TLDR : American public schools suck but there is an increasing number of extracurricular math programs that help talented kids learn advanced problem solving skills. Mostly only well-educated and well-off parents get their kids into these programs. That kind of sucks, and there are marginal efforts to reach out to poorer students. But the real story right now is, if you have kids in public school, their math education sucks and you might want to look into extracurricular options -- there are lots out there.
Now that I think about it, public education is great training for a future of working in open-offices. You learn to accept that you have to wake up at an arbitrary time, spend eight hours getting very little productive done, whilst being bombarded with noise, interruptions, and politics, then if you want to make any real progress, you have to do it afterwards on your own time, outside the school/work day.
One can make the case that, in California, the higher education system was purposefully, consciously stratified along career and status tiers, as you described.
Community college system = workers in the practical trades
Cal State system = office workers
UC system = technologists, scientists, managers
Big name, elite, private universities = executives and high level politicians, the people who actually run society and its institutions
And, if you look at the architecture on the various campuses, it more or less reflects that.
Also, all of the community colleges, and an awful lot of the Cal State schools are commuter campuses. You come and you go. It's not your home. You're a renter. The place shuts down around 10 pm. (Get out of here, kids.)
By contrast, the elite private schools have sufficient dorm/house space to allow most of the students to live on-site: the students have a lot more access to buildings and more or less "own" the place while they're there.
Having attended school in California at a community college, UC, and finally an elite, private university I couldn't more agree with your characterization. I don't know how much I would agree with the claim that the stratification was purposefully constructed (I'd argue it's more of a reflection of American society writ large - i.e. successful parents have more resources to ensure their kids are successful), but otherwise this rings very true.
The difference between "good schools" and "bad schools" is much more about the kids that go there than anything about the school itself. You're seeing this starkly in D.C. where gentrification in certain neighborhoods is shifting the student demographics from 90% low-income to 20% low-income over just 4-5 years. Test scores are shooting up, but it's not like they fired all the teachers and hired new staff at twice the salary.
American schools are fine. Our problems are social. For example, the U.S. has the second-highest rate of single-parent families along with one of the highest gaps in PISA scores between single-parent and two-parent households: http://educationnext.org/international-look-single-parent-fa....
The U.S. also has a larger fraction of children in the lowest income distribution than comparable countries: http://www.epi.org/publication/us-student-performance-testin.... Accounting for that eliminates a lot of the supposed gap in U.S. student performance:
> If U.S. adolescents had a social class distribution that was similar to the distribution in countries to which the United States is frequently compared, average reading scores in the United States would be higher than average reading scores in the similar post-industrial countries we examined (France, Germany, and the United Kingdom), and average math scores in the United States would be about the same as average math scores in similar post-industrial countries.
> Test scores are shooting up, but it's not like they fired all the teachers and hired new staff at twice the salary.
Why are you assuming that the schools are responsible for the higher test scores? In my immigrant, upper-middle class community, there's nearly universal use of after-school test prep and tutoring from companies like Kumon. I'd argue that's the reason you're seeing test scores "shoot up" once only few low-income families are left in a neighborhood.
This a really great, insightful and useful comment.
I think a lot of well-educated (or self-educated) tech folks think that if only we could fix our education system, poverty and income inequality would disappear under a massive rise in productivity and innovation. I know that I am guilty of thinking this way.
But you're right: family and socioeconomic status are highly predictive of education outcomes. So we need to directly address both schools and poverty at the same time in order to create a virtuous cycle of social improvement.
teachers in bad / poor areas in the states aren't paid less than teachers in the "good" areas. cps for instance, chicago public school teachers are among the best paid and worst performing in the country.
I didn't know the teachers were the ones earning the grades. See the posts above that cite what happens to re-gentrified areas, where the social-economic make-up of a school changes but the teacher make-up does not.
You're implying teacher quality and school financing are irrelevant, and yet every conversation about public schooling in the US brings those arguments up.
It's not as simple as that. There are a lot of rural areas where teachers make almost nothing. Chicago can afford to spend a lot of money (since it has rich areas it can tax). So they spend a lot on schools in poor areas of the city.
And then educational outcomes of the poor rural and poor (but expensive) urban schools aren't different.
That is general rule of thumb, but there are variations in this law at state and local level. In Texas, there is Robin Hood, basically a portion of a rich neighborhood taxes are used to subsidize poor ISDs.
Accounting for local, state, and federal spending, most states spend more money per student in their poorest districts than in their most affluent ones: https://www.washingtonpost.com/news/local/wp/2015/03/12/in-2.... In California, the poorest school districts receive almost 14% more money than the richest ones.
That doesn't seem too surprising. In rich areas, kids are off going to their private tutors and private after school activities. In poor areas, the kids need the extra push that a significant portion of them aren't getting at home.
Plus, in the case of NYC, rich PTAs more than make up the difference between what the state provides and what the students receive.
Unfortunately, the other kids variable is something that you can only control by moving away. I had to do that in the east bay, California, when the schools started taking more inner-county transfers and running busses. The greatschools score went from ~7.5 to 4 in 2 years. The test scores plunged and they pulled money from the school because it wasn't performing. Like that helps.
You can try to work with the school, the teacher, the principal, but you can't really work with the other parents. I can't even imagine how you'd begin that conversation. "Hey, little Johnny acts like a complete asshole and disrupts the class to the point that they are spending their heads down on their desk for half an hour a day. Can you step up and do something about his behavior?" Obviously I'm never going to be a politician, but how can that ever be phrased in a neutral way?!
This is a huge problem, yes, and probably far more important than what I'm about to say. But even in the best public schools, in places which lack economic and social problems, math education is still egregiously behind the types of learning and teaching described in the article.
Exactly this, as schools in SF have begun to experience re-gentrification, back from empty nesters and influx of poor immigrants, the new gentrification has anecdotally resulted in improving schools at the elementary school level, and as they grow (and if their patents remain in the city) middle and high would likely improve too.
One of the stark differences between improving and flagging schools is parent involvement and support, in addition to a culture of education and learning.
It's what I saw growing up, kids from blue collar families saw school as a reluctant obligation through which they had to pass. Kids whose patents were professionals took a different view of education and saw it as a station on the path to a richer [both meanings] life.
So, it's more than money or wages, it's a way of thinking, how the parents think of school, how the kids think of school, attitude towards academic achievement (over sports, for example), etc.
