In Praise of Open Source Textbooks
105 comments
> thank you, thank you
You are very welcome. Glad to help. :-)
(I'll just say that the TeX Users Group is very interested in improving the PDFs that LaTeX outputs in this regard, and has projects in this direction. They are at https://www.tug.org.)
You are very welcome. Glad to help. :-)
(I'll just say that the TeX Users Group is very interested in improving the PDFs that LaTeX outputs in this regard, and has projects in this direction. They are at https://www.tug.org.)
Oh, that's very good to hear! I'll definitely get in contact. I won't be able to, for the next two months or so, but after that I should have some free time when I can test/contribute with code/whatever else is required. (Hopefully, if this gets done, publishers that use LaTeX for typesetting might automatically offer accessible PDFs as well.)
Sometimes being a resource for developers, as someone who could be asked, can be valuable. Anyway, good luck with your studies!
Just wanted to say my thanks as well, while I have not worked with one of your books, I have a lot of respect for people that choose to release the source of textbooks they created.
You are welcome. Have a look at https://hefferon.net for the other books.
Could you elaborate on this? Like a link to a concrete project/discussion?
I am visually impaired too and I did my own research on this topic a while ago. It appears that in the past decade or two there have been a few attempts to improve accessibility of Latex generated PDFs, but none of them seems to have accomplished the goal and pretty much all of them are dead projects now.
I would be happy if there's an ongoing project.
I second this and would also like to add a request to clarify what it is that would even be possible in this space, because I have no idea beyond “have hidden MathSpeak text behind the mathematics notation”, which is probably both too vague and too specific to be useful.
Even more damningly, I actually have no idea what it is the accessibility users do, because I’m sure I wouldn’t understand half of the maths notation I’ve read or typeset if someone just spelt it out for me. I simply can’t manipulate things that long without writing them out, and when comparing two equations nothing beats placing them one above the other. Surely computers must be capable of something more helpful than forcing everything into one-dimensional form?
Even more damningly, I actually have no idea what it is the accessibility users do, because I’m sure I wouldn’t understand half of the maths notation I’ve read or typeset if someone just spelt it out for me. I simply can’t manipulate things that long without writing them out, and when comparing two equations nothing beats placing them one above the other. Surely computers must be capable of something more helpful than forcing everything into one-dimensional form?
Just having raw Tex code for the formula would be already immensely helpful. Right now we're in the situation that the information about formulas is lost for screenreader users. Once there's raw Tex formula, then screenreader developers, myself included, can come up with many different ways to present formulas in more convenient form. But again, so far, the raw tex code of the formulas is lost, and apparently it seems to be either incredibly hard to embed it into PDFs or something - judging by so little progress in this direction over the last decade.
There is a working group. See https://www.tug.org/twg/accessibility/. One of the reasons to have a TeX Users Group is to allow there to be a way to organize, and provide some money for, such things.
(I should say that my personal involvment goes no further attending presentations at the annual conference.)
(I should say that my personal involvment goes no further attending presentations at the annual conference.)
> interested in improving the PDFs that LaTeX outputs in this regard, and has projects in this direction
Can you elaborate on what / where those projects are? It's not clear from the tug.org website.
I love LaTeX and if I had a relevant skill set I'd be willing to help out.
Thank you.
Can you elaborate on what / where those projects are? It's not clear from the tug.org website.
I love LaTeX and if I had a relevant skill set I'd be willing to help out.
Thank you.
See https://www.tug.org/twg/accessibility/; I'm afraid I can't say more than that.
FYI, if you are a student with a 'qualifying print disability' (which includes visual impairment, dyslexia, and other learning disabilities), you may be able to get free access to hundreds of thousands of books/textbooks via Bookshare. [1]
They get digital versions of books from the publishers and make them accessible to people with print disabilities. This means adding image descriptions and offering various text alterations (different text sizes, special fonts and colors, etc.) to make them easier to read. They also offer math-based tools to make equations accessible.
Bookshare is 100% free to any US-based student who qualifies, and various other countries have agreements with Bookshare as well. They are part of the tech-for-good nonprofit Benetech and are based out of Palo Alto.
1: http://www.bookshare.org.
They get digital versions of books from the publishers and make them accessible to people with print disabilities. This means adding image descriptions and offering various text alterations (different text sizes, special fonts and colors, etc.) to make them easier to read. They also offer math-based tools to make equations accessible.
Bookshare is 100% free to any US-based student who qualifies, and various other countries have agreements with Bookshare as well. They are part of the tech-for-good nonprofit Benetech and are based out of Palo Alto.
1: http://www.bookshare.org.
I had a student with limited vision in a class once, who had a reader. Luckily, I had written the course notes (basically a textbook) in latex.
I consulted with the student and saw how the reader worked. All was fine, but it was slow because it said e.g. "backslash begin open brace equation close brace", so I made a perlscript to remove backslash and braces (and a few other things) and then it all worked really well.
People, especially those who don't use mathematics much, think latex is hard for humans. I think exactly the reverse is true.
I consulted with the student and saw how the reader worked. All was fine, but it was slow because it said e.g. "backslash begin open brace equation close brace", so I made a perlscript to remove backslash and braces (and a few other things) and then it all worked really well.
People, especially those who don't use mathematics much, think latex is hard for humans. I think exactly the reverse is true.
I have no idea how commercial textbooks for anything up to specialized, college-level classes are viable. You'd think that enough states (and countries) would put the work into the Wikibooks calculus book so it meets their standards and just use that.
I don't get it, either. I laugh when schools complain their textbooks are "old and outdated". So what? Has there been a revolution in algebra I didn't hear about?
I also laugh when teachers say they expend all this effort making "lesson plans". There are 3.7 million teachers just in the U.S. You'd think they could share them?
I also laugh when teachers say they expend all this effort making "lesson plans". There are 3.7 million teachers just in the U.S. You'd think they could share them?
English teacher here, working in Japan teaching English as a Foreign Language.
I would LOVE to use free textbooks and older books. I try to do so as much as possible. But the real problem (for me at least), is how can I get a copy for all of my students? I can't afford to print them all a copy of old stuff, and after about 5-10 years, the publishers stop printing the older books!
I came across this problem big time this school year -- planned on using a book I love and have been using for 10 years old to be told last minute it's now OUT OF PRINT. (It was in print just 6 months ago). sigh
Old is OK in many places, but only if you can get 50-100 copies of it each semester / year...
I would LOVE to use free textbooks and older books. I try to do so as much as possible. But the real problem (for me at least), is how can I get a copy for all of my students? I can't afford to print them all a copy of old stuff, and after about 5-10 years, the publishers stop printing the older books!
I came across this problem big time this school year -- planned on using a book I love and have been using for 10 years old to be told last minute it's now OUT OF PRINT. (It was in print just 6 months ago). sigh
Old is OK in many places, but only if you can get 50-100 copies of it each semester / year...
Open source textbooks are available and usable online for free. Why do you need printed copies?
Frequently, open source textbooks can also be printed on demand for much less than the cost of a new textbook, in any quantity. If you can afford new books, you can certainly afford printed old books.
“Out of print” is largely an outdated term, except for small print run books. If they sold well new, they should be available used, in quantity. Especially if you are only replacing lost or damaged books.
Project Gutenberg has many old books online and you can get them printed.
Frequently, open source textbooks can also be printed on demand for much less than the cost of a new textbook, in any quantity. If you can afford new books, you can certainly afford printed old books.
“Out of print” is largely an outdated term, except for small print run books. If they sold well new, they should be available used, in quantity. Especially if you are only replacing lost or damaged books.
Project Gutenberg has many old books online and you can get them printed.
Have you ever talked to any of these people you're laughing at? Maybe there is some nuance or background you're not aware of.
