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Math

There’s an op-ed piece in today’s New York Times about the ineffectiveness of “fuzzy math” instruction:

One of the most infamous fads took root in the late 1980’s, when many schools moved away from traditional mathematics instruction, which required drills and problem solving. The new system, sometimes derided as “fuzzy math,” allowed children to wander through problems in a random way without ever learning basic multiplication or division. As a result, mastery of high-level math and science was unlikely. The new math curriculum was a mile wide and an inch deep, as the saying goes, touching on dozens of topics each year.

I was shocked about this time last year when I was substitute teaching for a few weeks at the level of math juniors and seniors were working on. “We did that in fourth grade,” was K’s response.

K, studying for a national licensing exam for the last few weeks, recently revealed that the math she was working was “fun.” Matrices and such. “When did you learn that?” I asked, fearful of how her response might indict American education.

“Well, we started learning about it in primary school.” Around seventh grade (at the time, primary school in Polska was K-8).

Now some American educators are aiming for algebra by the seventh grade:

Under the new (old) plan, students will once again move through the basics — addition, subtraction, multiplication, division and so on — building the skills that are meant to prepare them for algebra by seventh grade. This new approach is being seen as an attempt to emulate countries like Singapore, which ranks at the top internationally in math.

The question is, what are students in Singapore studying in seventh grade math? I’d be willing to bet that, like in Poland, they’ve left algebra far behind by seventh grade.

The answer to catching up with some parts of the world in the education level of our schools lies not only in curriculum changes – rearranging deck chairs in the oft-used cliche. The answer depends, in part, on more educational time: a longer school day and a longer school year.

Out of the Closet

So I recently admitted to reading the Washington Times.

Sure, it’s a rough-and-tumble mouthpiece of the right wing, but it’s so much fun. Just look at this stuff from the op-eds:

  • The French irritation with America grows out of wounded pride, a sense that France is not as important in the world as it once was, but a President Sarkozy might restore some of that lost pride and with it an appreciation for stronger links with America. (Suzanne Fields)
  • The following are the chamber remarks of the fictional Lord Harold Reid (whose fictional grandson, in the 21st century would become leader of the fictional Democratic Party in the U.S. Senate).I regret to have to stand up tonight, on the day of defeat at the hands of the Germans of our French ally’s armies at Sedan and on the Meuse River to observe that on this solemn occasion Prime Minister Winston Churchill has chosen to politicize and cheapen the moment. (Tony Blankley)
  • Just as the mainstream media is fond of Bush bashing and calling all Republicans right-wingers — even when there is no conspiracy — the local press view politicians through biased eyes. They demonize pro-life politicians as anti-abortion rights; they view advocates of school choice as opposing public schools; they write profusely about a Jewish Democratic candidate Ben Cardin beating Kweisi Mfume, who has a African name, in Maryland with only 44 percent of the Democratic vote, and practically ignore the fact that Michael Steele, a black Catholic Republican, bested his primary run with 87 percent of the vote — nearly twice that of Mr. Cardin. (Deborah Simmons)
  • Yet the ephemerality of the sense of solidarity, to me, seems more an indication of its artificiality than of squandered sustainability. The United States, in the post-September 11 world, would be going places where few would be able to follow even if they were inclined to do so, starting with Afghanistan. Because Afghanistan was a quick success in terms of ousting the Taliban government and scattering al Qaeda to the four winds, people tend to forget the “graveyard of empires” analysis that swirled around the notion of dispatching the U.S. military to undertake “regime change” there. People also tend to forget the early reports of a bogged-down operation. (Tod Lindberg)

Good stuff…

Seriously, though, I find it difficult to understand folks who say, for example, “Oh, I never read the New York Times — too much liberal bias.” How would one know, then?

“I don’t watch CNN because it’s owned by Ted Turner.” “I don’t read the Washington Times because it’s owned by Sung Yung Moon.” I don’t see much difference.

Occasionally I’ll even find myself somewhat agreeing with the WT — but that’s for another day.

Blind Irony

I’m certainly not the first to comment on this, but it’s been rattling around in my head for a couple of days.