"Mostly only well-educated and well-off parents get their kids into these programs. That kind of sucks,"
It's really important not to let 201x social concerns get in the way of this stuff. The good stuff always starts out with the rich. Always. It is virtually structurally impossible for it to happen any other way. (Not quite, but very much the exception rather than the rule.) Rather than complaining that only the rich have the thing it is far more important to work out how to get it improved and shared more widely; complaining about the rich having the thing doesn't help that and in the modern political environment runs the risk of strangling the improvement in the crib. It is always easier to bring "equality" by cutting off the top than bring up the bottom, and you have to be very wary of that, because people will propose that in various subtle ways if you fall for the "class inequality" memeset too hard.
It's easy to want to simply to steal from the rich, as you point out.
But that's not our current style of failure, it's "hey poor district, you're not up to snuff compared to the rich district. We're going to fire all the teachers, gut your union, and generally make your life hell. That's sure to make you do better".
Poor management by the government is hardly a surprise. Systems have to be constructed to deal with that as a reality. Or we need to stop hiring managers based on how popular they are.
I wasn't talking about "styles of failure". I'm talking about this very thread, where people are popping up, looking at a program demonstrating success in mathematical education, a thing proved to be difficult by well-funded repeated and repeated and repeated failure, and all they've got to say about it is complaints about how it's not fair that it's just going to rich people.
This is not the time to be worried about fairness. This is the time to figure out what works. When you have that, then worry about fairness. Demanding that all the experiments be done equally to everybody at scale produces total paralysis, and is in no small part responsible for the total paralysis we witness in school reformation right now. You simply can't do anything that way.
I am not sure why you are seeing so many downvotes.
I have worked in a poorly funded chicago public school that had just that year become a "turnaround school". That's just a very cute euphemism for "we fired everyone, hired whatever assholes would work for the least amount of money (Yo!), more or less eliminated any budgets you would be working with, and are making no other real changes". I guess the logic is that if we were going to be set up for failure, we might as well do it on the cheap.
Then, a few years later, they wonder why the students who went to those schools are so far behind the rest of the students in the city.
I should also mention that many of the students going to these schools were already saddled with the disadvantages of being poor and black in Chicago, before having their entire educational world replaced with an even shittier and more dysfunctional one.
The funny thing is that I agree with both your cynicism in practice, and the parent commenter's optimism in theory.
At what point do you have to consider yourself an irresponsible parent if you leave your kid in public school while being able to afford homeschooling ? Are we rapidly approaching the point as a society where our public education feels more like daycare ? If that's not the case how do we measure it and where do we draw the line.
I've taught a summer program in number theory for high school students for the past several years. Each summer, my classrooms fill with high school students that are intrigued by the idea of math and extremely capable. That is nice and inspiring, and generally more rewarding than when I teach calculus classes to university students during the school year.
But my program is prohibitively expensive, and I'm acutely aware of the fact that when my students return to their high schools, they will almost certainly return to lackluster curricula. There are exceptions, of course. My summer program is filled with a far-above-average percentage of students attending private high schools.
The fact remains that students who attend the summer program are introduced to interesting math with no guided way to continue their exploration. Sometimes, students with supportive schools end up scheduling a self-study with some supervision from a high school teacher or counselor; I've been asked to help set up and guide self-studies, and I know at least a few of them have been successful. In my experience, this has been the best outcome for my students continuing exploration of advanced math. I'm not sure what this says about math and American high school education.
Why? Just curious if there's any brainstorming to be done.
Also expensive relative to what? Some people think Kumon is expensive. My kids did it for a couple years. Its about $100/month. Its very popular among immigrants who make a whole lot less money than I do. Of course Kumon isn't "real" math because its very drill -n- kill (which is why we quit, more or less)
Prohibitively expensive might not specifically reference to the monetary cost of the class. You could probably scrounge up $100 a month for Kumon even from much lower income families, but many children in lower income families end up having a real opportunity cost in going to a summer class. The parents may not be able to drive the children to the class, the children might be pressured to get a summer job to help pay for the family, etc.
> Why? Just curious if there's any brainstorming to be done.
I'm afraid that I don't know about the actual costs. There are several classes offered, and though students only take one at a time, they sometimes link a few and stay for up to 8 weeks. It's a pretty large board-at-the-university-for-x-weeks style summer program.
I'm an instructor, and I don't set prices. I also understand that there is a non-negligible cost to house and feed a student for a month. But program costs each student about $6000 dollars. I think that's enough to be called "prohibitively expensive," although I'm not sure how to compare these things really.
I am continually surprised by how many emails I get from teenage students thanking me for writing my math blog.
On top of that, I try to occasionally make it out to high schools to give guest lectures. I posted an example experience from one of these online [1] and I am usually looking for other opportunities to do this sort of thing. I think that if every math graduate student who is a reasonably good teacher took a day or two out of every year to visit a high school math class, we would see much more interest in math. Many of us (myself included) were not particularly interested in math in high school and didn't discover the cool stuff until college. So we were once the audience we'd be appealing to.
The sad thing is that the cool stuff isn't even always complex. It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules.
But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of my classes would have played up if a whole lesson was spent deriving and exploring concepts without rote learning.
Being a maths teacher has to be pretty rough, especially given the number of students who are openly hostile to it as a subject.
As an aside, I often think about my Religious Studies teacher who'd disparage topics like Maths as being irrelevant after school. We'd never use them she said. RS was vital to life success, Maths a pointless exercise. It still winds me up to remember.
>It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules.
Once you get in the mindset of deriving equations, rote memorization becomes insanely difficult, at least in my opinion.
During my last year as an undergrad majoring in physics I got a 4.0 in quantum mechanics, but very nearly failed introductory chemistry (which I was taking to fill a science distribution requirement at a liberal arts college), despite many of the chemistry concepts just being edge cases of applied quantum mechanics.
There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. I understood the solution to the problem itself, but when the professor started giving me hints I had to admit in front of the whole class that my issue wasn't with the number theory proof -- it was with the multiplication table we learn as children.
I was standing at the blackboard in front of the class. I've always been flaky on multiplication tables for some reason, and doing arithmetic in my head isn't my strongest suit.
That said I excelled in math throughout high school and college. It just goes to show that elementary math really has no bearing on the type of mindset one may have for "more complex", logic based math and computation.
Trust me -- since that experience of being humiliated in front of the best students in the math department at my college, I haven't forgotten what 9 times 7 is.
