## Monday, January 31, 2011

### PD Follies - part one, the Blind.

Professional Development Follies - part one.

Professional Development is one of those things that light up the stress meters in almost every teacher I've ever known. Bill Ferriter talks about it. So does Mr. Teachbad. Darren needed Google Translate to interpret the Educationese. What's my excuse? I have many things that trigger me and get my back up. Here, over the next couple of days, are some of those triggers.

When I went to get my commercial driver's license many years ago, I was faced with a guy who drove these vehicles every day. He knew the ins and outs, knew the laws, knew what was important and what had to be memorized for the test and then filed away. An expert who was teaching? How quaint.

How many times have I been in the room and the HIP, Highly Ineffective Principal, (thanks for reminding me, Richochet!) or an AP would get up and present as definitive fact a half-remembered workshop from the summer?

Too many times.

The more it was stressed that we were a "High School on the Move," the more stressed I got. With every new and improved "Best Practice," I wondered why no one, apparently, had never thought of this obviously brilliant idea before ... and then after maybe two seconds of thought, realized that it was pretty much what everybody tended to do anyway.

"We need to create A School Within a School."
"According to the Latest Brain-Based Research, students need to write about their feelings."
"I want all of the teachers to begin differentiating all classes with respect to the three Learning Styles."
"We're buying netbooks for each fifth grader because Maine did it and had the biggest gains in state history."

Before we should implement something, shouldn't there be at least one person who completely understands it? Perhaps we should rename this one as the "As Seen on TV" Initiative because it looks cool and shiny, no one understands it fully, it costs a lot (plus shipping and handling) and invariably doesn't work. Any of you suggesting we call it the "iRenew Initiative" can be quiet back there.

I'm not getting behind this nebulously defined initiative until someone clears it up and explains it. "You're being obstinate because you don't want to be a team player. You argue about every initiative."

Sorry. Got to do better than that. Argument by Accusation - not valid.

