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University of Minnesota Launches Review Project For Open Textbooks
New submitter Durinia writes "Minnesota Public Radio is running a story about the University of Minnesota's Open Textbooks project. The goal of the project is to solicit reviews of college-level open source textbooks and collect those that pass muster onto their website.
The project will focus first on high-volume introductory classes such as those for Math and Biology, because as David Ernst, director of the project, states in the interview: 'You know the world doesn't need another $150 Algebra One book. Algebra One hasn't changed for centuries, probably.'"
Requirements for inclusion include: Open licensing (Creative Commons Attribution/Share Alike), complete content (no glorified collections of lecture notes), applicability outside of the author's institution, and print availability.
I was talking with a history professor (rljensen) the other day, and he said that free textbook ebooks would never catch on because, quote, "They're all terrible. And if they weren't terrible, they'd be selling them."
Hopefully sites like this will not only prove him wrong, but bring education, world-wide, to the next level.
... not to mention Mayans or Incas ...
I'm reserving judgement of Mayan mathematical prowess until late December.
It's an absolutely silly statement. Teaching methodology has changed enormously just in the last fifty years. I've had the luxury of comparing 19th century textbooks to present ones—it's not something you'd want to be stuck with; they're more like reference texts with a few questions (or even a separate question book) if you're lucky. The didactic power has, quite simply, vastly improved.
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Even more interestingly the Greek were comparatively lousy at math. Good at geometry, tho. The Romans had a similar problem. Their number system did stink.
20 minutes into the future
Textbooks in which field?
Calculus Made Easy by Silvanus Phillips Thompson was probably the best of my early calculus books, it is off copyright due to its age, and is on amazon for less than $10 and can be found for free online. $150 a quarter just was not a reasonable expense for the other books.
They counted with their hands and feet (base 20 system) if that ain't kewl what is? Of course the thing is, people (particularly journalists) never quite understand the Mayans properly. The thing is just like we have leap years to correct the fact that the year isn't exactly 365 days they had a similar corrective system once a couple of decades were past where they added extra days. These days were in tradition associated with harmful events or whatever so they were usually holydays were people did nothing at all! Then there is the fact that they essentially did not bother extending that basic calendar past a certain year because they saw no use for it (they went extinct like in the XVIth century?). They do have a calendar system which is basically infinite but is seldom used. So the "end of the Mayan calendar" is a bit like the "end of the 32-bit Unix time_t epoch". A big DUH!
Classics and Math. I've also looked at 60s-70s Biochemistry and compared it with current stuff, and while the content is different, the difference is also huge in teaching style.
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Teaching methodology has changed, thats why students go to lessons. The teacher is reponsable for conveying the content in a modern manner. But the exercices, the theorems, etc... ? Gimme a break. A Calculus book from 1920 is as good as a modern one. It won't have flashy pictures or color photographs but who cares.
Here we go again, the pirates are at it again!
Do you know the enormity of the lost revenue for publishing/printing companies when all ancient knowledge would go open source?
With a lot of struggle, the publishers managed to make wikipedia sound untrustworthy, but now a real university is going to review textbooks. It's the end of the industry.
It's an absolutely silly statement. Teaching methodology has changed enormously just in the last fifty years. I've had the luxury of comparing 19th century textbooks to present onesâ"it's not something you'd want to be stuck with; they're more like reference texts with a few questions (or even a separate question book) if you're lucky. The didactic power has, quite simply, vastly improved.
That is indeed the kind of book I'd like to be stuck with. The signal to noise ratio is way higher, and it's the job of the teacher to teach. Today's teachers are much like typical mid-level management armed with Powerpoint in that they read a pre-digested presentation for a captive audience, without doing much teaching.
If "didactic power [...] has vastly improved", you'd think that kids today would know maths "vastly" better than old people. Really, now.
That's not what I see - I see tests that have been dumbed down to fit a smaller curriculum, and kids have been dumbed down with them.