Once in a graduate abstract algebra class (without being prompted) I interrupted the professor's lecture to remark that he had skipped the prime "15" in a list of primes he wrote on the board.
> There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was.
As do I, but the pressure of the situation didn't help, especially when the natural assumption of the professor/rest of the class was that I didn't understand the much more "complicated" aspect of the proof and not something most people take for granted as just "known" from elementary school.
I think that one main issue is that many people unfortunately equate math with routine calculations or rote memorization. I think it's valuable to communicate that actually math is the art of creative thinking. To do this, it helps to share some "gems", or examples with powerful "Aha" factors.
Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football:
There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there.
I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community:
Very nice video. I like how you actually made it out to a football stadium to start the video. One suggestion if you want to make this more 'shareable': start with the 2d graphics and then transition to video shot using a drone. This will let you get overhead video illustrating the defender/attacker scenarios. If your stand-in extras can't run fast, just have them run in slow-mo and then speed it up in post. Please keep up the good work!
Thank you for doing this. I would have appreciated someone like you in high school.
I remember going to the "best" math teacher in my high school with a math question about my science fair project. He couldn't answer it. That was so demoralizing. I had already taught myself so much of the math and stats I needed to know for analyzing my project, so I only went to him out of desperation.
It would have been awesome to have a more advanced instructor available to talk with and learn from.
Thank you, your students appreciate you way more than you may know.
Thanks, @j2kun for your contributions to the math scene! :)
I agree! I think that many people have interesting ways to communicate where they see the excitement in math. Your blog lets you scale your impact through the Internet, which is great, and it's even more powerful when coupled with the in-person experience from guest lectures. :)
Indeed, when thinking of effective ways to scale up the in-person outreach efforts that I was engaging in (as National Coach + teaching at CMU + expii.com), I started posting my weekly math enrichment discussion topics onto the Internet. I think that's the way that we'll ultimately be able to completely level the playing field for everyone in the world.
Reminds me of the math program that Jason Roberts is providing to a group of younger students in Pasadena. If you've never heard the TechZing podcast I'd recommend it: http://techzinglive.com/
The fundamental problem of education in public schools and its ineffectiveness is not being addressed.
It's great that many of these extracurricular clubs and institutes exist to impart advanced education to interested students. But it does not solve the underlying problem.
It's a step in solving the underlying problem, since at this point only someone studiously incapable of learning from history can think that the school system is going to produce a superior math curriculum on its own. I'd say "it had its chance", but that's hardly true... it has had its several dozen chances.
As the article clearly states, these math programs are only attended by the well off due to awareness and finances not being a hindrance.
What about the vast majority of students who don't get to attend these type of programs?
We need to come up with solutions that are inclusive and accessible to the vast majority of students. Clearly inclusiveness and accessibility are missing from these programs.
The methods that these programs use to promote the development of problem solving in students are novel. Maybe they can be incorporated into school curriculum and better train the teachers to handle this new approach to learning.
Well, see my other post in this thread. This is an example of exactly what I was talking about. If your only response to stuff like this is to complain about how it's not "fair", you take one step towards preventing it from even existing in the first place. Who wants to try anything new if the only thing they're going to hear is "But it's not being evenly distributed to everybody!"?
This is step one. Before we can "come up with solutions that are inclusive" we need to just plain come up with solutions! Don't kill that with complaining long before it's relevant about how "fair" it is.
Is it really so wrong that the rich are willing to be guinea pigs anyhow? It is, after all, ultimately disingenuous to complain that the school systems aren't seeing this improvement because whenever the school systems suggest trying this sort of improvement the complaint about using kids as guinea pigs and ohmigosh their futures will be wrecked immediately come up. You can't have it every which way. This is a significant chunk of the mechanism that has rendered national-scale schooling impossible to innovate with anyhow.
"But such initiatives cannot be a solution to a poor public school system."
I'd submit you're still asking for some sort of magical solution whereby we skip this step one somehow and leap directly to everybody having the good thing. But that involves skipping the experimentation phase that demonstrates the thing is good in the first place. It's why nothing, right now, can be the solution to a poor public school system... attitudes like this have utterly paralysed them.
If you want to see improvements, you've got to loosen up a bit on this fairness kick. Somebody is going to get them first. It is a mathematical necessity, because we should not do "experiments" by rolling things out to everybody at once in one shot. It's not like there's a guarantee that it's an improvement, after all.
You cannot conclude that the current school education is not ineffective(effective) just by looking at the number of Nobel Prize winners.
The USA is lagging behind many countries in key areas( especially STEM fields).
Anyway the point I was trying to make was that, these extracurricular initiatives are great, but it cannot be a solution to a poor public school system.
There is lots of research which suggests that the USA is indeed lagging behind in STEM fields. K-12 does not prepare students well enough when compared to many Asian and European countries. The numerous research articles are a Google search away.
Another indicator is the lack of sufficient skilled workforce in STEM fields in the USA. This forces many tech companies to hire from abroad.
To make a reasonable comparison to the United States, you'd have to lump a European country in with a third-world developing country to get the same level of racial and cultural heterogeneity. People always try to compare the US to Finland, when Finland has less population than New York City and the demographics of New Hampshire.
Tech companies hire abroad because it's cheap, not because there is a real skill deficit.
I don't how you would take into account all possible factors to make a perfect comparison, but objectively looking at the research and data available on this topic, it's clear to me that the USA is lagging in STEM fields.
Some tech companies do hire from abroad because it's cheaper, but there is a real skill deficit in STEM fields and there are just not enough skilled people available to recruit. This has been openly acknowledged by the tech companies, universities and the Government.
The question is not whether the USA is lagging in STEM, it is what should be done about the fact that the USA is lagging in STEM fields?
While imperfect, test scores provide some context for comparison.
The being said, back in 2013, this article was widely shared. It demonstrates that you can teach STEM ways of thinking (e.g. CS), starting from early elementary grades. It does not have to be a AP-level course.
I'm not sure basing a reasoning on extreme outliers makes much sense but anyway, the percentage of foreign born and educated American Nobel prize winner vastly exceed the percentage of foreign born citizens...
"The No Child Left Behind Act, which shaped education for nearly 15 years, further contributed to the neglect of these programs. Ignoring kids who may have had aptitude or interest in accelerated learning, it demanded that states turn their attention to getting struggling learners to perform adequately..."
teaching to population averages will prove disastrous to our long-term growth. thank goodness we have private institutions to pick up the slack where massive bureaucratic oversight often (so often) gets it wrong.
