What I like about option number 3 is that (in my opinion, at least) it would exclude curricula like Everyday Math (IIRC) that do not teach an efficient algorithm for long division or manipulation of fractions.
This would be a huge improvement in any state curriculum. Lack of fluency is the biggest problem we see when these kids get to college, nationwide.
In addition, the "Language Arts" requirement should include knowing the definition of "instantiation", since that is an important word in computer languages ... and also sounds cool.
I'm fairly sure that NCTM thinks it's important to teach both the use of algorithms and also an awareness that an algorithm is just an algorithm, not the Word of [your deity of choice]. I have no clue what Everyday Math is, as a series or text.
By the way, have you ever run across Jakow Trachtenberg's trick of doing long division without knowing division?
As a former math grad student, and college algebra teacher -- where is the visual aspect to all this?
To me, graphs and curves are the life of the party.
Also -- 139 pages???? yikes! I thought you said this was simpler?
Oh yeah, and this:
There was a time in American education that the secrets of algebra were reserved for college freshmen!
The history of algebra is interesting too -- the original addition of fractions with different denominators was
used for determining what your inheritance was!
And trade (dividing up booty???).
Although most persons with any real connection with mathematics realize that efficient algorithms are important, that understanding does not extend to all educators who produce K-8 curricula. The history of these abominations and the parental battles against them might make an interesting study, Sherman.
As Glen no doubt realizes, you can't do division with polynomials or do integration with rational functions unless you have certain skills that start with the ability to work with fractions and do the long division algorithm we learned as kids. That puts the victims of certain curricula at risk when they get to algebra.
Maybe the way to put it in context for you, Sherman, is to describe it as "look say". Rather than teach a simple algorithm for decoding and comparing fractions, the students guess at answers. One group of parents say the only advantage of the curriculum their schools use is that it is so bad the parents hire tutors, who actually teach their kids math.
And Glen, we are rapidly returning to the time you refer to, when "college algebra" (my high school algebra 2 class) was reserved for college freshman (as it was in my parent's day). I'd wager that the majority of high school graduates in your state of Florida have to take "college algebra" in college. College math placement testing statistics I have seen indicate that the passing level for the FCAT is somewhere around 8th grade in my high school curriculum. How many college freshmen start at or below college algebra in Florida?
Glen,
I don't see how the standards exclude graphs. The point of the "big ideas" (which are largegly identical to the NCTM focal points) is to prevent math standards from becoming a kitchen-sink ensemble.
CCPhysicist,
I am skeptical of claims that the NCTM 1989 standards destroyed math education. The evidence from NAEP is to the contrary. In Florida, for example, 8th grade NAEP average scale scores have been on an almost exactly linear trend upwards since 1990. That doesn't mean necessarily that NCTM's 1989 standards should receive the credit, but the criticisms are overblown. If you look at the 2000 standards, "compute fluently" is clearly in there.
Yes, the history of math education would be a great topic for a book. I'd have much broader questions than just the arguments over NCTM. How algebra replaced Latin as a "gateway" status topic is a big one. But there are others--maybe in 5-10 years?
Sherman, The only graphics I saw was the "figural rhetoric" of the layout of the 139 pages! 
When I taught College algebra 11 years ago, I was astonished at the range of student walking through the door. All different. One girl didn't know the diff between 2x2 and 2^2!
Some were coming from AP Calc in HS, but knowing nothing.
This even happened to a relative of mine.
Just reading about business and higher ed (1956), and how Eliot is winning the battle of Latin over algebra. I guess the arrogant Committee of Ten lose the war, though.
Some great quotes here, but flowery language, etc., make it very very difficult to read! 1956 author looking at 1860-1900 through the eyes of businessmen ...
CCPhysicist said: "I'd wager that the majority of high school graduates in your state of Florida have to take "college algebra" in college."
Hm ... Yeah, but the big change is that we NOW say EVERYONE has to meet this goal!
The minimum credential, algebra, keeps growing to encompass, not just those in college, but everyone, even those in HS.
This trend is untenable in the long term.
9th graders taking AP courses is eating your seed corn. This no longer has anything to do with learning, and I pity the masses of kids marched off into the maw of this Moloch, this new meatgrinder.
I don't see where I claimed that the standards have anything to do with the horrid state of education in Florida, nor am I impressed by a linear increase if it went from horrid to merely bad. Didn't Florida once have average HS grad reading scores down below the middle school level?
Math education was destroyed by elementary school teachers who hate math, and it can only be fixed by undoing that damage. (Oddly enough, I was led to your blog from profgrrrrl's, and led to hers when my brother pointed to an anecdote about future teachers celebrating never having to do math again after getting out of their hated math ed class.)
Glen, it is not the case that everyone has to take "college algebra" to graduate from college in Florida. It is not even required for teacher cert any more.
CC,
When I taught community college algebra, it was required for graduation. And it still is,
BUT there MUST be a way around it, somehow.
Let me describe an incident that has bothered me for years.
I once had a chance to tutor a 4 yr FL grad what previously graduated community college (including, I suspect, college algebra) -- for the FL General Knowledge (8th grade) teaching certification exam.
She was terrified of the math -- and for good reason: she did not even understand basic proportions ( a/b = c/d ).
Now, I think my dad showed this to me in sixth grade, but I don't think this woman had ever seen it before, ever.