I'm not a teacher, but I think often when they talk about old textbooks, the issue is that they are physically falling apart, not just that they were published a long time ago. These books are in continuous use by children, so you can't compare it to a book you've had on your shelf for 40 years. As for lesson plans, most teachers don't have the luxury to just pick a plan they think is best. Every state, district, individual school might have its own rules about what can and must be taught, and teachers often aren't given much say in that.
I'm not a teacher, but I think often when they talk about old textbooks, the issue is that they are physically falling apart, not just that they were published a long time ago. These books are in continuous use by children, so you can't compare it to a book you've had on your shelf for 40 years. As for lesson plans, most teachers don't have the luxury to just pick a plan they think is best. Every state, district, individual school might have its own rules about what can and must be taught, and teachers often aren't given much say in that.
I understand that textbooks fall apart and need replacement. I'm just talking about the complaints that they are outdated.
The complaint I constantly hear from teachers is they work their fingers to the bone preparing lesson plans. I ask why are they making them from scratch, why not share? and don't get a response.
> Every state, district, individual school might have its own rules about what can and must be taught, and teachers often aren't given much say in that.
Then why do they say they spend all this effort creating lesson plans, not even re-using what they used last year? One teacher told me she spent her summer writing lesson plans for next year. I asked why she didn't re-use the ones she wrote for last year? She said they had to be custom made for each student. I asked how could she custom make them in the summer, when she didn't know which students she'd be getting in the fall?
That was the end of that discussion.
The complaint I constantly hear from teachers is they work their fingers to the bone preparing lesson plans. I ask why are they making them from scratch, why not share? and don't get a response.
> Every state, district, individual school might have its own rules about what can and must be taught, and teachers often aren't given much say in that.
Then why do they say they spend all this effort creating lesson plans, not even re-using what they used last year? One teacher told me she spent her summer writing lesson plans for next year. I asked why she didn't re-use the ones she wrote for last year? She said they had to be custom made for each student. I asked how could she custom make them in the summer, when she didn't know which students she'd be getting in the fall?
That was the end of that discussion.
The teachers I know do reuse their lesson plans when they teach the same class. One of the biggest values of seniority is being able to teach the same class every year.
Why they don't standardize has everything to do with the kind of people who become teachers and what they want to be doing with their time.
Why they don't standardize has everything to do with the kind of people who become teachers and what they want to be doing with their time.
> The teachers I know do reuse their lesson plans when they teach the same class.
Of course they do. I knew I was being buffaloed.
Though the point stands that why don't they share lesson plans? Why do we need 3.7 million unique lesson plans? There ought to be plenty of off-the-shelf plans to use.
Of course they do. I knew I was being buffaloed.
Though the point stands that why don't they share lesson plans? Why do we need 3.7 million unique lesson plans? There ought to be plenty of off-the-shelf plans to use.
The teachers I know do start with standard lesson plans, but for reasons I don't understand they feel the need to customize them.
NIH is a powerful sentiment in many areas, not just tech.
Or perhaps every classroom is filled with unique individuals with differing learning needs?
How can they develop unique lesson plans the summer before they know which students they get?
Talk to teachers from the grade below, think about what hasn't worked well in your class the last few years, think about how your school district might differ from that of the lesson plan you're modifying.
For example, maybe you need to modify some take home science experiments because your kids tend not to have easy access to the right materials. Or, maybe the elementary school math program is more advanced than average, so as a middle school teacher you need to modify any standard lesson plan so you're not repeating material the kids already know. Or, maybe as a Spanish teacher you need to figure out how to effectively deal with a class where usually half the kids are children of immigrants and already close to fluent. Or, maybe as a history teacher you have an assignment the kids used to love where they make a Facebook profile of a historical figure, but now most kids aren't using Facebook anymore and the assignment isn't really engaging them. Or, maybe your town has some historical sites that you'd like to make field trips to, so you want to add some lessons to give some specific context around them. Or, maybe as a P.E. teacher the gym is being renovated and you're gonna have to work around that. Or, maybe a local private school just closed and you're expecting to get a bunch of its students in your class next year. Or, maybe a lot of your kids can't afford TI-84s but the school FINALLY got funding to purchase enough for the whole class. etc. etc. etc.
For example, maybe you need to modify some take home science experiments because your kids tend not to have easy access to the right materials. Or, maybe the elementary school math program is more advanced than average, so as a middle school teacher you need to modify any standard lesson plan so you're not repeating material the kids already know. Or, maybe as a Spanish teacher you need to figure out how to effectively deal with a class where usually half the kids are children of immigrants and already close to fluent. Or, maybe as a history teacher you have an assignment the kids used to love where they make a Facebook profile of a historical figure, but now most kids aren't using Facebook anymore and the assignment isn't really engaging them. Or, maybe your town has some historical sites that you'd like to make field trips to, so you want to add some lessons to give some specific context around them. Or, maybe as a P.E. teacher the gym is being renovated and you're gonna have to work around that. Or, maybe a local private school just closed and you're expecting to get a bunch of its students in your class next year. Or, maybe a lot of your kids can't afford TI-84s but the school FINALLY got funding to purchase enough for the whole class. etc. etc. etc.
Or perhaps every classroom has a unique teacher who has an individual teaching style?
Curriculum change is relatively frequent in some places. Different classes take to different material at different paces. Different resources are available to different schools and different classrooms (think science experiments). In the UK there are online platforms for purchasing and selling lesson plans. My partner has saved much time purchasing lesson plans from these platforms. They are available.
Teachers aren't paid very well in many places and, at least here, funds aren't made specifically available for purchase of lesson plans; teachers spend their own money buying lesson plans. It's easily worth it when there's a second income in your household. Perhaps not in places where teachers are very poorly paid and for those who are on a single income.
Teachers aren't paid very well in many places and, at least here, funds aren't made specifically available for purchase of lesson plans; teachers spend their own money buying lesson plans. It's easily worth it when there's a second income in your household. Perhaps not in places where teachers are very poorly paid and for those who are on a single income.
> funds aren't made specifically available for purchase of lesson plans
You mean no teachers set up a github repository where they give away lesson plans just to be helpful? Teachers are unable to pool their resources and help each other? "Hey Mr Hand, I'm teaching science for the first time next year. Can I use your lesson plans?" "Sure, Ms Halsey!"
Besides, teachers complain a lot about spending all their time devising lesson plans. They might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy plans, and spend the rest on a vacation.
You mean no teachers set up a github repository where they give away lesson plans just to be helpful? Teachers are unable to pool their resources and help each other? "Hey Mr Hand, I'm teaching science for the first time next year. Can I use your lesson plans?" "Sure, Ms Halsey!"
Besides, teachers complain a lot about spending all their time devising lesson plans. They might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy plans, and spend the rest on a vacation.
It is amazing how many strawman arguments you are getting, apparently from teachers. You requested clarification on specific items, yet the answers discuss entirely different things. Maybe that is the actual problem with how things are taught.
Simply googling would answer many of your questions in thirty seconds. For example, search for by lesson plans and you’ll discover there are many marketplaces for lesson plans.
People unfamiliar with problems frequently think they are easy, because they fail to understand the complexity of the problem.
A similar question might be “why would you invent a new programming language, when you could just use an existing one?”
Answering that question to a non programmer might require hours of explanation and background, and you might find yourself just sighing and saying “never mind”. That doesn’t mean you don’t have a reason, or it was a bad idea. It just means it’s not your job to explain things. Particularly to people who make it clear they have an agenda.
People unfamiliar with problems frequently think they are easy, because they fail to understand the complexity of the problem.
A similar question might be “why would you invent a new programming language, when you could just use an existing one?”