## Sunday, January 30, 2011

### Thanks for the Help

Gee, thanks Bill.
Joanne Barkan, writing in Dissent, argues that three big nonprofit foundations (the Bill and Melinda Gates Foundation, the Eli and Edythe Broad Foundation, and the Walton Family Foundation), working together, exert a “decisive influence” on public-school education. ”Whatever nuances differentiate the motivations of the Big Three, their market-based goals for overhauling public education coincide: choice, competition, deregulation, accountability, and data-based decision-making,” she writes.(h/t to the Freakonomics blog, Dubner and Leavitt.)
Unfortunately, this is not just about Bill, Eli and Sam wasting their own money.  It's about three foundations that are pushing an anti-public school agenda that aims to destroy the teachers' union and reduce the educational possibilities for the public. It's about the capitalization of an "industry" at all costs, using tactics that sound good on the face, but are mainly aimed at money.
But, Barkan warns, these market-based reforms are hardly a panacea: “[E]vidence is mounting that the reforms are not working. Stanford University’s 2009 study of charter schools—the most comprehensive ever done—concluded that 83 percent of them perform either worse or no better than traditional public schools; a 2010 Vanderbilt University study showed definitively that merit pay for teachers does not produce higher test scores for students; a National Research Council report confirmed multiple studies that show standardized test scores do not measure student learning adequately. Gates and Broad helped to shape and fund two of the nation’s most extensive and aggressive school reform programs—in Chicago and New York City—but neither has produced credible improvement in student performance after years of experimentation.”
Misguided reform coupled with tragically misguided legislation has left us with the same problems we had before coupled with many new ones.
• We have public schools in which the teachers at the top of their payscale (e.g., here in Vermont) with all the bells and whistles, degrees and seniority, still are earning less than the state median wage.
• You have charter schools opening up on the cheap, closing down significant public options, simply so that Green Dot and other groups can make a profit. The principal of such can look super while pulling in $200k to$500k but apparently a teacher making more than $30k is the AntiChrist. • You have organizations like Teach for America, set up solely to destroy teachers who want to make a career of teaching. How? By making it harder for serious candidates to get into places to establish themselves. Why would a school want a career teacher when it can hire a fancy thoroughbred that will seem flashy and pretty and fast, but ultimately flame out in two years? Instant gratification writ cynical. • You have reforms that are directly counter-productive, that "everyone knew were going to revolutionize education" but that really wound up wasting a significant portion of that budget that the pro-voucher, pro-private school advocates were pointing to as a problem in the public schools. • Think: Small Schools Initiative. (Break big schools into smaller ones and then bitch that the smaller ones don't have economy of scale.) • Think: Technology Uber Alles. Microsoft is the Education King! Every kid should have a laptop! Every kid should have a smartphone! iPod! iPad! Netbook! • Think: Parochial, Private, Charter, KIPP! Profit is better. • Think: Merit Pay! • Testing, testing, testing. Test them in October, release the scores in May. And I'm supposed to do what in the last six weeks of school to change my curriculum to help this kid? Like I said, Thanks. Now would you all please go somewhere and stop helping? ## Tuesday, January 25, 2011 ### Just be quiet and pay attention. Just once, I'd like the President to tell Congress to "Hold your applause until the end. Hey, you in the back. Do I need to keep you after class?" ## Saturday, January 22, 2011 ### It's a Rosy Picture, Rotten at the Core. I shouldn't need to add much to this: New York City’s top-ranked school is under investigation for cooking the books, reports the New York Times. Theater Arts Production Company School, a middle and high school located in a low-income Bronx neighborhood, graduated 94 percent of seniors, more than 30 points above the citywide average. The school earned a near-perfect score in “student progress,” based partly on course credits earned by students. The school’s no-failure policy requires teachers to pass all students who attend class, regardless of their performance; no more than 5 percent of students can get D’s. In practice, some teachers said, even students who missed most of the school days earned credits. They also said students were promoted with over 100 absences a year; the principal, rather than a teacher, granted class credits needed for graduation; and credit was awarded for classes the school does not even offer. When you tie teacher and admin pay to "performance", tie school survival to "attendance" and "graduation rates," it's not a stretch to imagine why people would lie. Should we blame Klein, Black, Bloomberg, Duncan, Obama, GWBII? Some combination of all of them? Or just go firing school officials? ## Thursday, January 20, 2011 ### Ray Allen wins again. Funny guys, those Boston Celtics. Winning on an awesome Ray Allen shot and immense Shaquille O'Neal shoulders. And yes, that tweet makes total sense. BTW, Reggie Miller: 2560 three-pointers. Ray Allen: 2533 three-pointers. 13-21 shooting threes for the last five games. When's the record gonna be? Data below the jump. ### Don't text and walk. 5 minutes of my life - gone. But it was funny. She was texting and walking, then tripped into a fountain. Splash. (You can see her there in the still, just about to fall in the water.) She instantly gets up and climbs out of the fountain, nothing hurt but her pride. "I fell in the fountain. I was so drenched." Mall security didn't rush out to help her. She called them the next day "I'm a mall employee. I don't want my employer to know." The story would have ended there but the surveillance video, as all video eventually does if it's embarassing or funny somehow, wound up on YouTube. (There's a lesson there, kiddies.) "I admit. It was funny, but (whiny sniffle) nobody took my feelings into consideration. Nobody called. Nobody went to my aid. It could have been anyone's mother." .... yeah, but it wasn't and she got up so fast that I'm not sure how anyone COULD have gotten to her before she took off. Naturally, she feels wronged and the lawyer smells deep pockets. A lawsuit is born. Lawyer wants to hold all responsible parties accountable, demand an apology, hold persons responsible for making the video public, blah, blah, blah. Aaaaaah, who gives a damn .... she walked into the fountain! But there is a message here. Swimmer girl's lesson: "Do not text and walk. Especially to the younger generation. The fountain could have been empty. I could have been hit by a bus. I could have been hit by a car. (sniffle)" Ain't that freakin' awesome? "I coulda been hit by a bus." How? YOU WERE IN THE FREAKIN' MALL! Let me think how this could have been avoided. ### PISA scores - another look. What do you see? When you look solely at schools with fewer than 10% of students on FRL (i.e., poor), US schools would be better than those of the top of the chart, Korea. When you include the whole spectrum of US schools and their students, the US is much lower. The US has a much bigger spread than any other country (the largest standard deviation of wealth in the developed world). Our overall scores are unspectacular because we have a high percentage of children living in poverty, over 20%. This is the highest among all industrialized countries. In contrast, child poverty in high-scoring Finland is less than 4%. For Cleveland and for the US as a whole, the major problem is poverty. Before we worry about teacher quality, institute longer school days, and increase testing, we need to make sure that all children are protected from the effects of poverty: This means adequate health care and nutrition, and access to books. When we do this, American test scores will be at the top of the world.-- Stephen Krashen ## Wednesday, January 19, 2011 ### Shocked. Alabama Governor is religious. "Anybody here today who has not accepted Jesus Christ as their savior, I'm telling you, you're not my brother and you're not my sister, and I want to be your brother," Bentley said Monday, his inauguration day, according to The Birmingham News. The Anti-Defamation League on Tuesday called Bentley's remarks shocking. "His comments are not only offensive, but also raise serious questions as to whether non-Christians can expect to receive equal treatment during his tenure as governor," said Bill Nigut, the ADL's regional director. Sorry to burst your bubble, ADL, but you're living in Alabama. What gave you the idea that everyone would be treated equally without fighting for it? Has Alabama EVER been anything but resistant to Muslims, Jews, etc? ### Techno-silly  Twain: Non sucky lecture. Rick Hess's blog was taken over by a guest (Meira Levinson, an assistant professor at the Harvard Graduate School of Education) who opined: As a professor, I am a techno-enthusiast: I'm constantly asking my students to do in-class activities using GoogleDocs or wikis, and I've moved all my lectures on-line on the grounds that it's criminal in 2011 to force a bunch of people to show up in the same room just to hear one person monodirectionally deliver information. Criminal? Interesting choice of words. Why should it be such an imposition for the students to show up to one place at a scheduled time? The reason they are (usually) required to be there is that lectures are rarely one-directional, unless the lecturer sucks. If I lecture, I am always looking for some kind of feedback if for no other reason than to ascertain whether any of them are awake. I guess if you're that boring or if you're just reading from, and never veer away from, a script then an attendance requirement should be waived, but that doesn't seem like much of a college to me. It's curious that the college manages to convince people that this online, easy-access, don't care if you do or not, video repeated for the third straight year is worth the tuition: Full-time Students Part-time Students Per Academic Year$35,568.00 Per Course/Per Term $4,446.00 If it doesn't matter whether or not the students are there, you might as well be running a video. Go ahead and put it online. ## Tuesday, January 18, 2011 ### Stupid I think Robert DeNiro is a brilliant actor. This does not necessarily translate over to education. "For the children, you just hope the movies do well enough so you can keep them in private schools." ### Algebra in the Third Grade? I got the NASCO 2011 catalog in my mailbox this morning. If you haven't dealt with them, they are a pretty typical school supply catalog - prices are double what you can find if you search diligently or ten times the scrounger's price. What it is really good for is as a wish list, a source for ideas. "How does that toy work? I could do that in the garage for$2 in materials."

