To Write A Textbook.

[Agent Intellect]

It's a popular topic around here (at least with me) that education is a broken system - or, outdated at best. Since I've gone to college a few years ago after having spent six years in the "real world" after high school, I've certainly taken a notice of this, and this summer semester especially. I'm taking calculus 1 & 2 as well as statistics, and I can't believe just how worthless these classes are.

Before I get started, here are a few TED talks about education (mainly about math) that I think are highly relevant, and I think you will get a sense of where I'm going with this from these:

Dan Meyer: Math class needs a makeover.
Salman Khan: Let's use video to reinvent education.
Conrad Wolfram: Teaching kids real math with computers.

One thing I had a problem with in my calculus class was when we spent an entire unit learning how to draw a graph using calculus (eg finding local min/max, inflection points etc). This is essentially how people had to do calculus before computers and calculators could graph functions for them. All this calculating is a useless exercise to drive home the point that when the derivative is zero, there is a local min or max, and that if it switches from negative to positive, it was a min, and positive to negative, it was a max.

My point is, this is time that could be better spent doing something else.

As is talked about in the videos, math is essentially taught in a plug-and-chug fashion. In my statistics class, we are supplied with formulas and parameters and we simply need to learn how to put those parameters into the formulas and have it regurgitate some numbers. I'm getting an A in my calculus and statistics class, yet I feel like I haven't really learned anything. In calculus I'm still terrible at the related rates and optimization problems*, because those actually require that I be able to extrapolate mathematical relationships between different variables, and it seems to just be assumed that if someone can calculate a bunch of numbers, that they should be able to do this.

In the third video, the speaker gives a list of four things that make up math:

1. Posing the right questions.
2. Real world -> Math formulation.
3. Calculation.
4. Math formulation -> Real world.

And it's argued that #3 is what gets taught in our math classes. I would mostly agree, although I think #4 is sometimes wedged in there. The idea behind the current math curriculum is to not only teach mainly calculation, but also to teach it in very abstract form. The logic is that, if someone can do something like calculus in an abstract form, then they should be able to apply it to whatever field they need it for.

I would argue that this is not the case. I can compute numbers like a champion in the style it's taught in math class, but I still have a difficult time bridging the gap between abstract computation and real world application. Being able to find the third derivative of a long series of symbols and spit out strings of numbers for certain values of X doesn't teach me A) what the numbers mean in any practical situation or B) how these formulas can relate to real life situations.

But, enough of my ranting.

I think the first two videos give some great ideas on how the teaching method, not just for math, but for almost any subject, can be improved. In the first video, the person talks about a method that would be more akin to guided inquiry as opposed to lecture. I think this would be powerful, primarily for the reasons he gives. I think that having students figure problems out by themselves using problem solving skills will teach them how to do the first two parts of math from the above list, inciting discussion and forcing students to look at a problem from every angle.

In the second video, one of the best points that he makes is that we don't teach students for proficiency. Whether or not you actually learned what was being taught or not, you get pushed along to the next topic, leaving large gaps in your knowledge that will be compounded every time a new concept is introduced - and even if you did well on the test, all that proved is that you could remember things for the test.

I titled this thread "To Write A Textbook" because as it is now, curricula are highly dependent on the information, the format, and the order of the textbook. In several classes I've had, one would not even have to go to the lecture if they had a good enough reading comprehension to just teach themselves from the textbook. This seems like a lazy way to teach, with the baseless assumption that there is a one-size-fits-all approach to learning material, and that only certain things are pertinent to ones education.

What I'm interested in is ideas on how the education system could be reformatted, or even overhauled.

Taking ideas from the videos, I think Salman Khan is on the right track. There is no need to go to school to get a lecture that one can get online from a place like Khan Academy. When one goes to school, they should be getting something more - and that is, essentially, what the first and third videos are talking about: learning to formulate questions, think critically about a concept, participate in problem solving activities, talking about ideas, and figuring things out on ones own. The straight up facts-to-remember and homework can be done in a Khan Academy like fashion.

Just off the top of my head, here's what I might like to see in a classroom:

Math: a real world problem is proposed by the instructor. The class, working together, must figure out a method for formulating this problem in a mathematical way, discerning what sorts of variables are involved, relating these variables to each other, finding a way to calculate them in a meaningful way, and then interpreting the results (a good example of this is in the first video). Because of the video lectures and exercises, the students know how to calculate, so the main focus is on the other three parts from the above list.

Science: given some information, students should be able to formulate a testable hypothesis and come up with an experimental design. A lot of science is learning to speak the language (as a biology major I'm painfully aware of this) but all that could be done in video lectures and exercises and from individual reading. What seems missing from a lot of science curricula is being able to ask the right questions in science, so a great exercise would be a guided inquiry environment that attempts to get students to ask the right questions to have the lesson move forward. For instance, instead of just being told that DNA is replicated in a semiconservative way, have the students come up with the question, based on what they know about DNA: where does the template DNA strand go during replication? In addition, students should be able to propose a hypothesis and come up with an experimental design for testing something like semiconservative replication.

History: a controversial subject from history is presented to class - for example (excuse my American bias) the events leading up to and reasons for the American civil war. The students are then charged with writing a research paper arguing for or against one sides stance (it could even be that the students must argue for the side they disagree with, perhaps at least in more advanced classes). The timelines of names and dates, once again, could be done in a video lecture and exercise format, but my main point is that the classroom is for a more involved, critical thinking method - perhaps even textual criticism of various historical accounts, comparative studies from opposing sides of issues, classroom debates, and ways in which both history itself and the way history is recorded have influenced modern times.

Political science and economics: I think it would be interesting to have students run computer simulations of their own societies - think sim city - or some sort of in-class game. Each student in a class would be a political official (maybe a senator or something) in one simulated society where political opposition, economic hurdles, and policy legislation come up. Perhaps a different simulation in which each student is in charge of a business or bank and must make real time decisions about what to do come up. Once again, information can be conveyed in an online format, but different political and economic schools of thought can be discussed, debated, and criticized in classroom discussions and guided inquiry.



