Skip to comments.School math books, nonsense, and the National Science Foundation
Posted on 11/12/2006 8:18:39 PM PST by wintertime
Problem: Find the slope and y-intercept of the equation 10 = x 2.5.
Solution: The equation 10 = x 2.5 is a specific case of the equation y = x 2.5, which has a slope of 1 and a y-intercept of 2.5.
This problem comes from a 7th grade math quiz that accompanies a widely used textbook series for grades 6 to 8 called Connected Mathematics Program or CMP. The solution appears in the CMP Teachers Guide and is supported by a discussion of sample student work.
Richard Askey, a mathematician at the University of Wisconsin at Madison, reported, I was told about this problem by a parent whose child took this quiz. The marking was exactly as in the text. Students instructed and graded in this way learn incorrect mathematics, and teachers who know better may be undermined by their less informed peers, armed with the solution. This example is far from the only failing of CMP. Among other shortcomings, there is no instruction on division of fractions in the entire three year CMP series, and the other parts of fraction arithmetic are treated poorly.
Is CMP just an anomaly? Unfortunately not. CMP is only one of more than a dozen defective K-12 math programs funded by the National Science Foundation. More specifically, the NSF programs were created and distributed through grants from the Education and Human Resources (EHR) Division within the NSF. In contrast to the NSFs admirable and important role in supporting fundamental scientific research, the EHR has caused, and continues to cause, damage to K-12 mathematics education.
At the elementary school level, one of the worst NSF funded programs is the widely used K-5 series TERC: Investigations in Number, Data, and Space. The program relies heavily on calculators and does not include textbooks in the usual sense. Harvard mathematician Wilfried Schmid evaluated it and concluded that by the end of 5th grade, TERC students were roughly two years behind where they should be according to the California, Indiana, and Massachusetts state mathematics standards, the best state math standards in the U.S. Schmid added, The TERC authors are also opposed to the teaching of the traditional algorithms of arithmetic, such as long addition, subtraction with borrowing, and the usual pencil-and-paper methods of multiplication and division. Not only do they refuse to teach the algorithms, they make clear their preference not to have the students learn them outside of the classroom, either.
(snip) The root cause is money badly spent. The NSF and corporate foundations maintain a gravy train of education grants and awards that stifle competent mathematics education. Although it is conceivable that ongoing NSF grants for new editions of defective math programs, such as those I have described, will improve matters, that is a poor strategy. It amounts to throwing good money after bad. The most that one can realistically hope for is that the original NSF-funded math programs will eventually rise to the level of mediocrity.
My own children used the Saxon Math books. They were admitted to college at the ages of 13, 12, and 13. By the age of 15, all had finished all levels of college calculus ( Calc III). The two younger were graduates of our flagship state university by the age of 18 with B.S. degrees in mathematics. The oldest of these two recently finished a masters degree in mathematics.
The oldest chose accounting.
So...Parents...homeschool, privately school, or be prepared to pay big bucks to the Sylvan Centers or for Kumon. But...even though the government school parent is doing the teaching or paying for the tutoring, the government school bureaucrats will take full credit for the high test scores.
Looks more like a specific case of x=12.5. That would be a line parallel to the Y axis. It should intercept the Y axis the next time I agree with a position taken by Nancy Pelosi.
My children were admitted to college at ages 12, 11, and 12. By the age of 14, all had finished all levels of college calculus. The two younger were graduates of Oxford and Harvard by the age of 17 with B.S. degrees in mathematics. The oldest of these two recently finished a Ph.D in mathematics.
So - parents - don't listen to those who utter platitudes and easy fixes to the complex problem of public eductation.
Widely-available education is a key advantage we in the United States have over the oligarchies of Europe and elsewhere. I believe anyone can achieve anything in the U.S.; provided they take advantage of public education, have sufficient innate intelligence, and work hard enough.
What is YOUR problem? Little sarcastic aren't we? Or jealous? Sheesh.
