The persistence and the dedication needed in skateboarding—that's what we need to be teaching. No one says to a toddler, 'You have ten weeks to walk, and if you can't, you get an F and you're not allowed to try to walk anymore.' It's absurd, right? But the same thing is true with math and science education. If you want to learn trig or calculus, it's set at such a pace in schools that it guarantees that only the absolutely best students will learn it.
Anyone watching a child learn will appreciate that the skill-level/time graph is not a straight line - this is particularly noticeable in sports where coaches appear to be far more aware of this fact that most teachers of academic subjects.
An example that pretty much stunned me happened with our son - he's now 11 and has been skiing since he was 3 and was pretty good, about what you would expect for the amount of time he has been doing it. However, last year he went from being pretty good to completely awesome (much better than me - to my horror/delight) - practically a step change in his skill level.
This got me thinking a lot about academic performance - I have my own history of "step changes" in performance (particularly in maths), but everyone - particularly teachers, seem to view skill progression as a simple linear progression when in reality things are an awful lot more complex than that.
From a systemantic perspective, the "purpose of a system is what it does" not what it says it does.
A large number of people are chasing a small (and decreasing) number of good opportunities so a major function of education is to weed people out and make them blame their failures on themselves, not to maximize the development of human talent.
We have a "meritocracy" that occasionally allows an exceptionally talented person to rise, generally allows the mediocre to inherit the status of their parents, and sometimes puts the kibosh on non-housebroken children of the elite.
Athletic coaching tends to be a lot more honest. Few of us expect to be judged on how we do in PE classes and extracurricular sports, we do it for fun, and hopefully give it our best. Good coaches work in that spirit.
Now, if you're one of the lucky people who'll go far in sports, performance is open ended (the top score isn't 100%) and, unlike schoolwork, you need unique training to develop your potential.
> A large number of people are chasing a small (and decreasing) number of good opportunities
The number of good opportunities is dramatically increasing all over the world... every breakthrough we make opens like five new potential avenues for breakthroughs.
Every generation thinks the sky is falling because old industries are being obsoleted or automated - subsistence farmers, shoemakers, textiles, horse buggy whip makers, horse breeders, typewriter makers and typists, telegraph operators.
Paper mills, traditional publishing, traditional media/television, and music are all happening now.
Old industries go by the wayside or become automated. But that's exactly where opportunity and progress comes from - here's tons more opportunity now than ever before. I can't think of any past era I'd rather live - I can see infinitely more opportunity today than at any point in history.
There's some truth in that (creative destruction and all) but we've also seen an incredible concentration of wealth from about 1980 onward. Much of this has gone to people working in just a few industries, such as finance and law.
What we've seen is an expansion of the bottom and the top and a "hollowing out" at the middle. The system of private retirement accounts based on 401K and IRA accounts has largely failed. The largest asset that many in the baby boom generation will have in their retirement will be their Medicare benefits.
The ultimate interpretation of the financial crisis is that the financial sector is currently unable to match capital with places where it can be invested properly. The power that this sector has over government and the culture of impunity surrounds it makes it possible that this situation will stretch on for another 10 to 30 years.
Sure, failing industries in the recession are going to create a few opportunities for people to do amazing things in the next 10 years or so, but look for rapid advances in A.I. to essentially wipe out white collar work within 20 years.
> "if you're one of the lucky people who'll go far in sports, performance is open ended (the top score isn't 100%) and, unlike schoolwork, you need unique training to develop your potential."
And that's how everything should be. Because that's true of learning in any other context. Sports, Music, Art, Mechanics, Science ... learning is learning and it's all open-ended. The only limits are self-imposed. And that's why our educational system is assembly-line garbage.
Most teachers are put in a situation where metaphorically they have 10 weeks to teach 30 toddlers to walk. They may be painfully aware that learning isn't a straight line, but the system limits what they can do about it.
Montessori is different. Kids stay in a mixed-age classroom for 2 or 3 years, and have a system conducive to self-paced learning. If you can get to Beverly, MA tonight there's an open house that will amaze you: http://www.stoneridgecms.org/
If you want to learn trig or calculus, it's set at such a
pace in schools that it guarantees that only the absolutely
best students will learn it.
The usual complaint against the school system is the inverse: stuff is set at such a pace that even the worst students will learn it. They can't have it both ways.
When I took math in elementary school, in the 80s, it was self paced. You really didn't get an F, you just kept studying a topic until you could pass it at 90%. On the other side, if you could pass a pre-test, you could skip the topic. It really enjoyed, because I could learn some topics in an hour, which would normally be 10 hours of boring instruction.
