Slashdot Mirror
Math Textbooks a Textbook Example of Bad Textbooks
theodp writes "Over at Salon, Annie Keeghan does an Upton Sinclair number on the math textbook industry. In recent years, Keeghan explains, math has become the subject du jour due to government initiatives and efforts to raise the rankings of lagging U.S. students. But with state and local budgets constrained, math textbook publishers competing for fewer available dollars are rushing their products to market before their competitors, resulting in product that in many instances is inherently, tragically flawed. Keeghan writes: 'There may be a reason you can't figure out some of those math problems in your son or daughter's math text and it might have nothing at all to do with you. That math homework you're trying to help your child muddle through might include problems with no possible solution. It could be that key information or steps are missing, that the problem involves a concept your child hasn't yet been introduced to, or that the math problem is structurally unsound for a host of other reasons.' The comments on Keeghan's article are also an eye-opener — here's a sample: 'Sales and marketing budgets are astronomical because the expenses pay off more than investments in product. Sadly, most teachers are not curriculum experts and are swayed by the surface pitches. Teachers make the decisions, but are not the users (students) nor are they spending their own money. As a result, products that make their lives easier and that come with free meals and gifts are the most successful.' So, can open source or competitions build better math textbooks?"
Entire exams have been ruined by incorrect questions. Apparently, reading and writing is not a hard requirement for being a mathematician.
Syllable : It's an Operating System
A great book, "Lies My Teacher Told Me" details the history textbook situation which is pretty bad too.
'Sales and marketing budgets are astronomical because the expenses pay off more than investments in product.'
Ah, so textbooks are the same as 'enterprise' software then...
HOORAY FOR AMERICA... Cultivating a nation of retards and morons. LETS HEAR IT FOR OUR CAPITALISTIC EDUCATION SYSTEM.... Pushes the red button. *Instead of a nuclear explosion, we hear another speach of gaseous substance from out president condoning the practices of quantity over quality"
This issue is found with all textbooks, and has always been a problem. Even in the 70s and 80s, pretty much every textbook I used in high school and university had mistakes, omissions, and unsolvable chapter-problems.
The difficulty with learning maths and sciences stems from the fact that they tend to deal with abstract concepts, procedures, and algorithms for performing mathematical calculations. In the age of calculators and instant-gratification web searches, not only aren't students willing to put in the time to learn "how" to do something, they aren't even interested in learning "why" they should do something.
Instead, they point to their computers and the web as being able to do the work for them, and question the sanity of learning "the old way" of doing things. If the only purpose of an education was to prepare people for the workforce, I'd agree with them -- but the point of an education is to learn how to learn, how to interpret, and how to understand material. An education isn't about the facts taught, but about the learning process that prepares you for a lifetime of learning as you deal with new technologies, products, and ideas during your time on this planet.
I do not fail; I succeed at finding out what does not work.
Its not like Math changes every year. The text book industry and publishers are just ripping students off every year. If they would just publish one edition of their text books, we wouldn't have this problem.
Bad title a titular example of bad titles.
I'm on my way out of teaching math, and the school I'm in doesn't have enough textbooks for the students to take them home at night. Which to my mind kind of defeats the purpose of having them in the first place. A lot of my learning in math class happened as I was struggling through the homework trying to make connections between the solution in the back of the book, the notes I had taken, the problem, and the worked examples in the textbook. To take two of those away, even if they're bad at times is just criminal.
At least the children (and possibly, their parents) will learn how to solve unsolveable problems.
Engineering Mathematics by K.A. Stroud.
Ken was my maths lecturer when I did my Engineering Degree at Lanchester Poly in the 1970's. I have a well thumbed signed 1st Edition.
Feynman wrote about the problems with textbooks and textbook selection in the 60s. Sadly, I don't think much has changed. It might have gotten worse. I do hope that open source textbooks and book readers might help, eventually, if we can prevent the systems from perpetuating textbooks as revenue generation first and teaching aids second.
Math perhaps but anything with any political aspect will be fought over, i.e. Texas re-writing history textbooks in an effort to lesson the constitutional barriers of separation of church and state.
http://www.washingtonpost.com/wp-dyn/content/article/2010/03/17/AR2010031700560.html
http://www.nytimes.com/2010/03/13/education/13texas.html
blindly antisocialist = antisocial
1. Life of Fred 2. Singapore 3. If you're going to go the traditional route, at least get people who know the subject and teach them to teach, instead of putting people who don't know the subject in front of the kids. Then the textbooks would matter less anyway.
-- Two men say they're Jesus. One of them must be wrong. - Dire Straits
If you can't even figure out that you can't figure out a problem - because there is something wrong with the problem - then you didn't understand what math is all about. Hint: It's not about rote memorization of solution recipes.
Slashdot Subjects the Subject of Bad Slashdot Subjects
Does this remind anyone of the saga recounted in Feynman's "Surely You're Joking, Mr. Feynman!" - reproduced here
Things don't change.
....as a former math teacher, I can assure you that teachers rarely get to make the purchasing decisions regarding textbooks. Teachers, even most rookies, can tell when a textbook is bad, but have to use what they are given for the most part. They are free to supplement the curriculum with their own created content, but of course they are expected to mostly teach the state standards with the given textbooks.
When I couldn't help my children solve "What is 1 + 1?" because the answer is "3". God bless America.
products that make their lives easier and that come with free meals and gifts are the most successful
Why are companies allowed to get away with bribing teachers into choosing their textbook? This article seems to be focused on K-12. So in the US at least, in many cases the money for those textbooks is public money. How is this any different than bribing an elected official to give your company a contract?
My son's elementary school uses "Math Investigations" which is part of that "new math". You know, the type that believes that it isn't necessary to learn multiplication tables, or that your really only need to learn a few fractions: 1/2 1/3 1/4 and that is it. Oh yeah, and you shouldn't "stack" numbers while adding. He doesn't have a text book. He only brings home photocopied worksheets.
I complained to the teacher. They referred me to the principal who referred me to the district's elementary math education supervisor. Long story short, when schools say they want parents involved, they are lying. That is the last thing that they want. They want you to chaperone field trips. They want you to help fund raise. But when you want to actually input on the fundamentals of education, they shut you out. Even though you might have been a physics major and tutor, and brought peer reviewed research sponsored by the Department of Education pointing out that their particular math curricula has students score lower on standardized tests they imply that you don't know what you are talking about.
Reading what Richard Feynman said about the way Maths textbooks are written and selected is so depressing. Not only would the questions be better proofread if more people had imput, but they could be put in a kind of a context that might make kids who have the potential to love maths actually see the point in it, and how it's like a game and a set of puzzles. Not just a bunch of meaningless formulae that you have to work through like a chimpanzee.
Investors valued Yelp restaurant and other reviews at $1.47B. How much is being spent on textbook reviews?
"It could be that key information or steps are missing, that the problem involves a concept your child hasn't yet been introduced to, or that the math problem is structurally unsound for a host of other reasons.' The comments on Keeghan's article are also an eye-opener "
Let's find out!
