Parents in several Washington, DC-area counties are fighting back against math textbooks they find confusing, convoluted, and just plain “wishy-washy” (free registration required):
In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra…
In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra.
How disturbing is it to see a math administrator claim, as one does in this article, that “memorization will only carry you so far” in basic math? Funny, but aren’t the basics something that should be memorized, so that students don’t have to draw pictures every time they need to use those basic skills to learn more advanced math?Â
The parents have started a petition here.Â
This is confusing.
Either this moron knows the students’ performance will reflect on him–badly–or he knows it won’t because there is no accountability.
Or he really thinks this is an improvement and, in fact, believes it so strongly as to risk accountability for his decision.
Or he knows nothing he does in this area can ever come back to haunt him. Because, NCLB and various other assessment tests notwithstanding, there is no accountability.
Good luck to those parents with the petition. We haven’t been able to do anything about our Fuzzy Math program (Everyday Math) even though students are getting to Middle School without being able to multiply or divide (some can multiply by drawing a lattice and filling in numbers, but it’s time consuming and takes up too much space to use in the margins of their paper.)
If schools want to do something radically different with math education they either need to get the parents on board and trained so they can help their children or the teachers need to be competent enough to teach it to the students without parental help.
Why is every new curriculum development automatically assumed to be better? New is always easier to sell. Sometimesd I wonder if kickbacks are a factor in curriculum purchases, but I have never heard of a scandal of this type.
I don’t think either the blog entry nor the linked articles give a very good picture of the size of the math wars going on. I don’t know all the details, but there have been a lot of parent groups formed in the last few years in opposition to the trends in math education promoted by the National Council Of Teachers of Mathematics. There are more web sites put up by these parent groups that I can keep track of.
My personal involvement began over a decade ago when our seventh grade daughter brought home a very interesting math book. “Interesting”, in this case, is not a compliment. This book seemed to exemplify everything that can be done badly in a math textbook. As a personal project I began to write up my analysis of that text. My perspective at that time was totally as a parent, not a teacher. However since that time I have returned to teaching math, and have become painfully aware that my daughter’s chaotic seventh grade text is not unusual in the brave new world of fuzzy math. I did finish that article I started then, and when I got a personal web site in 2004 I posted it. It is my most read article. Here’s a link. http://www.brianrude.com/chi-mth.htm
And, if I may take the liberty, here’s another article that I think addresses some of the important issues involved.
http://www.brianrude.com/disagr.htm.
I’ll quote from the article: “This has to be a decision made by everyone that’s affected by it,” said Cathie Dillender, a senior Pearson executive who handles math issues. “We have a lot of happy customers out there. We’re all educators, too, and we certainly wouldn’t publish a program that would not work with the kids.”
I just wonder if the curriculum that was replaced was also published by educators, and thus certainly would work with the kids?
Maybe someone somewhere needed a sale/kickback/excuse-for-staying-in-grad-school or something
These math programs are entirely focused on understanding the mathematical principles that underlie computations. Do they go too far? Probably, but this point is debatable.
Old school math wasn’t perfect, either. I took the standard college prep courses in high school — from Algebra to Trig to Calculus. The higher level courses got me into college, but provided no mathematical benefits. Every lesson was memorizing and practicing a new algorithm. I had the right answer every time, but I can’t tell you the underlying purpose for even one.
There needs to be some balance between memorization and understanding.
I hate to be the grinch all the time, but a think a healthy dose of skepticism is in order. J. says “These programs are entirely focused on understanding”. Well, they claim they are, but how is that to be accomplished? I am not familiar with the fuzzy math programs at all, other that what I read here and there. Over a decade ago I did become quite familiar with the math books my daughter brought home from junior high school. I can well imagine that the authors would be quick with the rhetoric of understanding, but the books I closely examined over the period of two years (the seventh and eighth grade book) appeared seriously lacking in coherence. That’s why I described them as “interesting”. What in the world were the authors thinking? I never had a chance to find out just how my daughter’s teachers used these books. I always figured they just did the best they could with the materials they were stuck with. How do you teach fractions if the book does not have a chapter on fractions? That’s what interested me. I made a stab at figuring that out.
My conclusion, and I’m sure many will strongly disagree with me, is that the Chicago Math books were only rhetorically focused on understanding. What they were really focused on, and I presume still are, is applying a few pedagogical ideas that are ideologically held. One very important idea is that practice is not necessary. I devloped that idea in my article, “Some Disagreements With The Standards”, which is on my website. Practice is not necessary? Tell that to an athlete. Tell that to a musician. Tell that to a college student facing an exam in the morning. Practice, unless you are a prodigy, is necessary.
