I completely disagree with Brady when he says that when they bring up the maths and people get lost or lose interest. I'm actually disappointed when in the videos Moriarty or anyone else starts to get into an equation or graph and they cut that section out. I always watch the extended versions of the videos where everything is more in depth. I think those are the most interesting videos of all.
Sasha Lane To add to that, if you lose interest in something because maths is brought up in regards to it... Then you're not going to be interested in physics anyway.
BlueCosmology True and not true. If you are into physics but you aren't that smart or aren't that well versed in maths then something as simple as the pythagoras theorem can be quite intimidating and can probably even turn people interested away simply because if you have no experience with numbers then i can imagine it being hard to just instantly gain some understanding of maths.
hermest99 There's a difference between knowing, and interest. If you don't know maths, then you're definitely not an actual physicist, but you most certainly can still be interested in physics. If you lose interest in something because maths is involved? Then you have no interest in physics. Physics is a subset of maths. Saying you're interested in physics but you're not interested in maths is like saying you're interested in books but you're not interested in literature.
BlueCosmology No it's not at all the same. I am interested in the human body and physiology, as a med student. But studying medication used to bore me and a lot of my peers, even though it's a vital part of being a med student and a doctor eventually. A lot of people have a tough time getting interested in medication, since it's not as cool as processes in the human body. So it's a real thing. Like how driving a car is cool, but knowing how the car works might not be your piece of cake. So you might love cars for driving, but not for the mechanics.
hermest99 That analogy isn't really fitting at all. Driving a car and building/fixing a car are different things. Driving a car, is not a type of building a car. Physics IS a part of maths. If you want to use an analogy of a car it would be like someone saying they really love driving cars, but they hate controlling automobiles.
How much physics can you even do in school without calculus? Our physics teacher introduced integral calculus before it was on the math syllabus because we really couldn't proceed without it in any meaningful way. But I guess we had quite an extraordinary physics teacher.
+pinkdispatcher My secondary school physics was completely without calculus (although we did introduce it in maths the last year). You can get all the way through up to some rudimentary introduction to special relativity and tiny bits of quantum physics. But in the process, you are often bound to special cases with constant quantities (so that you get rid of the derivations/integrals and replace them with a special formula, e.g. when dealing with constant acceleration) and static phenomena. You often can't explain where do the formulae come from, which makes it less of a subject to understand, and more of a subject to memorize. It takes away context. I definitely did not benefit from that, my understanding sky-rocketed almost overnight once calculus was plugged into physics during first year university.
Very little, actually. What you can do is learn what others have done, but you yourself, cannot do any physics. You can see the equation for constant acceleration( you can derive it without calculus actually, courtesy of Cauchy's mean-value theorem), but can you understand the thinking that went into it? No. Physics is more of a method that a collection of knowledge, but high school physics completely strips it of the former. You learn x and y and so on, but you don't learn the thinking behind x, you don't learn the thinking behind y, because you cannot deal with the math required. Look at Newton's law of cooling. It perfectly illustrates something basic about physics. Physics requires you to collect empirical evidence, and from there, build upon the evidence. We collect empirical evidence, which is the temperature at different times. From this, we can reasonably estimate the gradient of a graph. This is usually very easy to do, and in fact is an important method of collecting empirical data in physics. We love rates because they are so easy to measure. So most of our hypotheses start from rates. We can now see the gradient. We can guess a general trend. Maybe it's proportional to the temperature, or to the square of the temperature, or maybe the cube and so on (this sort of proportionality is easy to see from the graph). Could it be the cube? No way. If it was the cube, the rate of change would be huge, so temperatures would decay very quickly, and things would cool down much faster. Maybe it's the square? Could be, hard to tell. It could be the sin, or the cos, or the ln or something of temperature. It could be. We don't know. Let's take a guess - the simplest solution, because we are really lazy. So we try proportional to the temp. See? That kind of thinking, is the kind of thinking of physics. Guess something, use physical intuition to guide you. Be lazy (no really, the simplest solution is often the right one). We don't have that in high school courses. We just teach facts, not physics. And what now? Now we are stuck. Without calculus, we cannot solve the differential equation, which is how we express our rates mathematically. So not only do we not have the thinking, we don't even have the tools to follow the thinking. But let's say we did. How would it work out. We solve the differential equation, and end up with a proper expression for temperature. Now we see that our expression has all these constants. Well that's fine. We SHOULD use physical intuition to work these out, but what we were taught in math class about boundaries works too. We have an equation. Are we done? No. Now we need to test our equation. We see it has a constant. What is the constant, physically? We obviously see that different things cool at different rates. If the constant is bigger, our rate is bigger so perhaps that is what the constant means? Let's try it out with say, coffee and metal perhaps. Our experiment shows that our guess was right. It is what distinguishes between materials. Plus now, we just showed that our model worked. Our equation did indeed predict the cooling curve to an excellent degree, so yeah, we at least know we did the calculations correctly. Now we have to take our equation, predict something with it, and then test again. Then our equation would be validated. Validated in the range of its applicability, scope, and for a few years until a more accurate model comes along. It's always dynamic. But we don't show that. We just show, this is the fact, this is the question you will get on the exam, answer the question. Then when we get into college, and have to learn this thinking, we basically face-plant into our desk.