The real problem is the complete lack of qualified teacher's. A teacher needs to be a true master of all subjects so regardless of a text book the teachers should work with numbers like a mathematician. Bad text books can be overcome by excellent teaching and from what I remember my teachers were jokes. Don't blame the text books blame the unqualified teacher's.
At one point he was invited to sit on the committee that chose which textbooks to use for the California school system. He was unhappy with every single book he reviewed and made copious notes that he brought to the committee meeting.
It turned out that basically nobody else on the committee bothered doing more than skimming through the books, and in one case a book that hadn't even been written yet got a good score, something like 7 out of ten -- it was part of a 3-book series and it got slightly better scores than the two that were actually available to review!
PS: It's not "most teachers". Most teachers don't get any input into which books their district (hell, their state[1]) uses. That was a cheap dig, and politically motivated; OP is contemptible.
[1] Lots of states will just use whatever California uses, or whatever Texas uses.
Hail Eris, full of mischief...
E pluribus sanguinem
Keeghan doesn't name names and doesn't give any examples. She just panders to populist "This Is What's Wrong with America" notions. She's too close to the industry to actually write an exposé, much less offer any proposal for overturning the status quo. Her article comes off as a nostalgia piece for the mythical "good old days" of textbook publishing, where her career started. Any comparison to Upton Sinclair is unwarranted.
As someone whose published works have benefited from the collaboration with an outstanding editor, I feel for all the editors and writers out their that care about their craft. A writer creates a raw product, a good editor turns it into a work of art. When my editor was let go due to "financial constraints" I realized that the publication has begun the death spiral; and made sure my editor and I stayed in touch so I we could work together at some point in the future.
I'm a consultant - I convert gibberish into cash-flow.
Years back, I remember working through some of those SAT prep books for the math section. Seemed like every one of them had at least one error in the solutions, with Barron's seeming the best and stuff like Kaplan's having many mistakes. Well, obviously I was bored, so when my answer didn't agree with theirs, I wrote proofs proving their answer was wrong.
From a commenter: "The Internet is going to change textbooks forever. When retired Ph.D.'s in physics and mathematics and chemistry and biology can write a book and publish it online - without help from today's publishers - students win, elementary schools win, middle schools win, high schools win, colleges win."
I think part of the problem also is the ridiculous requirements put into textbooks by some of the states. Some locales have required multiculturalism parts of classes, even something like elementary school math, which should be pretty much a fact based class.
I live in Illinois, and I know my children's books are not up to the level of what I had 30 years ago. The books seem scatter brained with forced examples of what the states want put into the books. Also, the forced lack of focus on the fundamentals has gone a long way towards lowering the ability of students from the US to compete in a global academic environment, especially in the sciences and computer fields. Another item is what is wrong with timed drills, and letting students know that the world is not equal and that some people are better and faster in math than others. Welcome to the real world! I am not saying advertise who is the best, but don't stop doing timed tests and drills because some helicopter parent is complaining that their snowflake did not get the highest possible score. A friend of mine is a former principal at an elementary school, and he said that the biggest number of complaints he had were from parents who thought that it was traumatic for their children to not be able to complete timed math fundamentals tests.
Yes, the textbook manufacturers are sleazy and always trying to sell the new latest greatest edition, but don't forget some of the ever changing junk they have to put in to make the politicians happy in the big states (thank-you California and Texas). Let the experts decide what needs to be in an effective textbook, not the politicians.
My wife used to teach an Intro to Anthropology course (among others) and each year was a new textbook, which she would get a week before class started in Sept. Towards the end of her teaching career, the textbooks were less complete than the previous year and each book came with links to a publisher's website of 'supplemental material' which was the stuff that was missing plus some videos and flash demos... The links were embedded throughout the book. At the end of that school year, the website 'expired' making that textbook useless to be replaced by the current years' textbook and corresponding website. Pure evil.
In addition, there were lots of errors in the chapters causing my wife to have to spend a great deal of time fact checking each lesson plan against the book.. Eventually, she stopped simply telling the students about the errors and issued a challenge for students to identify the errors in the book, and then next class they would discuss the chapter focusing on the errors... It turned into a great teaching tool while simultaneously demonstrating to students not to believe everything they read.
1. A key part of any good text is the flow - how do chapters interrelate and build on each other, i.e. what is the story line? That needs an editor in charge that makes and enforces decisions; something noticeably absent from most OS products.
2. The people with the most knowledge are often the worst to have explain a concept - things that are initiative and simple may be obscure and hard to understand for a student. Writing a good text book means actually explaining stuff in enough detail for the reader to understand, and putting in stuff you think everyone would know when in fact they don't.
Even with simple concepts there are often multiple ways to obtain the same solution - do you put them all in; if not how do you decide which ones to include?
At least with math, if you avoid any historical context you can avoid some of the challenges that history text books would have, for example, with political and social views and arguments thereover.
I'm a consultant - I convert gibberish into cash-flow.
Why not go back to the math textbooks and curriculum that taught the men who put men on the moon? If the math was solid then, why is it not now? Do we have a new way to solve the problems now then we did back in the 30's and 40's? If high school still requires you to read books written in the 1800's, how is a literature textbook published today talking about it different then one from 1940? Is it not PC to use a textbook from that era? If the US was the leader in education then, go back to that type of education. This does not mean back to segregation in the school system. Other then the hard sciences were new discoveries can change the rules, why do the basic textbooks change that much?
I teach at the elementary level. I’ve pilot tested several textbooks in several curriculums. After using many publishers’ products, I’ve got a feel for what works well for me, and what materials I need. But what’s most important is how well the students work with the materials. If the students struggle with a pilot curriculum due to poor presentation, then that curriculum isn’t going to get my vote. And if there are mistakes in the materials, the sales rep is going to get an earful from me, but not my business (I hope).
There are always going to be typos and problems like that with text books. If that was the main problem with textbooks that would be something that could be fixed with errata.
. I taught 5th grade math in the Washington DC area for 2 years and avoided textbooks (for all subjects) as much as possible. Kids learn math by doing math and making it relevant. Same with reading, and spelling.
Really parents and (American) society's attitude towards math is to blame in large part. PARENTS: teach your kids math--tell them that you love it--or at least point out how often you need it. Stop making the education of your kids completely the responsibility of the school system. There are so many kids who aren't being properly prepared for school, whose parents don't think education is valuable.
I wonder if part of the reason teachers don't get paid a whole lot is because they produce an inferior end product? Why don't their unions enforce a higher standard, therefore justifying an increase in pay?
I know they could all just walk out at any time, leaving the nation's children uneducated, but then I suppose parents would start educating their own children. And if they did that, how could you justify taxing them? The system is flawed.
I had a organic chemistry text book that had a similar problems. I remember one question where it asked a question that you had to know about aromaticity. That would have been ok except aromaticity wouldn't be introduced for another 2 chapters. (The only reason I knew about it was I had read ahead a few chapters before looking at that problem in the text.) Come to think of it they also introduced resonance structures as the very first concept then proceeded to completely ignore the concept. (It only came up at the beginning of my orgo II class. Why they didn't move introducing the concept to right before it was going to be used instead of where they did and everybody forgot about it I'll never know.)
Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge.
Maybe the government could hold a competition and offer $10,000 in prizes for the best textbooks?
Remember how your college profs often seemed to be pushing the textbooks that they wrote - or at least co-authored? When the person teaching the course is also the person who wrote the text, you have accountability right in front of your for the quality of the text.
Now, obviously not every elementary, middle, or high school math teacher could or should write a math textbook. But if the books were actually written by teachers who are actively involved in teaching math, you could end up with a better product. It also improves subsequent versions as feedback from students on the text would be going to the author of the same.
Instead our current system favors a company that has little actual investment in the learning process writing the textbook, primarily competing only on cost with other companies who are trying for the same market. Houghton-Mifflin and others don't actually care that much about what the students actually learn, they just want to make money. And anyone who enters education only to make money isn't doing anyone a favor.
Damn_registrars has no butt-hole. Damn_registrars has no use for a butt-hole.
Emphasis added by yours truly.
I think that one paragraph sums up so many problems with the world today.
There have always been and will always be errors in text books. It seems the problem here is the teachers. If the teachers have already worked out the problems before they are assigned, they will know which ones have errors, and they'll be able to warn the students up front.
Inaccurate, incomplete, contradictory and poorly stated data and questions are par for the course.
Maybe it's a good thing for students to be exposed to some poorly worded and insoluble problems in their education.
Khan Academy
No, this ain't no "in soviet Russia" joke, though it could be I guess.
The best math textbooks I saw were the old soviet math school textbooks. They had one (1) textbook for a given grade for the entire country. It was the same book, with minimal adaptations and changes year after year. These books covered science without any "added sugar" - and they worked. Of course, none of that exists anymore - but that's a whole another story.
In any case, this is one field where open source and competition will likely result in more of what we already have. Central planning fails at delivering consumer goods and services, but it worked quite well delivering scientific education.
"That math homework you're trying to help your child muddle through might include problems with no possible solution. It could be that key information or steps are missing, that the problem involves a concept your child hasn't yet been introduced to, or that the math problem is structurally unsound for a host of other reasons."
That sounds a lot like the Langdellian case method we legal types are subjected to in law school.
Badly-written problems, like badly-written court opinions (Dred Scott would be a good examplar) can often be the best teaching opportunities. If a student can understand why a problem is unsolvable and be able to articulate the reasons, he or she will have come to a much higher-level understanding of the underlying operations involved than he or she would by simply crunching a perfectly set up problem.
It's still shameful that textbook publishers put so little effort into editing, but a resourceful teacher who can spot the flaws will not be at a loss for highly teachable moments.
i wonder how ebooks will play into this. if the new edition is merely bug fixes, should there even be an upgrade cost?
...
Guess who was the first man on the moon according to one of *my* textbooks (written by a teacher- no, not in the US).
Louis Armstrong.
Absolutely brillant.
Visit http://ringbreak.dnd.utwente.nl/~mrjb/growingbettersoftware to download your free copy of the book
Arthur Benjamin has an interesting TED talk suggesting that having our main math tract lead to calculus as the end point for most students is a mistake. He argues that statistics should be the targeted end point. As beautiful as the calculus is, I have to admit that our society makes more collective errors due to the public not understating statistics than not understanding derivatives.
Another great example of the current prevalent MBA driven short sighted corporate culture that we all know and love. There is a good reason why some industries should not be profit driven. Also who are those damn teachers that buy that crap?
Not related but good reading, "Retirement Heist: How Companies Plunder and Profit from the Nest Eggs of American Workers" http://www.npr.org/2011/09/29/140344871/retirement-heist-how-firms-trimmed-pensions
Teachers don't make the decisions, do they? I can't tell you how many times my mother (an elementary teacher) has come home irritated because the administration has chosen a new book which either sucks or is worse than the current book that she thinks she could still use. We were going over her new language arts book the other day and she was getting more and more upset as she flipped through the pages. She was supposed to be teaching grammar and she had to get a good 150 pages in before there was finally a portion on grammar. She'll work around it, of course, but it's so irritating that they spent all that money on new books that don't work with the curriculum.
My current Statistics Professor at University of Maryland, John Millson, regularly expresses his distaste for our textbook. He says that he is in the middle of writing a free online textbook but it is extremely difficult because he has to make the sample problems and the writing style significantly different from ALL textbooks he has ever used in a class. Otherwise, one of the publishers will sue him for copyright infringement.
So, can open source or competitions build better math textbooks?
There's no reason to write another Calculus book. This one covered the subject as well as it can be covered: Calculus Made Easy
The elementary math textbooks I had to slog through in grade school 30 years ago were apparently written by people whose first language was gibberish. It didn't help any that most of the (all public school) teachers didn't understand the concepts themselves at least half the time.
First off, anyone making comments on college or higher level math in this thread did not RTFA - its about kiddies, not college kids. K-8.
So why are we even talking about such stupidity? Has the "math" taught to K-8 today suddenly changed from.. 10 years ago? 30? 100? 300? Hmm.. lets see.. add, subtract, multiply, divide. Fractions. Percentages (same thing). "Word" problems. Maybe a touch of very very simple geomentry.
There is no need for a new mathbook for these kids. In fact, they would probably best be taught by grabbing one which was used in the 1920s or 1950s. Just wondering.. can your grandparents (or in some cases, if alive - great grandparents) add, subtract, multiply and divide? Or were the books and teaching "methods" just so atrocious back then that everybody ended up a dolt? Whats that? test scores ahve declined! Well maybe going back to what was used when the scores were higher might be a better thing to do? When in a hole the first thing to do is stop digging!
Bottom line: nannyism. school boards ptas publishers state and federal governemnt alll trying to find ways to justify their existence by fucking up what already worked quite well.
I don't know why anybody is outraged that the sales guy's commission is higher than the author's royalties. This is pretty standard in the intellectual-property industry, and not necessarily out of line with any idea of "fairness." (Authors, artists, screenwriters, etc. have always received the smallest cut of revenue in the IP industry.)
A huge textbook publisher like Harcourt might only have two or three series of elementary-school math textbooks which are then sold to the entire country. The textbooks only have to be written once, and then used for many years (maybe subject to minor revisions.) Meanwhile, selling those textbooks is going to require a lot more sales guys than it is textbook authors. Each textbook salesman is going to sell only a small portion of the production run of the book so it make sense that, in order to make a living, they are going to need a bigger cut of the sales than the author.
Lastly, if the author you want is satisfied with the royalties you are offering, why should you pay him/her more? It's not as if there is some acute shortage of people capable of writing down the precepts of basic arithmetic.
The advantage of open sourcing K-12 textbooks is that when schools finally go digital, they'll save a great deal of money per student. Free books = more educational money to go elsewhere. Also open sourced K-12 textbooks means you can buy kids in 3rd world countries a laptop through OLPC, and they'll have a chance at a first world education. Textbooks are just the beginning, I think all sorts of tutor software could be used too. People think it would be great for when we get Artificial Intelligence that it can teach our children, but we could make a software suite to help do it now.