My problem with them is that sometimes they really miss the mark. Here's the cover:

Really? Third grade and up? I rail all the time about my students arriving in 9th grade without a clear grasp of fractions and clueless about operations with fractions (sans calculator), limited fluency with percents and decimals, and an unsteady grasp of their multiplication tables and other basic stuff. I had usually blamed the 3rd through 6th grade teachers for not really understanding arithmetic and passing on any math phobias, but this seems like a major problem right here.

If the expectation is that this kind of thing is possible for 3rd grade and up, maybe it shouldn't be a surprise that fractions and arithmetic aren't getting as much attention.

My questions:
• Is this typical? Do third grade teachers really do this?
• Is it just a stupid cover by a catalog desperate to sell overpriced AlgeBlocks to a gullible school system?
• Shouldn't we be solidifying knowledge to the point of automaticity instead of spreading algebraic materials ever lower?
• I'm pretty sure that a few third graders could get this but is it appropriate for that level?
• Is it possible without manipulatives at this age?
Then, there's the other debate:
• Are manipulatives appropriate?
• Does the use of something tangible and obviously fixed in size get in the way of learning an abstract idea about a variable?

## Friday, January 14, 2011

### Not a two way thing.

 Genius, but not ignored or derided.
Many geniuses and their brilliant ideas are misunderstood, ignored or derided before being accepted by the mainstream as obvious.

This does not mean, however, that because you are misunderstood, ignored or derided, that you are a genius with brilliant ideas that deserve acceptance.

Just sayin'.

### Threats are threats, from either side.

WTMA reported:
An aide close to Sarah Palin says death threats and security threats have increased to an unprecedented level since the shooting in Arizona, and the former Alaska governor’s team has been talking to security professionals. Since the shooting in Tucson, Palin has taken much heat for her “crosshairs” map that targeted 20 congressional Democrats in the 2010 midterm election, including Rep. Gabrielle Giffords, who was the main target of Saturday’s attack.
So let me get this straight. Sarah Palin posts a map with crosshairs on it and she is a bad person because of this rather mild, yet undefined "threat" that only a certifiable nutjob would interpret as instructions and that everyone else should "tsk-tsk" and ignore. The appropriate response, according to the unwashed masses, is to send her death threats of their own? A vague threat warrants a specific one? In what universe are you all living?

Come on, people. Try to maintain logic and reason here.

## Wednesday, January 12, 2011

### Chinese Mothers and KIPP

The other day, I posted an article by a Chinese-American Yale Professor describing the way she brought up her kids. In it, she speaks of no play dates, hours of practice at the piano and the violin, drills and drills on homework, an endless desire to get As and harsh language when the lone B arrives on a report card.

The commenters on the WSJ site were, as might be imagined, SHOCKED that such behavior wasn't considered child abuse, that the woman was mistreating her children and that there was something terribly wrong with her parenting skills. All of those commenters would be SHOCKED if their little darlings were subject to that regimen.

It occurred to me that this is pretty much what KIPP does. Drill, drill, and more drill, extremely high demands on time, teachers driven nearly crazy in their enthusiasm for success and the need to produce, more drill, Saturday classes, no sports, summer school, more drill, and lots of test preparation.

All of those commenters would be THRILLED if there were more KIPP schools.
All of those commenters would be SHOCKED if their little darlings were subject to that regimen.

## Tuesday, January 11, 2011

### Tortured Logic

I thought I'd heard tortured logic before, and then I listened to this.

Apparently, the dying fish and the birds falling out of the sky, coupled with the heavy rains in Queensland, are the result of the repeal of Don't Ask, Don't Tell. It's a pattern, you understand. Correlation = causation. Proof by Pomposity?

Wow.

## Monday, January 10, 2011

### Parenting, Chinese mothers, and Stereotypes.

Very Interesting article from the WSJ.

Why Chinese Mothers Are Superior
By AMY CHUA

A lot of people wonder how Chinese parents raise such stereotypically successful kids. They wonder what these parents do to produce so many math whizzes and music prodigies, what it's like inside the family, and whether they could do it too. Well, I can tell them, because I've done it. Here are some things my daughters, Sophia and Louisa, were never allowed to do:

More after the break.

