What is Archimedes' principle? How does it relate to density? What is the association of density to volume? What happens to ice as it melts (or water as it freezes)?
The puzzle had me fooled twice (after 2 seconds: water level sinks, after the article: solution cant be determined), but thanks to your hint it finally dawned on me
Since water reaches its peak density at about 4 °C, the actual outcome will vary slightly depending on the initial and the final temperature of the water once the ice has melted.
The result of ice + water depends on the quantities and starting temperatures of both. You could have very cold ice in water resulting in freezing the entire volume. Or small amounts of warm ice in water resulting in water well above the freezing point.
No it wouldn't. The outcome will be the same regardless of the temperature, given the context of this problem. And the context is that the ice cubes are FLOATING, and that the temperature is hot enough for the ice to melt.
spindritf, not necessarily, we don't know the initial temperature of the water and on a hot day (as per the problem statement) the ice-water system will be absorbing some of the external energy.
In practical world, more likely that water will start at around 20-25°C mark and will be considerably cooler once the ice has melted but still above 4°C. So the water volume is likely to shrink a tiny bit due to the rising density and then some more due to ice and water evaporation.
But the effect might be barely noticeable and for some time water will stay level with the edges after ice melted.
I think that the standard form of this question assumes that the water+ice is initially at 0°C, so that there's no net warming of the water, only latent heat of melting.
Conversely, one could compute what relative volumes of ice and water would be required to arrive at a final temperature above 0°C. It's also possible (actually: likely) for ice to start at some temperature below 0°C, typically around -12°C for home refrigerator/freezer units.
So let's say we're starting with room-temperature water at 22°C, ice at -12°C, and a ratio of 50-50 water to ice, 100g total.
Latent heat of fusion for water is 80 cal/g, and latent heat is 1 cal/g.
We're heating 50g of ice by 12°C and then melting it. Additional heat, if necessary, is drawn from the environment.
The ice absorbs 200,000 calories.
Subtracting 200,000 calories from the 50g of water would cool it by 4000°C, not counting heat of fusion, or would pretty much freeze all of it solid, if we do. Or conversely, the water can release at most 1100 calories of heat energy before freezing. Working backwards, we find that our 50g of water would require only 12g of ice to cool it to 0°C, or a ratio of roughly 1g ice to 4.2g water.
It's a trick question. The question creates doubt because it asks you to choose between two wrong options. [Edit: no, it gives all three possibilities; I speed-read through that. Thanks to others for pointing that out. However it then does predominantly focus on the question of "up or down?", which isn't the right question.]
Ice is lower density than water, which is why it floats. As the ice melts, the runoff from the above-surface ice will raise the water level -- but the shrinkage from the below-surface ice will lower the water level. Assuming the above-surface and below-surface ice melts at the same rate, the water level will remain unchanged.
(Note that if this were a glass of hot water in a cold room, then you'd get non-uniform heating of the ice. The subsurface ice would melt first, causing the level of the water to lower, until the above-surface ice melted, at which point the water level would return to its original level. On the other hand, a glass of cold water in a hot room would initially overflow while the above-surface ice melted, and then its water level would lower when the subsurface ice melted. So the answer to the original question is, depending on context, either "neither" or "both".)
When water freezes, it expands. That's what full bottles in a freezer burst, as do pipes in winter. So 1 gram of water occupies less space in the glass (1 ml) than 1 gram of ice.
According to Archimedes' Principle, a floating object will displace precisely as much water as its weight. Which is why a log of wood floats - the water it displaces weighs more than the wood itself.
If 1 gram of ice is floating, it means it has already displaced 1 gram of water. When 1 gram of ice becomes 1 gram of water, it will occupy less space.
Or maybe the ice above exactly replaces the level of water, and on the whole it stays the same. The more I think about it the more confused I get, which seems to be the point of the article.
Yes, it does. As long as it's not resting on the bottom, the bouyancy of the ice underneath the top ice will push a little more of the top ice out of the water. The amount of ice matters for how far out it sticks, but the number of pieces it's divided into doesn't matter.
I've had this discussion many times w.r.t. global warming, and am amazed so many people, including scientists, just don't get it. The level the seas would rise is not so much dependent on floating ice (north pole) since the displacement is exactly the same, but on ice that was on top of land (e.g. Greenland, Antarctica, etc.).
Absolutely, although it's worth noting that loss of floating polar ice will change the albedo of the earth, so there's a positive feedback loop there that may result in further warming & consequent melting of land-based ice elsewhere.
So melting of the floating polar ice will not directly result in raised sea levels, but 2nd round effects of the melt might do so.
ok, water expands when it is frozen and contracts when it melts, so the question is by what factor to allow for the water to either overflow or not.
and are we talking about icecubes floating in the glass or filling up the glass so they are standing on each other (like a cube skyscraper) from the bottom of the glass?
When examining the ice you note that the cubes rise just above the surface of the water (like glaciers in the ocean), but do not extend to the bottom of the glass.
I find that I have the opposite problem. I think I know less than I actually know. Sometimes I feel (as a mathematician would) that I don't understand something unless I can prove it, assertion by assertion and line by line.
I dropped out of grad school after one year, and it seemed like a bigger risk/deal than it was. My sense is that the major benefit of having a PhD (especially from a top school) is the confidence that comes with it. It gives you faith that you know enough to tackle the interesting problems, and an assurance that people (usually uninformed people, often without the educational credentials they overvalue) won't try to peg you down as not up to it. Socially, it gives you the right to be an expert, which is not the same thing as expertise but just as valuable (if not moreso) in the work world.
So, even in traditional education, I'd argue that much of the benefit earned (maybe 85%) is confidence, both your own and others' in you. You can get a lot on your own by reading the papers and books, but you never get that official approval or that "proof" that you learned the right stuff.
