For fans of Mathematically Sane, here is their review of the National Math Panel report. My editorial comments are in green. They are not meant to intrude but to "enhance" your reading experience.
Friday, March 21, 2008
Really Says it ALL!
Presidential Math Panel Vows to Increase Learning Disabilities
Tuesday, March 18, 2008 5:17 AM
Gary Stager
In the last year of his term, the President of the United States and theDepartment of Education are now trying to do for math what they did for reading. The notable achievements of Reading First include massive fraud, profiteering, junk science, federal control over classroom practice, fear and hysteria. [Ed: They also found unprecedented success in school districts that had been written off by many.] While the National Reading Panel was stacked with ideologues sharing the same educational philosophy, the National Math Panel co-opted the National Council of Teachers of Mathematics (NCTM) by appointing the organization’s President to serve on the committee.
The National Council of Teachers of Mathematics, never known for its radicalism, swung hard towards “the basics” last year in its Curriculum Focal Points and now finds itself in the uncomfortable position of having to disagree with NCTM’s President and the President of the United States. “Skip” Fennell did neither his members nor millions of American schoolkids any favors by participating in this unnecessary process. These federal education expeditions seek to narrow both the range of content and pedagogy permissible in public schools. The private and religious schools the GOP wants to support with taxpayer-funded vouchers are immune from these intrusions. The one-size-fits-all prescriptions for what ails public education are justified by claiming that schemes are research-based. [Ed; "Research-based". Where have I heard that before? Aren't Everyday Math and Investigations "research-based"?]
The rigid definition of “scientific evidence” enforced by Department of Education may be fine in testing remedies for restless leg syndrome, but is ill-suited for the complexities of education. [Ed: Such reasoning may explain why teachers believe that teaching algorithms in the lower grades is harmful to such students]. But hey, these are the folks who have mangled the English language to imply that theory is merely an unproven guess.
There is a lot wrong with the recent math report, but making Algebra the holy grail of K-8 mathematics is wrong-headed and goes unquestioned. Stressing the importance of fractions as critical prerequisites forAlgebra adds insult to injury. In a world-class display of side-splitting math teacher humor, panel member Frances “Skip” Fennell told the New York Times , “Just as“plastics” was the catchword in the 1967 movie The Graduate, the catchword for math teachers today should be ‘fractions.’“ What Fennell doesn’t realize is that the person who said, “Plastics,” in The Graduate was emblematic of everything wrong with society. “Plastics,” was a metaphor for a shallow, superficial, inauthentic culture focused onthe wrong values. The National Math Advisory Panel’s greater focus on fractions represents a “plastic” version of mathematics that will do more harm than good.
It’s easy to see how someone might think that several years worth of fraction study prepares a child for Algebra. Fractions have numerators over denominators, separated by a horizontal line. Many algebraic equations have something over something else, also separated by a line.That’s all you need to know. Right? [ Um, uh...]Not only is the progression from arithmetic manipulation of fractions to Algebra tenuous, but neither of the assumptions underlying the value of teaching fractions or Algebra are ever questioned. [Uhh, well, they did discuss that at the very first meeting. Were you not there, or did you not read the transcript?] The President’s Math Panel, like most of the math education community maintains a Kabbalah-like belief in an antiquated scope and sequence. [Ed: A scope and sequence which managed to be successful for a great many people despite claims to the contrary in Mathematically Sane and other places] Such curricular superstition fuels a multigenerational feud in which educators fight over who has the best trick for forcing kids to learn something useless, irrelevant or unpleasant.
Despite the remarkable statement in the 1989 National Council of Teachers of Mathematics Standards, “Fifty percent of all mathematics has beeninvented since World War Two,” the NCTM has been in full retreat ever since. [Ed: Not everyone remains outwitted by stupidity.] Although much of this “new” mathematics is playful, practical, beautiful or capable of being visualized via the computer, little new content has made its way into the curriculum. [Ed. Well at last we agree. There is little to no content at all in NSF-funded programs like Investigations, Math Trailblazers, CMP, and others.] Against this backdrop of unimaginative heuristics and a leadership vacuum, math class has become increasingly torturous for too many students.