I took a math-for-teachers class that was taught by a Drama Major who insisted that there were 'many ways' to get a variety of answers. The PhD in Math guy, who was also required to take a SERIES of these inane classes, was just rolling his eyes. The Drama Major insisted on these 'new ways of looking at math.' She was from a well-respected university here in So Cal/ they were running the program for the state.
I left after 2 sessions. My brain hurt from the confusion the TEACHER was causing. I don't think teachers understand math, and the texts are awful too.
And that is why there are so many libs, I think. hahah.
Well, aren't they special?
Actually, my kids are not any smarter than any of the kids of the posters on this message board.
Hey...They haven't won any nation spelling bee, or published a New Times Best Seller.
I thought it was pretty funny. Reading it, I could really imaging the Jones' going on about their kids being just a little better than mine at everything.
Ummm-- They might be a wee bit smarter than some of our kids. My 12 year old is still doing pre-algebra and grumbling all the way about the Saxon books.
(age 11) in intermediate algebra.
By age 12 he will be ready for college level calculus.
What? Otherwise you wind up in Iraq?
I know a number of kids who have found the Saxon books to be excessively tedious and not really good at connecting the math to the real world. If you know a child who thinks that, be advised that there are other books out there, some of which may be better for that child.
Have found the Mathematically Correct website book reviews to be most helpful. http://www.mathematicallycorrect.com/
Oh, Saxon Math doesn't have any typographic errors at all, does it?
I've got no problem with homeschooling, per se. I do, however, have a beef with people who find every single isolated instance where the public education system - one of the largest industries of in the United States - messes up, and extrapolates it as though it applied to every school and every teacher.
So...Parents...homeschool, privately school, or be prepared to pay big bucks to the Sylvan Centers or for Kumon.
Horsecrap. There's still a lot of really good math teachers out there. They learn not to depend upon a book to the exclusion of their training and expertise.
I replied because I've grown tired of people posting unsubstantiated claims about public policy.
I could easily have said - my kid is well on his way to discovering a cure for Parkinsons made out of bicycle innertubes -- and he's only 9! So Mr. Fox can just stuff it!!!
The bottom line is: anecdotes may be interesting but they are ultimately irrelevant. In my opinion, what matters when discussing public education is not outliers who did not participate in public education, but rather real, tangible, repeatable solutions for those who do.
As a nation, we need to raise the level of our children's education, or else in 50 years they will be cleaning house and doing the laundry of others. Perhaps publicly funded education is not the answer; if not, please describe a well-thought-out alternative. My belief is that publicly-funded education is a fundamental part of how we as a nation will compete in the 21st century. The key question is: how we we improve it?
Yep. That's a huge problem. We should insist that only those who are properly prepared teach in public schools.
Step one in improving our education system.
Yup, unless the world has changed and nobody told me.
I wonder how much of the "another-reason-to-homeschool" obsession with every failing in the public schools is due to the individual parent's insecurity about their own decision?
heh heh heh, good one.
No. Of course not. I'm certain my kids are just as tangible as wintertime's kids. I'm simply trying to make a point.
Good one. That still ticks me off.
Good question. I'm sure there's a profound emotional linkage to any parent's decision.
Homeschooling is not for everyone, but some kids truly thrive when set free from the stultifying air of the classroom.
While I understand the concept that not all children learn in the same way, and this program addresses that, it still breaks down to total frustration on the part of parents who can't help their children because they can't figure out what is going on.
Example: Long Division
We all learned how to do long division the same way, and you need to know the multiplication tables in order to do long division. Not with this program.
Imagine dividing 20 by 2. With knowledge of multiplication tables you could easily say the answer is 10. But, with this math program they asked the kids to "guess" how many times they think 2 can "go into" 20. If the child guesses two times, they have you write a 2 off to the side, then subtract 2 from 20. Now you have 18 with a 2 off to the side. Now, how many times do you think 2 will go into 18? The child guesses 2 again. So another 2 goes under the first two and you subtract another two from 18. So, by the end of the problem the child will have 10 twos along the side and will basically have spent 20 minutes on a problem that would have been easily seen if they had been taught the math tables. I'm not exaggerating on this, it was a nightmare. Another scenario had this lattice work looking grid but I couldn't even figure that one out! They also had something they called Spiralling, which meant they would touch on a subject once or twice then a few months later if they touched on it again it would be "slightly" familiar to the kids.