## Sunday, January 9, 2011

### Can't Fix Crazy. Can't understand it Either

So this lunatic tried to assassinate Gabrielle Giffords. He shot her at point blank range in the back of the head, surprisingly leaving her alive though in critical condition. (Historical digression: probably the same type of wound that killed Abraham Lincoln. A phrase that sticks in my head: "When Doctor Leale probed the wound in Lincoln's thickened scalp, feeling for the bullet, he dislodged a blood clot, and Lincoln began to breathe again." Lincoln didn't die until 5:30 the next morning. Modern medical techniques would have undoubtedly saved him.)

Anyway, the usual blowhards are up and running. Dick Durbin, on CNN's State of the Union referred to the Palin map that listed Giffords as a target: "[sic] a sign of 'toxic rhetoric' that had gone too far" though he insisted he wasn't making a 'direct connection' between Palin and Saturday's shootings. Whatever you say, Dick.

Unfortunate though the map was, it is not the issue here. It annoys me and I think it was in incredibly bad taste but it wasn't the trigger.

Jared Lee Loughner is crazy. Crazy like the kids who shot up Columbine. Crazy like Manson who thought he was starting an apocalyptic race war. Crazy like Sam Berkowitz who figured his dog was telling him to kill people. Crazy like the Arabs who drove planes into buildings.

You can't understand crazy. Crazy means "cannot be understood." As humans, we need understanding so we tend to react to these senseless acts by lashing out, by making connections just as fragile as those the killers made, by overreacting, by passing laws in the heat of the moment that we regret deeply when the ardor cools.

After Manson called himself "Helter Skelter", did we ban the Beatles? No.

After Son of Sam, did we blame dogs? No. Well except for those two little old ladies walking down the street and one says to the other, "I KNEW that dog was evil."

After Columbine, we panicked and insisted on metal detectors and no black trenchcoats and talking to all kids as if they were potential mass-murderers. We instituted no-tolerance rules and suspended kids for carrying nail clippers. We blamed the NRA and violent video games and politicians and teachers who didn't pay attention. We blamed because we had no idea what else to do.

Remember John F. Kennedy and Robert Kennedy? Thousands of people worked on that case, from the Warren Commission to a computer security expert 50 years later. It still isn't settled for many people. There were people on the grassy knoll, shadows under the bridge, Zapruder film re-watchers who still can't deal with the killing, the "magic bullet" theory and it's debunkers.

Because we wanted reasons. We couldn't, and we can't, deal with death for no apparent reason. Random, senseless violence scares us stupid.

I wish the best for Rep. Giffords and I feel a tremendous sense of sorrow for the victims who didn't make it and for the injured who will carry this for the rest of their lives.

Jared Lee Loughner is the sole person responsible here. He would have gone off if Palin had said nothing. He would have gone off if Rush Limbaugh had a cheeseburger. He would have gone off if Nancy Pelosi had gotten up on the wrong side of the bed. He would have gone off if Obama and both chambers had passed gas, never mind the Health Care bill.

It drives us crazy, too. As I'm sure you've all seen, commenters on every news outlet on the web are losing their minds. The comments are not helpful to the conversation, but it may allow us to work through our fear.

"The shooter was a liberal pot smoking communist manifesto reading hippy."
"Republicans w/ their comments are murderers !!!"
and
"FOX MUST BE SHUT DOWN AND NO LONGER BE ABLE TO TELEVISE IN THE COUNTRY/////////"
were the most recent 3 out of 7,250 comments on one story on Yahoo!News. The rest were just as lunatic.

I hope we all heal soon.

## Friday, January 7, 2011

### Rules? Who needs those?

 Not the kid in question. I just felt you all needed a visual to fully appreciate how "rules governing the length of players' hair violate their son's right to wear his hair the way he wants."
So the basketball team has some rules. You have to wear a uniform. You can't be paid for playing. You need to be passing your classes. You need to attend at least 10 practices before being allowed to play. Lots of things all made clear up front in the extracurricular policy handbook (something set up and decided on LONG before the season). Oh, and you need a haircut.

This is too much for the kid so he sues on the grounds that girls don't have to have their hair cut to the same length, or as the story puts it so approvingly, "Obviously, the player and his parents decided to fight for his rights rather than acquiesce to the extracurricular policy's claim that a player's hair be above his eyebrows, collars and ears."

Then, they asked a few geniuses for opinions:
"I just think he should be stipulated to tie his hair up or something like that," said Anthony Johnson. "To cut it off, I think that's taking away a person's mind, body and soul sometimes."
Yup, can't fix stupid.

I had to laugh, too, when the story identified the parents as "Patrick and Melissa Hayden" but wouldn't breach confidentiality of the kid, saying "Their 14-year-old son, identified as A.H. in the lawsuit" like that protected his identity.

"One of the things that we're most concerned about is exactly that," said an administration official who was not authorized to speak publicly before the release of the report. The official described the government's plans in an interview with The Associated Press.
So why did you speak publicly, Dude?  This isn't exactly whistle-blowing and you're not leaking something to prevent injury or harm or corruption. It's just spots.

