Molly on junior high vs middle school

Looking back at my own junior high experience and comparing it to my kids' middle school experience, I think momof4 has hit the nail on the head. Junior high was about academics, and the adults trusted that the adolescents were cable enough to work through their personal growth issues on their personal time. Middle school seems to be about everything but academics.

In junior high, I had really solid instruction in writing,including extensive grammar instruction. We did science labs that required the exact same sort of write-up that my high school labs later required. We studied actual history and civics (as opposed to the nebulous social studies).

In middle school, my daughters don't write, they produce power point presentations. The few writing assignments are given as group projects - my oldest was recently assigned a group poem to write. While they do science experiments, these seem to be purely for demonstration value as the students are never required to record observations in any standardized form.

My middle school daughters frequently miss class in order to attend assemblies during which some nominally well-known person tells them how important it is to stay in school and get an education. The irony of cancelling class to have an athlete extol the virtue going to class seems lost on middle school administrators.

chemprof on docent science

Steve H on the STEM sessions at the Celebration of Teaching and Learning:

They are mostly about engagement (it's the student's fault and/or responsibility) or about selling something.

chemprof:

and "docent science," which is what my colleagues and I call it. Science appreciation is another good term. I guess I can see that they figure that most students won't actually go on and do STEM in college, but they are really limiting their students' options. Plus, I can't tell you how many students come to college thinking that there are careers in science appreciation. 

I've always had a simmering interest in math, and for years I bought 'math appreciation'-type books, which I always found somewhat unsatisfying and never finished reading.

Finally, after writing ktm for awhile and teaching myself math so I could re-teach math to C., I realized I didn't want to appreciate math. I wanted to learn math.

"Understanding math" - which I think of as a kind of feeling I have at times - is tremendously fun, but it's not fun when I can't actually do the math I'm "understanding." Hard to explain.

I've also learned the importance of "getting used to" math as opposed to understanding it. Or, at least, I've had the experience of learning to do something I can't understand and then, after awhile, coming to feel that it's "natural" and "logical" to do whatever it is I've been doing.

This process is starting to happen a bit with counting, which I have found utterly mystifying. Recently I discovered that a great deal of what I've been doing in counting problems involves the commutative property and the definition of multiplication.

Who knew?

I can't tell if all this self-teaching I've been trying to do is a good thing or a bad thing.

question about value-added measurement

My copy of the Harvard Education Letter arrived with an excerpt from a new book on value-added measurement. I have a question about this passage:

Misconception 2: Value-added scores are inaccurate because they are based on poorly designed tests. Most standardized tests are indeed flawed, but this is not a problem created or worsened by value-added.
Seven Misconceptions About Value-Added Measures
by Douglas N. Harris
Harvard Education Letter - March|April 2011
p. 8

Is that correct?

As I understand it, New York's state tests can't be used for value-added purposes. The tests are shorter in some years, longer in others, and somehow don't correspond to a one-year measurement of learning. Or so we were told. Certainly they don't provide any sense of where a child might be within a year's worth of content. New York tests are scored 1 to 4, so if your child scores a middling 3, what does that mean on a scale of 10 months? Nobody knows.

I had been assuming that in order to use a standardized test as a value-added measurement, the tests had to be normed month-by-month as the Iowa Test of Basic Skills is normed:

Grade Equivalent (GE)
The grade equivalent is a number that describes a student's location on an achievement continuum. The continuum is a number line that describes the lowest level of knowledge or skill on one end (lowest numbers) and the highest level of development on the other end (highest numbers). The GE is a decimal number that describes performance in terms of grade level and months. For example, if a sixth-grade student obtains a GE of 8.4 on the Vocabulary test, his score is like the one a typical student finishing the fourth month of eighth grade would likely get on the Vocabulary test. The GE of a given raw score on any test indicates the grade level at which the typical student makes this raw score. The digits to the left of the decimal point represent the grade and those to the right represent the month within that grade.

When your child takes the ITBS from one year to the next, it's simple to see whether he's made a year's progress in a year's time. If, at the end of grade 3, he scored a 3.10 on computation (grade 3, month 10), he should score a 4.10 on computation at the end of 4th grade.

But how would you make that determination using the New York tests?

Or is there some other comparison you make from year to year?

worse before it gets better

I went with a friend to the Celebration of Teaching and Learning conference in New York City.