It's time for the pendulum to swing back; that we start to demand something from our teachers and children. Like being able to absorb book knowledge even when not presented according to the latest pedagogic fad or directly targeting upcoming tests. Enabling the kids to do so is the teachers' job.
they're more like reference texts with a few questions (or even a separate question book) if you're lucky. The didactic power has, quite simply, vastly improved.
But that is excellent for a book that accompanies a lecture! And all books I have actually *used* during my academic career were composed in this way - the "pedagogical" texts (Tipler's "physics"...) waste countless pages on introductions, examples, essays and whatnot, while I can actually find what I am looking for in the, e.g., Bergmann-Schäger or Landau-Lifshitz class of textbooks.
Sadly, this type of book has become rather rare. Now everything tries to be completely self-contained, as if you could learn physics out of a book. In my opinion, this is very much misguided, and counterproductive.
Even more interestingly the Greek were comparatively lousy at math. Good at geometry, tho. The Romans had a similar problem. Their number system did stink.
Mathematics was held back quite a bit for quite a long time by religion. When institutionalized superstition abhors the concept of void (zero), you have a serious drawback.
(This is why 1BC is followed by 1AD, by the way.)
Similar for negative numbers, and more recently, infinity and imaginary numbers. The latter two still aren't taught below adult education levels in some particularly superstitious countries.
Everybody knows that if you don't open your textbook, it is easier to return as new at the end of the semester. This is just a ploy by the bookstore to foil my plot to save money.
If you want to troll, at least use a proper expression for equality.
This is a great concept, but who does this benefit in the end? I know quiet a few professors that I took classes from that the very books we used in 'their' classes were one's they 1) either knew a close colleague in their field that reviewed it or provided input into it (see liner notes for their names) or 2) endorsed or provided input on the writing or content of it themselves. Outside of that, there's always going to be that uber passionate professor that isn't going to like the quality, content or organization of the open textbooks they have to choose from and opt to still pick the book of their choice for the benefit of their students and curriculum.
So let's say this flies for gen-ed courses, which is totally could. I don't see it working at all for actual studies or specific majors with changing content or new adoptive technologies.
Hoping on the student loan bandwagon a second, let's say even half of a students book moved to an openly available one, it still wouldn't make a dent in reducing costs for the student in any manner of impact. I also thought my university's bookstore thoroughly enjoyed raping student's pocket books on the re-re-re-reselling of used books at a dirt cheap by-back tactic. Either way, if I see the fee or cost difference falling right back into the student's lap as some 'new' fee line-item.
I've been taking a Mandarin course aimed at British teenagers (though I'm much older). It is impossible to learn anything from the "textbook". It is almost entirely pictures and exercises. There is a very short dictionary, but absolutely no grammar. It's the kind of workbook I was getting when I was seven years old.
Call me an old fart, but I like learning from books. I'd much rather have a reference book than a picture book.
This is also in Project Gutenberg. I know. I had it scanned and submitted (though, as usual, lots of other people did the work of getting it proofed and assembled).
http://www.gutenberg.org/ebooks/33283
This kind of peer review is absolutely the most important missing part of the Open Text puzzle. One of the things text publishers still have going for them is the stamp of approval they give simply by publishing a text.
I take it your not actually a math teacher, or teacher of any other type. The exercises they were using during the 1920s are almost certainly not going to be relevant 90 years later. Buildings are larger and we can do things on calculators that would have taken them an entire page to do back then.
What's more there's been tons of studying done about how to present material and how to organize it that wasn't available back then. You'd be surprised how much of a difference it can make where you put particular concepts.
The difference is that kids today are expected to know more in general than back then. Teachers have less time and have to cover more material.
You're begging the question here. Kids today _do_ know more math than they did when you were a kid and when your parents were a kids. It's much more likely that they've taken calculus and even passed a third year of math in high school. What's more just compare what they're using it on compared with what was used 50 years ago.