Children who struggle to manipulate fractions do so because the skills are taught absent a meaningful context in a culture where fractions are rarely ever used. [Ed: Rational numbers are fast becoming passe as well.] Fraction fans might argue that fractions are important in following a recipe, but little cooking is done during fraction instruction. Even if kids did get to learn fractions by cooking, they might add, subtract or even multiply fractions, but one hardly ever divides fractions. The fact that there are four arithmetic functions doesn’t justify drilling kids for several grade levels. [Ed: Hats off to you, Mr. Stagers. Just when I think you can't outdo yourself, you do!] I wonder how many members of the Presidential panel can coherently explain how division of fractions works beyond repeating the trick – multiply the first fraction by the reciprocal of the second fraction? [Ed: Can't give you an exact number but I believe Wilfried Schmid, Hung-Hsi Wu, Vern Williams, Tom Loveless, Sandra Stotsky, and Liping Ma can do so. Maybe Deborah Ball. Not sure about Skip Fennel.]
The Report of the National Mathematics Advisory Panel does not dispute that teachers spend lots of time teaching fractions. The report merely urges that teachers do even more of the same while hoping for a different result. A definition of insanity comes to mind. It would be bad enough if wasted time was the only consequence of the fanatical fraction focus, but too many students get the idea that they can’t do math. This damages their inclination towards learning other forms of mathematics. Given the importance of mathematics and the widespread mathphobia sweeping the land, students can ill afford to a diminution in their self-image as capable mathematicians. Educators should not be complicit in creating learning disabilities regardless of what the President or his friends say. [Ed: I guess this means you won't be voting for George W. Bush again any time soon!]
It is statements like these that keep us from moving forward.
ReplyDelete"Mathematically Sane" ISN'T!
Hopefully their readers are curious enough to do a little research on their own. I'm sure they would agree that investigation is a good thing...
Maybe they have a vested interest in promoting mediocre math(?)
I wonder if any of their children have had to suffer through it...
And how many of them teach at the high school or college level to see first hand the results of these mediocre programs?
We need national math standards! Thinking that we can compete globally without a national curriculum is my definition of insanity!
"...but making Algebra the holy grail of K-8 mathematics is wrong-headed and goes unquestioned."
ReplyDeleteIt's clear that they are determined to redefine mathematics. They try to hide behind the idea that it's better, but it's really different and less rigorous.
"The National Math Advisory Panel’s greater focus on fractions represents a “plastic” version of mathematics that will do more harm than good."
Once again, we have the idea that they have something that is better, not different.
"Not only is the progression from arithmetic manipulation of fractions to Algebra tenuous, but neither of the assumptions underlying the value of teaching fractions or Algebra are ever questioned."
But they don't like algebra. It's not as if they have a better path to algebra. That's not where they are going. Silly parents who think that one of the jobs of K-8 schools is to provide a path to the high school AP calculus track.
"Although much of this “new” mathematics is playful, practical, beautiful or capable of being visualized via the computer, little new content has made its way into the curriculum."
It's not in Everyday Math or TERC.
"...math class has become increasingly torturous for too many students."
This must mean Everyday Math and TERC. They are the dominant curicula. My son started out with MathLand.
"Children who struggle to manipulate fractions do so because the skills are taught absent a meaningful context in a culture where fractions are rarely ever used."
Well, is mastery of fractions a goal or not? Redefine math and the problem goes away.
"The report merely urges that teachers do even more of the same while hoping for a different result."
Their solution is to change the goal because the problem couldn't possibly be the curriculum or teaching methods.
"...but too many students get the idea that they can’t do math."
Because fuzzy math doesn't explicitly teach the kids in any systematic way. It's not like fuzzy math hasn't been around for a long time.
"This damages their inclination towards learning other forms of mathematics."
And what other forms of math can be done without mastery of fractions or rational expressions? After you learn these other forms, then learning fractions is easier?
You don't solve a problem by claiming that the problem doesn't exist.
"Given the importance of mathematics and the widespread mathphobia sweeping the land, students can ill afford to a diminution in their self-image as capable mathematicians."
The importance of what kind of mathematics? If students don't know how to do fractions, then what kind of self-image can they possibly have?
"Educators should not be complicit in creating learning disabilities regardless of what the President or his friends say."
I guess you never have a learning disability if you never attempt to learn anything. If you redefine education enough then nobody ends up with a poor self-image no matter how bad the curriculum or teaching.