God spoke to me
I was going over some grade 10 math with my daughter. The questions in the book covered transformations of parabolas. Something I haven't touched in a dogs age. So I leaf through the textbook for how to do it. Nada, nothing, not a word. There were a few factoids about parabolas being used in satellite dishes and that was it. None of the formula needed or even a hint of how to solve the problems in the book. Online I had the method in 30 seconds.
Then there were many questions that were obviously written by English majors. "Draw all the different ways that 10 people could put on 8 different shirts." First is that 10 people sharing 8 shirts? Or 8 shirts per person? The first has quite a few different possibilities that would take quite a while to draw but the second is just absurd.
What bothers me is that there are so many great math books out there, "Jenny Olive's Student Survival Guide." "Mathematics for the millions" "Basic Math" "Calculus made Easy" and then the Great Courses people have some awesome lecture series; Why not have the teacher show those and then take questions?
One complaint that I have with all the textbooks is that they are based on really low expectations. The school board says we will cover this tiny portion of the mathematical body of knowledge and then the textbook stretches out what should be taught in a week or two into an entire year's effort. To use Jenny Olive's book as a text book you could go from basic algebra to calculus in 500 pages. That could be fit into junior high no problem. Or "Mathematics Describing the Real World: Precalculus and Trigonometry" by the Great Courses people is 36 lectures. So say one a week for the school year and you are ready to start calculus which that same guy covers in his next 36 lectures. If there are some students who fall behind, then you let them work at their own speed watching the lectures, working on the problems, and asking questions. There is no rule saying the whole class has to be on the same page.
That's news to me. Last I heard (at least in America) textbook selection goes like this: The state selects a handful of textbooks from which to choose, that list is given to local school administrators, who either present a smaller list for teachers to vote on or simply make the choice themselves. Teachers typical are given 2-4 textbooks to choose from, and have perhaps a month to review those textbooks on top of their normal teaching duties.
There are some good math texts out there. Art of Problem Solving http://www.artofproblemsolving.com/ has written a number of math text books. We homeschool, and after looking at *many* curricula chose AoPS for the spine of our daughter's math education. AoPS isn't aimed at homeschoolers -- it is aimed at kids in regular school who are not well served there. The texts are excellent, IMO. The online lecture meets once per week in a chatroom -- no video, no audio, but it *does* support direct entry of LaTeX. My daughter has thrived on it -- she is 12 years old and preparing for the AP Calc this spring (now you know why we homeschool).
The AoPS texts are available at a reasonable cost to anyone and I highly recommend them. The online classes move at a very rapid pace -- they are not for everybody. But you can take the text books at your own pace and get a great math education.
Another good set of online math lectures are put out by ThinkWell http://www.thinkwell.com/ -- the math lectures by Dr. Ed. Burger are outstanding. Burger is the math teacher you wish you had. These are not live, ThinkWell uses recorded videos. Very good and very reasonable priced.
Online classes are changing the world. Clayton Christensen (author of Innovator's Dilemma) wrote a book "Disrupting Class" about how online classes are causing a classic disruptive innovation in the world of education. I recommend it. If the world follows his time line, soon schools as we know them will go the way of the dinosaurs. About time.
Since I went through that in higher ed. I mean I had that more than once at university. At in at least one case the professor was basically incompetent.(IE couldn't write a proper test that generated a nice curve, couldn't answer questions in class even though he was the world authority on his branch of philosphy.) However he wrote "THE" text book on his subject matter but that made no difference. You couldn't get accountability because he was just so damn awful. (He was only kept around because he was a bigwig in philosophy and was considered a prime catch. So much so my CS professor knew of him and his rep. Of course my prof had no idea how truely incompetent an educator this guy really was.)
Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge.
More and more US schools are using math books from Singapore with some districts importing the teachers as well. http://www.nytimes.com/2010/10/01/education/01math.html?_r=1
"The average reporter we talk to is 27 years old......They literally know nothing." - Ben Rhodes
Unless these kids are getting PhDs, the same books that we used in the 80s to teach 3rd-8th grade math will suffice. Have any new discoveries been made in math for this grade level?
This is typical government bullshit. We shouldn't be buying them at all.
Back in the '60's and '70's I tutored Juniors, Seniors and Grad Students in Math and Physics. My secret weapon was "programmed instruction" books. People who hadn't done a lick of work all quarter would come to me and say, "I need a miracle." OK, I would assign them a programmed instruction course that covered the material they needed. Programmed instruction courses tend to be large volumes, but they typically take from 1/3 to 1/6 as long to finish as comparably-sized standard text. Furthermore, good programmed instruction was statistically tested so that there was 97% correctness and competency from frame-to-frame and to the overall content of the course.
Programmed instruction courses are few and far between now. Two long-lived examples are the Blumenthal English series (English 2200, 2600, 3200) and Ken Stroud's books on Engineering Mathematics. I attribute the decline in programmed instruction to a number of factors:
First, it worked, and it worked well without teachers. (God knows what would happen if the world found out that you didn't need teachers to learn! Why, we might have computers and parents teaching our kids!) Like I said, competency was statistically designed in for 97% success.
Second, it was based on research by B. F. Skinner and Norman Crowder. B. F. Skinner became controversial and his work was denigrated even though most of it was very sound. (Maybe Academics should stay away from expressing controversial opinions, but then what good does Education and Research give back to Society if you're afraid to let it loose?)
Third, Good programmed instruction is time-consuming and expensive up front. Not only is there writing and planning, but there are numerous tests and revisions to achieve that 97% competency. Computer projects and teaching machines used programmed instruction at a time when computers were VERY expensive. Control Data's Plato project was very successful for a long time. CBT today is a joke; it mostly reproduces classroom demogougery. However, there are a few programs like the web-based Logic Cafe http://thelogiccafe.net/PLI/ which show the possibilities of programmed instruction on the Web. It would certainly be easier to gather statistics and make adjustments to individual frames using a web-based programmed instruction format.
Fourth, programmed instruction is possibly not suited to every subject. My first programmed instruction courses were from IBM, covering Autocoder for the IBM 1401, but there have been many subjects, even flight training, done well and successfully in programmed instruction format.
Programmed instruction succeeded because Skinner's hypothesis was that people learned more from success than failure, and all content was arranged to make people successful at every step. (There were some formats from publishers that didn't test their frames; they simply broke up text-like content into small pieces and called them "frames" and the books "programmed instruction". Do not be fooled; PI is designed from the start to produce successful responses.)
Re-introducing Computer-Based Teaching on today's internet could have some amazing possibilities. Many of the illustrations could be replaced by animations that more clearly express the ideas. Programmed reviews could be short and sweet, and provide successful mental practice for people needing to develop knowledge that requires memory reinforcement. Basic skills in Math and English could be society-changing improvements.
"The mind works quicker than you think!"