Answering that question to a non programmer might require hours of explanation and background, and you might find yourself just sighing and saying “never mind”. That doesn’t mean you don’t have a reason, or it was a bad idea. It just means it’s not your job to explain things. Particularly to people who make it clear they have an agenda.
> A similar question might be “why would you invent a new programming language, when you could just use an existing one?”
I feel like this is a bad analogy if you are trying to support the idea that teachers need to make their own lesson plans. Could you imagine if every programmer had to build their own programming language before using it create software? Nothing would ever get done.
Instead, the vast majority of programmers just use one of the many existing programming languages.
I feel like this is a bad analogy if you are trying to support the idea that teachers need to make their own lesson plans. Could you imagine if every programmer had to build their own programming language before using it create software? Nothing would ever get done.
Instead, the vast majority of programmers just use one of the many existing programming languages.
> People unfamiliar with problems frequently think they are easy, because they fail to understand the complexity of the problem.
Please illuminate how 3.7 million teachers need to spend their summer drawing up a new set of lesson plans every year.
> A similar question might be “why would you invent a new programming language, when you could just use an existing one?”
Great question. Because I want to. I'm not complaining about it demanding sympathy because I lose my summers working on it.
I have no problem with teachers who want to create their own lesson plans, rather than using existing ones. I'm just not buying the complaining about what a burden it is to reinvent the wheel, when they can use last year's, or a fellow teacher's, or buy one off the internet.
Please illuminate how 3.7 million teachers need to spend their summer drawing up a new set of lesson plans every year.
> A similar question might be “why would you invent a new programming language, when you could just use an existing one?”
Great question. Because I want to. I'm not complaining about it demanding sympathy because I lose my summers working on it.
I have no problem with teachers who want to create their own lesson plans, rather than using existing ones. I'm just not buying the complaining about what a burden it is to reinvent the wheel, when they can use last year's, or a fellow teacher's, or buy one off the internet.
> You mean no teachers set up a github repository where they give away lesson plans just to be helpful
Your sample set of teachers is very different than mine if they can figure out how to do something technical like that.
Your sample set of teachers is very different than mine if they can figure out how to do something technical like that.
It's probably a bit late to bother replying to this, but hey, here goes anyway.
Believe it or not, I wasn't arguing against you. My main point was to agree with you, and to inform: markets exist for lessons. The prices are quite reasonable. Some are free. I hear free lessons are typically lower quality.
I also (indirectly) pointed out that lessons are necessarily different from one another. What I've observed is that some work needs to be done even when plans are obtained from another party. Though, from what I've seen, much less. Purchasing lesson plans is a big time-saver.
Perhaps next time someone complains to you about spending too long lesson planning, you should propose they purchase some lesson plans, and see what they say. To me, that's the interesting question. Do they know these are available? Do they find the cost reasonable? Are they opposed to purchasing these lessons in principle, because they already spend their own money for the benefit of their students?
> They might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy plans, and spend the rest on a vacation.
This statement is completely ludicrous to me. Humans should be given the resources they require to perform their jobs effectively. You might be strictly correct that individual teachers might be better off taking another job and buying these resources. But I think you should direct your ire at the employer of the teachers if you acknowledge that this is a problem. Consider the analogous statement:
> [Programmers] might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy existing libraries, and spend the rest on a vacation.
Believe it or not, I wasn't arguing against you. My main point was to agree with you, and to inform: markets exist for lessons. The prices are quite reasonable. Some are free. I hear free lessons are typically lower quality.
I also (indirectly) pointed out that lessons are necessarily different from one another. What I've observed is that some work needs to be done even when plans are obtained from another party. Though, from what I've seen, much less. Purchasing lesson plans is a big time-saver.
Perhaps next time someone complains to you about spending too long lesson planning, you should propose they purchase some lesson plans, and see what they say. To me, that's the interesting question. Do they know these are available? Do they find the cost reasonable? Are they opposed to purchasing these lessons in principle, because they already spend their own money for the benefit of their students?
> They might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy plans, and spend the rest on a vacation.
This statement is completely ludicrous to me. Humans should be given the resources they require to perform their jobs effectively. You might be strictly correct that individual teachers might be better off taking another job and buying these resources. But I think you should direct your ire at the employer of the teachers if you acknowledge that this is a problem. Consider the analogous statement:
> [Programmers] might do cost-benefit check on whether they might be way ahead taking a second job, using part of the wages to buy existing libraries, and spend the rest on a vacation.
The reused lesson plans still often need to be updated, either in light of curriculum changes or just because something “didn’t work” (too hard, too easy, messes up a dependency, want to emphasize something else, etc).
As for why there aren’t off-the-shelf plans:
You might want to adapt the curriculum to the current class of students or the broader community. The College Board does distribute a syllabus for AP US History classes, but it’s deliberately sparse so that teachers can plug in people and events that are “locally valued” (their words, not mine). A class in Alaska might spend more time on Native events and statehood; one in Boston might up the emphasis on the Revolutionary War events that happened nearby; Texas is going to go crazy with the Alamo. This is true for other subjects too. A science class might spend more time on local ecosystems that they can visit. A few of my literature class read a play and then went to see a production of it; that part presumably had to change every year, based on what was being performed nearby.
The other reason is that the teachers need to review the lesson plan anyway: no one can remember a thousand hours of material! While doing so, it makes sense to “refactor” them into something that matches your own mental model of the content. Teaching off someone else’s materials feels weird and often goes a little more poorly.
As for why there aren’t off-the-shelf plans:
You might want to adapt the curriculum to the current class of students or the broader community. The College Board does distribute a syllabus for AP US History classes, but it’s deliberately sparse so that teachers can plug in people and events that are “locally valued” (their words, not mine). A class in Alaska might spend more time on Native events and statehood; one in Boston might up the emphasis on the Revolutionary War events that happened nearby; Texas is going to go crazy with the Alamo. This is true for other subjects too. A science class might spend more time on local ecosystems that they can visit. A few of my literature class read a play and then went to see a production of it; that part presumably had to change every year, based on what was being performed nearby.
The other reason is that the teachers need to review the lesson plan anyway: no one can remember a thousand hours of material! While doing so, it makes sense to “refactor” them into something that matches your own mental model of the content. Teaching off someone else’s materials feels weird and often goes a little more poorly.
Obviously they do, here's one popular example from the national teachers union: https://sharemylesson.com/about-us
And of course teachers within any school will generally share whatever they can.
And of course teachers within any school will generally share whatever they can.
Yes. My wife had dealt with this nonsense for years.
She was ready to quit her school and the major negotiation point was reusing lessons from prior year. School finally relented.
Were they IEPs?
In the US, public school students with disabilities (learning and otherwise) are legally entitled to “Individualized Educational Programs”, which is supposed to be tailored to their particular needs and abilities. For example, a student with a speech impairment might be allowed to pre-record a presentation, or do it in private, rather than live in front of the whole class. There are a lot of requirements, and putting together something that passes legal muster and really tries to support the student seems like a lot of work.
https://en.wikipedia.org/wiki/Individualized_Education_Progr...
In the US, public school students with disabilities (learning and otherwise) are legally entitled to “Individualized Educational Programs”, which is supposed to be tailored to their particular needs and abilities. For example, a student with a speech impairment might be allowed to pre-record a presentation, or do it in private, rather than live in front of the whole class. There are a lot of requirements, and putting together something that passes legal muster and really tries to support the student seems like a lot of work.
https://en.wikipedia.org/wiki/Individualized_Education_Progr...
No, they weren't special ed teachers.
You're absolutely correct on your second point.