It strikes me that the problem is not the teaching of physics; it's the teaching of maths. Isn't the answer to start increasing mathematical literacy right from the primary school level? That way we keep the qualitative nature of A level physics that seems more appealing, but all students will be equipped (in parallel ) with the numeracy they will need for university.
I went to uni in the UK after going to highschool in france, for a chemistry degree (which is half physics really) and I was astonished at how much more literate I was in mathematics compared to the other brits.
Primary school maths is taught horribly in Britain, I was shocked when I was tutoring primary school kids for year 6 tests and assessments. Some of them barely knew basic algebra, were slow and confused with basic geometry, etc! Terrible school system. Conservative government always seem to make a right mess of education.
Outstanding observations and philosophy. I couldn’t agree more. I am a 68 year old retired engineer. I have asked my son , a highschool senior to watch the first half of your video. Couldn’t agree more.
When I was in high school, I asked my physics teacher how to show the first law of Kepler using Newtons´ laws, something he said to me was possible. His answer was: "I can´t show you with the maths you know."
@@ramind10001 Often when you reach physics to school kids, you get into a situation like: E = mgh or E= mv^2/2 or similar equations, and often, the school kid is not well enough versed in math to connect that if m increases and E is staying the same, then some other parameter have to decrease and other similar mathematical concepts.
@@RodelIturalde I understand that might be an issue. But the school system should've prepared that kid before taking the physics class. Personally, in college I wasn't able to get into a few calculus classes and couldn't take any intro to physics courses at my college, I had the option of taking physics at another college, which didn't require calculus, but ultimately I graduated a year late but took the calculus based physics at my own college; I was there to learn not just take classes and get over with it sooner.
In Brazil, we don't have Calculus in high school as well. The difference is that any science course in university is 4 to 5 years long. And most people take one year more to graduate. Personally, I'm graduating in Electrical Engineering next year and it'll be 6 and a half years of university (given that I spent one year in an exchange program in the UK). Our two first years are basically maths and physics (Calculus 1, 2 and 3, Physics 1 and 2, Mathematics for Physics 1, Complex Variables, etc). What I'm getting at is, maybe, you could solve the problem by teaching the maths first so, when they decide to do Physics, they can see all the maths on the course structure beforehand.
My dad showed me notes & worksheets his mother produced in a Calculus class around the late 1800's. I was shocked by the discipline & high level of understanding she displayed & compared it to my own maths work in the '60's. If the physics/maths education degraded noticeably then, I wonder what it's like now! Although my Calculus classes helped me understand the physics well enough to become an engineer, I'm sure that more thorough & intense maths education would have made me a better engineer. Professor Moriarty is right!
As a 2nd year (external) physics student at University who doesn't shy away from the math: Sixty Symbols videos make a great accompaniment to my studies - as an introduction to topics, for example.
Alrighty then, way to take a swing at my comprehension skills; I'll be the bigger man and fight the urge to correct your punctuation/grammar. You should know I wasn't disagreeing with you, only adding to your comment to dampen the connotation it carries. Why can't Sixty Symbols "movies" be a part of the Uni experience?
At the level of high school and even lower division math, most derivations are often a few lines and very rarely more than a page or two. I dunno how, but it would be lovely to get people in on derivations, because it feels like such a creative process.
I can completely agree with this. I did my A-Levels last year in germany and I started studying chemistry, which is not as math dependant as physics. In my very first lecture, which was revolving around simple thermodynamics and the concept of enthalpy the whole audience was shocked by the simple term dU= dQ + dW, because nobody in this room has ever dealt with Infinitesimals in this explicit way. Sure, everyone was getting used to it but this shows up the enormous difference between science in school and "real" science. There was barely anyone not being able to explain (not mathematically ofc) why fructose reacts positive on the fehling-test but this simple, crucial term was scaring the sugar out of everyone.
