic equation.
Chill, y'all. Some of this stuff[1] was know thousands of years ago... it would take you a few months to (re)learn all of high school math and solve all your math phobia issues. You're an adult now, you can totally handle that shit.
[1] https://minireference.com/static/conceptmaps/math_concepts.p...
It seems we have entered the Find Out phase of FAFO; which FA began with a lack of preparation in US educators in the 1960's for "New Math" which focused on conceptual understanding and abstractions, such as set theory and differential number bases. This lack of preparation, especially among primary educators (who had not themselves encountered mathematical theory in their own education) led to a regression; "Back to Basics" in the mid 1970's. Those missteps; both in educator preparedness, and in systemic regression to a rote memorization approach were substantially aggravated by reduced standards testing in the 1980's to hide the resulting weaknesses resulting from this regression.
First hand experience as a student through these epochs from the late 70's through the 80's and 90's in US academia led to thinking I was 'not good at mathematics.' For me the 'breaking point' of this pattern was the discovery that even with an undergraduate STEM degree from a PAC10 university, including 'advanced' math courses available therein, I was not sufficiently mathematically educated to qualify for enrollment in a post-graduate physics program at a leading scientific institute or to participate in advanced mathematics discourse at an international mathematics symposium.
During COVID lock-down I attempted graduate level bio-molecular studies from several tier-one US and UK online university programs and ran into proctored coursework where the educators opined that "some problems are simply intractable due to scope or complexity" and I was unwilling or unable to accept that there was no approach to solutions for these systems.
The ensuing self-directed relearning from international curricula and classical resources has remedied my misconception of inability; extended my approaches to include concepts such as p-adic bases and complex topological approaches. and shows that current cohorts of US students will need to become self empowered to learn conceptual math beyond what their educators believe achievable.
Those who do not grok math will always be in the position of being taken advantage of by those who do.
-- edit Paragraph Spacing --