But for the first point, as poor as research in education is, there have been improvements in educational methods. I read some examples about the Common Core mathematics pedagogy, prepared to be as angry as Feynman, but they were actually teaching kids how to do arithmetic the way I do (which is way better than New Math or brute force methods): 99x5 is 500-5 not 5+(4+5)*10+400. Are their changes more likely to be improvements rather than demerits? I do not know.
But for the first point, as poor as research in education is, there have been improvements in educational methods. I read some examples about the Common Core mathematics pedagogy, prepared to be as angry as Feynman, but they were actually teaching kids how to do arithmetic the way I do (which is way better than New Math or brute force methods): 99x5 is 500-5 not 5+(4+5)*10+400. Are their changes more likely to be improvements rather than demerits? I do not know.
There have certainly been changes in educational methods, but I doubt there are improvements. Math achievement has been flat for the last 50 years. The "new math" and "look-say" methods were largely invented to drive new textbook sales.
I think you should look into the complaints about common core; I think, if you're good at arithmetic (like I assume most of us programmers are), that you'll find the current methods an improvement over those and about as good as can be done by our grade-segregated, "no-child-left-behind", Prussian educational system.
Like I said, no measurable aggregate improvement in the last 50 years.
So many other factors have gone down, that might actually be an achievement.
I learnt arithmetic in the early sixties. 99x5 would be 9x5x10+9x5 = 450+45 = 495
Perhaps it helped that we all knew the 12 times tables.
Is there some new magical way of doing long multiplication that is more effective and easier to understand?
Perhaps it helped that we all knew the 12 times tables.
Is there some new magical way of doing long multiplication that is more effective and easier to understand?
999999*5 is far easier as 5000000-5 than 45+450+4500+...
Are you really arguing that the latter is faster and more effective to do in your head?
Are you really arguing that the latter is faster and more effective to do in your head?
Not at all. I didn't know we were discussing mental arithmetic.
Even on paper it's far simpler
(1000000-1)*5 => 5000000-5 => 4999995
Learning to find these patterns early sets up students for having an easier time with algebra later. Algebra is just rearranging equations. I don't understand, but students do struggle with going from "12/3=?" to "3*X=12 solve for X". We can't keep failing so many students every year and expect our country to hold together.
(1000000-1)*5 => 5000000-5 => 4999995
Learning to find these patterns early sets up students for having an easier time with algebra later. Algebra is just rearranging equations. I don't understand, but students do struggle with going from "12/3=?" to "3*X=12 solve for X". We can't keep failing so many students every year and expect our country to hold together.
Agreed! My copies of Calculus Made Easy and Calculus & Statistics are wonderful references even though they were written before I was born.
The amount of churn in (American) math education is bizarre. New hip curricula, textbooks, etc every few years, and yet the average high school graduate cannot prove the pythagorean theorem.
Not all subjects have the luxury of being so isolated from changes in the real world.
Let's see. Science? Nope. History? Nope. Exercise? Nope. Reading? Nope. Writing? Nope. Foreign languages? Nope.
Current events? Yup. Just bring a newspaper to class.
Current events? Yup. Just bring a newspaper to class.
> History?
Modern perspective on it is constantly evolving, especially on more recent bits, and there's plenty topics I'd rather have my kids being taught with a perspective from this century (E.g. to take my local German perspective, events surrounding WW2 and post-war development). Also, plenty things that happened while you were alive are History now. (remember, kids finishing high school now weren't born when 9/11 happened)
> Reading? Nope. Writing? Nope. Foreign languages? Nope.
Languages: Languages change (German literally added a letter in the past decade, new words are created, how people speak changes, ...). Language studies tend to be steeped in cultural aspects too, both for native and foreign languages (e.g. media literacy should probably cover internet material differently than it did when I was in high school, explaining the US media landscape in the English books probably also should look differently now). Being somewhat up-to-date with topics also helps students being interested.
> Science?
More stable, but also not frozen. Especially in biology and with medical topics you'll have changes, but other sciences too especially where discussing applications, but that's not as critical.
Some more examples:
Geography: If you'd given me 10 years old material in my first geography lessons even which country the lesson took place in would have been wrong.
Any kind of thing that deals with law/demographics/economics/politics (how exactly that's divided up into different subjects very much depends on where you are, it often comes up in material for other subjects) will benefit from regular review and updates.
A textbook being outdated doesn't mean the entire thing is useless now, often its just small sections that will stand out badly if not updated.
Modern perspective on it is constantly evolving, especially on more recent bits, and there's plenty topics I'd rather have my kids being taught with a perspective from this century (E.g. to take my local German perspective, events surrounding WW2 and post-war development). Also, plenty things that happened while you were alive are History now. (remember, kids finishing high school now weren't born when 9/11 happened)
> Reading? Nope. Writing? Nope. Foreign languages? Nope.
Languages: Languages change (German literally added a letter in the past decade, new words are created, how people speak changes, ...). Language studies tend to be steeped in cultural aspects too, both for native and foreign languages (e.g. media literacy should probably cover internet material differently than it did when I was in high school, explaining the US media landscape in the English books probably also should look differently now). Being somewhat up-to-date with topics also helps students being interested.
> Science?
More stable, but also not frozen. Especially in biology and with medical topics you'll have changes, but other sciences too especially where discussing applications, but that's not as critical.
Some more examples:
Geography: If you'd given me 10 years old material in my first geography lessons even which country the lesson took place in would have been wrong.
Any kind of thing that deals with law/demographics/economics/politics (how exactly that's divided up into different subjects very much depends on where you are, it often comes up in material for other subjects) will benefit from regular review and updates.
A textbook being outdated doesn't mean the entire thing is useless now, often its just small sections that will stand out badly if not updated.
For small sections, a pamphlet supplement would be all that's necessary, if that. The teacher can just say "that sentence is outdated, today we're pretty sure the dinosaurs were wiped out by an asteroid."
> Languages: Languages change (German literally added a letter in the past decade, new words are created, how people speak changes, ...).
If one learned German from a forty year old textbook the only problem related to that that you would experience in Germany would be that some people would think you were speaking rather more formally than expected. Learning it from an up to date text book isn't going to make you noticeably better at communicating with actual Germans in real life, that takes actual immersion in the language as it is really spoken.
And the German language authorities might well have added a new letter or changed the spelling of the word spagetti but that doesn't mean that every German has.
Textbooks are of very limited use in the real world.
If one learned German from a forty year old textbook the only problem related to that that you would experience in Germany would be that some people would think you were speaking rather more formally than expected. Learning it from an up to date text book isn't going to make you noticeably better at communicating with actual Germans in real life, that takes actual immersion in the language as it is really spoken.
And the German language authorities might well have added a new letter or changed the spelling of the word spagetti but that doesn't mean that every German has.
Textbooks are of very limited use in the real world.
Using a textbook with spellings that disagree with the dictionary in K-12 language education is going to be ... interesting. Not something you'd do if you can avoid it. And the bits talking about the GDR are going to be a bit out of place...
Can you use outdated material? Sure, but that's different than pretending it isn't outdated or that outdated material can't get in the way.
Can you use outdated material? Sure, but that's different than pretending it isn't outdated or that outdated material can't get in the way.
It is laughable to suggest that history does not change. Even studying history at the equivalent of high school had me comparing secondary sources from the 1960s, to the 1990s, to just a couple years prior. History, or rather our interpretation of it, is constantly evolving.
I expect it is the same for most of the humanities.
I expect it is the same for most of the humanities.
> is constantly evolving
Being an amateur historian myself, most of that smacks of political fashion. The (very) shallow view of history taught by K-12 doesn't need to change. The War of 1812 hasn't moved to 1814 yet. Hitler still lost WW2. Edison still invented the first practical lightbulb, despite all the attempts to dethrone him :-)
Being an amateur historian myself, most of that smacks of political fashion. The (very) shallow view of history taught by K-12 doesn't need to change. The War of 1812 hasn't moved to 1814 yet. Hitler still lost WW2. Edison still invented the first practical lightbulb, despite all the attempts to dethrone him :-)
The war of 1812 ended in 1815
Things are usually named by when they start, not end.