I'm glad private institutions exist too. But remember you can only get the education you can afford. Since brilliance is not necessarily related to parents' income, private education is a poor substitute for efficient, timely public education.
Exactly - that's why things like https://www.teachforamerica.org/ have to exist. It's a socio-economic issue that's holding back talent in developed countries across the world, where parental income directly impacts on academic success. Considering the imbalance is so pronounced in-country, it's a real shame...
I applaud Teach for America for the effort, but I'm not sure that's really that successful. I graduated with more than a handful of people that went into TFA, and around 90% of them burned out hard after a couple years. Most of them had no teacher training, and, really, no cultural context for understanding the cultures they got dropped into. Inner city ghettos, Cajun Bayous, and Appalachian hollers are a different world than white-bread East Coast suburbia.
I think if you want to fix the disadvantaged areas of the country, you've got to reverse the brain-drain that's sucking the best and brightest people out of these communities. Decentralizing the economy would be a good first step.
The deeper problem with TFA is that by hiring TFA teachers they are literally ensuring 100% turnover in 2-3 years since TFA teachers do not usually stay past their 2-3 year assignment in their placement areas. There are a few who do stay, however, as a pure numbers game, it is not enough. Also, you can Google (or Bing) away for stories of how TFA teachers are given inadequate training and special-needs students (or worse, disruptive students) are put into their classrooms.
Up the Down Staircase is a lightly fictionalized novel about teaching in the 1960s in a public school system. Bureaucracy, parents (or lack thereof), funding, burnout. Almost 60 years later, many of the same fundamental problems still exist.
It's not necessarily wrong to teach to population averages.
It sounds like you're suggesting that education effort/money should be distributed with an emphasis on high-aptitude students instead of low-aptitude students for long-term growth goals. This makes some sense, it seems likely that empowering high-aptitude students with better education will generate leaders, entrepreneurs, inventors, 10x engineers, and "growth".
But if you don't spend the extra money and effort to teach the low-aptitude students, they will not have a usable education, producing a "low aptitude class", likely condemned to poverty, unemployment, and suffering.
Growth is great, but suffering is not. Maybe the bureaucracy swings too far towards preventing suffering at the expense of future growth, but it's not a black-and-white wrong.
The example problem they give is pretty neat, but they don't mention the (IMO) interesting part of it. After sketching out the answer, I was suprised that the height you gain is independent of the size of the underlying circle. That certainly suprised me, as my intuition was that the height you would gain would shrink as the underlying circle grew -- after all, you'd be adding a constant length to an ever growing value. But the answer only depends on the amount of length you add, so the problem has the same answer whether it's the earth, the sun, or a proton. Neat!
I think that this (common) reaction probably illustrates a kind of over-correction among experienced problem-solvers: the knowledge that not everything is linear (e.g.: if you add a bit to the area of a circle, by how much does the radius change?) leads to the assumption that nothing is linear (or, at least, nothing that would crop up as a math-circle problem).
Thanks! :) We were really thrilled to post the problem.
Our rope question from expii.com/solve is a multi-layered math puzzle. If you haven't seen it before, the answer is often quite surprising: a human can walk under the circle even though the 710 inches of extra length are shared over the whole earth's circumference. Basic human intuition produces the most common answers, which are the bacteria or the ladybug. This helps to illustrate the purpose of math: to help us reason to determine the truth when basic intuition fails. If basic intuition were always right, then we wouldn't need math!
If you had seen the puzzle before though, you would already know that the rope lifts high, because it lifts by 710/(2*pi) inches, which is 113.0000095... taking us to the second layer of math embedded deeper in the problem. That is remarkably close to a whole number, which is surprising because pi is an irrational number. This means that pi is very close to 355/113, which brings us to the topic of Continued Fraction representations of irrational numbers, and amazing rational approximations of pi: https://en.wikipedia.org/wiki/Mil%C3%BC
So, this problem hits at both basic and advanced levels. :)
There are many interesting ways to teach math through multi-layered puzzles which have something for everyone, no matter where you are in the experience spectrum. Our goal is to provide these for free, disseminated over the Internet. :)
what a strange thing to subject your kids to, shame on these parents.
Has anyone done any studies on what these 'math wizards' end up doing in life.
I grew up in Indian community where this kind of stuff was the norm, many of my friends won regional championships but none of them do anything remotely related to math now.
Instead of associating math with magical patterns that explain the world, they now associate it with stress/anxiety/competition.
Please don't do this repulsive stuff to your kids, read Richard Feynman's bio and see how his parents inspired him to like math/science/world.
The sort of thinking in Feynman's bio is what drives math circles, though.
I taught at a math circle for a few years; we did 'looking at awesome stuff' for two thirds of the year, and competition prep for one third of the year. Different kids came for different parts, but will came out smarter for the experience, I think.
It's unfair to generalize about "these 'math wizards'" or "these parents" just based on the context of the article.
On the topic of "math competitions" or rewarding kids for "being the best," "being the smartest", etc... I gotta say that really didn't work for me. I'm very slow at math (in a 'big picture' way), even though I love it. So making me do that anxiety inducing speed competition actually just made me feel like I was awful at math. The whole "speed multiplication tables" thing in 4th grade honestly made it impossible for me to quickly remember my 7's, 8's and 9's calmly or easily consistently, and even to this day I still have to think about it.
So I see what you're getting at. But I'm not convinced that's all there is to the programs described in the article. While you're probably right that plenty of still parents put unwarranted pressure their kids to be good at math (or anything for that matter), I think you might be injecting your own experiences into this article a little bit.
edit: one more thought... for me, math is a kind of spiritual practice. It is a way of exploring perspectives of things that would otherwise be assumed, under the radar. So for me it's very important, even if I don't "do something with the math" to have a healthy, creative relationship with it. A lot of people are effectively superstitious about math. It's a bummer. So called "advanced math" is usually just the most elementary stuff. Number lines and venn diagrams, sets and groups... these are things that people use every day! I wish more people had confident intuition about these kinds of things so that we could elevate beyond just taking our cultural mathematical constructs and perspectives as givens and evolve them to other possibilities.
> read Richard Feynman's bio and see how his parents inspired him to like math/science/world.