These are just a few ideas, and may not be perfect, but the take home point is that what is done in classrooms right now (mindless calculations and long info-dump lectures) can be done in a Khan Academy like format, with 10-15 minute long videos conveying relevant information and online exercises geared towards proficiency as opposed to a pass/fail graded test. With all this done in an online setting, the classroom can actually be utilized for critical thinking, guided inquiry, and student-student and instructor-student interaction and discussion - eg stuff you can't actually do at home or on your own. This way, students are gaining a mastery and understanding of the subject by using the material to come up with and discuss ideas and by being guided towards conclusions (as well as questions) as opposed to being told information in order to pass the next test.

So, what do you (assuming you muddled through all this bullshit) think about the current state of education? Do you think the way students are taught works? Do you think that your own education has adequately prepared you? Do you know of any places that are actually making any sort of large reforms, and if so, how is it working out for them? What do you think about the videos posted? The ideas I proposed? How might you attempt to reformat or overhaul education? What would you like to see any a classroom of any particular subjects? What methods would you focus on?

*

Spoiler

Here's a little bonus for anyone interested in calculus 1 level optimization and related rates problems:

1. A piece of wire 10 meters long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed (in the triangle and square together) is A) a maximum? B) A minimum?

2. A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder.

3. In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end. It is believed that bees form their cells in such a way as to minimize the surface area for a given volume. The apex angle X has been measured and is amazingly consistent (all within 2 degrees). The surface area S is given by:

S=6sh-(3/2)s^2*cot(X)+(3s^2*sqrt(3)/2)*csc(X)

where s, the length of the sides of the hexagon, and h, the height, are constants. A) Calculate dS/dX. B) What angle should the bees prefer? C) Determine the minimum surface area of the cell (in terms of s and h).

4. A man stars walking north at 4 feet/sec from a point P. Five minutes later a woman starts walking south at 5 feet/sec from a point 500 feet due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking?

5. Water is leaking out of an inverted conical tank at a rate of 10,000 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 6 meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 meters, find the rate at which water is being pumped into the tank.

 

[Vrecknidj]

1) Long post. My attention span isn't that long.
2) I've been a high school and college math teacher for a little while.

Okay, on to some opinions.

First, classroom teaching is every bit as horrible as classroom learning. When I taught high school algebra, for instance, I would have to spend more time keeping kids from harming one another than actually teaching math. And, when I actually had the time to teach math, most of my students were at dramatically different levels (I'm sorry, a 16-year-old shouldn't be in basic algebra, and, worse, he shouldn't still be multiplying two single-digit numbers by counting on his fingers...).

One of the reasons why teachers and textbooks focus so much on calculation is that so many students are so bad at it. Solving simple quadratic equations (ones with two real roots, for instance) is a no-brainer for anyone who is really any good at math, once it's been learned.

x^2+8x+15=0

Anyone with a basic grasp gets rather immediately to (x+3)(x+5)=0,

and then to x = -3 or x = -5

But, some students have to do HUNDREDS of these to understand what's going on. The abstraction, from that problem, to the more complicated ability to start with:

a^2 + bx + c = 0

and end with:

x = (-b +- sqrt (b^2 - 4ac)) / 2a

is rather more taxing on most students. But, advanced students, the ones who don't have to do hundreds of these to "get it" can pretty quickly learn to convert between these two abstracted forms.

More generally, fighting to change the academic system is better left to people with nothing better to do for 4 or 5 decades. You'll be up against the public school unions in the big states, and those folks have a lot of political clout, have very wealthy sponsors, and have the ability to use political and financial inertia against you (no matter how much better your ideas actually are) until you give up.

As for me, I homeschooled my kids after 3rd grade. My oldest, by 14, was taking classes at the local community college. He's not a genius, heck, he's 22 and still needs 2 classes to finish his BA (he's been taking his time). But, he also didn't have to waste his entire adolescence in the bowls of the US "education" system.

Dave

 

[Agent Intellect]

1) Long post. My attention span isn't that long.

I know. I suppose I'm hoping people will at least watch the videos (very little reading involved!) and maybe at least read the last two paragraphs of my post.

2) I've been a high school and college math teacher for a little while.

Okay, on to some opinions.

First, classroom teaching is every bit as horrible as classroom learning. When I taught high school algebra, for instance, I would have to spend more time keeping kids from harming one another than actually teaching math. And, when I actually had the time to teach math, most of my students were at dramatically different levels (I'm sorry, a 16-year-old shouldn't be in basic algebra, and, worse, he shouldn't still be multiplying two single-digit numbers by counting on his fingers...).

I can sort of relate. I'm a tutor at my college right now, and some of the people I've had to tutor were completely clueless - I had one person that I spent about 45 minutes attempting in every way I could imagine to explain to him what an ion is (obviously I was tutoring for chemistry). I agree with you that it's just as bad for the teacher as the student, and I think this ends up showing and making it all that much worse for the student and vice versa...

I think a lot of this stems from the problems explained in the videos and in my post. The way that students are taught right now leaves them bored and either disengaged or simply cramming in order to get a good grade. I think the teaching methods explained above would help to get students engaged early on so that something like math is more of a fun puzzle and a way of looking at the world than a purely academic pursuit that only has application in the classroom.

By the way, I took Algebra 1 & 2 just two years ago at college when I was 24 years old.