Well rounded! As well, I'd like to say thanks to you, the other profs & Brady as well for making these videos. I had quite a bad education in our public schools here in the US, and as a result have had to do a lot of work to catch up to the level of my classmates in my university. Regarding market control of educational outcomes. We have that issue as well here in Florida - the amount of money paid for state standardized testing practice is outrageous. Our teachers teach the test, not concepts
Basics: Calculus is basically analyzing functions and their behaviors - or how they change, like Wiki says. The building blocks of calculus are "differentiation", which is a way of finding the slope of an algebraic equation from the equation itself, and the opposite, 'integration'. So if you have, say, a position function, you can differentiate to find a velocity function, and again to find an acceleration function. It's tremendously useful in physics and is often easier than algebraic methods.
You brought up an interesting point of not being able to hear explanations of complicated relationships from people or demonstrations. You said something to the effect of needing to read a clean cut, presentation of data and information and then piece it together yourself. In my experience as a high school senior going into engineering, your explanations are monumentally helpful. Hearing from an experienced professional that sees how students learn every day. Maybe you don't realize it but by going through what sounds like a tedious learning process, you have developed clear and communicable descriptions of phenomena in physics. It's almost as if you have skipped the formalities and unnecessary confusions for me. This allows me to dedicate my focus and critical thinking on the aspects of importance rather than some possibly unimportant and confusing details. However, I agree with your idea that this reduces our ability to analyze, breakdown, and formulate strategies to address problems. I think this is complex mathematics' role. The organization and consistency needed for accurately describing calculus problems builds this skill.
Well, I wouldn't call it useless. I'm currently studying physics at medical school and usually when I have a problem understanding certain topics I always try to understand them by myself and in most cases it works. Brady's videos not only give me different point of view on the topic but they help me understand it more clearly and it is thanks to you Prof. Moriarty and the other tutors at NU who help me see physics from a different perspective. And I'm thankful for that. - Martin :)
I love phil, he's so into it and energetic. Probably a function of the amount of coffee....but "irregardless"? IRREGARDLESS?! lol come on man...basic english
for the first year of physics, the firs semester should be all about getting students excited about physics and the next semester bringing in the math to physics and really showing how it relates.
I agree wholeheartedly with your last point, which really is the whole point. Schools are on league tables, and so are in competition with each other. Schools acting in their own interests rather than those of their students is damaging. It's a prime instance of market policies failing.
It's weird because the lack of mathematics in A-Level physics is what drew me away from carrying on with it at university level and instead went on to do just mathematics.
I must agree. When I understand chemistry like that, its really nice, and it gives a more rich and fuller clarity to the subject, just like the butter in a pastry.
I dropped physics when I was 17, and while struggling towards the end of my second year doing A-Level maths I decided to learn what the hell calculus really was. I went from getting failing grades to grades ranging from Ds to Bs. With this new found understanding I really, really regret not trying harder in my first year and carrying on with physics. I agree wholeheartedly with what this guy's saying!
Problem with school learning: No greater goals set -> Learn counting -> learn math -> Introduction to something interesting in physics -> Not going deeper into subject. - Versus how self study works: Find something interesting / have a goal -> Sub divide by category -> Sub divide problem where x is given-> Learn how to get first x. Result: small incremental (calculus) introductions + seeing progress + working towards goal.
I think you could also apply this "population inversion" to population sciences. To some people it is undesirable to live in a place like NYC or Brooklyn, or Atlanta, but because of a stimuli, be it a laser or a job opportunity, they will do so regardless resulting in a larger population in an unfavorable area, and a lower population in a more favorable area, and a general trend of favorable areas being less populated over time and less favorable areas being more popular. Correct me if I am wrong, but this is my understanding of it.
with the Open University in the UK, we had computer marked assignments which were essentially MCQ items. the thing was - the answers given were not exact, so we had to do the problem-solving in order to select the correct formula to use for something - and use it correctly in order to get the points.
I agree totally. i was going open lectures of university to study chemistry and got hit by alot of really tough mathematics just because they never taught us qm or VSEPR theory which is pretty easy compared to other subjects in chemistry. Also thermodynamics was pretty challenging but I loved every bit what really they are doing in university. I wish they course where you could study university level math in highschool for people who are really interested.