Action and reaction:

  • The pope makes comments that, when taken out of context, can be interpreted as implying that Islam is a violent religion.
  • Some Muslims react by shooting a nun and others by fire bombing a church.

I really feel like a wing-nut for saying this, but…

  • Why are we not hearing equal outrage in the Muslim world at these violent reactions?
  • Why, when Madonna used crucifixion imagery in her latest tour (BBC), did we not get riots and violent protests at the Vatican?
  • Why, when Jews are insulted, do we not see violent protests in Tel Aviv and Jerusalem?
  • Why can various Muslims (including the leader of Iran) call for the destruction of Israel while we non-Muslims are expected to tip-toe around troubling ideas found in the Muslim world?

Update: Just after posting this, I read in the newest The Week of a Dutch priest who, angered at Madonna’s depiction of the crucifixion, phoned “in a fake bomb threat to a Modonna concert. […] He was tracked down easily because he called from his home phone.” Google turns up a few stories about it.

Four Inches of Paper

The staff at the center I work has been, from time to time, encouraging me to take a look at the psychological profiles tucked away in each student’s file. The other day, I finally got around to looking at them.

It’s the closest I’ve come to holding anything “Classified” in my hands. Big thick folders filled with forms, evaluations, surveys, histories, and legal documents — all of it confidential.

While working in an EC classroom last year, I sat in on a couple of IEP meetings. The IEP (“Individual Education Plan”) is a road map of issues, proposed solutions, expected outcomes, and standards for quantifying success prepared for each student receiving special services.

IEPs are usually heafty tomes as well.

The discussion ranged from previous goals to the student’s medical issues, from how to incorporate the student more in regular ed opportunities to amusing things the student had said recently. Throughout the meeting, teachers, administrators, and parents alike referred to the child’s records on file — also a Tolstoy size packet of forms, notes, and evaluations.

It was a long meeting, but for me as an observer, fascinating.

“What if we had this kind of involvement for each and every student?” I muttered to my colleague as we left the meeting.

Fence

From our walk yesterday.

Fence

The weather has finally improved after at least ten days of clouds and rain. K and I made the most of it.

Reading List

Frederick Wirth writes in Prenatal Parenting of an experiment Anthony Casper conducted at the University of North Carolina regarding parental reading and prenatal development. He had mothers read Dr. Seuss’ The Cat in the Hat to their unborn children twice a day. A few days after birth, the infants were given a chance to hear the story again. However, using a device fitted with a special nipple, the infants could change the story being read by changing the rate at which they were sucking.

As demonstrated by their sucking speed, the newborns remembered The Cat in the Hat better. Furthermore, they preferred it read forward instead of backward. (Wirth, 37)

So I guess in a way I was wrong when I suggested that our daughter might prefer Shell Silverstein to Robert Frost.

Or, looking at it another way, here’s a chance to get my daughter interested in all the nerdy literature I love.

Of Mans First Disobedience, and the Fruit
Of that Forbidden Tree, whose mortal tast
Brought Death into the World, and all our woe,
With loss of Eden, till one greater Man
Restore us, and regain the blissful Seat,
Sing Heav’nly Muse

I aim to give L a headstart on senior lit…

Reading and Walls

Wirth CoverIn my “Currently Reading” pile of books lies Prenatal Parenting by Frederick Wirth, M.D. Most interesting so far have been the sections on fetal sensory development, particularly the development and growth of the auditory system. Wirth writes that at “twenty-two weeks of gestation the developing infant will respond to sounds from outside the womb. By twenty-eight weeks the infant responds to sound in very consistent ways.” (28) And so K talks to her walk driving to work, and I press my cheek to K’s belly nightly and tell our daughter how much we’re looking forward to meeting her.

K and I have been playing a little music box for our daughter nightly for some weeks now, but recently, we’ve added reading to the ritual.

It should have a noticeable effect:

I can always tell which of my full-term newborn infants have been read to. They have more mature orienting behavior to auditory stiumli. I can even tell which fathers have been active in reading to their unborn child. I do this by holding the infant between me and his father while we compete for the infant’s attention by calling the child’s name. If the dad has been actively involved in the reading and singing, his child will turn his head toward him, looking for the source of the sound. Invariably, when their eyes meet they both react positively. (Wirth, 29)

SidewalkOften, it’s selections from Where the Sidewalk Ends, not so much because L will like it more — obviously, fetal brain development at this point is not that advanced — but because K likes Silverstein’s playful language.