They redefine the goal but say that their methods are better anyway. Isn't that what EM says? We disagree with the goal, but we do it better anyway.
EM and TERC have been around for ages now. We should be seeing some results.
Show me the results.
I often mistakenly believe that general teachers couldn't possibly be stupid enough to fall for the edu-speak espoused in teacher's colleges or from the so-called upper echelon of quacks who define the next generation of edu-speak based on Dewey and Rousseau.
ReplyDeleteTo quote Hermione Granger from the first Harry Potter movie, "What an idiot!"
I have a degree in mechanical engineering and worked in a scientific and manufacturing area. If you wanted a decently paid skilled labor job (we're not even talking engineering) those guys needed to do algebra, and understand how to solve equations. They even needed trigonometry and geometry. Even an electrician needs to understand algebra and fractions.
To be an engineer (which isn't even as hard as being a genuine scientist), requires five college math classes--beyond calculus. If you can't understand and quickly do fractions, imaginary numbers, polar coordinates and other transforms, sovling equations, substitutions, rate-of-change, statistics, you will never, ever become anything other than a teacher in elementary school screwing up every other kid's ability to be an engineer or other high paying technical person.
The only people who don't need to know advanced math (including dividing fractions, trigonometry, etc) are sitting licking their own asses while teaching in teacher's colleges or telling teachers in teacher colleges what to think.
Gotta love this quote about Stager: "Mr. Stager's love for education is
ReplyDeleteevident in everything he does; he is a 'master teacher' who knows how
to lead children so that they experience learning without
being 'taught.'
http://www.stager.org/bio.html
It seems Mr. Stager has compared the traditionalist/conservative math camp to the Taliban. Who is more extreme?
Is this the same Stager who equates the National Spelling Bee to porn? Baaahhh!
ReplyDeleteSorry for broken link. Try this:
ReplyDeletehttp://www.huffingtonpost.com/gary-stager/spelling-porn_b_104441.html
One can make a good argument against the National Spelling Bee. But what, exactly, is that argument? The closest that Stager comes to making a valid complaint is when he assumes that schools take time away from other subjects to study spelling that is beyond what is already in the curriculum. He doesn't back that up at all. Bye, bye argument.
ReplyDeleteMy son likes the spelling bee. It inspired him to listen carefully to pronunciation, practice with spelling lists, and study word origins ... on his own time. I don't encourge him because (after a certain point) there really are more important things to study. I'd rather that he get involved with the Geography Bee, or something else.
But Stager opens up the door to a discussion of effective use of school time. I don't think he really wants to do that. I'll start talking about the school having my son draw a picture of his favorite scene in a book rather than learning how to write about it.
My 8 year old son saw some the National Spelling Bee last night. He was mesmerized. Within 10 minutes he said "I WANT to be on the spelling bee".
ReplyDeleteIt is too provoking; I must rant.
ReplyDelete“Fifty percent of all mathematics has been invented since World War Two”
I find myself just appalled at this argument. I expect it is true by some measures that mathematics has doubled in the last 50 years or so, but really learning (rather than looking at pretty pictures someone else has drawn) about _any_ of that new mathematics requires that you first know fractions and algebra thoroughly. _All_ of this new mathematics is way off at the frontiers of mathematics, and you can't get there without learning the same basics the people who created it learned. To say a student who doesn't understand the basics can still do fractal geometry, is like saying that I can do general relativity, just because I've found an applet that illustrates what happens when you get near light speed.
"Given the importance of mathematics and the widespread mathphobia sweeping the land, students can ill afford to a diminution in their self-image as capable mathematicians."
I really have a problem with the whole self image thing. We need people who can be capable mathematicians. In order to get some of these people, we need to be teaching fractions and algebra well, so that these people have a chance to develop.
Students should feel that they have valid and valuable options for their education and life even if they can't divide fractions: the world has need of plumbers and salesmen and writers and so forth, and none of these people really need to be able to divide fractions.
Students should feel valued for what they can do, but it isn't much good in the long run to pretend they can do things they can't. Having a country full of people who think they can do math and can't, just isn't going to get us anywhere.
students can ill afford to a diminution in their self-image as capable mathematicians
ReplyDeleteOf course the most direct approach to the "diminution in their self-image" problem would be to effectively teach students their math basics. So their self-image would corespond with reality.