Sure kids don't necessarily have as much declarative knowledge as was common previously, but complaining about teachers when you don't even have a clue what the situation is, doesn't reflect well on the schools you've been to.
At the university level you shouldn't even be using calculators or computers except if you take a course in numerical analysis which is obviously not the case for freshmen taking an introductory Calculus course.
Even Mathematica/Maple are tools, and if you as a student don't understand the limits of the software you're likely to get completely meaningless answers from certain types of problems.
Just because Mathematica spits out an answer doesn't mean it's the correct one.
The difference is that kids today are expected to know more in general than back then.
This is obviously not true. The books get less and less content (see GGP). Things that were taught before are now dropped, because (in part) of "no child left behind" and the focus on passing tests, not passing knowledge.
When did Charlemagne live? What's the capital of New Zealand? What's a cantilever bridge?
Tell me with a straight face that today's children know these things.
You're begging the question here. Kids today _do_ know more math than they did when you were a kid and when your parents were a kids. It's much more likely that they've taken calculus and even passed a third year of math in high school.
Calculus was mandatory and started in junior high back when I went to school. By ninth grade elective maths or first year high school, you were into derivates and integrals.
What's more just compare what they're using it on compared with what was used 50 years ago.
Yes, let's. They rely on expert systems to do the maths for them, served in task-specific packages.
They wouldn't even be able to do a simple trig calculation to figure out how long a ramp must be to not exceed a certain grade, or how much grain or how long a fence they need or for a non-rectangular lot. They rely on Home Depot to figure it out for them. And the clerks there depend on specialized calculating tools which were written by your mom and dad.
Hell, I can't even get the correct change back when a cash register is broken. And they run to Google when faced with horrible problems like "cook at 250 C" on a stove with F temperatures, because doing 1.8 x + 32 is beyond them.
I"ll bite--- which countries do not teach the concept of infinity, and imaginary numbers? Do they single these out, or just... not teach much math at all (e.g. to women for example).
The Japanese also had geometry that exceeded their mathematics.
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"You're begging the question here.
No, he's not. You should have had a better English textbook in your youth.
Teaching methodology has changed enormously just in the last fifty years.
No doubt. But has the actual education of average students in these subjects gotten better, or worse? (I say "average" students because the best students will always find a way to learn almost no matter what, and the worst students will find a way NOT to learn no matter what.)
I've had the luxury of comparing 19th century textbooks to present onesâ"it's not something you'd want to be stuck with; they're more like reference texts with a few questions (or even a separate question book) if you're lucky.
Why is that a bad thing? Sounds to me like this would mostly be a problem for the laziest teachers who basically delegate their entire job to the textbook. The textbook is supposed to be a reference, not the entire class.
You don't even have to go into infinity and imaginary numbers. Even real numbers are a problem with fundtards.
Do I have to remind you that there was legislation that said that PI = 3?
I really hate that the media gives those idiots airtime in order to provide "fair and balanced reporting".
But I do support the abolishment of 0 as a concept. It makes coding so much simpler. Also the letter "c" is not necessary. We kan do without it.
20 minutes into the future
Forget mathematical prowess, learn their marketing. Tip #1, if you're going to predict the apocalypse, predict it so far in the future that everyone you're talking to will be dead. Some will still be awed by your power to know such things, but never see you for the fraud you are. Today's crackpots always get that wrong, going around rounding up gullible souls for their commune or whatever because the world is going to end in May. Then June comes and they're revealed to be charlatans.
Love the ads for this story:
Fair enough, so we get a new edition of a textbook every 50 years. Let's be generous, and say every 10. Is that what happens now? No, it isn't. When I was in college not THAT long ago, using last year's edition was generally frowned upon but not quite forbidden. Not because the meat of the course was different, but because things like page numbers might be different, problems might be different, et cetera. Now, does that speak to a massive increase in didactic power, or precisely what you, the publisher, would do if you wanted to force students to buy new books instead of used ones?