It was a little more work for the teachers, since the system admitted that kids were at a variety of levels, but it was roughly a normal distribution, where a whole classroom of kids were on normal pace, some were a little bit ahead or behind, and a few were way ahead or behind. It seems like adaptive learning software could make this even easier.
You say teachers could do it in the 80's. Montessori could do it 100 years ago. I don't think the problem is lack of technology, it's that the principles of education have changed. Software won't fix that.
Sure you can, it's been done, it's not rocket science.
The problem with today's school system in America (and likely elsewhere throughout the industrialized world) is that it's very much aimed at teaching the wrong people the wrong things in the wrong way (and that's when teaching doesn't take a back seat to day-care). The main goal is for everyone to memorize as much of a broad swath of "material" as possible, it's very much a teaching-to-the-test least-effort system. It's not geared toward maximizing each individual student's learning. Nor is it geared toward teaching competency and fully mastering basic yet key skills. Nor is it geared toward teaching useful skills that are key building blocks in the workplace, as a member of society, and as a functioning citizen of a democratic republic.
The steps necessary to improve this situation are fairly straightforward. As a start, reduce class sizes and hire better teachers, which is possible without increasing per-student expenditures provided the bloat in non-teaching staff and unnecessary expenditures is cut back (per-student spending has more than doubled in the last 3 decades, adjusted for inflation, the money has not gone to improving education, it has been frittered away). End the farce of overstuffed curricula. There is a monomania about covering as much material as possible, so long as students can retain enough to pass a test, but students don't retain much of the material and when the fundamentals are neglected they miss out on that too. Take the basics back to basics, emphasize the fundamentals (reading, writing, mathematics, fundamental science), learning them, knowing them, mastering them. Continue to refresh and test students on those fundamentals throughout their entire K-12 educations. And provide enough funding to allow gifted students to work at a faster pace, either within existing classes or in classes of their own.
I could go on, but that's a good start. Unfortunately, the biggest impediments aren't knowing how to improve, it's all of the interests and bureaucracy protecting the status quo.
You make many assertions, but you haven't provided any reason to think that your approach is any better.
As a start, reduce class sizes...
This, in particular, is something that I've done a fair amount of research on. Although the jury is still out, the best conclusion I've been able to arrive at is that for most kids, class size isn't strongly correlated with achievement, at least not within a reasonable range. Class size only seems to make an appreciable difference for kids that are "at risk", i.e., those that don't get much academic support at home.
So I might be jumping on you for just one small aspect of your opinion, but from the part of it that I do know about, I have the impression that you're just jumping on board with conventional wisdom that hasn't had much testing.
You might be able to improve some things like this, but to deliver it as a factual answer is a disservice.
I was unclear: I meant that it's strange that people complaining about the educational system both criticise it for being 'aimed at the best' and simultaneously for being 'aimed at the worst'. I wasn't saying it couldn't both be true, but if it was, they wouldn't be complaining about a single extreme being the case.
Seems likely that it is "aimed at the average," and the complaints come from people who notice the "better" side or the "worse" side not being served and complain accordingly.
I'm curious what spending bloat you are referring to - because hiring more and better teachers is limited by money. It's limited by other things, too - such as figuring out a reliable metric for "better."
Sure you can: have more flexible pacing. Don't tie the different subjects' timelines together. There's no need to specifically have 5th grade reading, 5th grade math, and 5th grade history that all must be done at the same time. Have multiple tracks. Have many subjects be entirely optional.
"If you want to learn trig or calculus, it's set at such a pace in schools that it guarantees that only the absolutely best students will learn it."
Pardon my elitism, but only the absolutely best students need to learn trigonometry or calculus. I'd much rather high schools offer useful classes like personal finance or civics or creative writing than make average, uninterested students take a trig or calc class that they will have absolutely no use for later in life.
Since when is education about only learning the things that a student, in their current ignorance, project they'll need far into the future? Trig and calculus are trivial, learn them. (I'd argue that a solid understanding in both would make personal finance a lot better a subject too.) In any case, my high school offered all of those classes, with personal finance being required and trig being taught along the way in several required math courses.
Since when is high school education? High school is preparation for the real world: it has replaced the old apprenticeships and parental involvement that served as life preparation for centuries.
High school fails in this purpose when it wastes time teaching trigonometry and calculus to those who have no need for it. The majority of people do not graduate college; of the ones that do graduate college, many will never use trigonometry or calculus in their occupations or personal pursuits.