Oh, and the answer is that the water level stays exactly the same. Archimedes' Principle is that a floating object displaces as much water as it weighs. When melted, the iceberg (90% submerged) takes up as much space in the water as the submerged part occupies.
Luckily not a single student ever left traditional education with a single misconception about anything, or else this would seem like a ridiculously slanted article.
edit: on re-reading, he's still clearly using Khan and MOOCs as eye-catching buzzwords, symbolic of "bad education", but a) he mention (in passing) offline education having similar issues, and b) he intends to talk about how online education could fulfil his pet theory of learning in another article, so it's not quite the usual reactionary post, although it does lean that way.
The point is, if you have some kind of human discussion, close examination of coursework, etc., it’s possible for a sensitive expert teacher to figure out what kind of misconceptions and misunderstandings students have, and talk through them, making sure that students leave a course with a correct model in their heads. By contrast, this is very difficult to achieve via lecture alone, whether in person or online. [And certainly many traditional classes fail at this.]
In particular, all of the Khan Academy lectures I have seen (admittedly, this is only about a dozen random ones) do quite a poor job compared to the good teachers and professors I’ve had. They don’t seem to me to be grounded in much understanding or appreciation of how people learn.
(In theory, online courses should give people access to enough interactive tools and communication infrastructure to discuss and question and properly figure out the gaps in each student’s understanding. In practice, I haven’t seen any which do this at all well.)
And what about the people who will never have professors, and have never had sensitive expert teachers?
Do we just explain that they can't afford a good education and that it sucks to be them as the people who could afford that education are now fighting tooth and nail against any move to democratize learning?
To some extent it just requires more sweat. That's how the elite who figured it out the first time originally learned. Very little of hard science is revealed knowledge like (most) religious ed.
The problem with "gonna have to work harder" is a side marketing presentation of "it'll be faster and cheaper" in direct competition.
I think most students don't learn from direct interaction with teachers, anyway. My first uni calc course had about one kilostudents in an auditorium. Most recently I got one of 1100 meaningless certificates from a comp sci MOOC where a busy post in the discussion forum had maybe 100 reads and 10 posts. The other 90%+ who got certs ignored the forums. Unsure how many signed up and participated to some level but didn't get a meaningless cert. I got nothing out of the forums and mostly hit wikipedia / mathworld / google in general with my questions. About 90% of my questions were quickly answered by the textbook before I tried slower online research. Slower because the text was written much better than the average blog post on the topic, lots of slogging thru junk on line.
It does use Khan Academy as a strawman though. "Let's say that Khan Academy is the be-all end-all of education, then prove that it's not."
In reality, sites like the Khan Academy aren't intended to replace classroom education. They're meant to reinforce it. Get the lectures on your own time, so that you can get to the deep learning with teachers in the classroom. Spend classroom time on the socratic method, rather than lectures.
He beats up the tool that he should be using to improve the classroom experience.
Right? It seems like he's railing against the Kahn Academy but it's not as though a public school (or most private school) educations are much better. With a student/teacher ratio of 30:1 (or worse) and absolutely no tailoring of teaching method to student's optimal learning methods (verbal, visual, writing, etc) it's not as though traditional schooling is a paragon of getting everything 100% right and MOOCs are terrible by comparison.
Kahn should get a lot of credit for giving students the option to go back and re-watch things they didn't get the first time. If they learn by hearing or seeing (instead of reading) then that's an incredibly valuable tool.
If we want to complain about anything I think we should be complaining that there's no standardized testing of learning methods and then informing the students of their results (and what those results mean) so that they have the opportunity to try and optimize their learning and thus hopefully get a damn diploma. Why isn't that a national goal? Seems like it would be a small incremental change that would make a huge difference in terms of raising education levels across the board. It helps smart people and dumb people and everyone in between.
The reason I'm confident that in the long term MOOCs will succeed where traditional education fails is not that MOOCs will come out of the gate a superior product. The reason is that MOOCs can be tuned and developed over time in a way that a classroom experience can not, because every class room experience is too unique, delivered live, unrecorded, etc. It will take time for this to happen, but it is likely inevitable, and eventually the idea of flinging out an "education" into a room, where it shall disappear forever with no feedback or development, will be considered as archaic as the horse buggy.
(And also people can't seem to help comparing the perfect conventional education that does not exist to the worst of MOOCs, which may feel good, but is not relevant.)
I watched video tapes in the early 80s and before that, professionally produced film strips. Even film strips with 33RPM vinyl records, before tape. Also I saw a couple really old analog film movies in my youth. Currently, youtube videos and DVDs are supposedly popular. Why didn't they replace traditional classroom education using the same criteria you're applying to MOOCs?
You may be correct about outcome, but the reaction mechanism is lacking.
I'm a classically self educated well rounded kind of guy, so I feel education is developed from within not a mechanical external process much like weightlifting. The idea it merely requires butts in seats, and the result depends on what technique someone else applies to those seated butts, is more likely to disappear. Or at absolute most, perhaps "necessary but not sufficient".
"Why didn't they replace traditional classroom education using the same criteria you're applying to MOOCs?"
For the same basic reason that the computers of the 1980s didn't replace newspapers the way computers of the 2010s are; too hard to use, too expensive, not enough availability. The tech for editing a course may have existed but it wasn't wide-spread and easy, so there was not a feedback loop of improvement going on. Imagine being the teacher in 1980; you've recorded your lectures, you sent them away to be "edited", three months after your course was recorded they come back, you sample a couple of them just to see how they came out (you certainly aren't going to watch them all), and that's it. Even if you find an error, you're going to have to shrug your shoulders and at most issue a paper errata; you certainly aren't capable of going back and fixing it yourself, nor is anybody else going to pay for the skilled labor necessary to do so. For a feedback loop to occur there's a certain base level of ease that has to exist.