A college education is getting very expensive. This is okay, because a college education is enormously valuable. Nevertheless, we are entirely right to want to crush waste out of a very expensive system. I learned from my expensive econ textbooks that this is going to happen whether you like it or not because rich profits attract competition, and competition drives prices down. Switching around the pages, updating the examples in ways that doesn't change the content meaningfully, and changing the practice problems around is simply an artificial price support. Enjoy it while it lasts.
Hell, I can't even get the correct change back when a cash register is broken. And they run to Google when faced with horrible problems like "cook at 250 C" on a stove with F temperatures, because doing 1.8 x + 32 is beyond them.
While I'll admit, the inability for people to do the quick mental arithmetic required to give correct change quickly is astonishing to me, honestly, your second gripe seems a little ridiculous. Is that scenario truly something that happens often enough in a person's life that it should be committed to memory?
I mean, I'm all for knowledge for the sake of knowledge, but I'm not going to start shitting on people because they don't remember something that they were taught who knows how many years ago if they basically never use it in their daily lives. Most people only use basic algebra and geometry from day to day. Knowledge of higher mathematics (and unnecessary conversions) to them is about as useful as a shepherd having an encyclopedic knowledge of the history of the Roman Empire. If I've been on a boat 3 times in my entire life, do I need to remember the difference between a nautical mile and a terrestrial one? Or how to convert knots to mph/kph?
Would we have committed as much to memory ourselves in our scholastic careers if there had been an omnipresent internet with which to go looking for the answer at a moment's notice? I doubt it. It's just personal bias on our part, and I admit, I sometimes do it, too, when something that I always considered "common knowledge" is proven not to be so common in younger people I interact with, but such is the nature of common knowledge, it's constantly evolving. I remember a late 19th-century "basic" math test someone emailed me, it was loaded with agricultural conversions and surveying calculations...shit that virtually no one uses on a regular basis anymore. If we could travel back in time, they'd probably think we were a bunch of fucking morons, too, when we couldn't just spit out the answer to something they would consider trivial.
Can't really imagine how that is possible. Math textbooks are basically just a listing of basic proofs. Maybe they found simpler solutions in the meantime, but most of the proofs for basic algebra have been done hundreds of years ago. The only difference is probably the text markup.
Switching around the pages, updating the examples in ways that doesn't change the content meaningfully, and changing the practice problems around is simply an artificial price support. Enjoy it while it lasts.
Hence why some colleges are just building the cost of the eTextbooks into the tuition from the outset...you don't even get a choice anymore. Someone's palms are getting greased for that arrangement, I'm sure; like any other arm of the MAFIAA, they're not going to let an antiquated business model get in their way of increasing profits.
At least, that's how things are here in the U.S., based on the comments of extended family members currently in college. Textbooks were always a fucking racket, we all know that, but it's getting more and more ridiculous year after year. eTextbooks are great for the publisher...no more used market to compete with, no more kids scraping by using a library copy of their text, and since they're starting to add it in to tuition, they have a guaranteed sale with every admission.
[citation needed]
I actually read the Wikipedia page on the 0 (year):
http://en.wikipedia.org/wiki/0_(year)
Nowhere on that page does it mention religion as why there is no year 0. The most likely explanation is also the most logical: the year before the birth of Christ is 1BC, and the year after the birth of Christ is 1AD. There wouldn't be a year 0 because you wouldn't have an entire year in between "before the birth of Christ" and "after the birth of Christ", since the birth of Christ probably didn't take a year.
I don't doubt there was superstition over the year 0, but to blame no year 0 on religion without citations is disingenuous, at best.
A real racket is when your prof requires you to buy his textbook, which is not published and is 135 pages of (double sided) photocopied paper for $280 in 1996 dollars. I imagine now he'd charge $100 more now and e-publish it. I couldn't sell it back, either. At least that was the worst case - I had about 3 other self-published classes, but most were in the $30-40 range.
Mathematics was held back quite a bit for quite a long time by religion.