Tonight, Robert Frost, concluding with one of his best, one of the best, period: “Mending Wall.” It has one of the truest passages ever written:Wall

Before I built a wall I’d ask to know
What I was walling in or walling out,
And to whom I was like to give offence.
Something there is that doesn’t love a wall,
That wants it down.’

Such concerns seem largely forgotten these days.

Fan

Cleaning the Fan I

Cleaning the Fan II

Scorecard

ScorecardAt the day treatment facility where I work, we use the Teaching Family Model (see Teaching Family Association), a method of behavior modification that at first seems a little silly, but becomes more reasonable the more I work with it.

Basically, it’s point system, with each student (or “consumer” in the social services parlance) having a point card, which staff members use to help the consumer (really, I hate that term; what is being consumed?) keep track of beneficial and detrimental behaviors. Basically, for doing something good, they earn positive points, and that word choice is critical — we’re not to say we “give” them the points. For doing something negative, they earn negative points.

“Bob, I really liked the way you took the initiative when you saw the trash needed to be taken out. Take your point card out, please. I think you’ve earned a thousand points for that.”

“Sam, I need you to take your point card out. You know that using profanity is socially unacceptable, and can really lead to a bad impression of you as an individual in many situations. I need you to take of four thousand points for swearing…”

The points are then used as a gauge for moving up through the treatment levels, each of which requires more responsibility, but also has more privileges.

Usually, we staff members tie their points into their individual goals for the day, or their general program goals. That way we’re reinforcing the same basic things, rather than assessing random behavior.

“It all seems so artificial,” I initially thought. “People don’t go through life with point cards.” But watching the behaviors the students (I’m their teacher — I shall call them “students”! What assertiveness…) struggle with, I came to a different conclusion.

While no one carries point cards in the “real world,” we do go through our day assessing points mentally. If we meet someone who reluctantly holds out his hand when he meets us, weakly shakes our hand, mumbles, and refuses to make eye contact, we assign that individual negative points in our mind, consciously or not. On the other hand, meeting someone who seems gifted in conversation and immediately draws us to him/her racks up positive points. That’s what “making a good impression” is: positive points on our mental score card.

Making points depends on following the rules of society, which has “decided” that certain things are acceptable, others are not. Yet many of the students I work with are not aware of these rules — the rules of the game, one might say.

Soon after I’d started working at the facility, I was having a conversation with another staff member in the presence of the students, and the student butted in to tell me how I was wrong, how what I was saying was stupid, and how anyone with any sense would no better. Now, his tone was not overtly disrespectful, but his interruption certainly was, as was what he actually said. When I told him to give himself negative points for being disrespectful, he was genuinely puzzled, not to mention angered. A heated discussion almost ensued. Instead, we were able to calm him and explain that, while he might not have intended any disrespect by it, I felt it was disrespectful. “And unfortunately,” I explained, “disrespect doesn’t depend solely on the definition of the speaker, but also — more so, even — it depends on the definition of the listener.”

The Teaching Family Model’s point card system simply tries to make students aware of the mental point assessment that’s going on all around them. It’s intended to help them keep a positive score on the mental scorecard of those in authority.

Whether it works or not, I can’t say. Much of it depends on consistency. Perhaps key, though, is making sure the students don’t see point deductions as punishment, which is much more difficult than it might seem. Privileges depend on the number of points a student might have. There are “gates” at our program, thought they might be described as levels. With each gate come more privileges, as well as more responsibilities. Moving up to the next gate, in turn, depends on having a certain number of cumulative points. This is certainly not the only thing necessary to move up a gate, but it is an important facet. To gain points, a student must be consistently improving his social skills. Thus, taken altogether, it’s easy to see how students view a point deduction as a punishment. It’s too abstract for some of them to think of the staff as simply score keepers working within a framework imposed, even on us, from the outside.