Can't fix stupid.

## Thursday, January 6, 2011

### Always Bet on Black.

In Diamonds are Forever, James Bond bets on 17 Black. It is, of course, a European roulette wheel, with 18 red, 18 black and 1 green.

What is the probability of his getting the ball to drop in 17 Black twice in a row?

1/37 * 1/37, which equals 0.07%

How cool is that?

## Wednesday, January 5, 2011

### Tuesday Morning Quarterback on NCAA

"TMQ hates the celebration penalty. As long as there is no taunting, and there was none by Kansas State, why shouldn't players dance happily after a touchdown? Nearly all football fans, players and coaches hate the celebration penalty. Why does it exist?

The current NCAA stance seems to be that football players not graduating is a minor matter, athletes who break rules will be overlooked whenever bowl revenue is involved, but don't you dare act happy! Especially bizarre is the NCAA notion that celebration fouls should be a "point of emphasis." Punishing players for jumping around happily is a point of emphasis, while helmet-to-helmet hits are rarely flagged? Even considering the NCAA's reputation for hypocrisy, this is a bit much."

## Monday, January 3, 2011

Problem 01:
Just an extended fraction: $\dfrac{53}{22}$
Problem 02: 3
Problem 03: 2
Problem 04: 1/25
Problem 05: 4pi
Problem 06: 8/3
Problem 07: 30°
Problem 08: 125
Problem 09: 5

Problem 10: 10
Problem 11: 25% decrease
Problem 12: 1/2
Problem 13: 630
Problem 14: 6
Problem 15: 25/4
Problem 16: 6
Problem 17: 35/36
Problem 18: 225
Problem 19: 4008

Problem 20: 5
Problem 21: 6√3-3π
Problem 22: -4/5
Problem 23: 33/4
Problem 24: 0 or 4/3
Problem 25: 46
Problem 26: $\sqrt[3]{2}$
Problem 27: 139
Problem 28: 240
Problem 29: 35

Problem 30: (x,y) = (66, 55)
Problem 31: 3/4
Problem 32: 704
Problem 33: 1003
Problem 34: 1/6
Problem 35: 41
Problem 36: 9/8
Problem 37: 8√3
Problem 38: 42
Problem 39: 76

Problem 40: 1/20
Problem 41:
$(x,y)=\dfrac{3}{2},\dfrac{1}{2}$

## Sunday, January 2, 2011

### Driving While Impaired.

 Not to mention how ridiculous you look.
It's funny (meh) what the reality is:

Several studies, such as a 2005 paper in the British Medical Journal, have found that talking on a cell phone, even with a hands-free device, causes more driver impairment than a 0.08 BAC. A 2001 American Automobile Association study found several other in-car distractions that also caused more impairment, including eating, adjusting a radio or CD player, and having kids in the backseat.
h/t - Reason magazine

And then there is having a baby in the front seat, safely protecting you from a collision with the steering wheel and the airbag. Of course the airbag will kill your kid when it impacts his face at >100 mph. (There's the equivalent of three shotgun shell loads inside it to make it inflate fast enough.)  If it doesn't inflate fast enough, then your body will crush your child through the steering wheel. Of course, that's not something that would EVER happen to our BrittBritt.

You can't fix stupid.

### A call for parental input.

Not from me, actually. I'm not that enamored of the idea of "massive" parental input. If you're not a teacher, you don't have much that you can base your judgment on.

I can't remember all the times I've heard a parent tell me I should "use flash cards" or "not give homework" or "don't use flash cards" or "give more homework." Parents haven't been teaching high school for years and can't generally discern the good teaching from the bad, too often basing their judgments on fleeting or non-germane criteria.

"Is he passionate about teaching classes"? "Is the flow of his class natural"? "Does he maintain discipline at all times?" "Does he have a complete knowledge of his subject area?"

How is a student (with no actual classroom experience except for sitting in the back trying to see that girl's boobs without being noticed) supposed to answer these questions? How is the parent supposed to do any better?

Parental input should only go so far. For a parent to have "massive and sustained input" is simply a bad idea.
The Athens Banner Herald editorial, however, seems to like this idea a lot:
Frankly, what's missing in the tug of war between legislators and teachers over school funding versus classroom accountability, except for a passing mention in Senate Bill 521, are the voices of the people who are most qualified to speak out on the quality, or lack thereof, of the state's public schools and teachers. Any meaningful assessment of schools and teachers must include massive and sustained input from parents. (emphasis mine)