My gnawing question is how the heck can you pass college algebra, and NOT know basic proportions?
So, I conclude that there must be some way of getting around this.
I also have no idea what community college educational quality controls in the form of exit-testing there is to prevent this sort of thing.
I do know that there must be some way around the CLAST entry-level testing of CC students, because a couple of times over the 9 years I taught, I had semi-literate students, one with about a 2nd grade reading level. But that is another story.
CCPhysicist,
At one level, you're absolutely right that elementary school teachers who hate math are a central problem. That's one form of the generational challenge: how do we make sure that the next generation is smarter and perhaps even wiser than we are? ... or, in this case, learn and enjoy math more than we do. And if elementary teachers communicate a fear of math, or a perception that math is whatever they were taught poorly, then half the battle is lost right there.
At another level, there is a practical need for a greater teaching repertoire. You need to know both the underlying math and how to teach it (including identifying and correcting common errors that students make).
The third level is fighting against both of the dominant myths in the battle over math education: that math is either just calculation or just conceptual. I finally found some materials on Everyday Math, such as Math: An Inconvenient Truth, but I think the responses (part one and part two) by James Blackburn-Lynch are to the point: we need students who understand concepts and can perform standard arithmetic operations fluidly.
Another story: I struck up a conversation with a sixth-grade teacher during jury pool last year.
He said teaching was ok, if you got the students "to mind". Then, somehow, he mentioned "infinite numbers" -- what he meant were repeating decimals! I was shocked and dismayed by his ignorance.
My own romance with math (evident in the use of Cusp Catastrophe theory in my book) began in a 7th grade science class, when the teacher used d=1/2*a*t^2 to describe the distance of a falling object. I thought that was awesome. Still do.
I also thought the volume formulas were neat, too.
But fluency doesn't come out of a book. It comes individually, I think, and in different ways. If the focus is on the credential (on the test), then this detracts from fluency.
I was failing 10th grade geometry, but had a few sessions with a tutor my mom hired, and managed an A on the NY State Regents exam. Middle class advantages, of course.
But I still have those failing papers, and when I was in pure math grad school (again, not getting half of it, but some of it), I laughed about it.
Still, I had no business being in the PhD track, although I did pass 3 of the 4 masters level comprehensives. Problem was, I had no one (staff) to talk to, not even the idea that I needed someone to talk to about putting the credits into another masters program, like teaching math.
So, I left to get a 3 yr professional degree at Yale, which is also totally useless to me.
Yikes! That overview of TURK and Everyday Math was an eye-opener for me!
“The authors of Everyday Mathematics do not believe it is worth students’ time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole-number, fraction, and decimal division problems. Mastery of the intricacies of such algorithms is a huge endeavor, one that experience tells us is doomed to failure for many students. It is simply counter-productive to invest many hours of precious class time on such algorithms. The mathematics payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator. This said, the practical needs of students to succeed on standardized tests may require you to teach paper-and-pencil long division algorithms.”
No wonder kids are afraid of long division! It turns out, that their teachers are too! I think even the authors of this book "hate math"! Notice the contempt dripping over "paper-and-pencil" algorithms!
And the "fear of failure" here!
I can see some of the Deweyian concerns here, but let me back up a second.
A kindergarten teacher in NY that I know teaches basic reading and writing in kindergarten (!) using a full-blown constructivist curriculum. Through gleaning letters and words from the "everyday environment," they attach sounds to letters, etc., and gain mastery.
Some impressively so.
But "it doesn't work for math" she told me "because there only one right answer." I think about this a lot.
And you can see this "fear of failing" in the rejection of algorithms for multiplication and long division. Although cumbersome (very), they will get the answer, even without understanding digit-placements.
And that is were TURK fails -- by aiming at success for everyone, it gets stuck at a sub-par level of mastery that should be done virtually unconsciously in the background. It also takes a lot longer -- another obstacle -- given the short attention span problem.
Lastly, semi-constructivist "cluster" methods seem the result of the calculator invasion.
Another story. I was interviewing to teach 9th grade math at a vo-tech HS for students who failed FCAT. In that interview I learned that calculators are given to students taking the FCAT in 9th grade!
This may be another reason for the complete surrender in TURK. The inevitability of calculator use seems to cut off the teaching of division and multiplication at the knees.
A friend of mine was complaining that his kids weren't mastering long division (which HE associated with classroom "punishment"!!!), and consequently were being left back a year!
Lynch kept saying that math is about memorization, but this is wrong.
It is about solving problems. Word problems, etc.
He is right that the focus on textbooks obscures the political economy in which it plays a role.
But he has this assumption that everyone is supposed to get it, which I take to be a progressive myth of some kind. Everyone can only get it with prerequisites, and individual help if they need it.
He was right about 36/6, that we shouldn't stop with the answer without getting at the intrinsic numerical relations.
And to answer his question, what is math ed? there may not be an answer.
At the most cynical level, math ed is for those students who go for the next credential -- because in a world of calculators and talking heads, you do not need math.
No one counts their change anymore, and they might not even need to be able to read anymore either (some cannot, as I found - but they are gainfully employed anyway).
So, the cynical criticism says that all this is just job security for teachers and administrators -- and if you look at these math texts, you see the result of that.
Again, it is a result of the political economy.
Sheran said, "...no adult goes around thinking about things like number sense or measurement..."
Linguists do it all day.
Commenting by HaloScan