If I had not been given basic Physics education my first year of high school, I wouldn't have decided to go into Physics because I wouldn't have known anything about it.
9:08 "Get rid of the idea of having different proviers. Get rid of entierly the idea of a market anywhere close to something which is a pulic good like education. That doesn't matter if its primary school, secondary school, or higer education. Lets think about it as a public good thats something that should not be driven by market choices and profit." -Phil Moriarty
here in norway, idk if our physics is different, but i feel that we do "endless" problems about inclines etc. etc. i looked at my dads book about mechanics for a engineering degree from university and sure i didnt understand everything, all of it seemed familiar, just at a more difficult level than what we do
At A Level Physics we did some basic calculus, purely because we were told we had to do A Level Maths, or a Foundation Maths course to get some calculus, though this was starting A levels in 2007 before new modules in 2008. In our Cosmology option we did lots of Special Relativity, but this was through videos rather than teaching as our teacher didn't feel he could explain it. But it inspired me to do a degree and I'm looking at Nottingham for a Physics PhD
I'm currently a 3rd year physics student at uni. While I do think it was bad that calculus has been removed from the physics A-level it doesn't necessarily mean we didn't study it. It's a major part of the maths A-level which is required to study physics at uni. The problem I had though was putting the two things together and realising that all of these endless integrations and differentiations we had to do actually had some meaning in physics. It wasn't obvious at the time until I went to uni.
That problem has been the subject of Physics Education Research for a long time now. Your story should be collected by someone and made available to struggling students if the math and physics curriculums are not integrated yet.
PS7)I have recently asked Seton about this but I suspect their books "run very hot", about 6th grade in 4th and a staggering 12th grade in 8th. They offer testing but I wondered if the testing also places them, this for providing guidance for fellow parents who want to add something to their kids education or are worried that their child is struggling. And, thank you for your time.
The personal message I get from this video is that I should feel lucky that I enjoy calculus to the extent that I prefer the mathematics to be involved in a physics course? I see many fellow students struggling with even the most basic algebra, such as manipulating exponential expressions and factoring/expanding parentheses etc. So many people grasp the physics concepts easily, but can't solve the simplest problems because as soon as they formulate an equation, they can't solve that.
I remember my physics class in my final year. The first day we had to find roots of a quadratic equation and I remember thinking ``Man we`re in the big leagues now`` lol. Then in the coming weeks we had to learn about vector products, determinants, derivatives and matrices. We also stopped using ``numbers`` and started saying things like:`` Let M be the mass of the object and v the velocity, show that.....``. That`s when I got a taste of real physics and it attracted me not turn me away from it.
4)In the array of tools that are accessible to today's instructors they are easy to use, even for beginning instructors, and they are likely technologically advanced in other ways. I suppose my posts contain a small amount of minor speculation, but, I don't think I've jumped to any conclusions. One of the most free markets in the US is in home school curricula, and so it makes sense to consider the best performers in that market.
As someone just finishing my second year of a physics degree, I completely agree that the physics a-level is too different from a physics degree. I never even did further maths because I was unaware just how useful it would have been to have already got some extensive background knowledge of the mathematical techniques used in physics. I think unis definitely need to make prospective students more aware of what physics is like at uni
My schooling never made me curious, about science or anything else, it was the dead opposite. In fact (I'm a year removed from high school) now that I've made it out I'm trying to reunite with passions that school stood in the way of. Science is one of them, it seemed terribly interesting to me as a child, but I learned in high school it was all about being given an experiment, writing the hypothesis for it (which you already know), then doing it and getting the result you already knew.
4:17 I see what Phil is getting at here, but for A-Levels this is exactly the kind of thing that is covered in A-Level Mathematics - specifically the mechanics modules. The mechanics goes up to quite an advanced level, tackling quite tricky rotational problems that are more than sufficiently advanced for university physics.
He emphasises that this should be taught within physics so that those going to uni know that there not only going to learn the fun staff in physics but also prepare that the only way to understand is through maths
I think that there should still be the math-free videos that introduce the concepts, but I also think that there should be extra videos from SixtySymbols that go into the mathematics for those who want to know about the concepts in greater detail.
Thank you, good sir. When I was tutoring mathematics and physics - couple of decades ago now - I was getting this sort of question a lot. And, given the modular nature of the A-level in maths, we'd usually recommend further maths for anything involving maths, physics or electrical/electronic/civil/mechanical engineering. Again, thank you for your input. I think Thomas will find this very useful.