Only now do we have a world in which an instructor can give some bit of instruction, get a question from a student about something, and simply click "edit" to go back and fix whatever weakness in the original instruction the student's question reveals almost as quickly as they could answer the question in the first place. Run something like Physics 101 through that process over the course of 4 or 5 years and you'd quite likely end up with the best possible Physics 101-type course that could be developed. (The next step after that is fundamental rewrites of how we teach physics at all, but that will take longer.)
And indeed I'd suggest that we're still in the very early phases of that, too; it's going to get easier and more widespread. Once we start building educational resources over time instead of firing them like one-shot ammunition, the improvement feedback loop is all but inevitable.
Curiously, with MOOCs replacing OpenCourseware, we've shifted to an environment that's a little bit harder to iterate on. Editing text is easy. Editing something someone said in the middle of some video can be harder (continuity issues, availability of the original speaker, audio environment, etc).
Quite a few MOOCs have shifted up a notch in their production values recently. When you've flown to another country to interview a famous scientist for your MOOC, it's probably a bit trickier to make a minor edit to what was said next year.
"Editing something someone said in the middle of some video can be harder (continuity issues, availability of the original speaker, audio environment, etc)."
That's part of what I was thinking when I said this was early days. While the problems can't be completely glossed over, there's some stuff we can do to mitigate those problems.
An interview would be a primary source; of course you can't edit that, but good odds you've got some sort of summary that is part of the core course, where the interview is immediately available as a primary source. The summary would be as fungible as anything else, and the interview ought to be treated as a primary source and archived. (Possibly with one pass of audio cleanup, but not something to be modified wiki-style.)
On the topic of Wiki, some sort of editor-driven Wiki could help too. Many Montessori schools already adapt the idea of having the older students teach the younger, I believe; as MOOCs evolve it's very easy to imagine harnessing the students themselves to start fixing the courses they've already taken. They'd move from an isolated course to an integrated part of the whole education. Again, like I said, I fully believe these are the early days of a revolution, and writing MOOCs (and more generally, online education in general) off now is like writing off the automobile because it's a great deal less convenient in every way than a horse, and smells worse and is more expensive to boot. Yes, that was true... at the beginning....
That's because MOOCs (at least the new breed, not the original ones that had that name) are an attempt to fight back against open education by the establishment.
It's like Britannica putting their encyclopedia online, mostly a distraction.
Luckily neither Britannica nor the educational establishment actually have/had a coherent plan, but they can distract those who aren't paying attention.
"Only now do we have a world in which an instructor can give some bit of instruction, get a question from a student about something, and simply click "edit" to go back and fix whatever weakness in the original instruction the student's question reveals almost as quickly as they could answer the question in the first place."
To the best of my knowledge as a participant there are no MOOCs running internal processes anything like this. More likely in my experience is you get a wiki of errors for when its rerun again in a year with the same videos. Much like my film-strip example. "Advance to the next powerpoint slide at the beep" and then the record starts skipping.
As I think I said on my blog once, educators fancy themselves hip and cutting edge, but they are one of the stodgiest, resistant industries I know. They will get there. Silicon Valley will drag them, kicking and screaming, if necessary.
And I'd bet money there will be a lot of kicking and screaming, but the economics are inevitable. They'd be a lot more evitable if education had not rested on its laurels for so long and simply spent, spent, spent its social capital to suck in ever-more money, but that is what they chose, and that is where we are now.
WTF people!? Why is everybody discussing what the water is going to do when the article is about online education?
To stay on topic: I agree with the article, watching videos often leaves you with feeling of understanding but being unable to answer questions which require actual comprehension
I agree, I used to watch tons of nature shows and was always amazed at how I could recall very few of the facts presented in the show once the show was over. Retention doesn't occur until you have actually used the information in some way, not just passively watching it. I like the approach ULearniversity takes where you watch a short video and have to apply that technique before seeing the next video.
At one of the keynotes for the Association for Learning Technology back in 2007, the speaker had a variation on this question. His point, if I recall, was a little different --
As normally asked, the question is code for "parrot the Archimedes principle back to me". But on a realistic "hot summers day" there's not just the Archimedes principle. There's evaporation that can remove water from the cup. There's wind, and occasional movement of the ice cubes as they melt and slip over each other in the glass, that could cause spillage if it's really that full that it's on the verge of overflowing. As could interruption of the surface tension (e.g., condensation in just the wrong spot at the edge of the glass, causing the water in the meniscus to spill over.) The initial temperature of the water being unstated, its density will also change a very small amount, potentially in either direction.
Often when we ask our students scenario questions as teachers, we are essentially asking them to identify which taught principle we have flagged this question as being about, and base their answer on that, ignoring all other factors.
If the student answers "A. It goes down", did they fail to grasp the Archimedes principle, or are they a pedant grumbling that over that length of time there will be evaporation so it won't be exactly the same?
Take the question out of the context of a course, and suddenly the educational point of it can change. Is the person asking you this a physics teacher checking your understanding of Archimedes principle, or an ALT conference pedant checking whether you understand that in uncontrolled environments where bumps and spillages can occur you can't blindly expect the ideal result you'd get in a textbook?
The peril comes when questions are used outside of a teaching context. For example in technical interviews, where the same question can sometimes be a signal for many different teaching points, each expecting subtly different answers, and the interviewee does not know which the interviewer has in mind.
That's an excellent point and a flaw of many "reasoned conclusions" thought experiments. There's a world of difference between contemplating what might happen (which is a useful first step) and experimenting to see what actually does happen.
In the case of your hot summer's day instance, there are a number of things which could confound the experiment: how do you distinguish between water inside the glass (from the initial water + ice), and that on the outside (mostly from condensation, but possibly also from spillage)? How could you control for this? How might you run the experiment repeatedly? Etc. Actually, a chemistry lab where students each mix known weights of water + ice at specified temperatures and observe what happens, then collaboratively compare results might make for a useful group + parallel experiment exercise.