I've wondered why I haven't seen a movement toward an open-source model for textbooks whose subject matter doesn't change that rapidly such as history, math, physics, art, etc. Given budget constraints, I'd think schools would welcome such a development with open arms. Not to mention that for those who want particular emphasis on certain areas, customization would be easy. I watched a news show on the textbook industry and was surprised at the amount of ass-kissing it had to do for the largest school districts, with the result being that their products reflected those inputs and nobody else's. Make open-source versions and districts can opt out of Big Schoolbook if they want, and leave the rest to pay the exorbitant prices for what is frequently a dumbed-down, inferior product.
Teachers rarely get to provide input on the curriculum these days. In this atmosphere where teaching to the standardized high stakes state test is the norm, administrative clerks (principals and above) reach for any new scheme that they think will raise test scores. Most admin clerks have less teaching experience or curriculum knowledge than the teacher they lord over like demi-gods.
Cue Tom Lehrer
Contribute to civilization: ari.aynrand.org/donate
This wasn't a math problem, it's a logic problem.
If you don't do R&D, you don't have a product to market.
So, unless you are a political operative, you'd better work for a company that believes in the primary value of R&D.
Am I missing something here? Every statistics course I have taken has relied heavily on calculus.
Some of them even used nifty tricks, like Interchangeability of differentiation and summation for uniformly convergent series.
They should just print the cover and leave the rest as an exercise to the reader.
That some genius in the District/County/State discovers that there's all this money they can save by cutting texts entirely from their budgeting. As to using the money saved, probably it'll go to bonuses for them because they noticed it. That or they just will spend even less on education.
Not for content ("steak") but for presentation ("sizzle").
Some things like pre-college math and "established" history* simply don't change much.
A middle-school course on US history prior to WWI will cover pretty much the same things as
it did in 1980. Ditto Algebra or calculus.
But the delivery should be updated.
A 1980 history book that might have come with 2 or 3 16mm movies in a "teacher's package"
will instead come with both student- and teacher-oriented web sites and other
modern resources.
A 1980 calculus book was probably 3- or 4-spot-color with maybe a full color
page or two in each chapter. The "real world examples" were contemporary to
its time. A 2012 textbook - if it even exists as a book/PDF, will be
full-color and will use examples today's students can relate to. Cars will have higher
gas mileage, "mathematics in the work world" sidebars will have modern scenarios, etc.
But in both the history and the math texts, the concepts and even the very questions can
be carried over verbatim to today's students.
*"Established" history is typically history which 1) is factually established and 2) whose
interpretation isn't in flux. History from cultures that haven't left much in the way
of records isn't factually established, and the "preferred interpretation" of history of the past few decades is
still being written.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
http://www.themathpage.com/
I particularly agree with the ruminations in the Introduction of the Arithmetic section.
Knowing multiplication tables is useful but not in the way you might think.
It's not knowing them that's important, it's being able to do everyday math in your head
quickly that's important.
I'm at the grocery store buying supplies for my kid's Cub Scout meeting next week.
There will be 6 or 7 boys there and it never hurts to have extras, so I'm buying for 8
(I was going to buy for 10 but I'm not that generous).
So as I shop I keep a running tally in my head:
Cupcakes: two packs of 4 each, $2.50/pack. Food, not taxed. Total: $5.
Birthday candles: 1 package. $0.99. Tax is somewhere between 5-10% so call it $1.10.
Total: $6.10.
Matches: I've got a lighter at home. Skip it.
Party supplies:
I scoop up a bunch of things and the total is $14.20. With tax add about $0.70 to $1.40.
Forget the round-off error. Call it $15.60 for party supplies just to be safe.
Total: $21.70.
Oops, I was hoping to keep it under $20. I can splurge a little but
if I have to buy more stuff I'll have to put something back.
You see where this is going.
I knew how to multiply by 2, add, estimate 5% and 10% tax rates, and probably
had to multiply by 8 a few times in the party aisle.
And because I don't carry a calculator with me, I had to do this all in my head, and
fast enough to not waste time in the store.
If you can double, half, move a decimal point to multiply and divide by 10, and add and
subtract AND keep several "temporary" numbers in your head at once, you can do
fast estimates that are within 10-20% of precise in almost all everyday situations
that require seat-of-your-pants estimates.
Personally, though, I do find having multiplicaiton tables in my head handy for doing
things like estimating miles-per-gallon to 2 or 3 significant digits or estimating
taxes and tips to the same precision about as fast as it takes someone else to drag
out the calculator app on their smart phone.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
Most math curriculums teach the basics of probability and statistics long before they get anywhere near calculus. Unfortunately, you can't teach much more than the basics without getting into calculus.
This has been the status quo for many decades, unfortunately. Feynman was dealing with that problem in the 60s, and it drove him crazy and he had to stop participating. For what it's worth, my daughter's math materials for elementary school, coming from a big academic publisher, have substantial deficiencies and flat out lies. The section on probability (spanning a couple years) was done by someone who had no effing clue, heck, that person didn't even bother doing the simple experiments they were proposing!
A successful API design takes a mixture of software design and pedagogy.
Inserting things like multiculturalism into math class is a good thing, not a bad thing.
Well, it's a good thing if you want to teach your kids multiculturalism, otherwise
it's a waste of time.
Likewise, inserting practical applied math into social studies and even literature is
a good thing, as long as it's not contrived.
Here's a math lesson followed by the same lesson with subtle multiculturalism that
doesn't change the problem followed by the same lesson with additional text that
all but
force the student to think about multicultural concepts as he does the problem.
There is NOTHING wrong with example #2. The merits of example #3 in a classroom
where the teacher, school board, or state isn't intentionally trying to infuse multiculturalism
into the math curriculum is debatable.
No multiculturalism:
A class of 30 students went on a field trip to a museum 30 miles away. The school has several vans that
can carry 15 people each and several that can carry 8 people each.
School rules require two adults in each vehicle and a total of 1 adult for every 5 students
on the trip.
Using the 15-passenger vans will cost $1.10/mile to use.
Using the 8-passenger vans will cost $0.80/mile to use.
What is the most cost-effective way of traveling?
This being a modern full-color textbook, there is an background drawing of a
generic museum.
This time add a little subtle multiculturalism:
The text is the same but the background picture shows a photograph of real students inside
a real museum. The students and the adults in the picture are about half male and
half female and both students and adults represent a broad swath of ethnicities. They
have various skin color and there is at least one student wearing religiously distinctive
clothing from a small-minority religion.
Now the same problem but with some coerced multiculturalism:
As part of their lesson on Native Americans, a class of 30 5th-grade students from
George Washington Carver Elementary school went on a field trip to
their local science and history museum.
The museum is 30 miles away. The school has several vans that
can carry 15 people each and several that can carry 8 people each.
School rules require two adults in each vehicle and a total of 1 adult for every 5 students
on the trip.
Using the 15-passenger vans will cost $1.10/mile to use.
Using the 8-passenger vans will cost $0.80/mile to use.
What is the most cost-effective way of traveling?