It was depressing.

Vendors everywhere, technology, no books, Smartboards (it's the 20th anniversary of the invention of the Smartboard!), and, during plenary sessions, constant calls for Parent Responsibility, each one met with thunderous applause. Parents were not a popular group amongst the Celebrants.

During the session on bullying, three teachers asked plaintively, "Why is bullying our responsibility?" "Why is everything on us?" They were aggrieved.

The great and the good (Brian Williams, Cory Booker) thought teachers had a lot to be aggrieved about. Democracy is hanging by a thread, they told us: the only reason we have a country at all is teachers. And yet Americans fail to feel "reverence" toward teachers. What is to be done?

Mehmet Oz said pretty much the same thing; then he showed us a graph charting the rise of obesity in America and said rising obesity is the reason "there's no money for education." We need to lose weight! Because we need more money for education!

Also, the NEA wants the government to pay for college and graduate degrees for teachers. We'll need to lose a whole lot of weight for that.

My friend attended a session where there was a group of young administrators seated in the middle of the room. The teachers booed the administrators. Now that's interesting ---- what was going on? I wish I'd been there.

A fellow from the Department of Education told us that DOE is rolling out "an ambitious 5-year initiative": the moon shot of this generation. Which was.....a website. The moon shot of this generation is a Department of Education website.

We watched a lot of student videos, all created with a product called Adobe-something-or-other: raps about Haiti; a geography class in California making soup. In the soup video, a pretty girl who came to America from Nicaragua complained that nobody knows where Nicaragua is or that a person who speaks Spanish and has brown eyes might be from Nicaragua and not Mexico. Another student in the video said somebody thought "Guatemala" was guacamole.

Maybe the reason students don't know where Nicaragua is or that Guatemala is a country not a dip is that they're making soup in geography class.

A high-energy Brit pitched his Teacher Channel, I think it was called: there will be authentic content!! We watched an authentic video of a grade school class in Florida where the kids scotch-taped together little houses and stuck them in a line on a stage. Then the teacher walked along the stage blowing the houses with a leaf-blower to simulate a hurricane. Some of the houses blew apart and some didn't. Shots of fist-pumping little kids; fade-out.

The Brit told us we had just witnessed "learning" and said there would be many thousands such videos available on Teacher Channel, which was being sponsored or hosted or public-private partnered or some such with WNET, the host of Celebration of Teaching and Learning. Applause!

In the session on how to teach counting using a children's book, the Math for America Master Teacher banned the words "permutation" and "order" because "permutation" and "order" are words, not understanding. He told us, repeatedly, that he makes his high school students spend a full test hour drawing the answers to counting problems in order to show them that multiplying 5x4x3 is more efficient than drawing 60 houses with 1 of 3 pigs inside. At the end of the sessions, he advocated the use of children's books for teaching high school counting problems. "How many handshakes amongst the 7 dwarfs?" That was a good counting question we could base on a children's story, he said.

At one point a teacher said she'd made a counting tree, and the Master Teacher said, a look of mock incomprehension on his face, "Tree? What is a tree? Why do you talk about trees?"

Five minutes later he put up a Powerpoint picture of a counting tree -- an actual tree, with a trunk going down to the ground, and branches pointing up to the sky. I don't know why a real tree is good and an abstract tree is bad. He didn't say. The rule seemed to be that everything the teachers said was old-school and wrong, while everything the Master Teacher said was up-to-date and correct. 

The Master Teacher had no blackboard, whiteboard, or Smartboard, so you had to try to remember everything he had just finished saying while trying to follow whatever he was saying now, and his Powerpoint drawings were confusing, at least to me. He spoke too fast. He told us over and over again that we needed to hold with our students the kind of conversation he was holding with us: i.e., a conversation for understanding.

I don't recommend it. The "conversation" consisted mostly of our Master Teacher eliciting wrong answers and forbidden vocabulary from his class. There were probably 5 people of 30 who could work the problems, so he focused on them and didn't bother with the rest of us.