Problem 01: 4/5
Problem 02: 8 pounds
3/4 of the gas weighs 18 pounds. Gas = 24 pounds. Thus tank is 8
Problem 03: 30
$\frac{1}{(\frac{1}{5}-\frac{1}{6})} = \frac{1}{\frac{1}{30}} = 30$
Problem 04: 99%
Problem 05: 20°
BAD = 20° arcAC = 140° arcACE = 180°,
thus arcCE=40° and CAE = 20°
BAC = 60° thus DAE = 60° - 20° - 20° = 20°
Problem 06: 30°
Problem 07: -2+4i
Problem 08: 2008
$f(2002)=f(3*\dfrac{2002}{3})=\dfrac{1}{1+\dfrac{2002}{3}}=\dfrac{3}{2005}$
Problem 09: 36
4 years * 3 days * 3 months
Problem 10: 25%
$\dfrac{1}{\dfrac{4}{3}a}+\dfrac{1}{\dfrac{4}{3}b}=\dfrac{3}{4}(\dfrac{1}{a}+\dfrac{1}{b})$
Problem 11: -2 or 17
Cancel x+2, then multiply out both sides and simplify. Remember the x+2 when done.
Problem 12: $\frac{11}{21}$
The number of 3-element subsets with 3 evens: C(4,3) = 4
The number of 3-element subsets with 2 odd, 1 evens: C(5,2)*4 = 40
Problem 13: -1
The terms pattern out as 1, 2, -1, 2
Problem 14: $\frac{25}{6}$
(10-x)(0.4)+x(1.0)=0.65(10)
Problem 15: $\sqrt{6}$
Square the second expression.
Problem 16: $\frac{2}{3}$
Half-angle formula for sin divided by the half-angle formula for cos.
Problem 17: $\sqrt{3}$ or $\frac{1}{9}$
OMG, this was a pain. I'll post if requested.
Problem 18: 44
Problem 19: 12
Problem 20: -1
Problem 21: 26
Problem 22: $\frac{9}{2}$; 4.5
Problem 23: 11
Problem 24: 100°; length = $\dfrac{10\pi}{9}$
Problem 25: 9
Problem 26: 34
Problem 27: $6\sqrt{3}$
Problem 28: $\frac{29}{2}$; 14.5
Problem 29: $\frac{4}{9}$
Problem 30: $(\frac{3}{2}, \frac{5}{2})$
Problem 31: 264
Problem 32: 6π
Problem 33: d = 9/5 miles
Problem 34: n = 1, 2
Problem 35: 105 ways
Problem 36: 1001/334
Problem 37: 7/2
Pretty hefty polynomial expansion. I'll post it if requested.
Update: I'll post the "trick" (which I got from the test creators; my method was hairy):
Make the substitution $x=3^t-9$ and $y=9^t-3$
Then the student should notice that the equation becomes $x^3 + y^3 = (x+y)^3$

This is only possible if the middle terms of the expansion cancel each other.
So, $3x^2y-3xy^2 = 0$, and factoring gives us $3xy(x+y)=0$ and three corresponding results.
$x = 3^t-9 = 0$ which means that t = 2
$y = 9^t-3 = 0$ which means that t = 0.5
and $9^t+3^t-12 = 0$ and t = 1
Final answer is the sum of the three values is $\dfrac{7}{2}$
Problem 38: 22/3
Law of Cosines, solve for cos A: $cosA = \frac{11}{21}$, then plug back in for side AD.
Problem 39: -2
f(2002) = f(1001) + 1 = f(500) = f(250) + 1 = f(125) + 2 = f(62) + 1
= f(31) + 2 = f(15) + 1 = f(7) = f(3) - 1 = f(1) - 2 = -2
Problem 40: 4/3
FH is the altitude.
By similar triangles, AH/FH = 4/1 and HE/FH = AE/1.
Add the equations: AH/FH + HE/FH = 4 + AE; AE/FH = 4 +AE
Swap: FH = AE /(4 + AE)
1/6 = 1/2*AE*(FH) = 1/2 AE*[AE/(4+AE)]
Algebraic manipulation and x = AE: 3x² - x - 4 = (3x - 4)(x + 1)
AE is either 4/3 or -1.
Problem 41: 74
3 squares = 50. Original triangle + other easy triangle = 12.
Angle α in the upper left so the obtuse angle is 180°-α. Sin(α) = 4/5 = sin(180°-α), making the area of the upper obtuse triangle A = ½*3*5*4/5 = 6. Similar logic gives us the area of the lower triangle A = ½*4*5*3/5 = 6.
Total 62 + 6 + 6 = 74.

### What those first three years do for you.

Spencer has this list of things that all good teachers should be able to do without. He heads it with "How to Get Rid of Bad Teachers" but I think that needs to be qualified.

Some time ago, in his TED talk, Bill Gates opined that teachers don't improve after the first three years. He was saying, in effect, that test scores were the only thing that mattered and that brand-spanking new teachers improved their students' scores for three years only.

Okay, so Bill was wrong. (Is that sentence redundant?) What I think happens is that teachers grow into their jobs for the first three years. They start out by knowing very little and by making a ton of mistakes, teaching badly and inefficiently, and using methodologies that were just learned in education school - methodologies that don't work with actual students or anyone who isn't an education school guinea pig. Whew!

It takes about three years for them to figure out some truth. Some snippets are picked up from trade magazines, some from the kids or parents, but most are from the more experienced faculty once the newbie has gotten over his misconceptions about the "Old Guy" and the OG's total rejection of Shiny New Pedagogical Thought. "Old Guy doesn't use learning styles!?! WTF!?!"