And that's just for ice water. In a field I've got some interest in (practical and applied economics) there's an even greater tendency for assumptions and ideal circumstances to get constructed.
Interesting and challenging article about most current online education offerings. It would be interesting to see if the problems of maintaining engagement in a MOOC were at least partly due to students realizing that some or all of the requirements for authentic understanding were not being met.
As I understand it, there is a different MOOC philosophy that has not gained much support (probably because it's much harder to scale) - the connectionist approach. Perhaps that would support some of the requirements.
(PS: interesting that many of the comments here try to rise to the ice-cube challenge...)
I disagree with the article's assertion that, because I'd forgotten Archimedes' principle, I never truly understood it. I'd successfully worked the problem far enough to realize that my missing piece of information was how much of the ice cube stayed below water, then I watched the video and reacquired that information. No problems here, and the KA video was plenty sufficient for my needs.
As the responses to this HN post demonstrate so clearly, an intuitive understand of what Archimedes Principle means in the real world is not something that is easy to acquire: I'm sure most of the commentators on this HN post are intelligent people who probably did well at school, yet the majority of the responses here are completely wrongheaded.
If it isn't transparently obvious that the water level will neither rise nor fall but stay exactly the same then you don't really understand Archimedes Principle.
The author's question therefore is: how is the Khan academy approach supposed to improve on this situation? A bare explanation of Archimedes Principle clearly isn't enough, nor is the ability to parrot said explanation after viewing the explanation it as many times as required for the viewer to learn the required words. How then is a learner going to acquire authentic understanding from Khan academy videos?
(Note that traditional education has clearly failed here too! But that's a side issue: the question here is why should we expect Khan academy to do any better?)
can't agree more. I have been studying education sector in India, home to largest number of potential beneficiaries of khan academy. I would say khan academy is already bettering normal education. most teachers here would have no clue of archimedis principle atleast khan academy is giving the right information whether all the students are able to absorb is another matter
> If it isn't transparently obvious that the water level will neither rise nor fall but stay exactly the same then you don't really understand Archimedes Principle.
Surely it will overflow once the ice melts. At about 4C the water will reach it's lowest point, and then rise and start overflowing at about 8C.
The density change in the liquid water due to heating / cooling over the likely temperature range is tiny compared to the result of going from ice to liquid water. But I'll award you pedantry points nonetheless :)
The precise outcome requires knowing the volumes and shapes of the ice and water components, their initial temperatures and the temperature of the ambient environment so that you can calculate the path of the water volume over time as the ice has melts. In order to make that calculation you'd still have to make use of Archimedes Principle in order to know that you didn't need to worry about how much water was displaced by the floating ice in your calculations, which was the original point.
"If you answered “Yes” to this last question, then you just experienced the Illusion of Understanding first-hand."
Bzzt wrong it could mean you're thinking like an engineer instead of a scientist. And its not binary, so fuzziness would be partially one or the other reason at the same time.
Possible engineering challenges all contributing a really small delta, all of which add up to so few sig figs a good engineer can't predict what will happen to the water level:
1) You don't know how well mixed the cup is. I assure you, especially on the "summer day" in the article you can get a spread of 20 or more degrees in that cup. So the liq at the bottom is already way past the max density temp and expanding while the top still has some ice.
2) You don't know the starting temp of the water and ice. In addition to #1 above, the ice in my freezer is well below 32 and who knows the starting temp of the water. Maybe its barely melted meltwater or maybe its out of the tap or maybe the coffee maker. So its going to go thru some wild temp and density swings based on unknown initial conditions.
3) The pix shows massive condensation on the glass AKA they're running the experiment in New Orleans not Phoenix also in written form they're running it in the summer. Realize that there's nothing magic about surfaces and condensation... if a sq inch of 32F surface condenses 1 teaspoon per 5 minutes, the top will condense just as well as the sides. On the other hand if you run this in an environment with a dew point below 32F like where I am today, then water will steadily evaporate away depending on the intensity of energy striking the surface, although not too fast.
4) Ice stacks up nicely and clogs pipes. So you'd need more like a slushy to make sure that icecubes are not mechanically sticking up above the surface by being jammed by the cup walls. The supplied pix strongly indicates the middle ice cube is mechanically jammed way above flotation level. One thing for sure, liquids don't have much shear strength and thats going to eventually melt and drip down and raise the water level... how much, who knows.
5) How does water surface tension vary WRT temp? I donno. Probably does, a little. So how much the level can go up or down before it drips is a mystery. You might be able to tolerate a rise of 0.1% if the surface tension enables a "lens" above the top of 0.2% because of increased temp. Or maybe it goes the other way and surface tension drops so "just barely overflowing" at 32F means a flood (well, at least a drop...) at a liquid temp of 40F.
Its probably possible to very carefully engineer the perturbing contributions to a low enough, or counteracting against each other enough, level (oh the pun) such that the science principle will be demonstrated. Or given way the heck more engineering data, a properly engineered answer might be provided, maybe with enough sig figs to mean something. Or maybe not enough sig figs to mean anything. I'm feeling the latter.
The article conflates two separate connotations of "better" which are commonly applied in educational contexts. When we talk about better teachers like the author and Mr. Kahn himself, "better" refers to the average effectiveness of the teacher's methods on individual students. We would for example control for class size and socio-economic status of the students when deciding whether the author was a better teacher than Mr. Kahn himself.
But what "better" often means in terms of educational infrastructure is more access. We would measure the effectiveness by looking at the institution's effect on an entire population. Here we can look for the effects of access and raw numbers matter. A MOOC course could produce a significantly lower average achievement among individual students but produce orders of magnitude more highly successful outcomes.
It appears likely that they do based on my anecdotal experience. If there are 100x teachers and again I believe that there are in the context of adult education, then MOOC's can be better in both senses. Mr. Kahn may not be a 100x teacher, but he is a 100x educator.