This being a modern full-color textbook, there is an background photo showing real students
touring a pre-Colombian Culture exhibit at a history museum. As in example #2,
the people represent different genders and ethnicities. At least one person in
the photo is dressed in a way that makes it clear he is Native American (perhaps
he is in ceremonial dress, or perhaps he is wearing a t-shirt that has
a tribal symbol on it, it doesn't matter).
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
Explains a lot.
The best maths book ever is...Who is Fourier: A mathematical adventure. Many on Amazon reviews agree too. Should be used in school and universities where relevant.
You have to be able to do the "beginner's mind" trick - to think like a student at the appropriate level when writing.
I can't do that to save my life, and I doubt I'm alone. I can run classes and deliver lectures from lessons constructed by someone else, but on my own I'm an acceptable substitute for sleeping pills.
To a Lisp hacker, XML is S-expressions in drag.
The following is my opinion...you don't have to believe me: ;-)
Mathematics in the West is specifically taught to insure, most people are locked out of ever discovering its true meaning. This is done on purpose, and it is to create a class of people who become only familiar with Mathematics...but not knowledgeable about the topic. This is to insure the majority of people cannot use Mathematics for anything beyond what it is taught for. (i.e. Mathematics is taught for a job, for obedient workers.)
A good example is many of the engineering courses, which create idealized problems, with very little examples that clearly explain the connections between what I would call the secrets of Mathematics beyond a simple algorithm. You can see this in most textbooks, idealized problems, with a problem that is demonstrated step by step, but amazingly, none of those examples can be used to solve any of the problems in the problem sets.
I say secrets, because for example, Trigonometry is taught doing memorization, insuring the students never make the connections between anything but a triangle and a simple table of values for a given triangle on a unit circle. This is key. That way most people will be put off by Trigonometry with no connection of meaning, only memorization.
Also, only answers are given in the texts, if any problems are worked out they are done very lightly carefully planned, so that the individual cannot discern beyond the problem, and focuses strictly on the answer.
Have you ever noticed, after studying an entire chapter in a typical mathematics text, you can't do any of the problems, or very few of them? That is because you are not being taught mathematics, you are being taught obedience. You go to the instructor to insure you think "properly" about the problems in the text and that you do not ask any dangerous questions.
Another example is problems are then given with no worked out problems, and no answers. This is critical. It insures that if you somehow work out the problem, you do not understand the answer, or more importantly, you once again, have to check with the instructor to insure you are "thinking properly", and will often make you do the problem over in the "correct: manner. (State approved.)
This is by design, and it is to insure Mathematics continues to be a topic that "only smart people get". (Which there is no such thing. I can assure you, if you do a lot of work, outside institutionalized Universities and State organizations, and find your own way you will trounce these people. Most of them are nothing but idiot savants in my experience, with high skills in memorization and never straying far from text book material.) This is done this way and taught this way because if Mathematics and its meaning was clear, it could be used to ends many of the people that currently run our societies, do not want.
Things such as critical thinking, and independent thought are dangerous to these people. Remember, companies don't want individuals that are going to destroy their markets, by thinking differently. They want workers who think the same, so that the products which are turned out create predictable markets they can easily monopolize. Educational institutions are created with the same goals to support these corporations in most western countries.
You see this today right, with such terms as "disruptive technologies", for example. The most ridiculous term I have ever heard. The term is used for the small number of people who slip through the fingers of these institutions, and disrupt monopolized markets. There is no such thing as disruptive anything, there is only obedient citizens in the corporate fascist state, and "trouble makers or disruptive" people.
If you examine our current educational systems, they are specifically designed to insure everyone thinks the same way, and with no independent thought. It is very similar to brainwashing. It is so ingrained, that many of these people after spending an entire
Got Geometrodynamics? Awe, too hard to figure out? Too bad.
I know I'm late to the party, but another great read on the problems with text books is "The Muddle Machine: A Textbook Example of What's Wrong with Education" Available at: http://www.edutopia.org/muddle-machine
My company does typesetting, and that includes typesetting math for publishers. The quality of what we are asked to set is sometimes excellent, sometime abysmal. We use LaTeX for the work, regardless of what the publisher sends us, because we can trust it not to fall over and break under pressure, something we cannot say for other systems. As a result, we often get the publisher coming back to us asking how we got it to look so nice, which is very flattering (and we never tell them what we used), but supports Ms Keeghan's point that the publishers know that some of their product is rubbish. Some of the authors may well be to blame — we don't get to meet them — but publisher illiteracy plus publisher veniality is going to account for a lot of the problem.
Parent is not worth his salt (historical reference to an ancient monetary system.)
Parent does not know much about Arabic Numerals...
Yeah those Arabs and Indians were so genetically bad at math some alien must have given them the number system the world uses today! I seem to remember the Romans having something only slightly above drawing marks...
Democracy Now! - uncensored, anti-establishment news
Lectures are an efficient ways of learning something. Especially Mathematics. Most of the time (immersing yourself in some subject matter that exemplifies some part of Mathematics can be much more effective, but it takes more time and effort too). Besides, there is good reason why textbooks haven't changed: the subject matter has largely remained the same. Only people change (and their background knowledge and attitude).
What I see with Mathematics is that it just takes too much intellectual strength and concentration for 95% of the population to master under their own steam. Even if you gave them twenty years, they'd get absolutely nowhere. People in general simply haven't the smarts, the talent, and the perseverance it takes to discover Mathematics on their own.
This has a reason: Mathematics takes an effort to learn (unless you are lucky enough to be very gifted at it, which 99.9% of humanity is not). It's the mental equivalent of rock-climbing. It's not easy. However, just like rock-climbing, it's so much easier to climb up *after* someone than to climb in the lead.
Just consider the route you take: if you climb up after someone, you're guaranteed that the path up will lead you somewhere. Climb lead, and suddenly that's not a given anymore: you will need to *search* for the path. Apart from that there is the small matter of the rope that your lead climber can let down to you ... to help you over the tricky bits. You need a lot less strength, stamina, and knowledge to climb up after someone than to climb lead.
And that's why there are lectures. During a lecture, someone who has studied e.g. Mathematics guides you up, and drops you a rope. If you follow the lecture, you get to enjoy the view and (hopefully) enough understanding of what this particular part of the landscape looks like in order to apply the techniques you just learned to new problems. But no matter how good the teacher, you will have to expend the effort to hoist yourself up to the level of the subject matter. There is no "royal" way to learning.
Mathematics (even high-school Mathematics) is the product of more than two thousand years of struggle and groping by the best minds of their generation. Don't be surprised if you're not smart enough to hoist it all aboard without effort, and don't be disappointed if the stuff that's causing you trouble to learn is almost no different (apart from choice of subject matter) from the stuff that caused your grandfather trouble to learn. And unless humanity does something drastic to its brains, your grandchildren will have precisely the same trouble learning the same stuff as you do. That's not failure, that's normal.
This is because there is nothing that separates any of us from the level the Middle Ages, except for a mountain of accumulated knowledge and skills (e.g. the Scientific Method). Knowledge and skills that we learned about in school, through books, and nowadays through multimedia.