One of the reasons why teachers and textbooks focus so much on calculation is that so many students are so bad at it. Solving simple quadratic equations (ones with two real roots, for instance) is a no-brainer for anyone who is really any good at math, once it's been learned.

x^2+8x+15=0

Anyone with a basic grasp gets rather immediately to (x+3)(x+5)=0,

and then to x = -3 or x = -5

But, some students have to do HUNDREDS of these to understand what's going on. The abstraction, from that problem, to the more complicated ability to start with:

a^2 + bx + c = 0

and end with:

x = (-b +- sqrt (b^2 - 4ac)) / 2a

is rather more taxing on most students. But, advanced students, the ones who don't have to do hundreds of these to "get it" can pretty quickly learn to convert between these two abstracted forms.

Yes, people are often bad at calculating. But trying to keep tackling this problem with the same approach to learning isn't going to fix anything. I think it's the abstractness of pure mathematics that is both confusing and not very engaging to students - hence why starting from real life foundations and working toward abstraction would be a better approach. This gives students a more intuitive sense of mathematics.

Also, doing exercises in the style of the Khan Academy website would be a better approach for the reasons he gives in his TED talk - it's teaching to attain mastery rather than covering a concept and moving on whether everyone understood it or not. If students didn't attain proficiency in arithmetic and pre-algebra before moving on to algebra (maybe they scraped by with a C-) it leaves gaping holes in their understanding. It would be no wonder that students who do poorly yet were able to pass can't factor quadratics and have to do basic arithmetic on their fingers - they never became proficient in this before moving on.

More generally, fighting to change the academic system is better left to people with nothing better to do for 4 or 5 decades. You'll be up against the public school unions in the big states, and those folks have a lot of political clout, have very wealthy sponsors, and have the ability to use political and financial inertia against you (no matter how much better your ideas actually are) until you give up.

Hence why I would be more in support of privatized education.

 

[Melllvar]

I know. I suppose I'm hoping people will at least watch the videos (very little reading involved!) and maybe at least read the last two paragraphs of my post.

Actually I read the whole thing and wrote a few responses, just never posted them. Skipped the videos though, I'll check them out later (and I'm already pretty familiar with Salman Khan so I'm not sure what else he's going to say that I haven't already heard).

The main reason I didn't respond is that I've got a lot of ideas on the subject but it's one of the few areas where I don't want to just go spilling my best ideas out in a public forum. I've already spent a lot of time on trying to develop better educational systems (I mean like 12 hours a day, single-minded focus for months at a time), mainly involving computerized systems. Education in general is still being done extremely poorly, it's based on a system developed over a century ago that hasn't been innovated on significantly since. It's completely fallen behind all technological advances made in the meantime, and like Vrecknidj said there are entrenched interests to ensure that change will not just happen on its own. Not just the unions and such but the attitudes people have towards it: the old fashioned systems (think of the Ivy League schools) are viewed as inherently more prestigious than newer stuff like Khan Academy and such.

The whole thing is really a gold mine waiting to be exploited. Think of just how much money goes into education (the vast majority of it being a completely unnecessary waste). People fight tooth and nail for the privilege of paying hundreds of thousands of dollars to the most prestigious university just so they can have a chance at a piece of paper that may give them a slight advantage in life. Millions even if you think about what people are willing to pay for K-12 private schools just to boost their chances of getting into one of those schools. To say it's a billion dollar industry is still just an extreme understatement. I'm not even sure how much money goes into it between public schools, private schools, collegs and universities, textbook companies, and other stuff like tutoring, test-prep, SATs/ACTs/GMATs/LCATs/etc., in the US alone, much less worldwide, but you start to get the idea of just how much money is sitting there being funneled into obsolete systems just waiting to be out-competed by something that wouldn't even be that hard to develop.

(Also, this article seems somewhat relevant.)

Again, I really don't want to go into detail about my best ideas on it (not that they're necessarily good, I don't mean to be that arrogant), but as far as things already being done that are a step in the right direction, Khan Academy is good, and so was PLATO, and soles and somes too. People are taking steps in the right direction, but IMO they're still just scratching the surface of what's possible in this regard.

Regarding what you (AI) specifically said, it seems like a big part of your goal is to motivate the desire to learn. I tend to think that this desire is rather innate in people, at least to one degree or another, but structured schooling tends to kill it off. As someone else said, "Kids are really naturally curious until we force them to go to school." I'm not sure how much any kind of structured school can really do to facilitate that motivation beyond what would already occur naturally if people were just left to explore on their own. I'm more interested in how the actual learning process can be optimized and made more efficient, which is something that structured learning environments really fail at terribly. Of course everyone is different in how they learn (well, maybe not everyone, but there are obviously vast differences in how people do it best), so it may be that some people do learn better in a more structured arena (in the extreme case, even being forced into it). In general systems need to be adaptable to the learner, whereas the current ones (even Khan Academy and soles and somes) tend to assume that there is a best approach for everyone.

Edit: On reviewing your post I realized this isn't exactly what you said, but with regards to

When one goes to school, they should be getting something more - and that is, essentially, what the first and third videos are talking about: learning to formulate questions, think critically about a concept, participate in problem solving activities, talking about ideas, and figuring things out on ones own. The straight up facts-to-remember and homework can be done in a Khan Academy like fashion.

I suppose my feeling is that the learning to formulate questions, thinking critically, problem solving, etc. is something that comes naturally as people exercise those abilities, which structured schooling gets in the way of. I suppose I do put more emphasis on the importance of the rote memorization and facts-to-remember, assuming that if people are given the right tools to exploit when the desire strikes them, then they'll be better able to develop the other (admittedly more important) stuff that you're talking about. But I'm not sure it can be forced on them to any degree without hindering their progress, although I may be wrong here.

That's all I really feel like saying about it, right now.

Edit2: The other reason I didn't respond right away is because it's hard to write a post saying, "Yeah I think I have good ideas on this subject but I don't want to discuss them." It makes you sound like an ass, and I probably do.

 

[digital angel]

Interesting posts from people. I'll take some time before I comment.

 

[Artsu Tharaz]

I hope to one day write maths textbooks aimed at INFJs.