Dan Grossman of University of Washington has taught "Programming Languages" on Coursera. I took the second section. Here: http://www.youtube.com/watch?v=1T4IQrOJr5U he talks about data he collected from the first session. Particularly interesting are what "number of students" and "passing" mean.
The guest author is Professor of Education at the University of Texas at Arlington. It's good that educational research continues around the world. For the moment, it's especially important that education research focuses on what happens to young pupils in conventional classrooms, because they far outnumber older students who use MOOCs to learn. In that respect, I think the title "Khan Academy: The Illusion of Understanding" is unfair, because there are plenty of learners with illusions of understanding leaving the elementary schools of my country and yours, even though those learners have hands-on experiences in the classroom.
Michael Shayer in Britain[1] has been doing great research for years about how early experiences of children shape their understanding of the world. He has discovered that many of Piaget's findings about how children proceed through developmental stages in understanding no longer replicate in current children, because children today have different kinds of early life experiences from children in Piaget's era. What happens as society changes over time is that some experiences that used to be commonplace become rare, and other experiences that used to be rare become the most influential experiences in children's development.
The best way to gain intuition about Archimedes' principle (the example given in the blog post kindly submitted here) is probably to do the experiment repeatedly with differing experimental conditions and careful observation. The history of physics around the world shows that for centuries great thinkers could be badly confused about very elementary principles of physics. Galileo did the world a favor by insisting that physicists do more experiments to check their hypotheses. Teaching elementary pupils to hold their conclusions about the world tentatively and with an attitude of testing out everything they believe is the best kind of elementary teaching. Whether by video or in person, good teaching encourages learners to draw on their life experience between lesson sessions to test out ideas and to see what ideas are really correctly understood.
Schools find it easier to get students to memorize facts and techniques instead of getting them to really think and understand. This is a particular problem with Lecture-based learning, and it applies not just to middle-school students, but to Harvard students too:
I think we don't understand anything about how to teach.
Formal education started at least 4000 years ago (earliest writing is at least 4,000 year old, and I think you need a formal education to have scribes who can read and write). I don't think we have done any substantial progress in how to teach in that time frame, at least compared to how much progress we have done in most other subjects: medicine, math, engineering, metallurgy, you name it. heck, we are still discussing what methodology we should use to teach reading & writing, and we have had 4000 years to figure what's the best way.
On the other hand, anyone who has had a good teacher can attests that teaching quality can vary by a huge amount. So my theory for good education is:
1) find good teachers (which probably includes "pay them well")
2) let them do their stuff
Anybody who tries to do something better than the above should be able to explain why their pet theory has not been discovered before.
Don't let them "do their stuff". Have double blind randomised controlled studies (or as close as you can get) to test various teaching methods. The. Implement the good methods.
This has not been done because people have a built in desire for "fairness" and splitting a country or state into two groups means one group is getting a worse education. (Even though we don't know before the experiment starts which group that is)
Whenever I read these pieces, I always think that the establishment is getting worried. Whilst there are good points to be made, such inflammatory and sensational headlines make me think "Now why are they so upset about this?" - and unfortunately I often feel that it's because they feel threatened someone is walking on their patch.
Eric Mazur's Peer learning process https://www.youtube.com/watch?feature=player_detailpage&v=Ww... kind of highlights the problem and a solution for the same.
Namely, Flip the classroom. Ask questions that highlight the knowledge gap within the students. Let students debate among themselves and then actually provide the solution.
Though this is not sufficient, it at least improves the ability of the student to reason about the problem and question the models they have built around their heads on the given subject.
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[ 3.0 ms ] story [ 135 ms ] thread_Melted_ ice is 0°C.
The result of ice + water depends on the quantities and starting temperatures of both. You could have very cold ice in water resulting in freezing the entire volume. Or small amounts of warm ice in water resulting in water well above the freezing point.
In practical world, more likely that water will start at around 20-25°C mark and will be considerably cooler once the ice has melted but still above 4°C. So the water volume is likely to shrink a tiny bit due to the rising density and then some more due to ice and water evaporation.
But the effect might be barely noticeable and for some time water will stay level with the edges after ice melted.
Conversely, one could compute what relative volumes of ice and water would be required to arrive at a final temperature above 0°C. It's also possible (actually: likely) for ice to start at some temperature below 0°C, typically around -12°C for home refrigerator/freezer units.
So let's say we're starting with room-temperature water at 22°C, ice at -12°C, and a ratio of 50-50 water to ice, 100g total.
Latent heat of fusion for water is 80 cal/g, and latent heat is 1 cal/g.
We're heating 50g of ice by 12°C and then melting it. Additional heat, if necessary, is drawn from the environment.
The ice absorbs 200,000 calories.
Subtracting 200,000 calories from the 50g of water would cool it by 4000°C, not counting heat of fusion, or would pretty much freeze all of it solid, if we do. Or conversely, the water can release at most 1100 calories of heat energy before freezing. Working backwards, we find that our 50g of water would require only 12g of ice to cool it to 0°C, or a ratio of roughly 1g ice to 4.2g water.
Ice is lower density than water, which is why it floats. As the ice melts, the runoff from the above-surface ice will raise the water level -- but the shrinkage from the below-surface ice will lower the water level. Assuming the above-surface and below-surface ice melts at the same rate, the water level will remain unchanged.
(Note that if this were a glass of hot water in a cold room, then you'd get non-uniform heating of the ice. The subsurface ice would melt first, causing the level of the water to lower, until the above-surface ice melted, at which point the water level would return to its original level. On the other hand, a glass of cold water in a hot room would initially overflow while the above-surface ice melted, and then its water level would lower when the subsurface ice melted. So the answer to the original question is, depending on context, either "neither" or "both".)