I'm actually thinking about writing James Simons a letter.

from the Conference Program: 

Description: If three pigs live in five houses and each pig lives alone, how many living arrangements are possible? Participants will learn how a children’s book illustrates a simple way to solve counting problems like this without listing all possibilities. Teachers at all levels, from elementary to high school, will learn how students can find the answers without using confusing words like “permutation.”

the Celebration for Teaching and Learning on Twitter

mishegoss

Kick Me Out of School, I'm Irish


Have I mentioned Matthew K. Tabor has a new blog??

Education Debate at Online Schools

Blended learning that brings Khan Academy into the classroom

In California they're piloting a program that brings the Khan Academy into the classroom.  It sounds promising, with the potential to gain efficiency and raise achievement levels.

You can read more at Education Quick Takes.

momof4 on middle school versus junior high

My four kids all attended the same school between ES and HS, but it was a 7-8 JHS for my older two and a 6-7-8 MS for my younger two - over the strong objections of the parents in the attendance area. Apparently, the county required that a parent survey be done prior to the change but was not required to pay any attention to the results.

For my older kids, the JHS school had a strong academic focus and my kids and their friends LOVED the fact that the artsy/crafty, touchy/feely stuff had pretty much disappeared. Lots of girls who always had As in ES because they did lots of nice artwork were suddenly getting Bs and lots of boys who rarely got As in ES because they didn't care about pretty (or dioramas) were getting As because the correct answer was the main focus.

Three years later, when my third child entered the MS as a 6th-grader, the whole focus of the school had changed. The academic focus was GONE (even though many of the same teachers remained), replaced by teams, group-work and NEST (nurture, encourage, support and trust, I think). NEST was 20 minutes of daily torture; touchy/feely navel-gazing under the direction of the drama teacher. Lots of kids felt that their privacy was being invaded. The artsy/crafty projects were even more burdensome, since they had to be done in groups; often outside of school hours. It's SO easy and SO much fun to schedule 4 kids spread across 10+ miles of suburbs (irony alert) - and they all had significant extracurriculars, naturally. They also had to be driven by parents, of course. The only bright spot was that my youngest had a PE teacher for NEST and he didn't NEST - just expected the kids to be quiet enough to keep him out of trouble.

My experience was that the MS is awful; it focused on all of the worst aspects of adolescence and exaggerated them instead of minimizing them by focusing on academics. Also, the school obviously didn't understand adolescent (males, at least) very well because they didn't understand why the (male) winner of the Wonder Woman Award (best Women' History Month project) quietly dropped it into the trash can at the bottom of the stage steps - because guys should love the idea of being given a Wonder Woman award in front of 1500 peers. His parents were called in for a full-team conference. My kids could't wait to get out of that school.

Peter Meyer explains New York's contingent budget law

at the Irvington Parents Forum:

[S]tate law says that school districts are allowed to increase their budgets by up to 120% of the rate of inflation. I forgot the exact formula, but we've been informed (again, I'm on the BOE of a small (2000 kids) upstate district) that the CPI is 1.6%.

This might not mean much to Irvington, but to a poor (median family income up here is right around $30k and over half our kids are free and reduced lunch) district where more than 50% of revenues come from State aid, it means something close to a fiscal disaster.

Cutting to the chase, if we, the BOE, wanted to (the law says a board may vote to go directly to contingency if it wants, no vote needed!), we could increase our budget (it's about $40 million) by the 1.6% and make the local taxpayers make up the loss of state aid (projected to be over a million bucks) and loss of federal Edujobs money (another million and change) by having us property owners (all ten of us!) shoulder a 14.9 percent property tax increase. In that scenario we only layoff about 15 staff (including 7 teachers). There are other scenarios, none of them too pretty (and I'm one who believes pretty firmly in the proposition that more money does not buy a better education).

here's a followup:

The interesting thing, of course, is that the contingency law never anticipated the current economic crisis. The board COULD raise taxes 15% if it wanted to -- it has the legal right to do it. Would it? Probably not. So, no there are lots negotiations -- and lots screaming and yelling in executive session and elsewhere -- about whose axe gets gored. I think 4% tax increase scenario resulted in something like 70 layoffs. And yes, a salary freeze saves about 20 jobs (depending, of course, whose job).... It ain't pretty and it ain't too much fun....

It could always be worse, I suppose.

At least New York doesn't have a minimum budget requirement.

news from Headsprout

Headsprout bought by DYMO /Mimio

I don't know what this means, but folks are excited about it on the DI list.