Studying history formally isn't about memorising stuff you are interested in. I have a lot of sovietology books now, that doesn't make me a sovietologist because I don't consider myself able to really analyze the sources properly.
Teaching history is not about becoming a historian. Being a professional historian comes with it some standard practices and methods, which is irrelevant if you're not a pro. Though I have learned to not trust "history" books written by journalists, who usually write them because they have a political axe to grind.
As for historical facts, you cannot understand history without knowing any facts about it. For example, you cannot understand the American Revolution without knowing who the major players were and some idea of what their roles were.
BTW, I have an interest in Soviet history. I'm interested in your recommendations on the best books on the topic.
As for historical facts, you cannot understand history without knowing any facts about it. For example, you cannot understand the American Revolution without knowing who the major players were and some idea of what their roles were.
BTW, I have an interest in Soviet history. I'm interested in your recommendations on the best books on the topic.
I have a bunch of EM textbooks from the 40s and 50s on my bookshelves, the field has changed quite a lot i.e. I understand what they are saying, but the mathematical formalism is very obtuse and the applications are often irrelevant outside of the very basics.
The Feynman lectures were recorded prior to the standard model for example, still excellent but hopelessly out of date as an introduction to undergraduate physics in that particular area.
Also, old textbooks that didn't make it to still being in print today may not be out of date but they may be bad pedagogy. A certain percent of everything is crap, textbooks are no different.
The Feynman lectures were recorded prior to the standard model for example, still excellent but hopelessly out of date as an introduction to undergraduate physics in that particular area.
Also, old textbooks that didn't make it to still being in print today may not be out of date but they may be bad pedagogy. A certain percent of everything is crap, textbooks are no different.
My high school didn't teach EM, nothing remotely that advanced.
I thought you meant all textbooks, my bad. If this is just about high school then I mostly agree wrt to the amount of waste.
I think the solution would have to come down from the top however, in the UK at least the way our exams are marked means using an old textbook could be a fairly dangerous affair without an astute teacher (due to the ridiculously anal markschemes and philistine syllabus, this does bite people)
I think the solution would have to come down from the top however, in the UK at least the way our exams are marked means using an old textbook could be a fairly dangerous affair without an astute teacher (due to the ridiculously anal markschemes and philistine syllabus, this does bite people)
Most undergraduate textbooks are still fine. Though I agree that some topics change fast, like electronics beyond basic circuit analysis. Certainly comp-sci :-) Wow has that changed.
> A certain percent of everything is crap, textbooks are no different.
When it comes to classic literature, if you randomly choose a book that is still around after 100 years and randomly choose a book that was written in the last 5 years, odds are the older book will be a better book.
When it comes to classic literature, if you randomly choose a book that is still around after 100 years and randomly choose a book that was written in the last 5 years, odds are the older book will be a better book.
I kept nearly all of my textbooks from college 40 years ago. None of them are outdated. They still fetch high prices used on Amazon.
Here’s a terrible example.
Old textbooks used to use white names. Now, many schools are required to throw out prospective textbooks that don’t have names representing multiple minorities.
Old textbooks used to use white names. Now, many schools are required to throw out prospective textbooks that don’t have names representing multiple minorities.
> Now, many schools are required to [x]
In my experience, this is the sort of thing that, when un-cited often means "a school district somewhere had a proposed or implemented policy that, at its least in its least sympathetic interpretation, would require the school to do [x]" interpreted through a few layers of the outrage commentary telephone game.
In my experience, this is the sort of thing that, when un-cited often means "a school district somewhere had a proposed or implemented policy that, at its least in its least sympathetic interpretation, would require the school to do [x]" interpreted through a few layers of the outrage commentary telephone game.
In other countries textbooks are cheap because (as you say) the subject matter is more or less agreed-upon so there are just a few different textbooks largely distinguished by the quality of the writing and presentation.
In the US students are treated as a captive audience and publishers work hard to get professors and education authorities to specify particular books, which are then sold at a very high mark-up. The incentives ought to be purely academic but in practice are often material or financial.
In the US students are treated as a captive audience and publishers work hard to get professors and education authorities to specify particular books, which are then sold at a very high mark-up. The incentives ought to be purely academic but in practice are often material or financial.
Yeah. I'm not quite sure how it works in the US, but here in the UK we have strong student unions that often have a good relationship with the university whose students they represent. I think any professor attempting this would get shut down pretty quickly.
The word union is anathema to many in the US.
And they make sure to publish new editions with relatively minor changes every few years. Then they sell a Chem 101 text for $175. It's like the price is inverse to the number of readers.
While there are certainly incentive problems and simple cruft in that regard[1]...
Generally, writing textbooks is just hard and nobody really knows how to do it. Textbooks as they are usually understood[2] are, above all, books[3], that is, large flowing pieces of prose that tell a story about an area of knowledge in a generally linear manner.
This is not how knowledge works. At least the way I feel my knowledge is organized when I try to explain things is that I have a sprawling weighted (on a scale from “vague association” to “hard prerequisite”) graph with rather compact ideas as vertices of absolutely enormous degree (at least in regions I feel I have a decent understanding of). Only by several iterations of merciless pruning around the desired generating set can I get a subgraph that is concise enough that I have some hope of explaining it in the available time, parsimonious enough that I can toposort it onto the time axis without people’s heads spinning and stacks overflowing, and comprehensive enough that I don’t feel I’ve given people a horribly skewed impression and don’t risk choosing a perspective so narrow that would fail to engage some of them. Then comes the actual work of (choosing a) linearization, which I can kind of do in my head for stories of no more than a couple hours at the cost of something like 15 minutes of confusion-inducing backtracking per hour, but it gets exponentially harder as you go past these limits, and you have to go pretty far past them to reach good writing. All of these decisions are kind of like those in an optimizing compiler in that they really want to feed into each other, but actually letting them do so would cause the process to come to a grinding halt, so you interate and order and apply vague heuristics and make arbitrary choices and your inner perfectionist hates you the whole time you’re doing it. And you get to do this practically from scratch every single time because the given context and the desired focus are virtually never the same.
You might say at this point that this is what I get for choosing a wire representation (books and more generally stories) so unlike the in-memory representation (graphs of associations). That may be true to some extent[4], but it’s also important to realize that what is best for knowledge storage doesn’t have to be any good for knowledge acquisition[5]. In fact, the omission that bothers me most of the ones I made in the book-writing rant above is that I know of some things that are just so cute and smol sitting in my head, but when I try to get them out I either assume so many prerequisites that there’s nothing to get out or end up staring at a plan for what is at best a terse twenty-page essay I’m never going to write. I wish hard for viable alternatives to linear narrative, but I also realize I haven’t encountered any that were nearly as good or universally applicable. You can certainly point people at a pile of short-form hypertext, but that misses the issue of pruning: doing it effectively requires you to already know things you decide to prune and the general layout of the subject on a level that is, in classroom terms, several years beyond what you are trying to isolate; a learner is incapable of doing this or at the very least is going to waste tremendous amounts of time doing a mediocre job of it. (I certainly did when I was learning maths from Wikipedia.) I don’t mean to denigrate anyone’s intellectual capability here, or even dissuade them from literature surfing. Surfing in moderation is useful and efficient. I’m only saying that the apparently obvious solution of switching out books for a hyperlinked card catalogue fails and fails hard.