Soviet-era Mathematics shone for the same reason that Soviet-era ballet and musicians were such superb performers: it demanded (and got) extremely levels of dedication. Such focus actually *hurts*, so people in general don't do it (people aren't masochists). The people who do tend to do so either because e.g. it's their only clear ticket out of abject poverty (contemporary China or India), or their only chance to improve a life that would otherwise be without perspective life (the Soviet Union again).
If anything the US is lagging because people have it so good and because society as a whole values easy short-term results rather than hard-won long-term ones.
I believe that there is something about the fabric of US society that makes it more natural and attractive to join a gang and to goof off than to go to school, study, a
Capitalism simply does not deliver good education. There is no profit in a swathe of well-educated people, only the minimum needed to keep remaining consumers in line.
I don't mean to make it a political issue, but I recall President Obama's emphasis - at least, in public speaking, while the Congress remains embroiled otherwise - his emphasis on technology and innovation in the economy. Of course, those are goals that must be supported with sound technical education, with mathematics as at least one essential basis of the same. I don't know whether any regional school boards have quite caught a clue, at that, however.
Hypothetically, there is a motivation for - when being supported in developing a really solid education, as some regional (cough red state cough cough) school boards honestly might not give so much of a damn about - hypothetically, one can find a sense of motivation in pursuing education, like so: To be well enough educated to develop really useful innovations, ultimately for the purpose of their being useful innovations - to not get the cart in front of the horse, at that - ... whichmay therefore be of use in entrepreneurial development. That short line of reasoning put even shorter, as it were, there's motivation for innovation - motivation to develop a really solid education ... insofar as one regionally may, at least during public school, and there's always post secondary education, of course...
I mean, we could set out to get our public school systems to perform really up to par - or else, we could let the rest of the world outdistance us (further) in terms of common skilled labor. If we should take option number two, there, I'm sure that could go really well for us, in only a couple of generations's time - not.
Circa 1994, I remember that my Calculus III course teacher found some exercises in the book that had no solution and blame the publishers for that (Mc Graw Hill). Also he did apologize to us for waste 2 class trying to solve such exercises. And guess which questions were posted in his final exam? :D
Yes, only sadistic people want to learn maths as career. XD
Maybe what is wrong is the modern American business profit framework.
This is a case where a whole publishing industry was in place. All the small quality publishing houses were mature businesses with high costs, high quality, good pay for employees, and probably lots of American union printers. The market these publishers were in was getting price sensitive and as a result profit per share was declining. In business terms, the corporation with great assets and great competence but declining profit was ripe for the plucking.
Here is what I think is true: In the USA when an established medium size corporation slips into declining profit, the company can not resist being taken over. If the company turns down a buyout offer, the directors can be sued by stockholders, for example. The owners of Ben and Jerry's Ice Cream had to accept the highest offer even though the charitable activities of the company may have not been promised to continue.
Many changes in the math textbook business told in "Afraid of Your Child's Math Textbook? You Should Be" article by Annie Keegan are exactly the same in many other American businesses:
The company (or publisher) gets acquired, the new conglomerate company plays the same deck of profit improvement maneuvers: offshore typesetting, cheap no-benefit writing contracts, projects with impossibly short time frames, deliberate obsolescence of existing materials, construction of a labyrinth of side products that are all proprietary.
Notice that the corporate takeover game is a one-way transaction. Is there any way for a big corporation to become smaller? There is General Motors and Kodak as examples and both shrinkages required bankruptcy.
Here are the areas we should review for solutions:
1. Copyright and proprietary book products need to be bypassed. We need an open source mathematics textbook authoring system that produces open source reusable GPL books that can be decomposed and rewritten. Sections of the book can be signed and documented, enabling a book to have layers of authority and reputation. Every section of the book will be capable of hosting a "learn more" area. Every section will be capable of hosting a "related problems from the national college admission exam". The books should be downloadable documents where the cost of downloading is no more than 2x the cost of the Internet connection time.
2. American copyright used to have a statutory requirement that the work be first manufactured and published in the United States. American tax law used to allow a publisher to store an inventory of books for a period of years and not pay tax on the books before the books were sold. These protections were ended as part of a treaty I believe. It is time to revisit the effect of those trade agreements.
3. Here is one for you to check out: It seems to me the only small manufacturing businesses I have seen survive are where the business owner owns the land, the building, and owns the machinery and has low taxes due to being in one place a long time. The little businesses that survived ignored the ideas of maximizing cash flow. The only remaining problem these business faced is transfer of ownership which creates a debt situation. Paying the note on the business sale forces the new owner to play maximize cash flow. The new buyer gets increased taxes because the sale transaction establishes a new basis value for the business.
Teaching Math In 1950:
***** A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?
Teaching Math In 1960:
**** A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?
Teaching Math In 1970:
*** A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?
Teaching Math In 1980:
** A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.
Teaching Math In 1990:
* By cutting down beautiful forest trees, the logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels feel as the logger cut down the trees. (There are no wrong answers.)
Teaching Math In 2005:
El hachero vende un camion carga por $100. La cuesta de production es...
Have gnu, will travel.
The primary statistics course that is actually necessary stems from an older branch of math than calculus.
My daughter just went through grade 7 and 8. The textbooks were atrocious! Instead of teaching one method of performing a simple math problem, they taught three! My daughter quickly figured out how to do the basic method to find the correct answer but the school forced her to "learn" two other methods that didn't make sense to her. They marked her correct answers wrong if she didn't use the "correct" method! Instead of making it easier, it made it more difficult! The idea was that the newer methods were a graphical method of learning math. I've taken every math course when I went to college just for the fun of it and I now teach it at a post-secondary level. These graphical methods were extremely confusing. Just let the students learn one method and practice it until they are competent. They don't need to be overwhelmed with other methods. The other major issue is that they have teachers who know nothing about math trying to teach math. They need teachers who love math, understand it and see the beauty in it. Not the teachers who majored in english and history and are forced to teach math. That is a recipe for disaster. I would love to write a website that covers elementary and junior high math - just have to find the time...
I'm sorry, but there really isn't a lack of good mathematics textbooks for students. Math at the secondary and elementary level (especially the elementary level) hasn't changed: they're the same subjects they were now as they were 50, 70 years ago (more or less). The only difference is that the topics aren't nearly as rigorous as they used to be for the same curricular subject - especially with math. All the efforts to make the books "more accessible" to students have resulted in quite the opposite: it's now harder to figure out what in the world the books are talking about, and you've got to read a literal book chapter until it becomes clear. (Contrast this to short explanations for each new concept, followed by examples and further explanation - like what I remember from my childhood.)
The problem is that these books have gotten dumbed down and rewritten by people who were raised on New Math for No Child Left Behind curriculum. I have no idea why academia and the education industry feels the need to rewrite things which work, and continue to do so after their efforts have been proven not only ineffective but counter-productive. Chalk it up to governmental bureaucratic 'intervention' and the unionized "equality despite excellence for everyone" mentality of state education in America, I suppose.