If the DI people are excited, I'm excited.

Le Monde on the damaged nuclear power plants

The Times has just this moment posted a story headlined "Japan Faces Prospect of Nuclear Catastrophe as Workers Leave Plant" (the Times sends sound alerts to the iPad -- a couple of nights ago both the Times and Drudge woke me up in the middle of the night to tell me ---- what was it that night? Hosni Mubarak? Colonel Gadahfi? nuclear meltdown? I don't even remember at this point ---- )

Ed's reading Le Monde out loud; Le Monde is saying the Japan situation is worse than Three Mile Island, not as bad as Chernobyl. There's a French blogger on the scene, who says the Japanese government is not giving out very much information.

Lord of the Flies

from Peter Meyer's Education Next article on middle schools:

Parents and educators have begun abandoning the middle school for K–8 configurations, and new research suggests that grade configuration does matter: when this age group is gathered by the hundreds and educated separately, both behavior and learning suffer.

The Middle School Mess

by Peter Meyer
Education Next Winter 2011

merit pay fails in NYC

at Gotham Schools

Middle school kids did significantly worse.

I blame the middle school model, possibly.

And here is Peter Meyer on the middle school mess in Education Next.

Salman Khan at TED

Let's use video to reinvent education

still haven't watched this -----

I will

Mark Roulo on baseball statistics

re: the 32-parameter value-added model in NYC

One thing I like doing for discussions like this is to try and find a sports analogy. People tend no to get so hung up on non-PC conclusion in sports, but also often care a lot. This can lead to enlightenment.

So ... baseball:

(1) You can get a *VERY* good handle on how valuable a batter is with just two values, which can be combined into one number. You need on-base percentage (OBP) , which is, for every 100 times he comes to the plate, how often does he get on base? And you need slugging percentage (SPG) , which says how many bases he gets each time he has an at-bat. In both cases, more is better. And you can combine them with this: (OBP*3 + SPG)/2 to get a number that works the way most people who follow baseball can understand.

There ARE more sophisticated models, but they don't improve on this one by much. So ... two parameters, both of which are pretty easily understood.

(2) For pitchers it is a bit more complicated, but you can basically track strikeouts, walks and home runs and then put them together to get a single number. Again, one can improve (for starting pitchers, you also care about how "efficient" they are), but basically you'll get the right answer for ranking pitchers with just these three.

I get that teaching is more complicated. But 32 parameters is nuts.

tsunami

This is the first picture I've seen that gave me a sense of what the tsunami that hit Japan actually looked like.

And the aftershocks go on: 275 new tremors hit quake-torn Japan as fears grow for missing 10,000 in flattened port town
By Jo Macfarlane
Last updated at 8:55 PM on 13th March 2011

on film

group homes

Nearly 40 years after New York emptied its scandal-ridden warehouses for the developmentally disabled, the far-flung network of small group homes that replaced them operates with scant oversight and few consequences for employees who abuse the vulnerable population.

A New York Times investigation over the past year has found widespread problems in the more than 2,000 state-run homes. In hundreds of cases reviewed by The Times, employees who sexually abused, beat or taunted residents were rarely fired, even after repeated offenses, and in many cases, were simply transferred to other group homes run by the state. 

And, despite a state law requiring that incidents in which a crime may have been committed be reported to law enforcement, such referrals are rare: State records show that of some 13,000 allegations of abuse in 2009 within state-operated and licensed homes, fewer than 5 percent were referred to law enforcement. The hundreds of files examined by The Times contained shocking examples of abuse of residents with conditions like Down syndrome, autism and cerebral palsy.

At a home upstate in Hudson Falls, two days before Christmas in 2006, an employee discovered her supervisor, Ricky W. Sousie, in the bedroom of a severely disabled, 54-year-old woman. Mr. Sousie, a stocky man with wispy hair, was standing between the woman’s legs. His pants were around his ankles, his hand was on her knee and her diaper was pulled down.

The police were called, and semen was found on the victim. But the state did not seek to discipline Mr. Sousie. Instead, it transferred him to work at another home.

[snip]

In 25 percent of the cases involving physical, sexual or psychological abuse, the state employees were transferred to other homes.