Teaching and books are hard and nobody really knows the secret to doing them well, even those who are brilliant at them. There are a lot of arbitrary choices (not really, but heavily reader-dependent, including factors unknowable to the writer or even the reader) involved in making a book. We solve that problem by throwing a lot of them at the audience and seeing what sticks to whom. But that means a perfect book is impossible—not “drink the ocean” impossible, but “draw a round square” impossible[6]. The problem doesn’t even make sense; what’s a perfect book to you can be a hideous book to me, and what’s a perfect book for me right now was an impenetrable book for me ten years ago. There are objectively good books and objectively bad books, but objectively perfect is something a book cannot be.
[1]: Nobody is going to count your Wikibooks contributions towards your tenure; also, Wikibooks and MediaWiki in general managed to find that sweet spot where they’re simultaneously so expressive you can’t reliably process them automatically and so limited they don’t make good self-contained books, neither fixed nor reflowable.
[2]: Let’s say pre-1970—I find modern trends in English-language secondary and basic undergrad texts positively cringeworthy, but I haven’t ever had to use them in either capacity.
[3]: Can’t help but be reminded here of Michele Audin’s deliciously snarky Tautology 2.3.1 from “Conseils aux auteurs des textes mathématiques”, <http://irma.math.unistra.fr/~maudin/newhowto.ps>.
[4]: The only tool or process I’ve found which is even remotely adapted to this data model is TiddlyWiki <https://tiddlywiki.com/>, which I tried, but never could get over its many quirks and primitive organizational features to make it useful even for notes to myself, let alone as an interface with others.
[5]: For example, fluent readers of Latin/Greek/Cyrillic-script languages generally work by recognizing shapes of words on a page, often for several words in parallel, but teaching children or non-Latin/Greek/Cyrillic-literate adults to read this way is a famously useless affair.
[6]: This also means mandatory texts for students and even mandated curricula for teachers are an atrocity which sacrifices a whole lot of adaptation capability for a modest bit of ease in detecting incompetence and bad faith. The more often a curriculum is nailed down to the time axis with tests and metrics the worse it is.
Generally, writing textbooks is just hard and nobody really knows how to do it. Textbooks as they are usually understood[2] are, above all, books[3], that is, large flowing pieces of prose that tell a story about an area of knowledge in a generally linear manner.
This is not how knowledge works. At least the way I feel my knowledge is organized when I try to explain things is that I have a sprawling weighted (on a scale from “vague association” to “hard prerequisite”) graph with rather compact ideas as vertices of absolutely enormous degree (at least in regions I feel I have a decent understanding of). Only by several iterations of merciless pruning around the desired generating set can I get a subgraph that is concise enough that I have some hope of explaining it in the available time, parsimonious enough that I can toposort it onto the time axis without people’s heads spinning and stacks overflowing, and comprehensive enough that I don’t feel I’ve given people a horribly skewed impression and don’t risk choosing a perspective so narrow that would fail to engage some of them. Then comes the actual work of (choosing a) linearization, which I can kind of do in my head for stories of no more than a couple hours at the cost of something like 15 minutes of confusion-inducing backtracking per hour, but it gets exponentially harder as you go past these limits, and you have to go pretty far past them to reach good writing. All of these decisions are kind of like those in an optimizing compiler in that they really want to feed into each other, but actually letting them do so would cause the process to come to a grinding halt, so you interate and order and apply vague heuristics and make arbitrary choices and your inner perfectionist hates you the whole time you’re doing it. And you get to do this practically from scratch every single time because the given context and the desired focus are virtually never the same.
You might say at this point that this is what I get for choosing a wire representation (books and more generally stories) so unlike the in-memory representation (graphs of associations). That may be true to some extent[4], but it’s also important to realize that what is best for knowledge storage doesn’t have to be any good for knowledge acquisition[5]. In fact, the omission that bothers me most of the ones I made in the book-writing rant above is that I know of some things that are just so cute and smol sitting in my head, but when I try to get them out I either assume so many prerequisites that there’s nothing to get out or end up staring at a plan for what is at best a terse twenty-page essay I’m never going to write. I wish hard for viable alternatives to linear narrative, but I also realize I haven’t encountered any that were nearly as good or universally applicable. You can certainly point people at a pile of short-form hypertext, but that misses the issue of pruning: doing it effectively requires you to already know things you decide to prune and the general layout of the subject on a level that is, in classroom terms, several years beyond what you are trying to isolate; a learner is incapable of doing this or at the very least is going to waste tremendous amounts of time doing a mediocre job of it. (I certainly did when I was learning maths from Wikipedia.) I don’t mean to denigrate anyone’s intellectual capability here, or even dissuade them from literature surfing. Surfing in moderation is useful and efficient. I’m only saying that the apparently obvious solution of switching out books for a hyperlinked card catalogue fails and fails hard.
Teaching and books are hard and nobody really knows the secret to doing them well, even those who are brilliant at them. There are a lot of arbitrary choices (not really, but heavily reader-dependent, including factors unknowable to the writer or even the reader) involved in making a book. We solve that problem by throwing a lot of them at the audience and seeing what sticks to whom. But that means a perfect book is impossible—not “drink the ocean” impossible, but “draw a round square” impossible[6]. The problem doesn’t even make sense; what’s a perfect book to you can be a hideous book to me, and what’s a perfect book for me right now was an impenetrable book for me ten years ago. There are objectively good books and objectively bad books, but objectively perfect is something a book cannot be.
[1]: Nobody is going to count your Wikibooks contributions towards your tenure; also, Wikibooks and MediaWiki in general managed to find that sweet spot where they’re simultaneously so expressive you can’t reliably process them automatically and so limited they don’t make good self-contained books, neither fixed nor reflowable.
[2]: Let’s say pre-1970—I find modern trends in English-language secondary and basic undergrad texts positively cringeworthy, but I haven’t ever had to use them in either capacity.
[3]: Can’t help but be reminded here of Michele Audin’s deliciously snarky Tautology 2.3.1 from “Conseils aux auteurs des textes mathématiques”, <http://irma.math.unistra.fr/~maudin/newhowto.ps>.
[4]: The only tool or process I’ve found which is even remotely adapted to this data model is TiddlyWiki <https://tiddlywiki.com/>, which I tried, but never could get over its many quirks and primitive organizational features to make it useful even for notes to myself, let alone as an interface with others.
[5]: For example, fluent readers of Latin/Greek/Cyrillic-script languages generally work by recognizing shapes of words on a page, often for several words in parallel, but teaching children or non-Latin/Greek/Cyrillic-literate adults to read this way is a famously useless affair.
[6]: This also means mandatory texts for students and even mandated curricula for teachers are an atrocity which sacrifices a whole lot of adaptation capability for a modest bit of ease in detecting incompetence and bad faith. The more often a curriculum is nailed down to the time axis with tests and metrics the worse it is.
Finally, re high-school or undergrad “calculus”, I’m tempted to just quote Halmos (one of the foremost expositors of “higher mathematics”—that is, mathematics—of the 20th century) from his classic “How to write mathematics”[1] ...
> [T]here are many books that violate the principle of having something to say by trying to say too many things. Teachers of elementary mathematics in the U.S.A. frequently complain that all calculus books are bad. That is a case in point. Calculus books are bad because there is no such subject as calculus; it is not a subject because it is many subjects. What we call calculus nowadays in the union of a dab of logic and set theory, some axiomatic theory of complete ordered fields, analytic geometry and topology, the latter in both the “general” sense (limits and continuous functions) and the algebraic sense (orientation), real-variable theory properly so called (differentiation), the combinatoric symbol manipulation called formal integration, the first steps of low-dimensional measure theory, some differential geometry, the first steps of the classical analysis of the trigonometric, exponential, and logarithmic functions, and, depending on the space available and the personal inclinations of the author, some cook-book differential equations, elementary mechanics, and a small assortment of applied mathematics. Any one of these is hard to write a good book on; the mixture is impossible.