Don't get me wrong, we learned about differentiation, integration, linear algebra and complex numbers as well. We even saw some fractal-related stuff, which other schools didn't. But we could have seen so much more, and more adjusted to what is expected as prior knowledge for university mathematics in a physics degree. It was also the pace of teaching that took me by surprise, but simple things like hyperbolic functions we had not seen yet were expected to be prior knowledge at university.
I would suggest it would make more sense to standardize one test, but free market the school systems. The most successful are free market schools, you get to select a school, and the school gets paid for you choosing it.
I failed physics once in highschool :s but when i tried again the next year i loved it. it happened the same with math. I think one of the major problems with math is that teachers don't know how to make the lessons interesting for students. Also we should have math classses at least 4 times a week (insted of 3x) because the teachers barely have enough time to teach the entire program for the year let alone train some exercises in class. I'm Portuguese so i apologise for any mistakes.
I remember a quote from Star Trek: The Next Generation. As Picard is walking down a deck, you can hear a father and six year old son talking: "Dad, I don't want to learn Calculus!" The father responds, "Son, everybody needs a basic understanding of how the Universe works."
Also to add I think it should be compulsory to do A Level Maths if you are taking A Level Physics as that way you can include the more complex maths into the Physics as you are taking them alongside each other. But again you need to have communication at least within the institution where the courses are being taught to be able to get on the same exam board/decide when certain things are taught so the maths and physics are running together.
I came back to this set of videos a few times now. Once, when it came out and I was about to start with the final 2 years of the German Highschool equivalent, once when I started to study at university, and now, being a few semesters into undergrad physics. When I looked at these videos, after having finished my A-level equiv I was shocked at how little maths there was in the British system; we pretty much did the first third of a theoretical mechanics university course (all newton) and derived concepts from the newtonian axiom. Admittedly, we did not solve the kepler problem or any of these things, but we learned about vectors, about derivatives and integrals, so when I went on with solving this (and other) problems at university the hard stuff was understanding the physics concepts and solving equations, not figuring our what that strange S and these "dt" thingies are. I don't know why the US and GB shouldn't teach calculus given that they actually have more time slots, since they have to learn only one foreign language and not from 1st grade on.
I'd agree with what you said about Calculus. I am an engineering student (19) taking a HNC in Electrical and I am only now diving into calculus in my spare time. We have had very little experience with how it works and instead have focused on rote memorisation of formula. Im starting to find out how it works through talking to engineers where I work, but teachers at school shouldn't be dodging the questions students ask. At 15 I often got the response "Thats outside the scope of the curriculum."
For the vast majority, Maths often become interesting when its applied to "the real world" however it is getting ripped out of Physics lessons... That's a pure lose/lose situation for both scientific fields.
You can put something like this "catholic school performance evaluation cost per child comparison" into your search I used Google, clicked the first link, and it had a summary with sources. A good place to start. While you're looking up stuff for yourself consider looking here, Google link 1: "seton home learning Reading 4 for Young Catholics Comprehension (key in book)" And link 3: "seton home learning Reading 4 for Young Catholics Thinking Skills (key in book)"
I'm taking AS-Level maths in grade 9 (year 10 I think it'd be). Coming from the US, it's a different system, but I was prepared for the maths that I needed here in Switzerland. It's the IGCSE's, so it is a different system than pure GCSE's, but it's very easy to start from algebra/geometry and build up to calculus as long as you like maths.
I couldn't agree more with Prof Moriarty, In my view, League tables and rankings drive a race to the bottom. Rather than teaching to prepare you for further education or work it is all about grades. Unfortunately it has been like this for years. I did my A-levels near 20 years ago and then got a complete shock when I went onto to read Economics at university and had to do maths, when there was no maths in A-level Economics.
"I tried so hard and got so far but in the end It doesn't even matter I had to fall to lose it all but in the end it don't even matter." Linkin park, In the end. A summary of my past 4 to 5 years of Learning.
1)Which is why I sent you to the Seton home learning course. Also, I know of a good number of Catholic schools who are recognized as presidential blue ribbon schools. Of course there isn't much else in the area, and, also, we are fairly rural where I'm at, and the public school is quite good. I have had some discussion of this nature with friends and family who are school teachers. I home school my kids, and am on a Catholic school committee at the moment.