Understanding is important, in just about any subject. But I think there is a “fallacy of understanding”. The fallacy is in thinking that if I understand it now, I will understand it tomorrow, and I will understand it for the test, and I will understand it when needed to understand a new topic. Initial understanding, for the vast majority of people, is only one step among many. Understanding is important to enable remembering, and understanding is important to jog memory, but understanding is not enough. We still need to remember what we understand. There is not time enough when taking a test to reconstruct understanding that has slipped out of memory.
So I think the “understanding” claimed by the fuzzy math programs is almost all rhetorical and ideological. I don’t think they can deliver with any real substance. I admit I can’t speak from much first hand knowledge, but apparently there is a lot of frustration on the part of parents nationwide. Look at all the websites. All that frustration is no surprise to me after what I saw in my daughter’s Chicago Math books.
Every lesson was memorizing and practicing a new algorithm. I had the right answer every time, but I can’t tell you the underlying purpose for even one.
There needs to be some balance between memorization and understanding.
Here is the basis of the problem for almost every problem with modern education.
Modern education is based on curriculum written by education professionals, that is people who have been trained and educated in understanding underlying purposes and principles.
What most of them fail to understand, or have forgotten, is that the vast majority of people will never need, and do not desire, to understand the underlying purposes and principles. They just need to be able to get the right answer.
Elementary, Middle and High school students only need to learn how to get the right answers and memorize the basic facts. For something like 75% of the people, that is all they will ever need.
People who need to understand the underlying purposes and principles can go to college to learn them.
I have a few points of agreement with gahrie’s comment, and a few points of disagreement. I have become aware in recent years that many students think of learning math as a series of procedures to learn in order to solve problems of different kinds. They speak of “formulas”. They say they have a “hard time remembering the formulas”, and similar things. So I like to point out to them now and then that that’s doesn’t quite hit the nail on the head. Learning math, in my view, is a matter of thoroughly investigating and learning how to apply mathematical ideas. In algebra it is a basic idea that quantities may be represented by algebraic expressions, that algebraic expressions may be manipulated by faithfully following rules that derive from arithmetic, from what we know of numbers, and that the result of all this is a powerful tool for solving problems. But, with few exceptions, no math course is simply a collection of problem solving techniques. Problems may be intimately associated with math, and problems are a powerfull tool for learning math, but problems are not of the essense in math. Ideas are, and the logical development and consequences of these ideas are. This view is a hard sell to students who are struggling with problems. They know that doing problems is the key to success in homework, quizzes, and tests. So it’s hard to convince them otherwise, and I don’t try very hard. However I do point out that the solution to a problem is not the ultimate aim in their assignments. Rather a mathematical train of thought is. In algebra that translates to “show your work”. I learned by experience that with some kinds of problems trial and error can produce the correct answer, with no algebra used at all. Indeed on some types of problems (Train A leaves the station going east at 60 miles per hour. Train B . . . . . .) I have learned to give the answer. I will say in the problem “The answer is 2 hours and thirty five minutes. You will get full credit for declaring your variables, setting up and equation that accurately represents the problem, and solving that equation.”
The NCTM disagrees with me on this. In the Standards, they emphasize the desirability of finding “alternate solutions”. Once in a while that does happen in a good way, but usually “finding alternate solutions” simply means figuring out the answer by trial and error. At least in “story problems” that’s the way it usually works. In problems of manipulating algebraic expressions it usually means giving it the good old college try and scribbling down something. I have joked, not to students, that yes, I do give partial credit. I give one point per inch of nonsense.
Gahrie says our curriculum is written by “people who have been trained and educated in understanding underlying purposes and principles”. It doesn’t look that way to me. It looks much more the opposite. They talk about understanding, but it comes across as pretty empty. The result of their efforts is that they advocate “collaborative learning”, and projects, and open ended inquiry, and such. The result is fuzzy. It has a serious lack of coherence. It’s difficult to teach from and difficult to learn from. That’s what interested me a decade ago when I started looking at my daughter’s seventh grade math book. And that’s what frustrated me greatly in North Dakota (see http://www.brianrude.com/nds-mth.htm for the sad story there).
I disagree with Gahrie that most people need only to learn to get the right answers. They need some understanding of underlying principles or they have no ability to recognize a right answer, much less generate it. But understanding of underlying principles is not that hard. It is fostered by the legions of ordinary teachers who use the common sense and experience, not the latest education ideal, to focus their student’s efforts and attention, mostly through the medium of problems, to mathematical ideas, and over time build those mathematical ideas into a coherent and useful structure of knowledge. So it is my opinion that in the math wars it is the “worksheet teacher” who is the hero, not the advocate or follower of the NCTM’s ideals.
I have elaborated on some of these ideas in my article, The Math Curriculum, which is on my website. Here’s a link. http://www.brianrude.com/mthcur.htm