I think you misread the post:
> Does it rise and over-flow the glass, remain constant throughout the melting process, or go down?
Also,
> Assuming the above-surface and below-surface ice melts at the same rate
You don't have to assume anything about ice melting rates. All the info necessary to solve the problem is provided.
When water freezes, it expands. That's what full bottles in a freezer burst, as do pipes in winter. So 1 gram of water occupies less space in the glass (1 ml) than 1 gram of ice.
According to Archimedes' Principle, a floating object will displace precisely as much water as its weight. Which is why a log of wood floats - the water it displaces weighs more than the wood itself.
If 1 gram of ice is floating, it means it has already displaced 1 gram of water. When 1 gram of ice becomes 1 gram of water, it will occupy less space.
As the ice melts, the level of water comes down.
My only concern is the ice being "held down" by other ice cubes. It doesn't get the same treatment as the ice peeking above the surface.
The ice cube was previously floating and was therefore displacing 10g of water.
If we let our ice cube melt, we will have 10g of water than we can add back to the glass.
The net result is that the water level remains the same.
I've had this discussion many times w.r.t. global warming, and am amazed so many people, including scientists, just don't get it. The level the seas would rise is not so much dependent on floating ice (north pole) since the displacement is exactly the same, but on ice that was on top of land (e.g. Greenland, Antarctica, etc.).
So melting of the floating polar ice will not directly result in raised sea levels, but 2nd round effects of the melt might do so.
That makes it much more concrete.
and are we talking about icecubes floating in the glass or filling up the glass so they are standing on each other (like a cube skyscraper) from the bottom of the glass?
When examining the ice you note that the cubes rise just above the surface of the water (like glaciers in the ocean), but do not extend to the bottom of the glass.
I dropped out of grad school after one year, and it seemed like a bigger risk/deal than it was. My sense is that the major benefit of having a PhD (especially from a top school) is the confidence that comes with it. It gives you faith that you know enough to tackle the interesting problems, and an assurance that people (usually uninformed people, often without the educational credentials they overvalue) won't try to peg you down as not up to it. Socially, it gives you the right to be an expert, which is not the same thing as expertise but just as valuable (if not moreso) in the work world.
So, even in traditional education, I'd argue that much of the benefit earned (maybe 85%) is confidence, both your own and others' in you. You can get a lot on your own by reading the papers and books, but you never get that official approval or that "proof" that you learned the right stuff.
Oh, and the answer is that the water level stays exactly the same. Archimedes' Principle is that a floating object displaces as much water as it weighs. When melted, the iceberg (90% submerged) takes up as much space in the water as the submerged part occupies.
edit: on re-reading, he's still clearly using Khan and MOOCs as eye-catching buzzwords, symbolic of "bad education", but a) he mention (in passing) offline education having similar issues, and b) he intends to talk about how online education could fulfil his pet theory of learning in another article, so it's not quite the usual reactionary post, although it does lean that way.
In particular, all of the Khan Academy lectures I have seen (admittedly, this is only about a dozen random ones) do quite a poor job compared to the good teachers and professors I’ve had. They don’t seem to me to be grounded in much understanding or appreciation of how people learn.
(In theory, online courses should give people access to enough interactive tools and communication infrastructure to discuss and question and properly figure out the gaps in each student’s understanding. In practice, I haven’t seen any which do this at all well.)
Do we just explain that they can't afford a good education and that it sucks to be them as the people who could afford that education are now fighting tooth and nail against any move to democratize learning?
The problem with "gonna have to work harder" is a side marketing presentation of "it'll be faster and cheaper" in direct competition.
I think most students don't learn from direct interaction with teachers, anyway. My first uni calc course had about one kilostudents in an auditorium. Most recently I got one of 1100 meaningless certificates from a comp sci MOOC where a busy post in the discussion forum had maybe 100 reads and 10 posts. The other 90%+ who got certs ignored the forums. Unsure how many signed up and participated to some level but didn't get a meaningless cert. I got nothing out of the forums and mostly hit wikipedia / mathworld / google in general with my questions. About 90% of my questions were quickly answered by the textbook before I tried slower online research. Slower because the text was written much better than the average blog post on the topic, lots of slogging thru junk on line.
In reality, sites like the Khan Academy aren't intended to replace classroom education. They're meant to reinforce it. Get the lectures on your own time, so that you can get to the deep learning with teachers in the classroom. Spend classroom time on the socratic method, rather than lectures.
He beats up the tool that he should be using to improve the classroom experience.
Kahn should get a lot of credit for giving students the option to go back and re-watch things they didn't get the first time. If they learn by hearing or seeing (instead of reading) then that's an incredibly valuable tool.
If we want to complain about anything I think we should be complaining that there's no standardized testing of learning methods and then informing the students of their results (and what those results mean) so that they have the opportunity to try and optimize their learning and thus hopefully get a damn diploma. Why isn't that a national goal? Seems like it would be a small incremental change that would make a huge difference in terms of raising education levels across the board. It helps smart people and dumb people and everyone in between.
(And also people can't seem to help comparing the perfect conventional education that does not exist to the worst of MOOCs, which may feel good, but is not relevant.)
You may be correct about outcome, but the reaction mechanism is lacking.
I'm a classically self educated well rounded kind of guy, so I feel education is developed from within not a mechanical external process much like weightlifting. The idea it merely requires butts in seats, and the result depends on what technique someone else applies to those seated butts, is more likely to disappear. Or at absolute most, perhaps "necessary but not sufficient".
For the same basic reason that the computers of the 1980s didn't replace newspapers the way computers of the 2010s are; too hard to use, too expensive, not enough availability. The tech for editing a course may have existed but it wasn't wide-spread and easy, so there was not a feedback loop of improvement going on. Imagine being the teacher in 1980; you've recorded your lectures, you sent them away to be "edited", three months after your course was recorded they come back, you sample a couple of them just to see how they came out (you certainly aren't going to watch them all), and that's it. Even if you find an error, you're going to have to shrug your shoulders and at most issue a paper errata; you certainly aren't capable of going back and fixing it yourself, nor is anybody else going to pay for the skilled labor necessary to do so. For a feedback loop to occur there's a certain base level of ease that has to exist.