It makes no more sense to teach every high school student trigonometry and calculus than it makes to teach every high school student how to retread tires or operate a band saw.
I think it makes a great deal of sense to teach every student how to operate a band saw. And also how to dance, and how to read poetry, and how to draw with perspective, and how to use a potter’s wheel, and how to solve Newtonian mechanics problems, and how to build simple electrical circuits, how some basic cooking chemistry works, and how double-entry bookkeeping works, and some basic music theory, and how to operate a non-linear video editor, and on and on. Not every student necessarily needs to learn every thing, but schools should have the resources to teach many things to every student.
If kids are going to spend half of their time for 13 years (!) in school, I sure hope they’re learning all sorts of useful things. Drilling them on geography or historical dates or the content of 19th century “classic” novels, &c., certainly isn’t the only important thing in the world.
Okay, how about this: every student should learn trigonometry and how to dance and how to cook and how double-entry bookkeeping works and how to speak several foreign languages, most (personally I think all or nearly all) students should learn calculus, and a large (much larger than now) percentage should learn how to operate a band saw. Calculus is just absolutely fundamental to so much of the technology that we use every day that students who do not learn calculus are at a serious disadvantage comprehending our built environment.
Calculus is not fundamental to the technology that we use every day. I work an extremely technically challenging job and I'm serious, I haven't used calculus or trigonometry since my last physics exam in undergrad. Am I happy I know them? Sure, because I like knowing things. Are they even remotely useful in my everyday life? Not a bit.
Please, by all means, demonstrate a place where a person who doesn't know calculus is at a disadvantage interacting with the technology of the world around us. Until then, I'm calling bullshit.
Creative writing? I'd settle for plain old English composition. This is no "those darn kids" gripe - I get emails from people in their 30s and 40s that are excruciating to read and require a follow-up call just to find out what they were trying to say.
But at some point in understanding probability, as it is actually used in the real world, you need calculus. The same is true for economics, which you didn't mention but often comes up as something everyone should learn. I think by not covering calculus, students are forced to learn things (economics, physics, statistics) the hard way and without understanding them deeply. Unfortunately, calc generally requires trig. It should be taught while teaching calculus.
But at some point in understanding probability, as it is actually used in the real world, you need calculus.
At SOME point, true. But that point is very, very far off, and very few people ever get there.
It is possible to understand what the normal distribution is, and how to lookup significance values, without worrying about how to calculate it. This is how virtually every non-statistician does it, and is what statisticians themselves do more of the time.
The point where you have to calculate it and prove properties about it does require Calculus.
Unfortunately, calc generally requires trig. It should be taught while teaching calculus.
I'm sorry, but this is not a good idea. What Calculus requires from trig is a solid understanding of what sin, cos, and tan are (else the derivatives of the same won't make sense), and a solid understanding of trig identities for use in integration. Both uses require several layers of abstraction on top of the idea of trig. My experience is that it is a bad idea to layer abstractions on top of material before making sure that that material is solid.
I therefore want people to have a solid understanding of trig before they arrive in a Calculus course.
That said, I think that a lot of the use of trig in integration is a now useless skill, given the widespread availability of programs like Mathematica that can solve all of those problems very quickly and much more accurately. It was once important for people to learn those skills, but now it doesn't seem that useful to me.
You should be able to verify that the integral differentiates correctly. But integrating complicated expressions isn't in my view that critical of a skill.
I come from my own point of view that I have difficulty learning something when it is not likely that I will apply it. I learned basic calculus while learning physics, and it was immediately apparent why calculus was required. Without calculus, the problem domain available in physics is almost so trivial that it feels worthless to study.
Basic trig does have other interesting applications, such as computer graphics and what not, that could probably all be integrated into an interesting high school course. So much of a trig class is about memorizing identities, though, and it's hard to see why you might want to do that unless you had something else to do, like integrals. We end up re-learning trig in Calc 2.
I have heard arguments that setting calculus as a "goal" of math education leaves out the stuff of math that is actually "cool" and makes math seem boring. But calculus is interesting (at least) when you use its applications.
Mathematica can, indeed, solve a lot of problems, but is something lost when students never gain the ability to symbolically solve math problems? I suppose there is a wide space for research in this area, and I haven't heard of much being done.
That's a very interesting essay, but I don't think it squares with the view that the ability to do maths is extremely difficult to teach. Sure, you can teach proof techniques and do example questions, but the actual ability to see ahead and know what to do depends heavily on their natural ability, or, as some researchers claim, on their exposure to maths in the first few years of their life.
I think it may work for other subjects, but not maths.