I homeschool now.
Before you go any further with Saxon, check out Harold Jacob's Elementary Algebra, for Alg. 1, Jacob's Geometry, and Foerster's Alg. and Trig. for Alg. II. SirKit has a BS in Math and a PhD in Statistics, and he's seen a LOT of math textbooks during our kids' school years. He liked the Saxon middle school books, but he really enjoyed working with our homeschooled younger two in the Jacobs and Foerster books.
Actually I am considering doing a lot of the Math web links we have. He was excited last year when he was playing a puzzle game and realized it was algebra. I'll probably also give him my Painless Algebra book and see how he does with that.
I graduated in 2003 from TJHSST, a Virginia Governor's School for science and technology in Alexandria.
My math teachers used the books for homework problems and in some cases used textbooks custom developed by the math department. The computer science curriculum had its own textbook written in house.
My (conservative!) U.S. history teacher (famous for the sheer number of his students who would get 5's on the AP exam) never used our textbook.
So...it all depends on the school and the teacher.
Oh, Saxon Math doesn't have any typographic errors at all, does it?
In all my years using Saxon Math, I never found and error. This isn't surprising. Saxon Math has been around a long time, and their textbooks are not radically changed from year to year.
Actually his teacher that year was wonderful, probably one of the best he ever had. She was as frustrated to have to teach that method as the kids were. Her attitude was that whatever method the kids used was fine. If they knew their tables, they could do the problems that way, if not, try one of the others. Unfortunately, some of the other teachers made the kids learn each method and they were more confused by that.
Absolutely. Homeschooling is an excellent choice for many families. I'm not criticizing that. I am criticizing those who post unverifiable stories about a subject as if it is proof positive that their course is the right way to go.
I'm assuming you mean the AP US History test? What textbook had been assigned, and what kind of materials did he use instead?
I'm sorry the public schools in your area are so poor.
Such was not the case in my neighborhood.
It's too bad the public schools in your area are inadequate.
I encourage you to work hard to improve local government in your area. That would be far more fruitful than just sitting on the sidelines and not participating in local government; which I'm sure you would never do.
We had a pretty old, hard to read U.S. history textbook. I tried to read it over break, but it put me to sleep.
It never left my locker.
We used a thick U.S. history "summary" book (I forget the title)--this was mostly for reviewing for tests.
Our teacher actually taught us! (Surprisingly.) We did research projects in conjunction with our English class (integrated with U.S. history). The better parts were practicing for the essays and DBQs (document based questions) on the tests. Since my teacher was an AP grader, he knew exactly what the test was looking for.
We also held "Meetings of the Minds"--in which each student would pick a historical person and research that person's position on a particular topic, and we as a class would debate that topic (from our historical person's point of view).
Also--the U.S. History AP (and the SAT II test) were really really easy to begin with, imo. I got a 5 on the AP and 790 on the SAT II.
The same could be said for those who claim that the public school is the only way to go because their children had stupendous math teachers each year. Not everyone has that experience, even in private schools. Our kids only attended public school during their Kindergarten years, and only because the Catholic school didn't have Kindergarten at that time. They never had good math teachers, until our sons entered a very good, private Catholic all boys high school.
Our oldest is smart, but he wasn't as interested in Math, though he did go all the way through AP-AB Calculus and made a 5 on the test. He just passed the Bar Exam for MA.