 

[Agent Intellect]

The main reason I didn't respond is that I've got a lot of ideas on the subject but it's one of the few areas where I don't want to just go spilling my best ideas out in a public forum. I've already spent a lot of time on trying to develop better educational systems (I mean like 12 hours a day, single-minded focus for months at a time), mainly involving computerized systems. Education in general is still being done extremely poorly, it's based on a system developed over a century ago that hasn't been innovated on significantly since. It's completely fallen behind all technological advances made in the meantime, and like Vrecknidj said there are entrenched interests to ensure that change will not just happen on its own. Not just the unions and such but the attitudes people have towards it: the old fashioned systems (think of the Ivy League schools) are viewed as inherently more prestigious than newer stuff like Khan Academy and such.

It's most likely that a 'system overhaul' would not be the best approach. Probably starting private schools with a new system would be best, and the results could speak for themselves. My biggest problem with privatized school is the idea of prestige - as was mentioned in the article you posted, there is an idea that paying more for school means you are paying for prestige. Either the private school would have to be expensive, which would make it exclusionary and select, or it would be cheap and then would either be seen as lacking something, or worse yet, would actually be lacking something.

The whole thing is really a gold mine waiting to be exploited. Think of just how much money goes into education (the vast majority of it being a completely unnecessary waste). People fight tooth and nail for the privilege of paying hundreds of thousands of dollars to the most prestigious university just so they can have a chance at a piece of paper that may give them a slight advantage in life. Millions even if you think about what people are willing to pay for K-12 private schools just to boost their chances of getting into one of those schools. To say it's a billion dollar industry is still just an extreme understatement. I'm not even sure how much money goes into it between public schools, private schools, collegs and universities, textbook companies, and other stuff like tutoring, test-prep, SATs/ACTs/GMATs/LCATs/etc., in the US alone, much less worldwide, but you start to get the idea of just how much money is sitting there being funneled into obsolete systems just waiting to be out-competed by something that wouldn't even be that hard to develop.

(Also, this article seems somewhat relevant.)

I agree with you about the fact that the current system is entrenched - and not just with those making money off of it. I think there is an aversion to 'experimental' schooling because traditional schooling is, well, traditional. If something experimental ended up a failure, it's not like we could just reset the children and try again with something else. The traditional method of schooling can put the onus on the student - this is how we've schooled children for hundreds of years and some people have gone on to be very successful. But, in an experimental school, the onus is on the school - if the student doesn't perform well, it wasn't the students fault, it was the teaching method that hasn't shown that people can be successful with it yet.

Change requires that people take risk, and people will be afraid to take risks with their or their children's education.

Again, I really don't want to go into detail about my best ideas on it (not that they're necessarily good, I don't mean to be that arrogant), but as far as things already being done that are a step in the right direction, Khan Academy is good, and so was PLATO, and soles and somes too. People are taking steps in the right direction, but IMO they're still just scratching the surface of what's possible in this regard.

I think a more eclectic approach would be best. I think these people have great ideas, too, but my approach is to synthesize them. I think technology is definitely the way future education should be taught, but I think that technology and the classroom (human interaction) should work side-by-side.

Regarding what you (AI) specifically said, it seems like a big part of your goal is to motivate the desire to learn. I tend to think that this desire is rather innate in people, at least to one degree or another, but structured schooling tends to kill it off. As someone else said, "Kids are really naturally curious until we force them to go to school." I'm not sure how much any kind of structured school can really do to facilitate that motivation beyond what would already occur naturally if people were just left to explore on their own.

I completely agree, and hence why I think the structure of the classroom should be downsized. I would advocate for a more guided inquiry style, where the students are the ones that progress the lessons, with the instructor simply there to propose questions and allow the students to bounce ideas off of them. The classroom would become more of a discussion (similar to this forum) for topics and concepts to be discussed, while all of the necessary facts can be covered in short videos online.

I'm more interested in how the actual learning process can be optimized and made more efficient, which is something that structured learning environments really fail at terribly. Of course everyone is different in how they learn (well, maybe not everyone, but there are obviously vast differences in how people do it best), so it may be that some people do learn better in a more structured arena (in the extreme case, even being forced into it). In general systems need to be adaptable to the learner, whereas the current ones (even Khan Academy and soles and somes) tend to assume that there is a best approach for everyone.

I agree with the idea of adaptable learning processes, but I could see that being a large sticking point for the PC crowd. One of the foundations of "equality" is that people should all get the same treatment. If there was a policy of teaching children in different ways, people would get upset when their child isn't being treated like the genius the parents think he or she is when the neighbors kid is being taught differently.

Edit: On reviewing your post I realized this isn't exactly what you said, but with regards to


I suppose my feeling is that the learning to formulate questions, thinking critically, problem solving, etc. is something that comes naturally as people exercise those abilities, which structured schooling gets in the way of.

My idea is that the classroom would become more like a gym for exercising this natural inclination, for cultivating what's already there, not for teaching it like it's information to be conveyed. I don't picture any lesson plan where it goes step by step on the "process" of critical thinking and problem solving, but having an environment where one can meet with their peers and the guidance of an instructor and explore ideas and concepts using these natural tendencies in a way that further develops such skills while at the same time attaining the raw information that schools dump on students in lecture form right now.

I suppose I do put more emphasis on the importance of the rote memorization and facts-to-remember, assuming that if people are given the right tools to exploit when the desire strikes them, then they'll be better able to develop the other (admittedly more important) stuff that you're talking about. But I'm not sure it can be forced on them to any degree without hindering their progress, although I may be wrong here.

My problem is that dumping information on students in a lecture format is boring and only teaches students methods for remembering information long enough to pass a test. I tutor at my college, and a lot of the people I tutor (I mainly do science tutoring) are simply taking the class as a prerequisite or to get the requisite credits. People have told me straight up that they don't give a shit about the subject material and that all they care about is getting a C- or better so they can move on. This is the learning style that rote memorization and info-dumping fosters - the kind of learning that discourages proficiency in lieu of the path of least resistance.