That's not entirely true:
- Guys like Pythagoras (c 500 BCE) and Aristotle (c 400 BCE) were living in a polytheistic society where religion was not really the force that it became under Christianity. Everyone seems to have paid at least lip service to worshipping the official state gods, but it was nothing like an environment where if you didn't profess a particular faith you were killed. Roman documents were very clear that they were generally fine with people believing whatever they wanted unless that belief encouraged them to revolt against Rome (which Nero thought the Christians were doing). And the BC / AD split (now BCE / CE, of course) obviously wasn't something that happened until Christianity became fairly well established.
- The Abbasid Caliphate actively encouraged and funded the study of mathematics and science from about 750 CE to 1250 CE, in what has been termed the Islamic Golden Age. The difference between the math that was being used by the Romans and the math that was available for Isaac Newton to draw on are largely the result of Arabic mathematicians (who in turn drew from mathematicians in India) - they had codified writing of numbers including fractions and decimals, created algebra and trigonometry, and vastly improved understanding of irrational numbers.
- The aforementioned Isaac Newton was incredibly religious, writing a great deal about alchemy and metaphysics. Same with Renee Descartes: his magnum opus was a philosophical proof (in his mind at least) that God exists.
If you mean that mathematics was held back in Europe in the Middle Ages due to dogmatic Christianity, then you'd be somewhat right, but that's different from all religion holding back all mathematics.
I am officially gone from
Math textbooks are basically just a listing of basic proofs.
It sounds like you were educated in the 60s - 70s, because that is what textbooks were at the time. No decent math textbook today just lists basic proofs. That would be a reference book, intended for someone who already knew the math and needed to look-up the steps. A good textbook is more explanatory, breaks out the steps, includes historical anecdotes, footnotes, examples of applications, etc. Since the 60s we have learned that drilling proofs into people's mind is not the optimal way to teach math.
Not that education or textbooks today are perfect, but there have been advances.
These new textbooks sound great! Anyone know where I can steal a copy? My fast-food job doesn't provide me with enough money to lurn.
That whole Bourbaki thing just went right over your head, huh?
They did use base 20, but the way most people count with their hands and feet is in base 1, regardless of whether you use 10 fingers or 20 fingers + toes. You can somewhat reasonably count in binary on your fingers, but only up to 10^10 - 1 = 1023. Adding more states to each finger gets really difficult, and who needs to count so high on their fingers anyway?
According to this page each digit was written as some bars, each with value 5, plus some dots, each with value 1. You could imitate this system on your hands--eg. right hand for bars, left for dots. If you were good enough you could do the same with your feet for a total of two base-20 digits, though counting in binary nets you a larger maximum with hands only.
But I do support the abolishment of 0 as a concept. It makes coding so much simpler.
Hear hear! I'm sick and tired of all these "null reference exceptions" and "segmentation faults" my programs keep throwing. Each time I debug them I find a 0. If 0 didn't exist, neither would my problems!
You can somewhat reasonably count in binary on your fingers, but only up to 2^10 - 1 = 1023.
FTFY
I have to agree with this. I'm in an accounting class right now. The instructor is using the pre packaged textbook website for our quizzes and homework. She is using a syllabus provided by the book company to teach her classes. She knows nothing outside of that. This is a woman that presumably was a teacher before this pre-packaged era, but often says, "I don't know, it's not in this chapter's package." There is literally nothing in this class, that could not have been done at home, and online because there is no teaching being done.
That's exactly what a textbook should be. Now, we have about 1/2 a page of actual useful information per 10-20 pages of chapter. A student can actually carry around a reference text. Textbooks today are mostly just question books with no teaching value. I can use Infinite Math to generate questions. What students need is a book that actually helps explain things.
Instead, because the textbooks are useless, they have to rely solely on notes.