I noticed a perfect parallel between Feynman's relationship with his dad and Steve Wozniak's relationship with his, in his autobiography iWoz. It's all about encouraging and exploring curiosity, rather than trying to do well on tests.
I was frustrated by this article because I find it taking for granted the idea that math is only accessible to a small group of people - 'talented, gifted, with an affinity for, confluence of specific abilities'. I find similar language around programs like the Russian School, Brilliant and quite obviously the 'gifted' programs.
Yet in this article they quote the following statistics:
- High achievement in math: US 9% to SK 30%
- Ratio of high achievers affluent vs poor: US 8 to 1, SK 3 to 1
These statistics communicate to me that half of all students are capable of high achievement in mathematics. From my experience tutoring and visiting classrooms of various grade levels and demographics, most students are capable of the rich problem solving described in the article.
US education's biggest issue is social justice. We spend the least resources on the children who need it most. It's funny to me that the closing of this article suggests that it's time for the advanced mentors to step in to the public education scene. What would a group of people that cater primarily to the best-served students in the system have to say about how to help the worst-served? What would they know about the obstacles faced by poor children and parents; overworked, undertrained and unsupported teachers; and underfunded schools?
> We spend the least resources on the children who need it most.
Actually we spend a lot more with no returns. No amount of investment will ever offset bad parenting. Short of removing the children, which will never happen, what can be done?
"What would a group of people that cater primarily to the best-served students in the system have to say about how to help the worst-served? What would they know about the obstacles faced by poor children and parents; overworked, undertrained and unsupported teachers; and underfunded schools?"
Hopefully they wouldn't get caught up in all that and just teach some math to whoever's interested, regardless of income level.
One of my teacher friends taught 6th grade math. In his classes, he had to account for 4th through 8th grade math skill levels. Those with 8th grade being Khan Academy-style motivated learners.
>These statistics communicate to me that half of all students are capable of high achievement in mathematics. From my experience tutoring and visiting classrooms of various grade levels and demographics, most students are capable of the rich problem solving described in the article.
I think that excellence in math is actually in everyone's reach. The main questions are why and how to reach it. :)
The article surveys the field of enrichment programs and activities, many of which are available only to people in certain areas. I've witnessed the immense local impact of those outreach efforts, while visiting Math Circles, high schools, and academic competitions around the country. The people who lead those events (mostly after-hours or on weekends) are an incredible bunch, and many of them do it out of their passion for the subject.
However, I think we would all gain if we could engage everyone in math/science, no matter where they live. The success of these programs shows that interesting content increases interest! The Internet allows us to level the playing field, and scale the impact of free educational resources to the world.
I was once at a math education conference where groups were pitching ways to develop math talent. These programs sometimes need financial sponsorship from governments or foundations, so that they can remain accessible across socioeconomic lines. On the second morning of the conference, I suddenly thought: how much money does our public school system spend trying to teach soccer each year? (I don't think it's much.) It seems that many students achieve fairly high levels of proficiency regardless.
Of course, there is still much value in funding the current math education efforts, but that made me think about whether significant gains could come from finding out how to communicate educational content in the most engaging way. That would take a page from the startup playbook (optimizing for engagement).
So, I got my hands dirty. I launched a startup (expii.com) to crowdsource and rate free interactive lessons in math and science, to quantitatively evaluate an organized collection of these resources, distributed at scale across the world. The objective is to turn every smartphone into a pocket tutor, delivering the most engaging lessons produced by the combined creativity of the world.
That's a big project. In the meantime, while the content is crowdsourcing, I also am broadcasting interesting nuggets of math each week at expii.com/solve (again free). These deliver the same topics I talk about in person at middle- and high-school math enrichment events around the country when I visit them to give guest talks: https://www.youtube.com/watch?v=9sxVgJ_wPaM&feature=youtu.be...
My thought process is that if I'm taking the time to develop the materials to deliver to only 200 people at a time, then we should harness the Internet to scale the distribution to the world, while also packaging the content in a fun way, to show to the mass audience why math is actually a very interesting subject. :)
Ultimately, I think that the global project to build interest and excellence in math is an enormous task, which needs the insight and hard work of a great multitude of people, and a diversity of ideas and approaches. Thanks to everyone who is pitching in on this mission! :)
"Nearly everyone in the accelerated-math community says that the push to cultivate sophisticated math minds needs to start early and encompass plenty of thoughtful, conceptual learning experiences in elementary and middle school."
What hope do I have to study advanced math when I've begun to teach myself in my mid 20's?
Per that, the drop between 25 and 40, is only around 15%.
Becoming better at learning, and wiser in how you spend your time, can offset some of the cognitive decline that comes with age versus the raw capability of youth that is perhaps more squandered due to lack of wisdom.
You'd benefit from a title "How We Learn". Contrary to pop culture portrayal, skills acquisition is more about short bursts of frequent repetition than sitting down quietly with a textbook for three hours.
Learn something quickly, repeat it at certain intervals, test yourself frequently, and your brain will develop a "muscle memory", a toolkit of handy learned concepts.
96 comments
[ 2.7 ms ] story [ 163 ms ] threadCommunity college system = workers in the practical trades
Cal State system = office workers
UC system = technologists, scientists, managers
Big name, elite, private universities = executives and high level politicians, the people who actually run society and its institutions
And, if you look at the architecture on the various campuses, it more or less reflects that.
Also, all of the community colleges, and an awful lot of the Cal State schools are commuter campuses. You come and you go. It's not your home. You're a renter. The place shuts down around 10 pm. (Get out of here, kids.)
By contrast, the elite private schools have sufficient dorm/house space to allow most of the students to live on-site: the students have a lot more access to buildings and more or less "own" the place while they're there.
American schools are fine. Our problems are social. For example, the U.S. has the second-highest rate of single-parent families along with one of the highest gaps in PISA scores between single-parent and two-parent households: http://educationnext.org/international-look-single-parent-fa....
The U.S. also has a larger fraction of children in the lowest income distribution than comparable countries: http://www.epi.org/publication/us-student-performance-testin.... Accounting for that eliminates a lot of the supposed gap in U.S. student performance:
> If U.S. adolescents had a social class distribution that was similar to the distribution in countries to which the United States is frequently compared, average reading scores in the United States would be higher than average reading scores in the similar post-industrial countries we examined (France, Germany, and the United Kingdom), and average math scores in the United States would be about the same as average math scores in similar post-industrial countries.