Edit2: The other reason I didn't respond right away is because it's hard to write a post saying, "Yeah I think I have good ideas on this subject but I don't want to discuss them." It makes you sound like an ass, and I probably do.

I'm not sure why you're apprehensive about sharing your ideas. Unless you're afraid someone will steal them and claim them as their own, I can only imagine that you're afraid of criticism? Or possibly that you'll write a long essay and nobody will read it (as is what happens to most of my posts)?

 

[Cogwulf]

I'm terrible at maths. I used to be at the top of the class through school, then when I moved on to higher maths at 16, I just started to struggle because I was at a point where it was no longer good enough to just memorise rules. I'd never been taught to do maths any other way.
My education in maths was always just "for question A, do function B" So the only way I know how to do maths is by spotting familiar questions and trying to copy what I did on previous ones.
I wish I was taught the principles of mathematics. Instead of memorising functions I should have been taught how and why they work.

 

[Melllvar]

It's most likely that a 'system overhaul' would not be the best approach. Probably starting private schools with a new system would be best, and the results could speak for themselves. My biggest problem with privatized school is the idea of prestige - as was mentioned in the article you posted, there is an idea that paying more for school means you are paying for prestige. Either the private school would have to be expensive, which would make it exclusionary and select, or it would be cheap and then would either be seen as lacking something, or worse yet, would actually be lacking something.

I agree on the system overhaul part, but I think brick-and-mortar schools themselves are as out-dated as anything else. For the most part education could be cheap or even free at this point. Put it all online and let it be paid for with advertising, the same way all of google's services are. That may not work for every single subject, for example a hands-on chemistry experiment or electronics lab would be hard to teach in a non-interactive way, although I'd say that games and virtual worlds or augmented reality could facilitate that a lot. To the extent that it isn't as good or can't replace it, that could just be a function of things like public libraries. It'd be massively cheaper than having an entire school just because a small few subjects require a more hands-on approach that can't easily be conveyed through a computer screen.

As far as testing in such a system would go, simply make it skill and knowledge based with an accreditation system. You're required to demonstrate your knowledge of the subject, not just pass a test and forget the material a day later. The "test" (or demonstration of knowledge or whatever, wouldn't necessarily have to be a traditional test) could be taken and passed at any point, no reason to make people all move at the same pace of quarters and semesters. This also has the advantage of being able to rank people by proficiency in the subject, and allowing them to be made to retake the tests at later times to prove they are still proficient in the subject at a given level (this would be good for companies when hiring). As it is people accomplish something once in their lives, never use it or exercise it again, and ride that status forever regardless of what their actual proficiency level is. I knew a guy with a master's in engineering physics who was an example of this: at the age of 45 he'd been out of work for over a decade and couldn't even get hired because he'd forgotten half of what he ever knew, but still liked to go around bragging about his genius in the subjects.

On another level too, traditional schools themselves are just bad. They're basically prisons for kids, and jobs programs for people too stupid, incompetent, cruel, corrupt, and worthless to do anything else with their lives. Much like prisons, they're breeding grounds for all kinds of, for lack of a better term, generally unwanted activities, particularly public schools (although to the extent that some may avoid it, it's generally due to enhancing the prison-like aspects of the whole thing). Bad environments for both the students and the teachers. Among students they mostly just encourage delinquency, and to the extent that people do enjoy it, it's usually because of the social aspects rather than the educational ones. All the people I met in college who were going to be teachers had these idealistic, noble ideas of what they were getting into, while all most of the old teachers I've met hated their jobs, hated the students, and it was reflected in their performance. I really can't think of anything more beautiful or beneficial to society than to just put the entire fucking thing out of business and watch all those sacks of shit that perpetuate it for their own personal gain have their livelihoods ripped away from them.

I agree with you about the fact that the current system is entrenched - and not just with those making money off of it. I think there is an aversion to 'experimental' schooling because traditional schooling is, well, traditional. If something experimental ended up a failure, it's not like we could just reset the children and try again with something else. The traditional method of schooling can put the onus on the student - this is how we've schooled children for hundreds of years and some people have gone on to be very successful. But, in an experimental school, the onus is on the school - if the student doesn't perform well, it wasn't the students fault, it was the teaching method that hasn't shown that people can be successful with it yet.

Change requires that people take risk, and people will be afraid to take risks with their or their children's education.

Yeah, there's also that bias about things: if someone does badly in school it is considered their own fault, rarely a failure on the part of the system. I think there's a simple solution to this though: there are plenty of places in the world where people are eager for education and can't really get a high quality one. Open up an experimental program in some place like Africa or India, promising free schooling for people and their kids, or even agree to support the mind-bogglingly low cost of living in return for people's participation. If that isn't incentive enough, there's the added benefit that people would hopefully develop skills enough to be competitive workers in industrialized places and could send part of their earnings back to the poorer communities they came from.

As far as places with entrenched educational systems being unwilling to change, who gives a shit. They'll most likely adopt a better system when they realize it's more profitable or that they're about to be out-competed, and if they're unwilling to then that's their own problem. They'll either change eventually or suffer the consequences. Which actually brings up another point, part of why I'd rather keep my best ideas to myself: education is a powerful weapon in itself. A company, nation, military, or whatever that has a vastly better "training program" than others will have an obvious advantage over the others. I suppose I just mean that developing a superior system is profitable even beyond the pure financial interests involved.

I think a more eclectic approach would be best. I think these people have great ideas, too, but my approach is to synthesize them. I think technology is definitely the way future education should be taught, but I think that technology and the classroom (human interaction) should work side-by-side.

