We've completed the upgrade to Movable Type 3.33. Readers of this web log will notice nothing. Those stupid enough to host with us will notice prettier icons on the backend. That is all.
I think I may have found my all time favorite staging of Les Filles de Cadix on YouTube of all places. Oh, YouTube, your hilarious opera videos fill me with great pleasure yet your ability to let anybody post videos of themselves doing stupid things fills me with sadness.
When I first decided to enter the educational arena I was told that I would always have a job but would be continuously disappointed because those in charge of educational reform would generally be clueless and the media would write about education without having much of a clue about how it actually works.
I'm beginning to understand the truth in these words. Education is a tricky subject because everybody thinks they're an expert on the basis of having gone through the system. Math education is especially tricky at the elementary and middle school levels because everybody thinks they know how to do elementary and middle school mathematics and, hence, can teach it well. I was recently dismissed from a project because, God forbid, I had the audacity to tell the developers that their content wasn't mathematically sound. (You can teach decimals by examining yardage on a football field! Speed isn't a rate! What do you mean there's not ONE general equation to describe ALL motion?!? Can't you calculate the position of an object at any time by dividing distance by time? DING! DING!! DING!!!) I envy mathematicians because their knowledge is so specific and expert. Joe Schmoe down the street isn't going to argue with a mathematician about the Poincaré Conjecture. [But this loop on my basketball converges to Jerry West's ankle!]
Add to this the low opinion of educators and educational researchers and I'm beginning to understand that I'd be better off telling people that I'm an expert trash collector rather than a wannabe math educator. Sadly, that reputation is sometimes warranted. I've gone to conferences where "cutting edge" research shows that students in poor neighborhoods have less technology at home than students in rich neighborhoods. [Really?!? Oh, my fucking God! Well, I quit! My work here is done!] Another time, a tenured faculty member claimed in a talk that countries in Asia are moving toward a more constructivist curriculum. Somebody in the audience reasonably asked: "Could you tell us in which countries that change is happening?" A perfectly legitimate question. The response? "Well, I actually don't know. But if some Asian person from one of those countries is here today perhaps you could talk to us about it." My mom was right. I should have stood right up and said, "Hello. I'm an Asian person and hence universally represent all Asians. Furthermore, I am a researcher at the University of Asia and no such thing is happening in our country."
So I suppose it shouldn't surprise me that articles out of major newspapers last week commenting on the new NCTM guidelines were written as if the writers hadn't even read the guidelines. Now, I'm not defending the entire guidelines. Some of the stuff in it is actually pretty idiotic, but surprisingly enough no one mentions those things. Instead, most articles and editorials are painting this to be a major shift that will ameliorate all of mathematics education. It's as if we've been teaching nothing for the past 17 years. The one from The New York Times is particularly great for its pithy uselessness.
In a major shift from its influential recommendations 17 years ago, the National Council of Teachers of Mathematics yesterday issued a report urging that math teaching in kindergarten through eighth grade focus on a few basic skills.
If by "a few basic skills" you mean the mathematics curriculum from kindergarten to eighth grade. What the writer means by "a few basic skills" are actually curriculum focal points, 3 per grade. Each focal point contains more than just "a few basic skills."
For example, here's the curriculum focal point for whole number multiplication.
Students use understandings of multiplication to develop quick recall of the basic multiplication facts
and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized
groups, arrays, area models, equal intervals on the number line), place value, and properties of operations
(in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and
generalizable methods to multiply multidigit whole numbers. They select appropriate methods and
apply them accurately to estimate products or calculate them mentally, depending on the context and
numbers involved. They develop fluency with efficient procedures, including the standard algorithm,
for multiplying whole numbers, understand why the procedures work (on the basis of place value and
properties of operations), and use them to solve problems.
Yes, the basic fact here is to develop fluency with multiplication. But it also includes an intimate knowledge of place value, distributive property, modeling multiplication, and understanding the multiplication algorithm. If you think that's easy then ask yourself if you can accurately justify and prove each step in the multiplication algorithm. To me, this focal point is more than just knowing a basic skill.
If the report, "Curriculum Focal Points," has anywhere near the impact of the council's 1989 report, it could signal a profound change in the teaching of math in American schools. It could also help end the math curriculum struggles that for the last two decades have set progressive educators and their liberal supporters against conservatives and many mathematicians.