Why are you assuming that the schools are responsible for the higher test scores? In my immigrant, upper-middle class community, there's nearly universal use of after-school test prep and tutoring from companies like Kumon. I'd argue that's the reason you're seeing test scores "shoot up" once only few low-income families are left in a neighborhood.
I think a lot of well-educated (or self-educated) tech folks think that if only we could fix our education system, poverty and income inequality would disappear under a massive rise in productivity and innovation. I know that I am guilty of thinking this way.
But you're right: family and socioeconomic status are highly predictive of education outcomes. So we need to directly address both schools and poverty at the same time in order to create a virtuous cycle of social improvement.
Also well off parents could help school in other ways.
And then educational outcomes of the poor rural and poor (but expensive) urban schools aren't different.
Plus, in the case of NYC, rich PTAs more than make up the difference between what the state provides and what the students receive.
http://www.thenewyorkworld.com/2014/08/06/pta-2/
http://www.bondbuyer.com/news/regionalnews/california-school...
You can try to work with the school, the teacher, the principal, but you can't really work with the other parents. I can't even imagine how you'd begin that conversation. "Hey, little Johnny acts like a complete asshole and disrupts the class to the point that they are spending their heads down on their desk for half an hour a day. Can you step up and do something about his behavior?" Obviously I'm never going to be a politician, but how can that ever be phrased in a neutral way?!
One of the stark differences between improving and flagging schools is parent involvement and support, in addition to a culture of education and learning.
It's what I saw growing up, kids from blue collar families saw school as a reluctant obligation through which they had to pass. Kids whose patents were professionals took a different view of education and saw it as a station on the path to a richer [both meanings] life.
So, it's more than money or wages, it's a way of thinking, how the parents think of school, how the kids think of school, attitude towards academic achievement (over sports, for example), etc.
It's really important not to let 201x social concerns get in the way of this stuff. The good stuff always starts out with the rich. Always. It is virtually structurally impossible for it to happen any other way. (Not quite, but very much the exception rather than the rule.) Rather than complaining that only the rich have the thing it is far more important to work out how to get it improved and shared more widely; complaining about the rich having the thing doesn't help that and in the modern political environment runs the risk of strangling the improvement in the crib. It is always easier to bring "equality" by cutting off the top than bring up the bottom, and you have to be very wary of that, because people will propose that in various subtle ways if you fall for the "class inequality" memeset too hard.
But that's not our current style of failure, it's "hey poor district, you're not up to snuff compared to the rich district. We're going to fire all the teachers, gut your union, and generally make your life hell. That's sure to make you do better".
This is not the time to be worried about fairness. This is the time to figure out what works. When you have that, then worry about fairness. Demanding that all the experiments be done equally to everybody at scale produces total paralysis, and is in no small part responsible for the total paralysis we witness in school reformation right now. You simply can't do anything that way.
I have worked in a poorly funded chicago public school that had just that year become a "turnaround school". That's just a very cute euphemism for "we fired everyone, hired whatever assholes would work for the least amount of money (Yo!), more or less eliminated any budgets you would be working with, and are making no other real changes". I guess the logic is that if we were going to be set up for failure, we might as well do it on the cheap.
Then, a few years later, they wonder why the students who went to those schools are so far behind the rest of the students in the city.
I should also mention that many of the students going to these schools were already saddled with the disadvantages of being poor and black in Chicago, before having their entire educational world replaced with an even shittier and more dysfunctional one.
The funny thing is that I agree with both your cynicism in practice, and the parent commenter's optimism in theory.
But my program is prohibitively expensive, and I'm acutely aware of the fact that when my students return to their high schools, they will almost certainly return to lackluster curricula. There are exceptions, of course. My summer program is filled with a far-above-average percentage of students attending private high schools.
The fact remains that students who attend the summer program are introduced to interesting math with no guided way to continue their exploration. Sometimes, students with supportive schools end up scheduling a self-study with some supervision from a high school teacher or counselor; I've been asked to help set up and guide self-studies, and I know at least a few of them have been successful. In my experience, this has been the best outcome for my students continuing exploration of advanced math. I'm not sure what this says about math and American high school education.
Why? Just curious if there's any brainstorming to be done.
Also expensive relative to what? Some people think Kumon is expensive. My kids did it for a couple years. Its about $100/month. Its very popular among immigrants who make a whole lot less money than I do. Of course Kumon isn't "real" math because its very drill -n- kill (which is why we quit, more or less)
I'm afraid that I don't know about the actual costs. There are several classes offered, and though students only take one at a time, they sometimes link a few and stay for up to 8 weeks. It's a pretty large board-at-the-university-for-x-weeks style summer program.
I'm an instructor, and I don't set prices. I also understand that there is a non-negligible cost to house and feed a student for a month. But program costs each student about $6000 dollars. I think that's enough to be called "prohibitively expensive," although I'm not sure how to compare these things really.
On top of that, I try to occasionally make it out to high schools to give guest lectures. I posted an example experience from one of these online [1] and I am usually looking for other opportunities to do this sort of thing. I think that if every math graduate student who is a reasonably good teacher took a day or two out of every year to visit a high school math class, we would see much more interest in math. Many of us (myself included) were not particularly interested in math in high school and didn't discover the cool stuff until college. So we were once the audience we'd be appealing to.
[1]: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...
But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of my classes would have played up if a whole lesson was spent deriving and exploring concepts without rote learning.
Being a maths teacher has to be pretty rough, especially given the number of students who are openly hostile to it as a subject.
As an aside, I often think about my Religious Studies teacher who'd disparage topics like Maths as being irrelevant after school. We'd never use them she said. RS was vital to life success, Maths a pointless exercise. It still winds me up to remember.
Once you get in the mindset of deriving equations, rote memorization becomes insanely difficult, at least in my opinion.
During my last year as an undergrad majoring in physics I got a 4.0 in quantum mechanics, but very nearly failed introductory chemistry (which I was taking to fill a science distribution requirement at a liberal arts college), despite many of the chemistry concepts just being edge cases of applied quantum mechanics.
There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. I understood the solution to the problem itself, but when the professor started giving me hints I had to admit in front of the whole class that my issue wasn't with the number theory proof -- it was with the multiplication table we learn as children.
Is there a reason you didn't whip out a calculator and do it there? Although I must say that I remember everything till 20x20 :P
That said I excelled in math throughout high school and college. It just goes to show that elementary math really has no bearing on the type of mindset one may have for "more complex", logic based math and computation.