Yeah, that's generally all I'd try to do too. I can't claim to really have that many groundbreaking ideas, it's just that even the experimental programs aren't taking advantage of the other experimental programs and progress that has been made in the subject. Khan Academy lacks all the interactivity that was included with PLATO, while soles and somes requires interaction with actual instructors instead of measuring which ones have done the best jobs with particular students and reusing their methods for other similar students, just as examples. I really could go on like this for a while, but I'd rather not lay out a full business plan for someone else who actually knows investors or has a better skill-set for implementing it to come along and exploit first. Although I admit most of the good ideas are already out there to some degree, they just aren't being used effectively.

I completely agree, and hence why I think the structure of the classroom should be downsized. I would advocate for a more guided inquiry style, where the students are the ones that progress the lessons, with the instructor simply there to propose questions and allow the students to bounce ideas off of them. The classroom would become more of a discussion (similar to this forum) for topics and concepts to be discussed, while all of the necessary facts can be covered in short videos online.

No major disagreement, although again I'm not sure about the need for a classroom or real instructors at all, when things like this forum already exist and people already enjoy using them. Stuff like Yahoo Answers and Wikipedia already exists to let strangers share knowledge and learn together, although the quality could use some improvement (particularly with the various Answers sites). I suppose Wikipedia itself makes a pretty good model of an interactive, online sort of 'classroom', with the editing and discussions gradually reaching a level of accuracy that rivals the big paid encyclopedias. The main limit with it is that it doesn't get enough people involved in the learning, debate and discussion.

In general I'd like to see education integrated with social networking and gaming (that's honestly a large part of the stuff I'd rather not going into detail about). PLATO basically tried to do the first part of that, it just tried it 40 years ago. Integration with gaming has been tried some too, and it's been effective but for some reason no one seems to catch on that "we can make learning fun!!" (and not just fun but interactive too)

^Regarding the learning/games integration I should also probably link to Jesse Schell's DICE talk from 2010, all of which is good but mainly because part of it focuses on gaming as a motivator (that part's here, the first few minutes are most relevant). To be fair the idea of needing to motivate people to do things that they 'should' want to do anyway is somewhat debatable. (Also the full presentation is here, but it's 30 minutes, unlike the 10 minute clip linked to above).

I agree with the idea of adaptable learning processes, but I could see that being a large sticking point for the PC crowd. One of the foundations of "equality" is that people should all get the same treatment. If there was a policy of teaching children in different ways, people would get upset when their child isn't being treated like the genius the parents think he or she is when the neighbors kid is being taught differently.

Maybe, but there's already a lot of imbalance that people are willing to accept with different college tiers, AP classes, honors programs, etc. In my mind this wouldn't differentiate between students even that much, more like, for example, making interactivity with other students and instructors optional for those who need it, when they need it, but not forcing it on those who learn better just sitting alone in a room with a book (from talking to my friends about this kind of stuff, it's become apparent that some people really do need interactivity with other people to stay interested in a subject, while I find it's just a distraction that makes it harder on me - until I talked to them I'd thought everyone must learn the same way I do, "why do we even have classes and lectures? just give me the book and leave me alone." - but it's become apparent that this is one area where people are different).

What I was really thinking was more along the lines of, back to your example of using real-world examples to teach math rather than starting with abstraction, measuring how students respond to different methods of conveying the information and formulating the future lessons in the ways they've responded best to the past ones. Real-world examples may be better for some people, abstractions may be easier for others (personally, I think I've always found abstract math more interesting than applied math - seeing how things like addition, multiplication, division, etc. are all just special cases of a larger concept [binary operators], or vectors/covectors/gradients/linear operators/etc. are all special cases of tensors, always got me more excited than stuff like being able to calculate optimal traffic flow at a traffic light or how the rate at which water flowing out of a cone is changing). Considering how much time people spend in school, or just learning stuff in general, it should be possible to measure their progress via different methods and formulate new material in the way they find most interesting and easy to digest.

Also it should be possible to combine lessons so that people are learning multiple things at once. For example using historical examples in mathematical word problems, just to come up with something off the top of my head. One interesting thing about math in general is that you're often learning lots of other subjects at the same time: physics, chemistry, economics, biology, etc. Their needs to be more of that for optimal efficiency.

Stuff like that wouldn't seem to have a lot possibilities for vast inequalities in education, particularly if it was just a by-product of what the learning algorithms determined was optimal for a given person. Sure some people may be more suited to a faster or more efficient method, but that just goes back to some people being faster learners at certain things than others. If people wouldn't like it based on the idea of inequality then they're basically choosing to slow down their own education because they don't understand their own optimal learning style.

My idea is that the classroom would become more like a gym for exercising this natural inclination, for cultivating what's already there, not for teaching it like it's information to be conveyed. I don't picture any lesson plan where it goes step by step on the "process" of critical thinking and problem solving, but having an environment where one can meet with their peers and the guidance of an instructor and explore ideas and concepts using these natural tendencies in a way that further develops such skills while at the same time attaining the raw information that schools dump on students in lecture form right now.

No disagreement at all. Part of the problem is just that it's easier to teach straight facts, and optimize the teaching of such things, rather than get people really thinking about stuff. The only way to do the latter is to make them genuinely interested in the subject, which I suppose comes from showing the potential of what is being learned and exposing them to interesting problems and material (from personal experience, I generally find solving math and physics problems to be boring as hell, but sometimes one just gets me hooked and it keeps me awake at night - those are the kinds you want to expose people to, particularly before they're interested enough in the subject to push themselves by simple force of will).

My problem is that dumping information on students in a lecture format is boring and only teaches students methods for remembering information long enough to pass a test. I tutor at my college, and a lot of the people I tutor (I mainly do science tutoring) are simply taking the class as a prerequisite or to get the requisite credits. People have told me straight up that they don't give a shit about the subject material and that all they care about is getting a C- or better so they can move on. This is the learning style that rote memorization and info-dumping fosters - the kind of learning that discourages proficiency in lieu of the path of least resistance.