We learn calculus at A Level in Maths, and for our A Level course (the year before it changed again) we did have a little bit of calculus in our Physics course. Then when I started University we had 2 maths lectures a week which started with calculus and went through to complex numbers, matrices and partial derivatives. The problem we had was the lecturers didn't communicate so we were assumed to have knowledge of maths we hadn't learnt yet. I think it's down to communication between departments
Something I had in the mid 1980's,( in addition to three large lecture classes a week), was a "Calculus Lab". The "Calculus Lab" was a smaller group of about a dozen students taken from the large lecture hall class. We met with a graduate student who acted as a tutor/teaching assistant and helped us with questions about the lecture, assigned textbook problems (Stanley I. Grossmann) and supplementary exercises on certain points. I think the graduate student was in close communication with the Professor that gave the lectures.
Yes, I learn a lot as well, however what we learn from these videos is the gist of the idea. If you want to learn on a deep level, you need to sit down with with pen and paper and work through explanations, examples, problems sets, which are best conveyed through a written format. A thorough, video of a lecture that can be replayed over and over again can be useful as well, but I really do think the written word is the best for reviewing.
I had a lot of mathematics in high school (as much as I could choose) and even then the difference with university physics was very big. The initial adjustment took me quite a while and I think this could be solved by increasing the slope of mathematics in high school. Maybe not for everyone, but certainly for the science students. Then you have more room to manoeuvre in physics as well. If you're interested in physics and you're good at maths, you should have the opportunity to explore more.
(4)If you are the actual professor, you could tour a regulated free market system, such as in Norway. You regulate with a standard exam (just one, not a bunch to choose from, all of which are so extensive that they force the teacher use the test a curriculum) and by publicizing the results. The schools compete directly, then, and the parent can choose which to send their children using public funding, and possibly more if they choose.
Some people have inductive minds and they can do what you are saying, learn the logic from equations, practise their minds by seeing the result of logical reasoning. But most of the people need to know why they are learning, and where it applies and then how..
The maths in physics is almost trivial. I shat my pants with complex analysis. I went to Nottingham in 1986 and left with a 2:1 inspite of never going to any lectures
You don't need calculus for the first year of physics. Students can learn calculus in the first year while they are learning the basic concepts of physics. Calculus isn't that hard anyway. People expect it to be hard because videos like this treat it that way.
I don't think the video made calculus come across as hard in anyway. On the contrary, the professor is astounded that they took the fundamental language of physics out of the courses and dumbed it down to such a degree that students suffer when they find out the true form of physics.
I am sorry, which school have you studied? Can you please tell me how do you want to do mechanics without calculus? And mechanics is the first topic in any physics class. Just think that acceleration and/or velocity is and how it is calculated. That is the lesson ONE! And from mechanics it gets only worse.
2)The Seton home school students do quite well on the college entrance exams. Of course the curriculum is regularly updated and is not without expense, though not as expensive as private schools (in general), so, the parents are likely dedicated and not poor, which are excellent indicators for their children. The same can generally be said of kids at private schools, but, more so the money and less the parent involvement.
I failed maths at school... but the idea of coming out of school (even at GCSE / 'O' Level level - let alone at 'A' Level) not knowing what calculus is boggles my mind.
patrickJMT on RU-vid does a really good job of working through Calculus (I, II, & III) with problems and examples. There's also online open course ware (through MIT, for example) for the entire spectrum of Calculus, so there's definitely resources throughout the internet for the intellectually curious people watching these videos. It's a good idea to make them more widely accessible, too.
In 2023, I'm still trying to find a BRILLIANT course or Khan Academy mastery exercises on Geometric Calculus. The open course ware is often antiquated and doesn't use a unified notation system.It is also a lot of passive viewing of Professors working problems rather than getting me to try my hand at it.
That's true to some degree, but if you compare any RU-vid lecture by someone competent in their field to a tutorial session with them, the level of benefit you receive is a completely different one. RU-vid videos cannot cater to your questions, learning methods or individual tangents of interest to anywhere near the degree personal interaction with an educator can.
5)There is a certain strain here between science and opinion. The clearest way forward is to put aside our generalizations, and look at individual components. I am an industrial engineer, and I can't begin to unravel all the nuances of statistical analysis that people make mistakes about. Statistically, what would we expect in a more free market system? Probably more variance, which means negative anecdotal evidence, which is important, but needs to be placed in context, for instance...
Students are kicked out of school, but they aren't banished from receiving an education - indeed, their parents are still legally obliged to ensure they receive an education. If a law which makes education compulsory doesn't qualify it as a public good, what does?