Trust me -- since that experience of being humiliated in front of the best students in the math department at my college, I haven't forgotten what 9 times 7 is.
If it's any consolation, the great mathematician Alexander Grothendieck (https://en.wikipedia.org/wiki/Alexander_Grothendieck), when asked to supply a prime number (at some point in a lecture)—and being puzzled by the idea of actually naming a specific prime number—famously thought for a while before suggesting 57. (https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics)
Spread out your fingers. Number them from 1 to 10, left to right (i.e. left-hand little finger = 1).
For 9 * 7, simply curl finger 7 downwards.
Now you have 6 fingers on the left, and 3 fingers on the right. Voila, 63. :-)
Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football:
There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there.
I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community:
https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1...
I think that by thinking of and packaging cool nuggets of "math" like this to share, we can help rebrand the image of math. :)
I remember going to the "best" math teacher in my high school with a math question about my science fair project. He couldn't answer it. That was so demoralizing. I had already taught myself so much of the math and stats I needed to know for analyzing my project, so I only went to him out of desperation.
It would have been awesome to have a more advanced instructor available to talk with and learn from.
Thank you, your students appreciate you way more than you may know.
I agree! I think that many people have interesting ways to communicate where they see the excitement in math. Your blog lets you scale your impact through the Internet, which is great, and it's even more powerful when coupled with the in-person experience from guest lectures. :)
Indeed, when thinking of effective ways to scale up the in-person outreach efforts that I was engaging in (as National Coach + teaching at CMU + expii.com), I started posting my weekly math enrichment discussion topics onto the Internet. I think that's the way that we'll ultimately be able to completely level the playing field for everyone in the world.
It's great that many of these extracurricular clubs and institutes exist to impart advanced education to interested students. But it does not solve the underlying problem.
What about the vast majority of students who don't get to attend these type of programs?
We need to come up with solutions that are inclusive and accessible to the vast majority of students. Clearly inclusiveness and accessibility are missing from these programs.
The methods that these programs use to promote the development of problem solving in students are novel. Maybe they can be incorporated into school curriculum and better train the teachers to handle this new approach to learning.
This is step one. Before we can "come up with solutions that are inclusive" we need to just plain come up with solutions! Don't kill that with complaining long before it's relevant about how "fair" it is.
Is it really so wrong that the rich are willing to be guinea pigs anyhow? It is, after all, ultimately disingenuous to complain that the school systems aren't seeing this improvement because whenever the school systems suggest trying this sort of improvement the complaint about using kids as guinea pigs and ohmigosh their futures will be wrecked immediately come up. You can't have it every which way. This is a significant chunk of the mechanism that has rendered national-scale schooling impossible to innovate with anyhow.
But such initiatives cannot be a solution to a poor public school system.
I'd submit you're still asking for some sort of magical solution whereby we skip this step one somehow and leap directly to everybody having the good thing. But that involves skipping the experimentation phase that demonstrates the thing is good in the first place. It's why nothing, right now, can be the solution to a poor public school system... attitudes like this have utterly paralysed them.
If you want to see improvements, you've got to loosen up a bit on this fairness kick. Somebody is going to get them first. It is a mathematical necessity, because we should not do "experiments" by rolling things out to everybody at once in one shot. It's not like there's a guarantee that it's an improvement, after all.
If it so ineffective, how come americans win so many nobel prizes, have thriving high tech industry ect
http://graphics.wsj.com/which-country-has-the-most-nobel-pri...
The USA is lagging behind many countries in key areas( especially STEM fields).
Anyway the point I was trying to make was that, these extracurricular initiatives are great, but it cannot be a solution to a poor public school system.
Lagging how?
Test scores are not a good way to measure the "lag", imo.
Another indicator is the lack of sufficient skilled workforce in STEM fields in the USA. This forces many tech companies to hire from abroad.
Tech companies hire abroad because it's cheap, not because there is a real skill deficit.
Some tech companies do hire from abroad because it's cheaper, but there is a real skill deficit in STEM fields and there are just not enough skilled people available to recruit. This has been openly acknowledged by the tech companies, universities and the Government.
The question is not whether the USA is lagging in STEM, it is what should be done about the fact that the USA is lagging in STEM fields?
I did some googling around this but all the research uses test scores to come to that conclusion.
I would like to see some other methodology.
The being said, back in 2013, this article was widely shared. It demonstrates that you can teach STEM ways of thinking (e.g. CS), starting from early elementary grades. It does not have to be a AP-level course.
https://neil.fraser.name/news/2013/03/16/
http://www.huffingtonpost.com/james-witte/nobel-laureates_b_...
So that's not especially vindicating the American high school.
teaching to population averages will prove disastrous to our long-term growth. thank goodness we have private institutions to pick up the slack where massive bureaucratic oversight often (so often) gets it wrong.
I think if you want to fix the disadvantaged areas of the country, you've got to reverse the brain-drain that's sucking the best and brightest people out of these communities. Decentralizing the economy would be a good first step.
Up the Down Staircase is a lightly fictionalized novel about teaching in the 1960s in a public school system. Bureaucracy, parents (or lack thereof), funding, burnout. Almost 60 years later, many of the same fundamental problems still exist.
https://en.wikipedia.org/wiki/Up_the_Down_Staircase
It sounds like you're suggesting that education effort/money should be distributed with an emphasis on high-aptitude students instead of low-aptitude students for long-term growth goals. This makes some sense, it seems likely that empowering high-aptitude students with better education will generate leaders, entrepreneurs, inventors, 10x engineers, and "growth".
But if you don't spend the extra money and effort to teach the low-aptitude students, they will not have a usable education, producing a "low aptitude class", likely condemned to poverty, unemployment, and suffering.
Growth is great, but suffering is not. Maybe the bureaucracy swings too far towards preventing suffering at the expense of future growth, but it's not a black-and-white wrong.
Our rope question from expii.com/solve is a multi-layered math puzzle. If you haven't seen it before, the answer is often quite surprising: a human can walk under the circle even though the 710 inches of extra length are shared over the whole earth's circumference. Basic human intuition produces the most common answers, which are the bacteria or the ladybug. This helps to illustrate the purpose of math: to help us reason to determine the truth when basic intuition fails. If basic intuition were always right, then we wouldn't need math!