Personally I get nothing out of lectures, but again, from talking to other people, I seem to be the minority here. Books do a lot more for me, but it seems most people are of the opposite inclination. Anyway, it does seem like interactive learning ('doing' something) tends to ingrain the material better than simply having it wash over you, whether it's from watching or reading. Examples, you can watch a video of how to solve a math problem, but you won't remember the process as well until you've actually worked through the problem yourself. Same with other things, you can watch someone show you how to play guitar, but you won't get the hang of it at all until you actually practice. Even with stuff that's typically viewed as a simple "read it and memorize it thing", like learning foreign vocab, you remember it better when you actually write the words down or use them in a sentence. I suppose the point is that practice > watching. My main point with memorization and arbitrary facts isn't that it's better than other stuff, just that it's easier and having it makes doing the other stuff easier. You can't learn a foreign language just by memorizing vocab, but if you already know thousands of words and their approximate translations, you can start to pick up the grammar a lot easier. Similarly with chemistry, just memorizing lots of reaction mechanisms or chemical structures won't let you understand the real chemistry, but if you already have those in your head then figuring out what is really going on will be a lot easier, since you have a lot of information to reference it against.

The problem with people not giving a shit or only taking things to pass doesn't seem so much a matter of the importance of memorization (and I don't mean strictly memorization, but just the "fill your head with facts" type of stuff that's at a lower level than stuff like problem solving, deeper understanding, etc.), just that the entire experience is boring/painful/etc. and they aren't learning out of any particular desire to be proficient in the subject. People go to school for the most fucked up reasons: just to get a degree, because it's easier than getting a job, because they have to live up to their parents expectations, to try and find a husband, because they want to party and get laid... those are the reasons the vast majority of people are in school (from my experience, at least). I think that could all be solved by just eliminating the whole structure more in favor of what I've been describing, particularly in the first few paragraphs of this post. Then it isn't about credentials, it's about demonstrating proficiency (and acquiring that proficiency in the first place). The entire social aspect of it would be made secondary to the educational aspect of it, where as currently the educational aspect is secondary (or worse) to the social aspects.

I'm not sure why you're apprehensive about sharing your ideas. Unless you're afraid someone will steal them and claim them as their own, I can only imagine that you're afraid of criticism? Or possibly that you'll write a long essay and nobody will read it (as is what happens to most of my posts)?

Trust me, not being able to get feedback and criticism is the worst part of not just spilling everything I've ever thought about the subject. It's purely the money thing. Not that I'm really that kind of person (avaricious), but as they say, "If the world's worth saving, it's worth saving at a profit." Beyond that I personally have to worry about how I, as a college dropout who isn't particularly social or good at fitting in, am going to acquire resources for the next however many decades of my life. The problem with most of my ideas is that either a) someone already had them a long time ago and they're already being done, or b) they couldn't possibly be implemented by one person working alone. Building a vastly improved, highly profitable education system is one of the few that passes both tests. I admit it's probably silly and I'll probably never need to worry about any of this, but I'd rather not lay out a full, detailed business plan just so someone else with connections and investors can come along and capitalize on it while I'm still thinking about it and working on it.

Also I wouldn't be so hard on yourself about people not reading your posts (I think you've made those comments in a few places), a lot of times they're reading but don't know what to say, or feel that what they would say isn't good enough (this is basically why I didn't respond right away, I wrote three long responses and then decided "not satisfactory" after each one). For some reason the trite bullshit always gets more responses, and not just here (this place is probably better than most). It's just easier to throw stuff out on a not-at-all-serious topic than a serious one, usually, even if you find the serious one a lot more interesting. I guess this is my way of saying that I don't think most people find your posts bad or not worth their time or anything (probably the opposite, really). Although honestly I feel like most of my threads die off pretty fast as well. The only one that really took off was that "INTP Dating" thread where all I did was post a Questionable Content strip.

Also I still haven't watched those videos, I'll get around to it soon (maybe tonight but probably tomorrow). Might have a lot more to say after that, I'm looking forward to the Wolfram one in particular.

 

[Melllvar]

I'm terrible at maths. I used to be at the top of the class through school, then when I moved on to higher maths at 16, I just started to struggle because I was at a point where it was no longer good enough to just memorise rules. I'd never been taught to do maths any other way.
My education in maths was always just "for question A, do function B" So the only way I know how to do maths is by spotting familiar questions and trying to copy what I did on previous ones.
I wish I was taught the principles of mathematics. Instead of memorising functions I should have been taught how and why they work.

You might be one of those people who's better at calculating than at abstract stuff like proofs and theorems. I'm really terrible at calculating but better at abstract theory, so I'd always fuck up easy problems in my engineering classes because I'd make simple mistakes (add when I should have subtracted, integrate when I should have differentiated) but do a lot better at the 'harder' stuff we'd do in physics (they'd give us an order of magnitude less problems but they'd take hours or days each, usually requiring some level of 'insight' or connecting multiple ideas to solve). Calculation type math is the kind of stuff you do in arithmetic, or like the calculus problems listed above, where as 'real' math is more like the proofs you see in geometry, or advanced calculus/real analysis, topology, abstract algebra, etc. People can be great at one and horrible at the other, because they're almost completely unrelated.

 

[digital angel]

Wow, there's a been alot of comment since I last stated any thing. I agree that the education system has been in place for a long time and a complete overhaul is a huge task. As a hopeful future professor, I find this interesting.

I haven't been in school for awhile. From what I remember, most of my college courses were lecture style. My courses in law school were lecture style but with the socratic method. It was the same for my LL.M. courses. I enjoyed the interaction and the reading. I think what many law schools are doing now is to permit students to access lectures online. This gives students flexibility.

I'm not sure much can be done if a student really doesn't care. The question is how can we provide meaningful education efficiently? Perhaps a blend of lecture and technology is the way to go. Perhaps some schools are doing this already. I don't know enough about some of the educational styles that people have discussed so I'm not comfortable commenting on them yet.