The state initiated termination proceedings in 129 of the cases reviewed but succeeded in just 30 of them, in large part because the workers’ union, the Civil Service Employees Association, aggressively resisted firings in almost every case. A few employees resigned, even though the state sought only suspensions.

In the remainder of the cases, employees accused of abuse — whether beating the disabled, using racial slurs or neglecting their care — either were suspended, were fined or had their vacation time reduced.
At State-Run Homes, Abuse and Impunity
By DANNY HAKIM
Published: March 12, 2011

Rubber rooms are expensive, but we clearly need them.

And we need cameras. Cameras in every room.

thinking about Japan

The Lede

synchronicity

Apparently, God wanted me to a) think of Vlorbik today and b) Google his blog, because look what I found there: Notices of the American Mathematical Society - math education issue.

Here is H. Wu: The Mis-Education of Math Teachers (pdf file)

getting used to it

Young man, in mathematics you don't understand things. You just get used to them.

Reply to Felix T. Smith who had said "I'm afraid I don't understand the method of characteristics."

—as quoted in The Dancing Wu Li Masters: An Overview of the New Physics (1984) by Gary Zukav footnote in page 208.

John von Neumann

I know people here have quoted this before (I think Vlorbik might have been the person who I first heard this from). But I just stumbled across it today and had to quote it again.

For what it's worth, this observation describes my own experience of learning math - quite a bit of it, at any rate.

up

 cross posted at the Irvington Parents Forum ^*

Proposed Tax Rate Increase: 4.31%

Average assessment in Irvington = $24,500
Approximate full value = $731,000
Estimated increase in school taxes for the average assessed home = $604.17

History of Irvington tax rate increases:

2005-06: 13.42%
2006-07: 9.41%
2007-08: 5.87%
2008-09: 8.86%
2009-10: 0.42%
2010-11: 0.28%
Proposed 2011-12: 4.31%

In the years 2005-2009, we saw increases far beyond the rate of inflation.

Inflation for 2010 was 1.6%, so again we are far above inflation. (Core inflation - excluding food and energy prices - was only 0.7% from October 2009 to November 2010.)

Here’s a chart of core inflation since 1971: ^**

If you superimpose Irvington’s percent change in tax rates on this graph, the problem becomes obvious. Annual tax rate increases well beyond inflation make school spending unsustainable.



BLS Consumer Price Index – January 2011 (pdf file) 

Forecasters Expect Solid Growth, Low Inflation in 2011 (pdf file)



^* If any of you would like to join the Irvington Parents Forum, please do. We have members from around the country.  
^** I don't know why the label on this chart is "Core inflation, previous 12 months." UPDATE from gasstationwithoutpumps: Inflation is usually measured as a ratio of two index values taken at different time points, divided by the time between the points. The label is saying what index is used and what pair of time points (the core index at time on the x-axis divided by the same index 12 months earlier).

the Times on public sector pay

terrific set of charts, graphs, and summaries

2nd SAT

Debbie took the SAT today!

A hundred kids in line waiting for accommodations -- and they separate the twins.

death by data

A teacher in my town posted a link to this story:

The Lab School (Lab School at US News) has selective admissions, and Ms. Isaacson’s students have excelled. Her first year teaching, 65 of 66 scored proficient on the state language arts test, meaning they got 3’s or 4’s; only one scored below grade level with a 2. More than two dozen students from her first two years teaching have gone on to Stuyvesant High School or Bronx High School of Science, the city’s most competitive high schools.

“Definitely one of a kind,” said Isabelle St. Clair, now a sophomore at Bard, another selective high school. “I’ve had lots of good teachers, but she stood out — I learned so much from her.”

You would think the Department of Education would want to replicate Ms. Isaacson — who has degrees from the University of Pennsylvania and Columbia — and sprinkle Ms. Isaacsons all over town. Instead, the department’s accountability experts have developed a complex formula to calculate how much academic progress a teacher’s students make in a year — the teacher’s value-added score — and that formula indicates that Ms. Isaacson is one of the city’s worst teachers.

According to the formula, Ms. Isaacson ranks in the 7th percentile among her teaching peers — meaning 93 per cent are better.

This may seem disconnected from reality, but it has real ramifications. Because of her 7th percentile, Ms. Isaacson was told in February that it was virtually certain that she would not be getting tenure this year. “My principal said that given the opportunity, she would advocate for me,” Ms. Isaacson said. “But she said don’t get your hopes up, with a 7th percentile, there wasn’t much she could do.”