The best physics class that I've seen (and that I've taught) is the Physics 101 autotutorial class. Students get three chances to take each test, but they need to get a passing grade on each unit before they move on to the next. This is contrast to the usual physics course, where the average grade on a test might be 35, but they do it on a curve so that 35 gets you a B-.
The class is aimed at premed students, and experience shows that Physics 101 students do better on the MCAT than students who take a conventional class aimed at premeds. Because it's aimed at premeds, there's a heavy dose of fluid mechanics and other subjects that often get missed in intro physics.
It's particularly fun, as a teacher, to work with students to "debug" their thought process. So often I'd hear "I understand the concepts but can't do the problem" but then once they started explaining how they tried to solve it, I'd see that they missed important concepts.
"The code is right but something is coming out wrong" was one of the favorite things I would hear from my intro to programming students.
I would call them out on it, too. The attitude they had was part of why they couldn't debug their program. They needed to adopt a question-and-test-assumptions approach, which can be intellectually uncomfortable. I hoped that by explaining to them why that comment was obviously wrong that they could start to learn the debugging process without me walking them through it, constantly asking pointed questions.
I think it's important for students to have critical self-feedback alone. The problem with tests (generally) is that it's feedback for the student (which is good) but also feedback for the teacher, with grades with implications. So basically you have to get everything the first time, and to pace and time that is tricky.
I do like your approach, as it does not penalize you for trying hard, even if you reach deadends, or made some assumptions that can be sniffed out easily by a test. My physics professor did a variation of this sort, where the final consists of all the topics, and your previous test grades gets overwritten by the final if the final grade is higher.
Uhm... Early Childhood Educators do give F's in walking and block stacking and a variety of gross motor, fine motor, cognitive skills. They might not call it that to the parents, but that is exactly what it is. They do screenings like the Denver, LAP, and eLAP that tell where a child is in development and point to exercises to do or the very real need to get specialized help for the infant / toddler. Failure to get help could cost us taxpayers big bucks (1M+) over the course of the kids life.
So, yes, your child can flunk walking or block stacking.
It's true. I failed something called "Running, Skipping, and Jumping," when I was in kindergarten. I was a clumsy child, and I also had difficulty understanding what the gym teacher was barking at me. My parents found it hilarious.
I can do all three of those things just fine now, by the way.
"There was a lot of pressure from my family not really to have a career path in mind, just to get good grades. Getting something less than an A wasn't a disappointment, it was an outright failure. I didn't consider that a very nurturing environment."
Funny how many smart and successful people come from this kind of background but don't want to share it with anyone else.
When you're raising a brilliant kid and want him to have a good academic work ethic, you have to hold him to standards that don't have any other pragmatic justification. They raised their standards to a level that made him work hard in school, which is perfectly appropriate. There are other things they could have done, such as home-schooled him, pushed him to excel at academic extracurriculars (if they were available), or forced him to abandon his friends and attend university early, but they may not have been aware of those options, and pushing him to do well in school is a decent approach. Holding a kid that smart to "reasonable" standards means allowing him not to work at all, which means he's in for a big shock when he gets to the real world and realizes that sitting around being 20% smarter than everybody else isn't actually rewarded (or rewarding).
He doesn't say precisely what he's complaining about. Since everything else seems to have worked out well for him, I can only speculate that maybe he has some personal problems he attributes to the way he was raised -- but who doesn't? It's much easier to understand how our own problems could have been avoided than to imagine the problems we would have had if we were raised differently.
P.S. Any other mistake parents make -- like making a kid feel deficient or unloved -- is separate from holding them to high standards and making them work hard. If a kid's feeling of being loved or being a valid human being hinges on what his parents say about his grades, they've screwed something else up already, and they can't fix it just by giving a thumbs-up to his grades.
P.P.S. Just wanted to clarify I'm not presuming to talk about details of the real Kim here; I'm talking about a situation we've extrapolated from a few words in the article, which is as good as hypothetical.
So many times at college in computer science I heard the idea that math == computer science and that it is impossible to grok one but not the other.
I've heard the famous Dijkstra quote "Computer Science is to computers as Astronomy is to telescopes", but one aspect of computer science education strikes me as fundamentally different than math education: The technological revolution brought by the compiler. While it's true that a compiler can't tell you if your algorithm is correct and is thus useless for algorithm analysis (although there are other tools for that), its ability to check syntax, etc. makes it an invaluable tool for the beginning programmer who once he is comfortable with programming can use it as a tool to explore computer science. The compiler is like a computerized instructor giving feedback for elementary programming in the same way that a human instructor gives feedback to students for elementary math. Of course in advanced math the student must reason out complex proofs, but at the beginning stages of any algebra or calculus course there’s a lot of "You must do X before Y" and its that kind of basic rules that are analogous to programming language syntax and grammar.