End the math curriculum struggles when every district is free to set the curriculum as they see fit? That seems like a dubious claim at best. Also, it's a fallacious claim that every time a new set of guidelines is released every teacher in the United States suddenly has a soul searching moment and says: "Gosh, darn it! I've been teaching it all wrong! Time to change the way I teach!" Teachers teaching in their first five years are mainly trying to understand classroom management. That is, they're just trying to get by. Also, most teachers teach the way that they were taught and only incorporate new methods when they find that it radically makes their lives easier. Case in point: the general reaction of California teachers when asked about the math wars and curriculum change during the 1990s is: what changes? But it seems like every time new guidelines are released, the commentary is that the entire educational scene is going to change overnight. What we really need to do is take the business of teaching math teachers more seriously. We may even, I don't believe I'm actually suggesting this it's so radical, have math methods courses taught by people who have actually taught mathematics! And we might even want to teach elementary school teachers a bit of math content instead of telling them that as long as they have the answer key they're a-okay!
At a time when most states call for dozens of math topics to be addressed in each grade, the new report sets forth just three basic skills for each level. In fourth grade, for example, the report recommends that the curriculum should center on the "quick recall" of multiplication and division, the area of two-dimensional shapes and an understanding of decimals. It stopped short of a call for memorization of basic math facts.
Having deep understanding of these topics relies on intimate knowledge of the entire rational number field which some students don't even have by college. Also, last I checked "quick recall" is isomorphic to memorization. Honestly, though, NCTM members: "quick recall"? As opposed to what? Slow recall?
The 1989 report is widely seen as an important factor nudging the nation away from rote learning and toward a constructivist approach playing down memorization in favor of having children find their own approaches to problems, and write about their reasoning.
"It was incredibly influential," said Chester E. Finn Jr., a Department of Education official in the Reagan administration. "More than half the states explicitly acknowledged it in devising their own standards. This report is a major turnaround."
Dr. Finn added, "This is definitely a back-to-basics victory, emphasizing the building blocks children have always learned that a large part of the country believes are important, and moving away from the constructivist approach some educators prefer, in which children learn what they want to learn when they're ready to learn it."
Did anybody read the guidelines? Yes, NCTM specifically talks about algorithmic importance throughout the strands. They also spend a hell of a lot of time talking about having an understanding of these algorithms, using alternative methods, and connecting the algorithms with problem solving. The problem with most mathematics students (up to and including college) is that they have a bunch of algorithms and formulas memorized but little sense of how to use and compose them to solve complex problems. They're able to do particular classes of problems but ask them to do a similar problem that has different wording or context and they're lost. It's akin to being able to paint, sand, hammer, etc. but having no clue as to how to build a chair. So these back-to-basics people look at he guidelines, see "memorize" a few times and declare: "Now we've fixed mathematics education! Huzzah!" Sorry, folks. It'll take a lot more than memorizing a few algorithms before everyone is fluent in the Calulus. In fact, I'm surprised these back-to-basic people aren't terrified. The guidelines call for being able to have fluency with adding and subtracting decimals by fifth grade. I'm sorry, but if you can't add and subtract fractions by fifth grade you're in a world of trouble.
Finally, the term constructivist now has the connotation of an entire room of students not doing math but instead writing essays about how they feel about math. However, teaching a true constructivist curriculum is a lot of hard work. It requires generating tons of curriculum material and, most difficult of all, actually listening to kids to find out what their thinking is and instantly being able to target misconceptions. This means having extensive content knowledge (you'd be amazed at how much kids can learn if you know how to frame questions and answers) but also an intimite understanding of how they learn and how to challenge their thinking at any moment. It also means doing lots of formative assessments during a lesson so the right activities and treatments can be given in a timely manner to effect instruction. Overall, a ton of hard work and not fuzzy at all. I don't think any true constructivist would say that constructivism is just about letting kids explore the world and suddenly they'll invent mathematics before our eyes without any direct instruction. But again, I doubt anybody who declares constructivism in these terms has actually read any of Piaget's work with kids. Oh, well. Par for the course I guess.
Well, my beloved Oakland A's have clinched despite not having a .300 hitter, having their best hitter and pitcher on the DL for most of the season, and, in general, having a team that on paper looks like they should have won about 50 games.
Sadly, with the 2000 - 2003 disappointments, I will reserve celebrating until they're a strike away from winning the World Series.
Entertain me phooeyhoo. I have resorted to Google Video because you have no new posts. I don't care about your fancy dancy car anymore.
Hmm ... seems like a rather sad commentary on Wilderness's life if he resorts to reading this web log for entertainment. However, ask and ye shall receive in the form of random thoughts.