That's when he learns what education really is and what it entails.

Excepting with respect to the newbies, I'd like to comment on Spencer's list:
Take away the Teacher's Guides and if they claim that they are unable to teach, they are right. They can't. As long as you're at it, take away the standards and the curriculum maps. Any decent teacher should be able to know what is vital in his or her content area.
Teacher's Guides/answer books are a convenience, not a crutch. Real handy for the repetitive and annoying work of producing paperwork that your building requires. There is probably a set of lesson plans tailored to the standards - photocopy them for your anal-retentive principal to get him off your back. Then go teach the class. Copy the curriculum map and hand it in. Then consult it once a month to stay roughly where you want to be. Taking away the standards entirely seems good in theory but not so much in practice. There needs to be some kind of plan, some kind of guidelines so the teachers don't go off in random directions.  Some of the best programs in the country have been fairly tightly controlled - Escalante's, for example.
Take away the computers. Tell them that there's no electricity. Even if it's a computer class, there's still a lesson to be learned. If they can't teach without the gadgets, then they aren't teachers. They're technicians and they have no business in a classroom.
To make a point, yes. Everyone should be able to "wing it." A blackboard is a whiteboard is a smartboard. But to say that ALL classes could do this for more than a couple of days is denying the use of available tools. Saying "you COULD walk to school, it's only 4 miles" is different from making it a common occurrence. There are topics that make no sense without tech and topics that have been phased out because tech took over.  Like it or not, some things are gone.
Take away the School Discipline Program and have the administrators leave for a day. If they can't lead a class without the intervention of an administrator, they probably need to leave.
Maybe. Maybe not. It seems that all teachers have the need for capable administration at various times although I've never seen one who required help every day.In that rare case, this is a valid point.
Take away the grades and get rid of the homework. Toss out the token reward system and the points and the gold stars. If they claim that they can't motivate a class without these things then they're missing a big part of what it means to motivate.
Homework and grades aren't for motivation. They're for practice and measurement, respectively. The token reward system is often effective, especially for the younger grades. Just because I don't use gold stars doesn't mean it's bad practice.
Take away the classroom for a day and have the teacher lead a group of ten kids. Meet outside. I don't care where. A lake, a river, a mountain, a busy intersection of the city. If the teacher can't see how the subject connects to life and struggles to get a point across without a Word Wall or a chalkboard or a set of worksheets, then the teacher is missing the point of education.
Whatever. I was never big on "class outside" and I fail to see where this ability is all that important.  Many things don't translate outside real well.  To say that the teacher is missing the point of education if they can't move into some random mountain meadow and teach algebra ...

YMMV

## Saturday, January 1, 2011

Problem 01: -14/29 just plug, crank, and pull.
Problem 02: 5/3
Conjugates are the red herring here.
(4√2 + √2)÷(4√2 - √2) = 5√2 ÷ 3√2 =5/3
Problem 03: 2
Draw a vertical line down the middle and the students will quickly see that the two halves are 2x2 and the red portion is 1+1 = 2
Problem 04: 112
Choose three consecutive integers: x-1, x, x+1
(x+1)³ - x³ = 666 + x³ - (x-1)³
x³ + 3x² + 3x +1 - x³ = 666 + x³ - x³ + 3x² - 3x + 1
Stuff cancels all over the place: 6x = 666; x = 111; Answer is 112
Problem 05: 1
Problem 06: 17
(x+2)² = x² + 8²
x² + 4x + 4 = 64 + x²
4x = 60; x=15; hypotenuse = 17. Even if you missed the Pythagorean triple.
Problem 07: 15
Problem 08: 36
Problem 09: 117
Problem 10: 59
Problem 11: 2
9x + 2(3x+2) = 243
32x + 18(3x) = 243
complete the square for U = 3x
u² + 18u + 81 = 243 + 81 = 324 = 18²
u + 9 = +- 18
3x = 9, -27 .... 2 is only real answer.
Problem 12: 13/14
Problem 13: 930
Problem 14: 140√2
ab = 28; ac = 20; bc=70
a²b²c² = 28*20*70
abc = √(4*7*4*5*7*2*5) = 140√2
Problem 15: 6/31
In these simple dice rolling questions, I like to imagine the full sample space of 36 possibilities. We are told that 6 is not an option and that occurs 5 times, leaving 31 total.
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
Thus, P(7) = 6/31
Problem 16: 48
Problem 17: 62
Build a rectangle around the figure and subtract the four triangles.
10*10 - ½(4*7 + 3*7 + 3*3 + 6*3) = 62
Problem 18: 1/5
Problem 19: 6/55
Problem 20: 16
Problem 21: 10
Problem 22: 1/13
Problem 23: 8
Problem 24: 4013
Problem 25: 6
log144(3a * 2b) = c
144c = 3a * 2b
24c * 32c = 2b * 3a
Problem 26: a=3, b=2/13
Problem 27: 1/6
Problem 28: 49
Problem 29: 5π/8
Problem 30: 300
Problem 31: 64/175
Problem 32: 18√3
ABC is a 30-60-90, with B=90o. AC is 12, split 3,3, and 6. If the altitude is BN, then AN=3 and BN=3√3, making the area = 18√3
Problem 33: 3
Problem 34: 339
4a+4b+4c=124, so a+b+c=31. Square it
a²+ab+ac+ba+b²+bc+ca+cb+c²=961
2ab + 2ac + 2bc = 622
a² + b² + c² = 339, which is also d²
Problem 35: 250
Assume first that p is odd. The list of integers is symmetric:
x-2, x-1, x, x+1, x+2; 5x = 57
In general, then px = 57, making p a power of 5.
p=5, x=56. 5 terms
p=25, x=55. 25 terms
p=125, x=54 = 625 terms.
p=625, x=53. Impossible because x was the "middle" number and we can't have 312 on either side.