The compiler in computer science education is different from a calculator or a system like matlab or even those online assessment tests like "Webwork" found in higher math education because those tools are only binary in their feedback: "Either you're completely right or completely wrong, and I'm not going to tell you why you're wrong. Good luck!" If you had worked the problem out on the board with an instructor hopefully they tell you “You were close, but you messed up here, you can’t take the square root of that without doing this other thing first” or "you used the chain method incorrectly over here"
It is my goal to one day develop an open source "math compiler" that allows you to write out the steps of your problem line-by-line (either through pen input or some sort of math symbol input system) and let the compiler give you that sort of feedback that would otherwise take a dedicated tutor to give. I know that there’s a million ways to solve a given math problem, but math textbooks usually teach things in certain orders, so you more or less know what the student will know at that point in the semester, and if someone is already thinking beyond the material then they don’t need this helper at this point anyway.
It’s a crazy idea, but it is my hope that in the years to come we will see technology not necessarily replace human educators, but rather supplement them, allowing feedback that would normally consume all of one instructor’s time and being able to simultaneously provide that to an entire classroom.
I heard the idea that math == computer science and that it is impossible to grok one but not the other.
IMO that's bullshit. I started university majoring in math with CS as secondary, but ended up switching as I was struggling to pass in math while getting straing As in CS.
Funny thing is, I still had to take some "pure" math lectures and during an oral test for one of them the professor asked which part of the lecture (group theory) I found most interesting. I told him it was the algorithm for ennumerating co-sets, since as CS major, algorithms were bread and butter to me. He laughed and said that this was the part most math majors had problems with...
Have you ever used Wolfram's Mathematica? He may be a huge crank, but the software is really awesome for doing mathematics research and learning. It can do all sorts of calculations automatically, but you can also easily program it to do them manually; it shows you a step-by-step derivation of pretty much anything it can compute.
Many mathematicians use it for their day-to-day research, and for learning something like calculus it can be enlightening to have millions of examples of anything you can think of at the tip of a finger.
Automated theorem provers behave much like this. As you lay out the steps of a proof they will check that each step is correct and show you what you have remaining to prove. You can start with a vague proof outline and refine each step until there is enough detail for the compiler to infer a full formal proof. Check out the Isabelle/HOL tutorial for a good example: http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation....
Forgive me for not knowing, but don't we already have pass/fail in some courses. Some of the more radical colleges have gone completely pass/fail. The premise being that once you've mastered the material you are qualified to move to the next level and if not you try again until you understand.
BTW, In elementary school the only Bs I ever received were in Handwriting. It didn't make sense to me then to give a grade on it and it doesn't make any sense now. But now I live in a country (France) where some companies give a graphology test to interviewees. A personality test based on your handwriting.
In theory, yes... but there are a number of problems, the most obvious one is that those "units of knowledge" used in the pass/fail process are extremely coarse.
Grades are handed down per activity... and in general on a monthly or even bi-monthly basis. In theory, this should provide feedback to the teacher to adjust the pace of the learning. In practice, the study program is set in stone and the students who cannot catch on their own will be left behind, no questions asked.
The only pass/fail test is at the end of the year, where everything is shoveled together. If the student completely fails to grok subject 3... but excels at subjects 1, 2 and 4. This liability gets lost in the numbers, remaining as a time bomb that will blow on his face in a couple of years when subject 3 is a building block of more complex stuff.
This problem is exacerbated by the fact that grading is extremely lax also. This is my personal opinion, any grade less than "B" shows knowledge in either immature (student needs to study more) or flawed (students have inaccurate assumptions that need to be detected and corrected by instructor) stage. If C and D students are allowed to proceed to later stages, they are being set to fail, because the teachers there are unlikely to devote any attention to correct deficits from previous years.
right on. our artificial reality education system has so many mistaken premises. but fortunately, they are given forever to get it right.
The real problem, of course, is its coercive nature. This way of doing things would never have achieved such a total monopoly without coercing students to participate and taxpayers to fund it. Not to mention that you're turning your children's minds over to the unions for indoctrination.
Murray Rothbard picks apart the whole system in chapter 7 of For a New Liberty. mises.org has a podcast of the entire book.
Reminded me of the essay "Everyone Should Get an A": http://www.inference.phy.cam.ac.uk/mackay/abstracts/exams.ht...