I've probably e-mailed this to everyone, but just in case, MOST hilarious and yet MOST disturbing at the same time:
In the Great Spams of the Internet department we have: a tea that will dissolve fat. I can just see this being turned into one of the essay questions on the GRE: assess the validity of this advertisement.
I have a great idea for the sport of tennis that will revolutionize the sport, get increased fan interest, get those lazy scientists off their asses, and, best of all, give a degree of comeuppance to players who annoy me. With all the people who have played The Adventures of Link, I'm surprised that no one has ever thought of this idea.
Okay, here's the deal. Before a tournament, every tennis player will have a genetic clone made of them. The winner of the tournament will have to face his or her doppelganger in the "true final" battle. The doppelganger will be genetically isomorphic to the player with one exception: everything is magnified by a factor of 2. So, for example, Sharapova's doppelganger would be twice as loud on her shrieks and eat twice as many bananas during a match. Henin-Hardenne's doppelganger would be twice as bitchy, twice as likely to shout "Allez!" during the match, and twice as likely to lie about raising her hand. Lleyton Hewitt and Rafael Nadal's twins would pump themselves up on virtually every point win or lose. This would slowly teach players who do annoying things like shriek on every point, pump their fists when their opponent hits a ball into the net, and constantly shout "Come on!" or "Allez!" after each point a bit of restraint. Since the doppelganger is made before each tournament, if a once terribly annoying player becomes less annoying before a tournament, then so will their doppelganger.
Of course, in some ways this could benefit the actual player. Amelie Mauresmo's doppelganger would have twice as much variety to her game but would be twice as likely to choke at critical points in the match. Henin's twin would be twice as likely to retire from a match due to stomach cramps. Some players would actually really benefit from playing their doppelganger. Kim Clijsters's doppelganger would be twice as nice and would want twice as much to talk to the other girls rather than her trophies after she retires. This would probably lead to strange moments where Clijsters's clone would challenge a call to benefit her opponent. Roger Federer's clone would also be twice as nice and would send get well cards to anyone who so much as scraped their knee during the tournament.
Of course, unlike in Adventures of Link, players will actually have to beat their doppelganger at tennis: crouching in the corner of the screen and thrusting with a sword won't cut it. ATP tour and WTA tour: it's in your court now!
In Match Point, the lead character is asked who it was tougher to play against: Agassi or Henman. For the non-tennis folks amongst you who are wondering why I would mention this, it's akin to asking a former NBA player who was harder to guard: Scottie Pippin or Harold Miner.
How is posting to your blog to tell your side of the story a postmodern moment? I guess it shifts power somewhat to the blogger to create experience. That's somewhat of a stretch though. It's too bad that Hakuin isn't around now as a postmodern Zen Master. His blog might look something like this.
David Nalbandian on Lleyton Hewitt: "I'm not his friend, nor is anyone else, but that doesn't worry me."
Headline: "Super-sub Kukoc set to call it quits." In related news, nobody really cares.
On that subject: what the hell is a super-sub? Where do they come up with these terms. That's like saying: super-utility-infielder or super-middle-reliever.
I am finally free of television! Well ... almost. Last January the service at my apartment was switched from cable to DirecTV. Others in the apartment rejoiced. Free DirecTV and more channels! I, however, was a bit more subdued as the DirecTV does not lend itself to being recorded by GBPVR unless you manually change the receiver channel which was way too much work for me except during the French Open and Wimbledon. So I essentially watched very little television from January until the summer when the watching approached an epsilon greater than zero due to work. Lo and behold: I didn't miss it! I was free! But then comes the almost. When Alex was in town we taped a few episodes of Weeds. Fantastic little show. Oh, well. It's only 30 minutes a week. Plus, since Sibel took her television from the living room when she moved out there are technically no televisions in the apartment which will curtail random TV watching.
Rich Harden goes against Cleveland on Thursday. Do I dare get my hopes up? With a pitching staff of Harden, Zito, Haren, and Blanton we now have as much chance as anyone to win the pennant. Without Harden? Hmm ... maybe we could convince that Toe-ma guy to pitch.
Some of you know that I amuse myself by attending graduate school in math education. I've made a terrible mistake. The system is irrevocably broken and will never be fixed. Those who are in power don't care and, actually, have no real power anyway. Send your children to a private school. My work here is done.
What did we ever do before video sites. Oh, right. We actually got useful work done.