If you had seen the puzzle before though, you would already know that the rope lifts high, because it lifts by 710/(2*pi) inches, which is 113.0000095... taking us to the second layer of math embedded deeper in the problem. That is remarkably close to a whole number, which is surprising because pi is an irrational number. This means that pi is very close to 355/113, which brings us to the topic of Continued Fraction representations of irrational numbers, and amazing rational approximations of pi: https://en.wikipedia.org/wiki/Mil%C3%BC
So, this problem hits at both basic and advanced levels. :)
There are many interesting ways to teach math through multi-layered puzzles which have something for everyone, no matter where you are in the experience spectrum. Our goal is to provide these for free, disseminated over the Internet. :)
Has anyone done any studies on what these 'math wizards' end up doing in life.
I grew up in Indian community where this kind of stuff was the norm, many of my friends won regional championships but none of them do anything remotely related to math now. Instead of associating math with magical patterns that explain the world, they now associate it with stress/anxiety/competition.
Please don't do this repulsive stuff to your kids, read Richard Feynman's bio and see how his parents inspired him to like math/science/world.
I taught at a math circle for a few years; we did 'looking at awesome stuff' for two thirds of the year, and competition prep for one third of the year. Different kids came for different parts, but will came out smarter for the experience, I think.
On the topic of "math competitions" or rewarding kids for "being the best," "being the smartest", etc... I gotta say that really didn't work for me. I'm very slow at math (in a 'big picture' way), even though I love it. So making me do that anxiety inducing speed competition actually just made me feel like I was awful at math. The whole "speed multiplication tables" thing in 4th grade honestly made it impossible for me to quickly remember my 7's, 8's and 9's calmly or easily consistently, and even to this day I still have to think about it.
So I see what you're getting at. But I'm not convinced that's all there is to the programs described in the article. While you're probably right that plenty of still parents put unwarranted pressure their kids to be good at math (or anything for that matter), I think you might be injecting your own experiences into this article a little bit.
edit: one more thought... for me, math is a kind of spiritual practice. It is a way of exploring perspectives of things that would otherwise be assumed, under the radar. So for me it's very important, even if I don't "do something with the math" to have a healthy, creative relationship with it. A lot of people are effectively superstitious about math. It's a bummer. So called "advanced math" is usually just the most elementary stuff. Number lines and venn diagrams, sets and groups... these are things that people use every day! I wish more people had confident intuition about these kinds of things so that we could elevate beyond just taking our cultural mathematical constructs and perspectives as givens and evolve them to other possibilities.
I noticed a perfect parallel between Feynman's relationship with his dad and Steve Wozniak's relationship with his, in his autobiography iWoz. It's all about encouraging and exploring curiosity, rather than trying to do well on tests.
Yet in this article they quote the following statistics:
- High achievement in math: US 9% to SK 30% - Ratio of high achievers affluent vs poor: US 8 to 1, SK 3 to 1
These statistics communicate to me that half of all students are capable of high achievement in mathematics. From my experience tutoring and visiting classrooms of various grade levels and demographics, most students are capable of the rich problem solving described in the article.
US education's biggest issue is social justice. We spend the least resources on the children who need it most. It's funny to me that the closing of this article suggests that it's time for the advanced mentors to step in to the public education scene. What would a group of people that cater primarily to the best-served students in the system have to say about how to help the worst-served? What would they know about the obstacles faced by poor children and parents; overworked, undertrained and unsupported teachers; and underfunded schools?
Actually we spend a lot more with no returns. No amount of investment will ever offset bad parenting. Short of removing the children, which will never happen, what can be done?
Hopefully they wouldn't get caught up in all that and just teach some math to whoever's interested, regardless of income level.
But in public school you have to teach math to everyone. Any they aren't all interested.
Are Americans the same as South Koreans?
The article surveys the field of enrichment programs and activities, many of which are available only to people in certain areas. I've witnessed the immense local impact of those outreach efforts, while visiting Math Circles, high schools, and academic competitions around the country. The people who lead those events (mostly after-hours or on weekends) are an incredible bunch, and many of them do it out of their passion for the subject.
However, I think we would all gain if we could engage everyone in math/science, no matter where they live. The success of these programs shows that interesting content increases interest! The Internet allows us to level the playing field, and scale the impact of free educational resources to the world.
I was once at a math education conference where groups were pitching ways to develop math talent. These programs sometimes need financial sponsorship from governments or foundations, so that they can remain accessible across socioeconomic lines. On the second morning of the conference, I suddenly thought: how much money does our public school system spend trying to teach soccer each year? (I don't think it's much.) It seems that many students achieve fairly high levels of proficiency regardless.
Of course, there is still much value in funding the current math education efforts, but that made me think about whether significant gains could come from finding out how to communicate educational content in the most engaging way. That would take a page from the startup playbook (optimizing for engagement).
So, I got my hands dirty. I launched a startup (expii.com) to crowdsource and rate free interactive lessons in math and science, to quantitatively evaluate an organized collection of these resources, distributed at scale across the world. The objective is to turn every smartphone into a pocket tutor, delivering the most engaging lessons produced by the combined creativity of the world.
That's a big project. In the meantime, while the content is crowdsourcing, I also am broadcasting interesting nuggets of math each week at expii.com/solve (again free). These deliver the same topics I talk about in person at middle- and high-school math enrichment events around the country when I visit them to give guest talks: https://www.youtube.com/watch?v=9sxVgJ_wPaM&feature=youtu.be...
My thought process is that if I'm taking the time to develop the materials to deliver to only 200 people at a time, then we should harness the Internet to scale the distribution to the world, while also packaging the content in a fun way, to show to the mass audience why math is actually a very interesting subject. :)
Ultimately, I think that the global project to build interest and excellence in math is an enormous task, which needs the insight and hard work of a great multitude of people, and a diversity of ideas and approaches. Thanks to everyone who is pitching in on this mission! :)
What hope do I have to study advanced math when I've begun to teach myself in my mid 20's?
Your brain starts to slow down around 25-30 years of age or so, based on the major studies I've read. Eg:
http://time.com/63500/brain-aging-at-24/
Per that, the drop between 25 and 40, is only around 15%.
Becoming better at learning, and wiser in how you spend your time, can offset some of the cognitive decline that comes with age versus the raw capability of youth that is perhaps more squandered due to lack of wisdom.
Learn something quickly, repeat it at certain intervals, test yourself frequently, and your brain will develop a "muscle memory", a toolkit of handy learned concepts.