Work Safe Porn
I'd be OK with electronic texts as long as I get to keep a copy forever and it's in a format that guarantees it's not just an encrypted useless blob at some point in the future. Obviously, that's not how the publishers want to do it. One of the reasons I'm where I am today is because my aunts and uncles left old college textbooks at my grandparents' house. I read them and was inspired to go learn. For the same reason, I never sold back a single college textbook.
)Nowhere on that page does it mention religion as why there is no year 0. The most likely explanation is also the most logical: the year before the birth of Christ is 1BC, and the year after the birth of Christ is 1AD. There wouldn't be a year 0 because you wouldn't have an entire year in between "before the birth of Christ" and "after the birth of Christ", since the birth of Christ probably didn't take a year.
I assure you, the year he was born in took a full year.
A few years ago I was a grad student at the U of M and the job that put me through school was in educational technology. David Ernst was my boss's boss's boss. When I met him I thought he was a returning grad student whom I hadn't met yet and doing the same job as me, and he was very funny about the encounter. Anyways, they've been working on addressing stuff like this for a long time and it's amazing to see the project blossoming.
His statement about algebra one not changing is perhaps a little careless and distracts from the point of the project. There are plenty of good open source texts out there, and to have a knowledgable group diligently working to locate and promote the best ones is great for students.
Thank you so much for telling me that I should look for an old book next time.
> Not that education or textbooks today are perfect, but there have been advances.
An interesting question is whether the rate of advancement would be faster or slower using an open source approach. Personally, I wouldn't bet on the gatekeepers.
Actually, I cringed a little bit with that line. George Polyas "How to Solve it" seems to have had at least a mild influence on all of the math textbooks I have at home. Not that that will hold back an open text book, just that the quote is a little exaggerated.
He's wrong. Algebra 1 is different in Texas
Oh, speaking of limits: up until the 20th century they weren't used in teaching Calculus whatsoever. Infinitesimals (the idea that a number could have a smallest possible value) were, instead. Another example of how things have changed.
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To each his or her own, I guess, but keep in mind that you're probably an exception in saying that. Improved teaching methods do not necessarily need to coincide with lazier students; that's more of a result of anti-intellectualism than anything else. There are, also, some very good reasons for not knowing as much: some material simply isn't relevant to the students' vocation, and the reduction in mental clutter for people in many mentally-intensive professions has made it easier for them to focus on that field itself. (I don't have a citation for this, but I hope it's apparent.) The most prominent example would be the removal of Greek and Latin from the standard curriculum over the course of the 20th century, and a success story of the idea of streamlining people for specific tasks might be Grigori Perelman.
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Yeah at our school around the middle of the time I was there we had teachers self-publishing. Almost all of them made it really cheap (Either free for ebooks, or like 10-20 dollars for 150-250 page self published books.) The only time I got rankled by the whole thing was one when of them had 'Pearson Publishing' stamped on the second page and one of those page long copyright notices in it.
If you're going to self publish, at least do it through somebody other than the bastards who've driven costs up and quality down enough to require you to write your own course material!
But then again, most of my professors in the computer science/business department wouldn't have (or in fact ducked in there from) the real world, where they were almost as big of slackers as their teaching showed (there were like 2 exceptions, plus one who hadn't had another job since college! Boom! College, Professor. Real Elitist prick too).
Anyhow with any luck we'll get some crowdsourced books from experts who'd rather stick it to the man than make obscene profits. But I won't hold out too much hope, rare are the visionaries who both have the focus and the skill to make such things happen.
I believe the attitude there is to provide backup in case the professor fails to do an adequate job in lecture, the student misses lecture, or something in between. I've seen a lot of classes where the recommended approach is to read the material that will be covered in the lecture the night before; this exploits a facet of human memory that significantly improves retention by ensuring the student is exposed to it twice. If students actually bothered to do the readings (I, for one, didn't), it would be a significant boon to student performance; better than a naked reference for most people and situations during the normal course of the semester. (That being said, reference works are still indispensable. I have a Greek book from the 1880s where the latter half of it is nothing but a list of rules; over a thousand in all. It can tell you pretty much anything.)