That’s not the only problem Ms. Isaacson’s 7th percentile has caused. If the mayor and governor have their way, and layoffs are no longer based on seniority but instead are based on the city’s formulas that scientifically identify good teachers, Ms. Isaacson is pretty sure she’d be cooked.

She may leave anyway. She is 33 and had a successful career in advertising and finance before taking the teaching job, at half the pay.

“I love teaching,” she said. “I love my principal, I feel so lucky to work for her. But the people at the Department of Education — you feel demoralized.”

How could this happen to Ms. Isaacson? It took a lot of hard work by the accountability experts.

Everyone who teaches math or English has received a teacher data report. On the surface the report seems straightforward. Ms. Isaacson’s students had a prior proficiency score of 3.57. Her students were predicted to get a 3.69 — based on the scores of comparable students around the city. Her students actually scored 3.63. So Ms. Isaacson’s value added is 3.63-3.69.

[snip]

The calculation for Ms. Isaacson’s 3.69 predicted score is even more daunting. It is based on 32 variables — including whether a student was “retained in grade before pretest year” and whether a student is “new to city in pretest or post-test year.”

[snip]

In plain English, Ms. Isaacson’s best guess about what the department is trying to tell her is: Even though 65 of her 66 students scored proficient on the state test, more of her 3s should have been 4s.
But that is only a guess.

Moreover, as the city indicates on the data reports, there is a large margin of error. So Ms. Isaacson’s 7th percentile could actually be as low as zero or as high as the 52nd percentile — a score that could have earned her tenure.

Evaluating New York Teachers, Perhaps the Numbers Do Lie
By MICHAEL WINERIP
Published: March 6, 2011

I have four reactions.

1.
A 32-variable teacher evaluation scheme does not sit right with me if only because it lacks transparency. This teacher has no idea why her score falls in the bottom 7% of all teachers in NYC, and neither does anyone else including her principal and students.

2.
Is this teacher running afoul of a ceiling effect? Her students were already scoring well above average coming into her class -- isn't it harder to bring above-average students further up than it is to bring below-average students to average? Working on SAT math with C., I'm convinced that the jump from 550 to 600 is a shorter leap than the one from 600 to 650. Whether or not that's true for the SAT specifically, I'm pretty sure people have shown it to be true with other tests.

[pause]

Yes. It's a well-known effect. ^*

3.
I flatly reject the assumption that New York state tests are capable of distinguishing between a group of students earning 3.57 on average and a group of students earning 3.69 on average. A few years back, when C., who is a fantastically good reader,^** scored a 3 on reading, I got in touch with our then-curriculum director, who told me that NY state tests in some grades have essentially no range of scores in the 4 category at all. That is, if you score a 37 or 38 out of 38 correct, say, you earn a 4; score a 36 and you're a 3. I checked the test and sure enough. She was right. There was no range at all for the 4. I don't know whether David Steiner has changed the tests in the year he's been in office, but even if he has, I reject the idea that the tests are now valid and can accurately assess what the gap between a 3.57 and a 3.69 means (if anything) and whether it is equivalent to the gap between a 3.01 and a 3.13.^***

4.
On the other hand, suppose the 7% ranking is right. What might account for that?

One possibility: the Lab School is a constructivist enterprise (here's the Math Department), and this teacher was trained at Columbia Teachers College. She is teaching English and social studies to 7th graders. New York state requires that teachers have a Bachelor's degree in their field of specialty beginning in 7th grade, which means that most 7th grade teachers are teaching English or social studies, not both. One of her students says, "I really liked how she’d incorporate what we were doing in history with what we did in English,” Marya said. “It was much easier to learn.”

Interdisciplinary teaching at the middle school level tends to be shallow because students aren't expert in any of the fields being blurred together (and teachers are expert in just one field), and the only commonalities you can find between disciplines tend to be obvious and current eventsy. e.g.: back when one of our middle school principals explained to us that henceforth character education would be 'embedded' in all subject matter, the best example he could come up with was that the father in The Miracle Worker is an angry patriarchal male who is abusive towards his handicapped child. That "interdisciplinary" reading of The Miracle Worker is anachronistic, simplistic, and wrong.