Only now do we have a world in which an instructor can give some bit of instruction, get a question from a student about something, and simply click "edit" to go back and fix whatever weakness in the original instruction the student's question reveals almost as quickly as they could answer the question in the first place. Run something like Physics 101 through that process over the course of 4 or 5 years and you'd quite likely end up with the best possible Physics 101-type course that could be developed. (The next step after that is fundamental rewrites of how we teach physics at all, but that will take longer.)
And indeed I'd suggest that we're still in the very early phases of that, too; it's going to get easier and more widespread. Once we start building educational resources over time instead of firing them like one-shot ammunition, the improvement feedback loop is all but inevitable.
Quite a few MOOCs have shifted up a notch in their production values recently. When you've flown to another country to interview a famous scientist for your MOOC, it's probably a bit trickier to make a minor edit to what was said next year.
That's part of what I was thinking when I said this was early days. While the problems can't be completely glossed over, there's some stuff we can do to mitigate those problems.
An interview would be a primary source; of course you can't edit that, but good odds you've got some sort of summary that is part of the core course, where the interview is immediately available as a primary source. The summary would be as fungible as anything else, and the interview ought to be treated as a primary source and archived. (Possibly with one pass of audio cleanup, but not something to be modified wiki-style.)
On the topic of Wiki, some sort of editor-driven Wiki could help too. Many Montessori schools already adapt the idea of having the older students teach the younger, I believe; as MOOCs evolve it's very easy to imagine harnessing the students themselves to start fixing the courses they've already taken. They'd move from an isolated course to an integrated part of the whole education. Again, like I said, I fully believe these are the early days of a revolution, and writing MOOCs (and more generally, online education in general) off now is like writing off the automobile because it's a great deal less convenient in every way than a horse, and smells worse and is more expensive to boot. Yes, that was true... at the beginning....
It's like Britannica putting their encyclopedia online, mostly a distraction.
Luckily neither Britannica nor the educational establishment actually have/had a coherent plan, but they can distract those who aren't paying attention.
To the best of my knowledge as a participant there are no MOOCs running internal processes anything like this. More likely in my experience is you get a wiki of errors for when its rerun again in a year with the same videos. Much like my film-strip example. "Advance to the next powerpoint slide at the beep" and then the record starts skipping.
And I'd bet money there will be a lot of kicking and screaming, but the economics are inevitable. They'd be a lot more evitable if education had not rested on its laurels for so long and simply spent, spent, spent its social capital to suck in ever-more money, but that is what they chose, and that is where we are now.
To stay on topic: I agree with the article, watching videos often leaves you with feeling of understanding but being unable to answer questions which require actual comprehension
It's easier to argue about 'right' rather than the harder issue of deep understanding as it relates to MOOCs.
As normally asked, the question is code for "parrot the Archimedes principle back to me". But on a realistic "hot summers day" there's not just the Archimedes principle. There's evaporation that can remove water from the cup. There's wind, and occasional movement of the ice cubes as they melt and slip over each other in the glass, that could cause spillage if it's really that full that it's on the verge of overflowing. As could interruption of the surface tension (e.g., condensation in just the wrong spot at the edge of the glass, causing the water in the meniscus to spill over.) The initial temperature of the water being unstated, its density will also change a very small amount, potentially in either direction.
Often when we ask our students scenario questions as teachers, we are essentially asking them to identify which taught principle we have flagged this question as being about, and base their answer on that, ignoring all other factors.
If the student answers "A. It goes down", did they fail to grasp the Archimedes principle, or are they a pedant grumbling that over that length of time there will be evaporation so it won't be exactly the same?
Take the question out of the context of a course, and suddenly the educational point of it can change. Is the person asking you this a physics teacher checking your understanding of Archimedes principle, or an ALT conference pedant checking whether you understand that in uncontrolled environments where bumps and spillages can occur you can't blindly expect the ideal result you'd get in a textbook?
The peril comes when questions are used outside of a teaching context. For example in technical interviews, where the same question can sometimes be a signal for many different teaching points, each expecting subtly different answers, and the interviewee does not know which the interviewer has in mind.
That's an excellent point and a flaw of many "reasoned conclusions" thought experiments. There's a world of difference between contemplating what might happen (which is a useful first step) and experimenting to see what actually does happen.
In the case of your hot summer's day instance, there are a number of things which could confound the experiment: how do you distinguish between water inside the glass (from the initial water + ice), and that on the outside (mostly from condensation, but possibly also from spillage)? How could you control for this? How might you run the experiment repeatedly? Etc. Actually, a chemistry lab where students each mix known weights of water + ice at specified temperatures and observe what happens, then collaboratively compare results might make for a useful group + parallel experiment exercise.
And that's just for ice water. In a field I've got some interest in (practical and applied economics) there's an even greater tendency for assumptions and ideal circumstances to get constructed.
As I understand it, there is a different MOOC philosophy that has not gained much support (probably because it's much harder to scale) - the connectionist approach. Perhaps that would support some of the requirements.
(PS: interesting that many of the comments here try to rise to the ice-cube challenge...)
If it isn't transparently obvious that the water level will neither rise nor fall but stay exactly the same then you don't really understand Archimedes Principle.
The author's question therefore is: how is the Khan academy approach supposed to improve on this situation? A bare explanation of Archimedes Principle clearly isn't enough, nor is the ability to parrot said explanation after viewing the explanation it as many times as required for the viewer to learn the required words. How then is a learner going to acquire authentic understanding from Khan academy videos?