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There are plenty of cases in which a long drawn-out explanation of the material is beneficial: the teacher could indeed be lazy, or they could be too busy, or the student may not grasp the teacher's approach, or they went too quickly... when you add up all of the reasons, I would argue that you go from the majority of teachers down to a small minority of them. In addition, you have students missing class and students studying for the exam. And actually, all of that is beside the point: the ideal teaching style for these textbooks is for the student to read a section the night before it's covered in the class. Both hearing and seeing the same content within 24 hours can greatly improve retention.
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I am completely and totally in support of everything you just said, yes. Textbook companies are far too parasitic to pass as the well-behaved symbiotes they ought to be.
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Infinitesimals never really went away -- they may not be formally used in calculus any more, but the practice of treating "dx" as though it were a real number (which works surprisingly well for many types of problems) is a powerful holdover from their era.
The correlation between ignorance of statistics and using "correlation is not causation" as an argument is close to 1.
Infinitesimals are a better approach for learning calculus, and most nonmathematicians who use calculus (e.g. physicists) think in terms of infinitesimals because of their usefulness.
Well, like it or not, textbook publishers' pockets are so perversely deep that they can actually afford to pay the writers of their flagship books a fair sum. Most professors I've talked to believe it's had a non-negligible effect on the books' quality. Until the open source movement really takes off we won't really know if that's true or not—but they certainly seem to be too scared to find out, given that they've started throwing lawsuits around.
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They're as easy to come by as anything else on the Internet.
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There are, also, some very good reasons for not knowing as much: some material simply isn't relevant to the students' vocation, and the reduction in mental clutter for people in many mentally-intensive professions has made it easier for them to focus on that field itself. (I don't have a citation for this, but I hope it's apparent.)
It is not. It is likely false, and there are good reasons to believe that the more you learn, the greater your ability becomes to learn even more. See "Renaissance man" and "polymath".
The only good reason I can see for removing the study of less relevant fields is if that time is used to study more relevant fields.
Thus the removal of Greek and Latin from the standard curriculum, as you said, not because it would "clutter up" the students' heads, but because that time could be better spent learning other studies.
whoosh!
GPP is unintentionally correct: he's assigning the value "socialism" to "open textbooks," where no such equality previously existed.
The correlation between ignorance of statistics and using "correlation is not causation" as an argument is close to 1.
Maybe a 3% savings on your total school bill? Who cares.
Creating value equal to 3% of the general education outlay, scaled to the English speaking world, would be kind of a big deal. Particularly when it also creates open courseware that can be freely used by non-enrolled students as a happy externality.
My thoughts exactly.
Of this I am aware! And they are even used formally in many contexts because it's more convenient, even though we don't have the theoretical underpinning to justify them properly. Personally, I think I would've been more comfortable in a first-year calculus course that used them instead because they seem more intuitive.
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we don't have the theoretical underpinning to justify them properly
Sure we do. Nonstandard analysis has been well-established since the 1960s. Haven't you kept up with those developments?
But I do support the abolishment of ... the letter "c" is not necessary. We kan do without it.
I agree, but I think we need new glyphs for the letters sh, th, and ch (especially with c going away on that last one). Sick of seeing words like "sweetheart" and not being instantly sure if it is pronounced with the "th" sound or a separate "t" "h" sound.
Being the sort of compulsive student of many fields in question, I would honestly argue that there are mixed benefits. Learning ability is improved because you've been exposed to more fundamental concepts (and are better at seeing new angles, because that's a skill you've developed), but actually turning around and applying that knowledge takes more practice. The associative nature of human memory means that when you're trying to recall something under pressure, you have a higher tendency to stumble onto spurious knowledge—you remember a lot of things from other fields and areas that get in the way. In addition, having a breadth of knowledge can actually be a source of frustration when studying depth in a very narrow area, as the lack of variety in the topics being discussed becomes frustrating; behold, the misery of the student with the general degree who can't decide what he or she wants to do with his or her life.