... But I should probably explain the general picture somewhat for the reader who’s unable to follow the deluge of terminology here.
The problem with calculus, in terms of my parent comment, is that it hasn’t been a singular cluster or clique of ideas in any working mathematician’s association graph since the time of Euler; the list of topics that is presented under that name has never been such—it’s both anachronistically rich in trying to include insights from Weierstrass’s rigour to Tychonoff’s point-set topology and anachronistically poor in avoiding Newton’s motivation from algebraic geometry and differential equations or Euler’s motivation from complex analysis and homotopy theory.
So, if we don’t have a justification from either history or state of the art, why do we insist on this low-resolution camrip of Newton and Leibniz’s writings sprinkled with an arbitrary selection of later work? I don’t know, but I suspect that this is simply the best people could fit into the allotted time when they last tried to incorporate actual, live mathematics into the general curriculum at the beginning of the 20th century, after a hundred years of vulgarization erosion and haphazard contradictory pushes for modernization and practicality.
Why should you even care how mathematicians think now or thought in the past? You don’t have to, of course, though in that case I would much prefer that you avoid diluting the brand “mathematics” by attaching it to the result[2]. But a course should be about something; either you’re teaching mathematics as a matter of culture and way of thought (you sure as hell don’t have time to teach it as a field of study), or you’re reaching for a particular application (but you better know which one, because an applied course left adrift soon becomes a patchwork zombie).
Either way those funny mathematicians in their ivory towers can be of use for you, because they haven’t simply spent all these years playing with impractical abstractions: they broke every subject including old-school calculus into patterns, distilled those patterns into their most elementary possible forms in the form of impractical abstractions, then went back and rearranged their understanding of each subject to make the forms they found more evident, then did it again and again. For decades.
Unfortunately for us lovers of simple answers, their conclusion was, “calculus is not a single thing”. Is there a course or two struggling to come out in the general vicinity so labelled? Yes, but while I have some speculations as to what they are, I don’t have a actual plan—that takes years of regular experimentation with and on classes of real students. It probably includes more varied topics compared to the current approach, certainly some formal series and a glimpse beyond dimension one, probably even a bit of linear algebra as a geometric foundation for it all. (Also a pony while we’re at it.) Should we teach them when combinatorics is infinitely more accessible and probability theory is infinitely more practical? I think so, if not for the cultural significance and life wisdom[3], then because any physics worth speaking of is practically inexpressible without it.
Sorry, I don’t have an answer for you; if I had, it would’ve already been one of those many, many books.
(Took me until the middle of the second of my two answers to realize they both essentially say “Your question is ill-posed” from different points of view; hope they are a bit more helpful than just that.)
[1]: https://www.mathematik.uni-marburg.de/~agricola/material/hal...
[2]: https://www.maa.org/external_archive/devlin/devlin_03_08.htm...
[3]: <https://www.basicbooks.com/titles/jason-wilkes/burn-math-cla...>, <https://www.blackdogandleventhal.com/titles/ben-orlin/change...>
> [T]here are many books that violate the principle of having something to say by trying to say too many things. Teachers of elementary mathematics in the U.S.A. frequently complain that all calculus books are bad. That is a case in point. Calculus books are bad because there is no such subject as calculus; it is not a subject because it is many subjects. What we call calculus nowadays in the union of a dab of logic and set theory, some axiomatic theory of complete ordered fields, analytic geometry and topology, the latter in both the “general” sense (limits and continuous functions) and the algebraic sense (orientation), real-variable theory properly so called (differentiation), the combinatoric symbol manipulation called formal integration, the first steps of low-dimensional measure theory, some differential geometry, the first steps of the classical analysis of the trigonometric, exponential, and logarithmic functions, and, depending on the space available and the personal inclinations of the author, some cook-book differential equations, elementary mechanics, and a small assortment of applied mathematics. Any one of these is hard to write a good book on; the mixture is impossible.
... But I should probably explain the general picture somewhat for the reader who’s unable to follow the deluge of terminology here.
The problem with calculus, in terms of my parent comment, is that it hasn’t been a singular cluster or clique of ideas in any working mathematician’s association graph since the time of Euler; the list of topics that is presented under that name has never been such—it’s both anachronistically rich in trying to include insights from Weierstrass’s rigour to Tychonoff’s point-set topology and anachronistically poor in avoiding Newton’s motivation from algebraic geometry and differential equations or Euler’s motivation from complex analysis and homotopy theory.
So, if we don’t have a justification from either history or state of the art, why do we insist on this low-resolution camrip of Newton and Leibniz’s writings sprinkled with an arbitrary selection of later work? I don’t know, but I suspect that this is simply the best people could fit into the allotted time when they last tried to incorporate actual, live mathematics into the general curriculum at the beginning of the 20th century, after a hundred years of vulgarization erosion and haphazard contradictory pushes for modernization and practicality.
Why should you even care how mathematicians think now or thought in the past? You don’t have to, of course, though in that case I would much prefer that you avoid diluting the brand “mathematics” by attaching it to the result[2]. But a course should be about something; either you’re teaching mathematics as a matter of culture and way of thought (you sure as hell don’t have time to teach it as a field of study), or you’re reaching for a particular application (but you better know which one, because an applied course left adrift soon becomes a patchwork zombie).
Either way those funny mathematicians in their ivory towers can be of use for you, because they haven’t simply spent all these years playing with impractical abstractions: they broke every subject including old-school calculus into patterns, distilled those patterns into their most elementary possible forms in the form of impractical abstractions, then went back and rearranged their understanding of each subject to make the forms they found more evident, then did it again and again. For decades.
Unfortunately for us lovers of simple answers, their conclusion was, “calculus is not a single thing”. Is there a course or two struggling to come out in the general vicinity so labelled? Yes, but while I have some speculations as to what they are, I don’t have a actual plan—that takes years of regular experimentation with and on classes of real students. It probably includes more varied topics compared to the current approach, certainly some formal series and a glimpse beyond dimension one, probably even a bit of linear algebra as a geometric foundation for it all. (Also a pony while we’re at it.) Should we teach them when combinatorics is infinitely more accessible and probability theory is infinitely more practical? I think so, if not for the cultural significance and life wisdom[3], then because any physics worth speaking of is practically inexpressible without it.
Sorry, I don’t have an answer for you; if I had, it would’ve already been one of those many, many books.
(Took me until the middle of the second of my two answers to realize they both essentially say “Your question is ill-posed” from different points of view; hope they are a bit more helpful than just that.)
[1]: https://www.mathematik.uni-marburg.de/~agricola/material/hal...
[2]: https://www.maa.org/external_archive/devlin/devlin_03_08.htm...
[3]: <https://www.basicbooks.com/titles/jason-wilkes/burn-math-cla...>, <https://www.blackdogandleventhal.com/titles/ben-orlin/change...>
There is a lot of knowledge where the world would benefit from a basic level of open ubiquity and the participation of experts who might be incented to contribute in a manner similar to Wikipedia.
Here are two publishers releasing in the open:
https://www.openintro.org/
https://openstax.org/
Here are two publishers releasing in the open:
https://www.openintro.org/
https://openstax.org/
This is pretty interesting. You should also consider cross-posting this request in other teaching communities, for example:
https://www.reddit.com/r/teachingresources/
https://www.reddit.com/r/edtech/
https://www.reddit.com/r/matheducation/
https://www.reddit.com/r/ScienceTeachers/
https://www.reddit.com/r/CSEducation/
https://www.reddit.com/r/highereducation/
https://www.reddit.com/r/teachingresources/
https://www.reddit.com/r/edtech/
https://www.reddit.com/r/matheducation/
https://www.reddit.com/r/ScienceTeachers/
https://www.reddit.com/r/CSEducation/
https://www.reddit.com/r/highereducation/
We use openstax currently in our AP Biology class. It's incredible to not have to scroll through a scanned PDF for an obscure 2010 textbook. In addition, the questions that we are assigned are completely unique so I don't believe that this will contribute to the (very pervasive) problem of cheating.