Assume p is even.
x and x+1 are the middle two terms.
x-3, x-2, x-1, x, x+1, X+2, x+3, x+4 : 8 terms => 8x + 4
In general, p terms = px + .5p = p(x+1/2).
Since x is integer, we need a 2: q(2x+1) = 57.
5(2x+1)=57: x=56, means ten terms.
25(2x+1)= 57: x=1562, 50 terms
125(2x+1)=57: x=310, 250 terms
625(2x+1)=57: x=62, impossible for x to be the middle.
Problem 36: 46
logab + 10logba = 7
logab + 10/logab = 7
U + 10/U = 7
U² + 10 = 7U
U² - 7U + 10 = 0 ... (U-5)(U-2) = 0 .... logab = 2, 5
a5 = b has three candidates in range: 2,32; 3,243; 4;1024
since 45² = 2025, a² = b has 43 candidates in range. 2² = 4 through 44² = 1836
46 candidates.
Problem 37: 19
Problem 38: a=9 and b=11
Two equations:
386a = 272b
146a=102b
Starting with the second: 1a² + 4a + 6 = 1b² + 0b + 2
a² + 4a + 4 = b²
(a+2)² = b² gives us a+2 = b
Substitute into equation 1
3a² + 8a + 6 = 2b² + 7b + 2
3a² + 8a + 6 = 2(a+2)² + 7(a+2) + 2
expand
3a² + 8a + 6 = 2a² + 8a + 8 + 7a + 14 + 2
3a² + 8a + 6 = 2a² + 15a + 24
a2 - 7a - 18 = 0
(a+2)(a-9) gives us a = -2, 9
a = -2 is impossible so we're left with a=9 and thus b=11
back to number 38.
Problem 39: 224x³
Simplify by canceling an x³ and then by substituting u = x³.  Now for some long division. Yay!

      u666 +2u663 +3u660 + u657 + ...
-----------------------
u3-1) u669 + u666 + u663 + u660 + ...
u669 - u666
-----------
            2u666 + u663
2u666 -2u663
------------
                  3u663 + u660etc.

So each column adds one and projecting down the line gets you to a remainder of 224x³
Hang on. I messed that up. Must revisit.

      u668 + u667 + u666 + u657 + ...
.   -----------------------
u-1) u669 +  0    + 0 +   u666 + 0 + 0 + u663 + u660 + ...
u669 - u668
-----------
u668 + 0
u668 - u667
------------
u667 + u666
u667 - u666
------------
2u666 + 0

When you are finished, you will have 224/u-1 but we can't leave it there. We removed a x³ from numerator and denominator so the last bit is really 224x³ / (x6-x3) so the remainder is really 224x³.

Good thing I wasn't taking the test for real.
Problem 40: 3/2
d² = x² +(2x)² +(5-x)² + (2x)² + (5-2x)² + (5-x)² + (5-2x)² + x²
Expand all that and cancel/clean up
sum of d² = 20x² - 30x + 50
min when d(sum)=0
40x - 60 = 0
x = 3/2
Kids get in trouble here because they want to differentiate the square root or get off the idea that the sum of the distances must be at a minimum.
Problem 41: 150
Cleaning up Jonathan's comment a bit:
The semiperimeter, S = (5+6+7)/2 = 9.
Heron's:
A = √(9*4*3*2) = √216 = 6√6.
To get Altitude (height):
Area = ½*5*h = 6√6 so h = 12/5√6
Use CA = 6 and h to find that CPh = 6/5.
Using h and Pythagoras:
q1 = (1/5)² + h²
q2 = (4/5)² + h²
q3 = (9/5)² + h²
q4 = (13/5)² + h²
Sum:
4(12/5*√6)² + (1+16+81+196)/25.
(4*144*6 + 1+16+81+196)/25 = 3750/25
= 150

Eric P said:
First find cos(C) by law of cosines
Cos(C)=[6²-7²-5²]/(-2*7*5)=19/35
q1² = 49 +1 -2(7)(1)(19/35)
q2² = 49 +4 -2(7)(2)(19/35)
q3² = 49 +9 -2(7)(3)(19/35)
q4² = 49 +16-2(7)(4)(19/35)
Lining it up this way and using some quick mental math tricks makes the addition simpler: SUM=4(49)+30-2(7)(10)(19/35)=150

I think I have to side with Eric on this one.

### Test

$2x + 3 = \frac{1}{2}$