There are still publishers who do "just the math, ma'am" mathematics. Let me offer Saxon Math to those who are interested. They're not nearly as good as they used to be due to having fallen to the Houghton Mifflin Harcourt conglomerate, but they're still more than a cut above the rest and fairly true to their roots.
~/ssh slashdot.org ssh: connect to host slashdot.org port 22: too many beers
This is what math educators refer to as the "Death March to Calculus". The problem is that a lot of more interesting and very useful math falls by the wayside to make time to do everything necessary to prepare for calculus. I agree statistics is more useful for the general population. And for computer science, discrete mathematics is more important than calculus. Still, calculus is the language of science and engineering so anyone in those disciplines needs it. We need a more thoughtful approach to math curriculum choices -- so I guess I'm agreeing with Benjamin that basic numeracy should include a sound understanding of statistics. But that doesn't do a lot of good unless coupled with good critical thinking skills, which is something that is totally missing from most education systems.
I often say that the corner office doesn't go to the person with the highest IQ, it goes to the person with the best bullshit detector. (Bullshit detector == critical thinking skills.) First we need to teach kids to *think*, then make sure they understand enough statistics to support decision making. Calculus and discrete math can be added as needed.
Many years ago, I helped a girl I knew with her math homework. I remember one particular word problem involving a car traveling at X km/h and slamming on its brakes. Given a rate of deceleration in m/s and an initial speed of the car in km/h, what would be the length of its skid mark? The numbers given seemed a bit odd, particularly the rate of deceleration.
I solved the word problem easily but when I looked at the answer, I thought, "a 200-metre-long skid mark? What?". The skid mark was hilariously too long given the car's speed. 200 *feet*, maybe.... um... oh my god, you're kidding...
The text book in question was originally a U.S. text book and they "converted" it to metric (I'm in Canada) by just replacing the names of the units rather than actually converting the numbers. Worse still, they equated "feet" to "metres". Almost every single word problem I could find was skewed as a result, to a greater or lesser degree.
The only parents who have such luxuries of time and money will be (and have always been) fine. You don't re-do (or reading between the lines: kill) public education for their benefit. You adequately fund public education (decouple spending from property taxes which are always cut by the already rich) for the ever-increasing sector of the contemporary US economy: the working poor - who literally don't have time for such niceties as attending school district or local government meetings (almost always held in suburban enclaves, btw).
They were good enough for me, and they are good enough for my kid. Same with Halliday, Resnick (and now Walker).
Teachers make recommendations, but the books are selected by school superintendents and school boards. I am a math teacher, and I agree the textbooks are crap. Good teachers are selective about the problems assigned at home, and use the textbook primarily as a resource, not as the primary mode of instruction.
I have been working at a free digital textbook on probability and statistics for almost two years now. It receives quite a lot of visitors and some visitors e-mail me to thank me and ask me to cover more topics. There is an interesting fact though: visitors from the US spend half the time (and visit half the pages) spent by visitors from Europe and Asia. What does that mean? Is it because US students are less inclined to spend time reading maths? An if so, why?
Setting aside for a moment that the article is concerned with K-8 specifically, college textbooks are just as horrible. Math (calculus) is the worst. TFA says that: "It could be that key information or steps are missing." If you wanted to teach yourself calculus, my calc book was the worst. Sure there would be some examples, but, in almost all cases, some term would magically turn out to be zero, one, or negative one, meaning that you got to skip a number of steps in solving the problem and never actually learned how to use the technique that was being taught. Fast forward to the problems for that chapter, and none of them are anything like the example.
Come on the educational system is a scam (not to say education.. Santorum... yes you.. sit back down..)
The professors palm off the shittiest lectures they can get away with using as little of their time as they can, the books are overpriced and under featured and tuition has the enviable position of being able to take government money without in any way being restrained by the same government.
That last point is why people think they hate government "interference" in the marketplace btw It's not that the government is in the market- the government is in the market in a million ways you'd never think of getting rid of- it's that it's been hobbled in the marketplace as a mere hapless payer of bills the politically connected coke snorting class of university administrations dream up.
If your class or teacher sucks, can you get your money back because your product is defective? Ditto on the shitola they force you to buy at the bookstore. It's unreadable, the questions range from the useless to the impossible (I really enjoy being told by the book after working on one problem for say three or four hours that there was no known solution or the solution when first discovered represented an advancement in mathematics... fuck you, assholes.
Which pretty well sums up everything anyone with any common sense has to say to the university- fuck you.
Fuck you for your insane and baseless inflation which you pursue relentlessly because your salary is positively correlated to the cost of tuition.
Fuck you for not changing - in 250 years - how people are taught even one iota - the fucking sage on the stage.
Fuck you for deliberately and maliciously keeping your courses and books offline. You had your fun kicking me out of university for trying to put course lectures online 12 years ago but trust me, I haven't been wasting my time and I haven't forgotten. Our company is going to take a baseball bat to the collective skull of your business model and by the time we're done, minding Khan Academy's servers is going to look like a good career move to you.;
Fuck you for systematically colluding with banks to steer people to worst-deal-ever student loans.
Fuck you for not giving a fucking shit about all the students I saw who earnestly wanted to learn something only to be met by a wall of blistering cynicism and indifference- a business in the real world would last exactly 6 months with your level of "service".
Fuck you for systematically lying and colluding to falsify the qualifications of in state students for the purpose of fattening your bottom line with daddy- can-pay-full-freight foreign students.
Fuck you for screwing over your TAs and paying them minimum wage while your fucking university presidents do shit like, oh, million dollar redecorations of their entire office floors so their fucking daughters can get fucking married there.
Fuck you for having zero quality control over your courses and fuck you for trying to present this as some type of fucking "academic freedom".
Fuck you for your lavish financial attention to fucking sports and fucking glitzy shitty pizza joints whose only purpose is to get another two three grand off mom and dad each semester while your academic cultural and social activities are starved of resources.
Fuck you for your coddling and rewarding of political skullduggery as a means to career advancement in your faculty. Do you really not know what goes on and can you really not think to counter it in any way? Oh that's right, that's who YOU are and how you got YOUR position.
Nevermind.
Count your fucking days, bitch. They're numbered.When the financial aid bubble bursts and people discover they have cheaper and better- both- ways to get an education, which is going to be at most one two years now? when that day comes I sincerely hope the crushed collective future you face leads directly to your putting a gun into your fucking collective mouths and pulling the fucking trigger.
Why do you need to rewrite math textbooks at all? It's not like our basic math has fundamentally changed in decades. Just print more of the old stuff. Hell, the publishers can even profit more as some becomes public domain, right?
It turned out that the blank book had a rating by some of the other members!
Richard Feynman complained about math books in 1964 seems nothing is really better. http://www.textbookleague.org/103feyn.htm
I was at university in a cell biology class. The teacher picked me and four other top students from the class to go to a local pizzeria with the sales rep from the textbook publisher. They gave us copies of the textbook and paid for lunch. We recommended the textbook, even though it was almost certainly too advanced for the population of students who would be using it.