(And to any who would make cynical remarks along the lines of "maybe you're just stupid," I don't think you're doing cognitive psychology any benefits by implying that there is some group of superhuman with infinite retentive ability that deserves exclusive consideration.)
Bio questions? Ask me to start a Q&A journal. Computer analogies available for most topics!
Apparently not. Thanks for the update.
Bio questions? Ask me to start a Q&A journal. Computer analogies available for most topics!
Man, your records don't back far enough for me, it seems. ;-)
I would rather that academia focused more on open minds that open textbooks.
Naked men should use base 21.
AC
The problem with counting on your fingers is that things get messy when you start using fractions.
Can't really imagine how that is possible. Math textbooks are basically just a listing of basic proofs. Maybe they found simpler solutions in the meantime, but most of the proofs for basic algebra have been done hundreds of years ago. The only difference is probably the text markup.
You clearly never studied math at university level. Proofs can be written in different ways, some easier some harder to read. The choice of which theorems to include and which to leave out also means a lot. Having good exercises lists is also part of being a good book. Sometimes, some math techniques lose relative importance, because their applications lose relative importance.
Also, in older books it was prohibitively expensive to include many figures or graphs. Equations were also expensive to typeset, so older books have less equations. Even the choice of how to write equations was different (as typesetting a large fraction of many variables was much more expensive than just doing "alpha^2 beta bla bla * / ( \int_{x=0}^{1000} gamma bla bla bla)" on a single line of text.
And they run to Google when faced with horrible problems like "cook at 250 C" on a stove with F temperatures, because doing 1.8 x + 32 is beyond them.
Hey, I resent that remark. I can handle the arithmetic, but I just don't have any reason to remember the conversion, because it's Not That Important. I spend far more time converting between different bases than different measurement systems.
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Mathematics was held back quite a bit for quite a long time by religion. When institutionalized superstition abhors the concept of void (zero), you have a serious drawback. (This is why 1BC is followed by 1AD, by the way.)
Oooh! Religion bashing! How unique and original.
The Greek philosophers spent a heck of a long time asking themselves whether something could be nothing. There is a fundamental difficulty, therefore, in naming something as "0". The first year of the Julian calendar existed. How can you call it nothing? Look at very young babies. Do we call them "zero-year olds"? No, we call them 4-week olds, three month olds etc, because we have to call them something. And how many brothers do I have? I have three. How many mothers? I only have one. How many dogs? I don't have any. You can't say "I have zero." You don't say "I have zero." Zero is not, and never has been, a genuine "number" to us psychologically. Of course it took a long time for people to accept it.
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The main thing they forget to say on that wiki page is that the Romans counted their years as ordinal numbers (ie 1st, 2nd, 3rd), just like we do with days. There is no "zeroeth" except in certain notations of convenience within computer science. (Although to me x[0] will always be the first element of the array....)
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How many dogs? I don't have any. You can't say "I have zero." You don't say "I have zero."
I would argue that some would say that, especially if used to filling out forms. Quite a few more would say "I have none" or just "none".
Zero is not, and never has been, a genuine "number" to us psychologically.
Most numbers aren't natural to us psychologically. You are unlikely to have a built-in psychological concept of "thirteen".
If anything, the lack of something is very fundamental to our existence. It's because we have zero meat we go hunt.
Recommended reading: "The Nothing that Is: A Natural History of Zero" by Robert Kaplan.
And this shorter one: http://www.etymonline.com/zero.php
If anything, the lack of something is very fundamental to our existence. It's because we have zero meat we go hunt.
And yet you would not say that if I hadn't prompted you to.
Zero was a technology that was not properly understood, so people didn't use it. That's perfectly natural. There are plenty of examples of this. Don't drop it at the door of religion.
(And for the record, no, I don't believe in God/a god/gods/divine enlightenment/reincarnation/life after death. I just believe that most religion bashing is ignorant and unjustified.)
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