It's impossible to say whether these scores mean anything.

But if they do, they suggest to me that a 7th grade teacher needs to focus all of her efforts on English or on history, not on both.

English literature and history are very different disciplines.

I wonder how other teachers in the school fared - and, if they did better, how true they were to the middle school model?

^* The article doesn't tell us whether the city's statisticians correct for ceiling effects and regression to the mean.

^**C. typically missed just 1 or 2 items on SAT reading & writing tests.

^*** Of course, given the very wide range for 3s, perhaps a .12 difference is significant. It's impossible to know -- and that's the problem.

parents on schools and time

re: Richard Elmore's observation that family's time is a gift, not an entitlement:

This is exactly how I feel about most of my kids' homework -- it's throwing their childhood away.
FedUpMom

One of the reasons we are currently homeschooling the elementary kids, I couldn't take one more scrap booking assignment disguised as literature or math. Not to mention the hours lost to drug awareness, school fundraising pep rallies and watching "Finding Nemo."
Lisa

help desk - what does this mean?

A problem from Dr. John Chung's SAT Math:

Between 500 and 1000, how many integers are multiples of 5?
page 68

How do I read this?

Are 500 and 1000 excluded?

So that I would be finding how many integers are multiples of 5 starting at 501 and ending with 999?

The solution seems to start with 500 and end with 999 ------

[pause]

Reading (& re-reading) Chung's solution, it's apparent he means that 500 and 1000 are excluded, but his way of writing the solution is so different from the way I would write it that it looks like he's including 500 but excluding 1000.

His solution also seems to imply that you find the number of integers between 100 and 199 inclusive (i.e. how many integers starting with 100 and ending with 199) is to subtract 100 from 199.

Chung's book seems to be fantastically useful, but I'm wondering whether you need to be already scoring a 700 or so to understand it.

I will soldier on.

wrong answer

C. and I both got question 15 on page 773 in the Blue Book wrong.

15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible? 

My friend Debbie Stier got it right -- ! After she explained it to me, C. and I saw what we were doing wrong (double-counting the trainee pairs, basically), too, but we wanted to watch the Khan video to see how he did it.

Turns out Salman Khan did the problem the same way C. and I did.

Which makes me feel somewhat better.

Best explanation for novices on College Confidential:

Best way to approach this:

Fact 1: There are 4 different experienced plumbers.
Fact 2: There are 6 different combinations of 2 trainees in a total group of 4 trainees. If this isn't obvious, let the 4 trainees be A, B, C, and D.

All the possible trainee pairs:

AB, AC, AD
BC, BD
CD

and each of these trainee pairs can go with any of the 4 experienced plumbers, so we multiply 6 X 4 for the total number of possible teams, which gives 24. A common error here would be to erroneously consider AB a different pair from BA, when really order doesn't matter in this problem. That is how you would get a wrong answer of 48. 

a mathematician on math and writing

re: math & writing:

In both math and writing, the core idea that you are trying to express exists somewhere in the aether. In both math and writing, you start out staring at the blank page, trying to figure out how to summon the idea, make it yours, and commit it to the page. In both math and writing, you make false starts (unless you are very lucky) and work hard (unless you are very lucky) to express the idea with precision and clarity. In both math and writing, your familiarity with the idea that you are trying to express and your prior practice at expressing ideas can sometimes give you a head start in knowing in which direction to start.

Math is writing. Most of math is persuasive writing; math is an exquisitely structured argument.

(I am a professional mathematician.)

I love this.

This passage captures what writing is for me.

This one does, too:

Writing is easy. All you do is stare at a blank sheet of paper until drops of blood form on your forehead.
— Gene Fowler

Richard Elmore on time

It would be an enormous step forward if adults in schools treated the time that children and their families give to schools as a precious gift rather than an entitlement.


Three Thousand Missing Hours
Where does the instructional time go?
By RICHARD F. ELMORE
Harvard Education Letter
Volume 22, Number 6
November/December 2006

Somewhere along the line I began to see my middle school with its required "health class" and its required "technology class" and its required PowerPoint assignments for Spanish class (create a menu; pack a suitcase and label the clothing) as scooping up huge, heaping armloads of my son's childhood and simply tossing them in the trash. 