The next youngest was just scary he loved Math so much. He was always interested in numbers; I taught him to add and subtract, but it was my Mama, during a visit who taught him to 'carry over'. His first grade teacher, on the day of his orientation to the school, knew she was in trouble when he raised his hand and asked if they were going to get into long division that year. ;o) The best year, academically, he had in elementary school was in the 3rd grade, when we transferred him to a school that said they were into the child learning as much as he could in whatever he wanted. He surprised even THEM when he blew through ALL the math workbooks they had, all the way through 6th grade. Unfortunately, they wanted the kids to conform to their 'nonconformist' liberal ideas, and he wasn't interested, so we brought him back to the Catholic school, where he was bored stiff until his Dad 'afterschooled' him in Alg.I. By then, his Math education was mostly self-directed, though he did take all the math classes the high school had by 10th grade, then did two semesters at Holy Cross He finished Carnegie Mellon in 3 1/2 yrs. with double majors in Computer Science and Psychology and is working on a PhD in Comp. Sci. Bragging enough for ya?
Our two homeschooled kids have done well in Math, our daughter taking up through pre-Calc at the Community college, and our son just fixing to get into Alg. II in his Junior year. It is a struggle for him, mainly because of the crappy early Math years. We regret not pulling him from school earlier.
I thought wintertime was just making the point that homeschooling was the right choice for HER kids. They DID excel in that environment, after all.
Sounds like a fantastic class!! Our boys used Brinkley's US History for their AP class, and our daughter used the same text when she homeschooled, though she didn't take the AP test. She liked the text, though she recognized his liberal leanings in the writings. One thing about his text that we liked was the part where he shows what other historians have to say about the matter, especially those who hold different conclusions from his. We're using the Brinkley text again with our youngest this year.
Would be nice, in a perfect world, but not all School Departments are amenable to change. Homeschool message boards are filled with people who followed just the route you mentioned. They volunteered, tried to talk to principals, Superintendents and School Boards. They got tired of beating their heads against a wall and realized that they didn't want to sacrifice their children's education just so they could say they were working for change.
You bet it was! Our U.S. history summary book was mostly filled with facts (names, dates, treaties, people, places, etc.) and sample essays/DBQs.
Idiocy. But mathematicians are happy to get anything from the NSF, which is much more interested in sinking money into the pit of the various forms of snake oil research.
If you want to improve education, make sure you have nothing to do any University departments of education.
Especially in mathematics. We know what mathematics is. Most math teachers couldn't get a Bachelor's of Science in mathematics.
What kind of mathematics?
I have a better one for you. I am teaching calculus and at a review session somebody asked me a question that required them to divide, say, x^3-3x^2+2x-10 by x-2 and get a quadratic polynomial plus a leftover term.
I said that they learned it in 4th grade and proceeded to do long division of polynomials.
It was as if I wrote Greek on the board. Not only had they not learned this in high school (and many claim to have had "calculus" in high school) they couldn't even understand that is the same thing. It wasn't "long division" as they knew it because it had variables.
There's no teaching of the basics nor is there any creativity. It's the worst of both worlds.
"Oh, Saxon Math doesn't have any typographic errors at all, does it?"
That was NOT a typographical error. It was an error of ignorance. There is a major difference.
And yes, I realize that people should not rely on the answer sections anyway, but an error of ignorance makes me question the system a lot more than a simple typo does.
Somewhat unrelated question: What text were you using?
We use Varberg, but that's really just a topic outline for me.
The new books come with these interactive problem-solving programs that you can use online. They're useful for me. Students can get individual help even in a huge lecture class (which I have two of now).
I think this refers to Pick's Theorem.
For some reason this has become a fixture of elementary math education. I guess because it's fun and unexpected, which makes it suitable for the popular exploration style lesson plans, as here.
There's nothing particularly wrong with it, but it does seem like a confusing approach to simple area concepts. It's simple, but why is it true? Note the lesson plan doesn't address this, and expects students to accept it because it seems to work. The proof requires a fair degree of sophistication.
Perhaps it's not going too far to see an insidious purpose behind it, namely mystification. You rejected it because you "couldn't figure it out", but the children are being taught that they should not expect to understand how or why it works, and that is math.