I donated to Openstax as well: https://riceconnect.rice.edu/donation/support-openstax
I donated to Openstax as well: https://riceconnect.rice.edu/donation/support-openstax
It would be nice to have this thread as a "collection" place for different open textbooks. I personally use OpenStacks, they're quite good. https://openstax.org/
This is my favorite text on electronics, open or otherwise: https://www.ibiblio.org/kuphaldt/electricCircuits/
The explanation of impedance (volume II, chapter 14) was the first one that made intuitive sense to me, after struggling with the concept for years. The whole thing is beautiful, but that chapter especially.
The explanation of impedance (volume II, chapter 14) was the first one that made intuitive sense to me, after struggling with the concept for years. The whole thing is beautiful, but that chapter especially.
The thing that disappoints me about Openstax is that, while they're free/libre, they don't seem to be open source anymore. They used to provide access to the raw XML (CNXML) used to generate the books, but I can't find that anywhere.
It would be nice if there was something like OpenStax, maybe even a fork of it, that could be held in a Git repo and anyone could make pull requests.
It would be nice if there was something like OpenStax, maybe even a fork of it, that could be held in a Git repo and anyone could make pull requests.
It looks like they're transitioning/have transitioned to editing the books with Google Docs:
https://openstax.org/blog/saying-goodbye-cnx
https://openstax.org/blog/saying-goodbye-cnx
I highly recommend Interactive Linear Algebra for learning undergrad-level linear algebra mostly in the R^N. It has a PDF version available, but the real magic is in the interactive embedded 2D and 3D visualizations.
There's a couple of variations available - it was written by some professors at Georgia Tech, one of which moved to Duke and teaches off of it there - but the UBC version is my favorite, as it makes some changes in the lesson order to teach vectors before matrices.
https://www.math.ubc.ca/~tbjw/ila
There's a couple of variations available - it was written by some professors at Georgia Tech, one of which moved to Duke and teaches off of it there - but the UBC version is my favorite, as it makes some changes in the lesson order to teach vectors before matrices.
https://www.math.ubc.ca/~tbjw/ila
Openstax is the best source of extremely high-quality alt descriptions I've ever found.
If you need inspiration for good alt descriptions of STEM / computer science / software engineering related images, just look at how Openstax does it. I'm a screen reader user myself and I'm very impressed.
If you need inspiration for good alt descriptions of STEM / computer science / software engineering related images, just look at how Openstax does it. I'm a screen reader user myself and I'm very impressed.
Oh, I had never thought about this. Thanks, shall see what I can do. I never thought the latex source would make any sense to anyone but me
When I publish my book, I will also publish the source. Knowledge is universal. Praise all the authors who release their sources.
I publish all my code these days as Open Source.
not about the subjects that you mention, but if you ever need to learn probability and inference, this is easily among the best books on the subject: http://www.inference.org.uk/mackay/itila/book.html
if you read the latex source, there are even some easter eggs in the comments
if you read the latex source, there are even some easter eggs in the comments
Could a equation OCR system like [1] be combined with a screen reader? It seems to support asciimath
[1]: https://mathpix.com/ocr
[1]: https://mathpix.com/ocr
this looks interesting, and I think would be perfect for the kind of stuff I deal with. Unfortunately, the pricing looks less interesting (about $100 for a 1000 page pdf, if I'm reading it right, although possibly I could attempt to break the pdf up into pages which have the math). There was an older solution for this which costs about $200 as a whole.
Stuff like this exists, and is possibly pretty reasonable monetarily, but not being in the U.S., exchange rates hit me hard.
I've bookmarked this and will look into this more, though, thanks!
Stuff like this exists, and is possibly pretty reasonable monetarily, but not being in the U.S., exchange rates hit me hard.
I've bookmarked this and will look into this more, though, thanks!
There is an option for 5000 snips per month for $5. If you annotate the pdf every time you convert to latex, it should be much cheaper
Many books/websites let you view the Latex code, despite not technically being open source. If a website uses MathJax, you can change the renderer to "plain source" by opening the context menu on any math equation. "Paul's Math notes"[1] is a good example, and a really great free website for college-level math.
If you're a screen reader user, the context menu may not open for reasons unknown. Try routing your mouse to the equation and simulate a right mouse click, that should do it. Moving your focus to the equation with the tab key may also be an option. Alternatively, you can just use Voice Over for MacOS, it can do it just fine.
If you're a screen reader user, the context menu may not open for reasons unknown. Try routing your mouse to the equation and simulate a right mouse click, that should do it. Moving your focus to the equation with the tab key may also be an option. Alternatively, you can just use Voice Over for MacOS, it can do it just fine.
Yup, I have been using this extensively. Paul's notes are something I forgot to mention-I referred to them almost daily, back when I was taking the equivalent of Calculus 1, and they're still very useful now that I'm taking differential equations.
Unfortunately, this doesn't quite work on OpenStax-I can't get LaTeX, all I can get is MathML, and that's not very easy to read. There's a way to navigate the math (using something called mathplayer), but it's quite inefficient as compared to LaTeX, specially as I go into higher math. The books are still very, very good, though.
Unfortunately, this doesn't quite work on OpenStax-I can't get LaTeX, all I can get is MathML, and that's not very easy to read. There's a way to navigate the math (using something called mathplayer), but it's quite inefficient as compared to LaTeX, specially as I go into higher math. The books are still very, very good, though.
Try playing with Mathjax's own accessibility settings. Not sure how well that works on Openstax, will work well if they're using Mathjax 3, badly otherwise.
Alternatively play with MathPlayer's settings (in the control panel), some of the other reading modes work better in certain contexts.
If you can, also try VoiceOver on the Mac, it has its own math support, which works pretty well.
We seem to be in similar situations, if you want to share tips or something, my hn username at gmail dot com.
Alternatively play with MathPlayer's settings (in the control panel), some of the other reading modes work better in certain contexts.
If you can, also try VoiceOver on the Mac, it has its own math support, which works pretty well.
We seem to be in similar situations, if you want to share tips or something, my hn username at gmail dot com.
I would like to add only a link to a public organization that is working on the problem. Have a look here https://www.fondazionelia.org/en/
I remember seeing a (trained) image-to-text approach that claimed to translate scanned math equations to latex sourcecode. Might be 3-4 weeks ago here on HN.
jeff erickson's 'algorithms, etc.' is the textbook for our university's algo class. it's brilliant.
in case, link: https://jeffe.cs.illinois.edu/teaching/algorithms/
in case, link: https://jeffe.cs.illinois.edu/teaching/algorithms/
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Have you tried any epubs with MathML? If so how do they compare?
As a person who has to use a Screen Reader, math in PDFs is almost impossible to read for me. The problem is almost insurmountable if the PDF is a collection of images, but even if it is a LaTeX-generated PDF, reading anything but the simplest of equations is very, very hard. In these cases, having the LaTeX source to read is a godsend.
To the authors who publish the source of their books: thank you, thank you. I cannot express how grateful I am. To anyone who is related to /working in the publisher space: it would be incredibly useful if there was a process to get the LaTeX source of books upon request, although I understand how copyrights/etc might make this difficult.
Some other books I would like to point out for being open source: Apex Calculus, Open Data Structures.