 

[Trebuchet]

This is a subject I have considered quite a bit. I've taught and tutored math, both for high school (so students could meet requirements) and vocational school (so students could actually get a job in a technical field). Now that I am a mom, I have to face the fact that our daughter's education is up to us, and we simply can't leave it to the schools.

One thing my 6-year-old taught me is that there are two subjects, both called math. At school, math is arithmetic and terminology. At home, math is finding a fun phenomenon or puzzle and playing with it. (One example: how many ways are there to hit my blot in backgammon, and is that likely or not?) She started complaining this past year that math is boring, but then at home getting out a calculator or drawing little squares or asking me for puzzles.

I started drawing a distinction between two kinds of "math." "School math" is learning arithmetic and techniques, and it is like learning the alphabet before reading. Those tools are essential and very useful, even if learning them isn't so much fun. "Real math" is finding a way to figure out a problem when you don't know how to solve it or what the answer is. Failure and creativity are both inherent in real math. I've seen her try such a problem again and again, for days, until she got it, so I know she likes doing that.

The reason for making the distinction is that I can't deny that school math is boring. She has a right to feel that way. But generalizing that to "math is boring" seems like a dangerous attitude to have, especially since so many parents and teachers still think girls aren't very good at math. Seriously, I hear that a couple of times a month. (What century is this again?)

I don't have a solution for overhauling the system. It is rigid, and at least in the US the textbooks are chosen by school boards in Texas, and they are not well-written. I don't know that there is a way to save it, but I don't think we can afford to give up, either.

 

[Agent Intellect]

Too much to respond to piece by piece, so I'm making a more general response (although Mellvar is probably the one I mainly have in mind).

I see two problems with the autodidact style of education, one practical and one philosophical.

In a practical sense, the school acts as a day care, especially for younger children. If we got rid of the school facility as part of the education, children would need to be babysat, would require a parent to stay home, or would have to be home alone. All three choices are impractical. Also, if you have a babysitter, why not a tutor? If you have a tutor, why not a place where multiple people can be tutored at the same time?

In addendum, I think schools not only teach students academically, but also socially. In school, we are taught, in practice, how to interact with peers, how to work together, how to stand in line etc. In higher education (high school level) this can even come in the form of on-the-job sort of practice. Even just the idea of having to get up every day, get ourselves dressed and ready to go, and arrive on time, is good practice for the real world. So, in a practical sense, the act of going to school will prepare us for adult life.

Also, in a practical sense, while I disagree with standardized tests, there does have to be some way of gauging someones abilities. I think the exercises on Khan academy is an interesting way of doing this, and would be much better than the way it is now.



In a philosophical sense, I have a problem A) believing that everyone will have the self-motivation to teach themselves and B) that people will be able to filter through information and misinformation, and C) that people can get a full overview of a subject.

As far as A) is concerned, I do think that the vast majority of people have an innate tendency to want to learn, or at least they do as children. But, I think putting this responsibility in only their hands will allow them to be lazy - both in a mental way, and a practical way. If a person has an obligation to go to a gym five days a week, they'll jog on a treadmill five days a week, but if you just give them a treadmill at home, only those truly motivated will use it for more than a coat rack. I think the same thing can be said about education - if someone is obligated to go to school, they will learn something, but if you just give someone an internet connection, only a small subset will come to places like this or go to Wikipedia and Khan academy while most will spend their time reading celebrity gossip and watching the latest viral youtube video.

As for B), I have seen it in some of the people I have interacted with on this forum. The people who come here are generally self-motivated to learn, but generally do it on their own. What I've found is that people like this will sometimes completely misinterpret something, or they will convince themselves so deeply that what they believe is correct. This mainly happens because, as self-learners, people will read and study material that they agree with already (eg confirmation bias). When people are left to their own devices, they construct schemata about reality without any opposing views, and this stifles critical thinking about ones own knowledge (and ultimately opinions). I don't want to name names, but I've seen this in a few people I've interacted with on this forum.

For C) I think that schools are a good place for someone (an instructor) who is a recognized expert in their subject to compile all the relevant information on a subject into a single lesson plan. While I would want to veer away from the idea of a one-size-fits-all lesson plan, having an instructor at least ensures that certain fundamental topics will be covered in a certain subject. If there is one thing I like about school (despite my ranting in the OP) it's that it brings everything together. In many of the subjects I find most interesting and that I have read extensively about, there have always been small gaps in my knowledge and disparate outlier 'facts' about certain things which going to school has sort of bridged together into a completed big picture. I think without a school facility, students would have inquiries that lead them down certain avenues of thought before they have all of the relevant knowledge and techniques of adequately analyzing and understanding the complete picture.


As I stated in an earlier post, I would see the school facilities as being a gym for peoples minds. I do think that having more personalized learning experiences would be beneficial, based on an individuals learning style and even personality. But, I think it would be to every students benefit to have at least some interaction with both peers and instructors, both to challenge our own notions and force us to think critically, and to guide students toward pertinent information that can be useful in the real world.

I think that the school should only be a part of this education. Tools such as the internet (both as videos, exercises, and discussion forums) should have a large part in any future paradigm of education, working in synergy with the "mind gym" of a school facility.

I think there should still be some semblance of a curriculum, where students must be proficient at certain subjects (primarily math, language, computers, science, and politics/history) and have attained the proper techniques of analyzing each of these topics (critical thinking, problem solving, application etc). Various topics in arts and humanities I think are just as important to have students exposed to as well.

My problem with having the autodidact method of education is that, even if the student doesn't fall into the pitfalls I enumerated on above (points A and B), the student will still have limited exposure, and will only play to their strengths and atrophy their weaknesses - if I'm not good at working with computers (or I believe this about myself) I may not have the self-motivation to learn about them.