(Note that traditional education has clearly failed here too! But that's a side issue: the question here is why should we expect Khan academy to do any better?)
Surely it will overflow once the ice melts. At about 4C the water will reach it's lowest point, and then rise and start overflowing at about 8C.
The precise outcome requires knowing the volumes and shapes of the ice and water components, their initial temperatures and the temperature of the ambient environment so that you can calculate the path of the water volume over time as the ice has melts. In order to make that calculation you'd still have to make use of Archimedes Principle in order to know that you didn't need to worry about how much water was displaced by the floating ice in your calculations, which was the original point.
Bzzt wrong it could mean you're thinking like an engineer instead of a scientist. And its not binary, so fuzziness would be partially one or the other reason at the same time.
Possible engineering challenges all contributing a really small delta, all of which add up to so few sig figs a good engineer can't predict what will happen to the water level:
1) You don't know how well mixed the cup is. I assure you, especially on the "summer day" in the article you can get a spread of 20 or more degrees in that cup. So the liq at the bottom is already way past the max density temp and expanding while the top still has some ice.
2) You don't know the starting temp of the water and ice. In addition to #1 above, the ice in my freezer is well below 32 and who knows the starting temp of the water. Maybe its barely melted meltwater or maybe its out of the tap or maybe the coffee maker. So its going to go thru some wild temp and density swings based on unknown initial conditions.
3) The pix shows massive condensation on the glass AKA they're running the experiment in New Orleans not Phoenix also in written form they're running it in the summer. Realize that there's nothing magic about surfaces and condensation... if a sq inch of 32F surface condenses 1 teaspoon per 5 minutes, the top will condense just as well as the sides. On the other hand if you run this in an environment with a dew point below 32F like where I am today, then water will steadily evaporate away depending on the intensity of energy striking the surface, although not too fast.
4) Ice stacks up nicely and clogs pipes. So you'd need more like a slushy to make sure that icecubes are not mechanically sticking up above the surface by being jammed by the cup walls. The supplied pix strongly indicates the middle ice cube is mechanically jammed way above flotation level. One thing for sure, liquids don't have much shear strength and thats going to eventually melt and drip down and raise the water level... how much, who knows.
5) How does water surface tension vary WRT temp? I donno. Probably does, a little. So how much the level can go up or down before it drips is a mystery. You might be able to tolerate a rise of 0.1% if the surface tension enables a "lens" above the top of 0.2% because of increased temp. Or maybe it goes the other way and surface tension drops so "just barely overflowing" at 32F means a flood (well, at least a drop...) at a liquid temp of 40F.
Its probably possible to very carefully engineer the perturbing contributions to a low enough, or counteracting against each other enough, level (oh the pun) such that the science principle will be demonstrated. Or given way the heck more engineering data, a properly engineered answer might be provided, maybe with enough sig figs to mean something. Or maybe not enough sig figs to mean anything. I'm feeling the latter.
But what "better" often means in terms of educational infrastructure is more access. We would measure the effectiveness by looking at the institution's effect on an entire population. Here we can look for the effects of access and raw numbers matter. A MOOC course could produce a significantly lower average achievement among individual students but produce orders of magnitude more highly successful outcomes.
It appears likely that they do based on my anecdotal experience. If there are 100x teachers and again I believe that there are in the context of adult education, then MOOC's can be better in both senses. Mr. Kahn may not be a 100x teacher, but he is a 100x educator.
Dan Grossman of University of Washington has taught "Programming Languages" on Coursera. I took the second section. Here: http://www.youtube.com/watch?v=1T4IQrOJr5U he talks about data he collected from the first session. Particularly interesting are what "number of students" and "passing" mean.
Michael Shayer in Britain[1] has been doing great research for years about how early experiences of children shape their understanding of the world. He has discovered that many of Piaget's findings about how children proceed through developmental stages in understanding no longer replicate in current children, because children today have different kinds of early life experiences from children in Piaget's era. What happens as society changes over time is that some experiences that used to be commonplace become rare, and other experiences that used to be rare become the most influential experiences in children's development.
The best way to gain intuition about Archimedes' principle (the example given in the blog post kindly submitted here) is probably to do the experiment repeatedly with differing experimental conditions and careful observation. The history of physics around the world shows that for centuries great thinkers could be badly confused about very elementary principles of physics. Galileo did the world a favor by insisting that physicists do more experiments to check their hypotheses. Teaching elementary pupils to hold their conclusions about the world tentatively and with an attitude of testing out everything they believe is the best kind of elementary teaching. Whether by video or in person, good teaching encourages learners to draw on their life experience between lesson sessions to test out ideas and to see what ideas are really correctly understood.
[1] https://kclpure.kcl.ac.uk/portal/en/persons/michael-shayer(5...
http://harvardmagazine.com/2012/03/twilight-of-the-lecture
Though having read it, the only conclusion I can make is that I don't really understand anything about the subject.
Formal education started at least 4000 years ago (earliest writing is at least 4,000 year old, and I think you need a formal education to have scribes who can read and write). I don't think we have done any substantial progress in how to teach in that time frame, at least compared to how much progress we have done in most other subjects: medicine, math, engineering, metallurgy, you name it. heck, we are still discussing what methodology we should use to teach reading & writing, and we have had 4000 years to figure what's the best way.
On the other hand, anyone who has had a good teacher can attests that teaching quality can vary by a huge amount. So my theory for good education is: 1) find good teachers (which probably includes "pay them well") 2) let them do their stuff
Anybody who tries to do something better than the above should be able to explain why their pet theory has not been discovered before.
This has not been done because people have a built in desire for "fairness" and splitting a country or state into two groups means one group is getting a worse education. (Even though we don't know before the experiment starts which group that is)
Though this is not sufficient, it at least improves the ability of the student to reason about the problem and question the models they have built around their heads on the given subject.