 C. told me a funny story. One of his brainier friends was up late one night, reading stuff for health class. His dad saw that his son was still up and asked what he was doing. When C's friend said, "I'm reading health," his dad barked at him: "Put that away! Get to sleep!"

Dad is a physician.

math museum

Ralph Gardner on math versus writing:

I don't want to say I'm skeptical about the idea of a museum devoted to mathematics. Indeed, I can recall the deep satisfaction I felt on the all-too-rare occasions at school when the concepts or formulas fell into place. It seemed an entirely different discipline from writing, where something arises from a blank page through a combination of hard work and patience, with a sliver of creativity. With math, the experience is more like discovering something that's always existed and finally decided to stop playing hard-to-get.
Making Math Fun (Seriously)
March 9, 2011
Wall Street Journal

I'm curious.

Do people who work in math or math-related fields feel this way?

Or is this more aptly a description of the way it feels to learn math when your expertise lies elsewhere?

Choosing Carnival Junk Food

It’s standardized test time in Connecticut and my child will be busy participating in this painfully drawn-out process over the next couple of weeks.  While I should clarify that I think testing *can* be useful for diagnostic purposes, I consider the following question from the eighth grade CMT Mathematical Applications section to be yet another example of why I find my state's manner of assessing students quite useless:

Sample Item 8-5 (Numerical):  Buying Tickets

The carnival offers you two different options for buying tickets.

                OPTION A:  $2.00 per person plus $0.75 per ride
                                                                OR
                OPTION B:  $5.00 per person plus $0.25 per ride

If your uncle gave you $10 for the carnival, which option – A or B – would you choose.  Show the mathematics you used to determine your answer.

OPTION CHOSEN: _______

Explanation:

This poor excuse for a word problem is just one example of why we started homeschooling.  While I’m assuming the objective of the question is for the student to show mathematically that option B is the better choice because you can go on 20 rides as opposed to only 10 rides with option A, the question does not indicate that the goal is to go on as many rides as possible.  I can easily imagine any of my children (including the 8-year old) coming up with alternate scenarios that could make either option the better one.  Unfortunately, I can just as easily imagine a scenario where the person responsible for grading 200 tests containing these strange open-ended mathematical responses before the end of their shift would mark their mathematically and numerically accurate answer WRONG.
 

Let's say the student were to choose OPTION A since he really likes to eat junk food at carnivals (just like his favorite uncle who spots him the $10) but hates the rides because they make him dizzy (thereby leaving him with $8 to spend on food instead of $5).  Would that be counted as a correct answer?  I would argue that either option could be the better choice depending on the objective—which was not made clear.  Mathematics is supposed to be clear, precise, and accurate. This question is just silly.

These types of  Everyday Math word problems (I'm being generous here by calling it a word problem) used to make me crazy when my child would come home with them in 4^th grade.  Now here we are in 8^thgrade running in circles all over again.

Meanwhile back in Singapore children are answering this:

Hooke's law for an elastic spring states that the distance a spring stretches is proportional to the force applied. If a force of 150 newtons stretches a certain spring 8 cm, how much will a force of 400 newtons stretch the spring? (New Elementary Math 2 Placement Test)

 *sigh*

People are starting to pay more attention to what is "behind the curtain" in our public schools

I caught a few minutes of a school board budget meeting in the school district next to mine, which happens to be near the one that is the subject of this post.  Residents were complaining about what they considered to be outrageous compensation packages given to school administrators. Some speakers expressed surprise about the way that school employees are able to carry forward so many personal/sick days and bump up their compensation during their last year of employment. Of course, the incentive to do just that lies in the fact that lifetime pensions are based on the last year or so of pay.

A couple of speakers compared their situation to that of Dorothy in The Wizard of Oz, as they were only now learning what was "behind the curtain".

The quote from the movie is, "Pay no attention to that man behind the curtain." Well, people are certainly starting to pay attention now.

(Cross-posted at Education Quick Takes)

Bronxville school taxes

A good article in the Times today.

The only problem is that it doesn't mention the Triborough Amendment, which you need to know something about in order to understand why the union would choose to work without a contract.

Also, in the illustration below, substitute the words "since the crash" for "in the last several years."

bubble this

C. and I take sample SAT tests together every day just about.....and I make bubbling errors.

Bubbling errors!

I bubble in the wrong bubble!

Today I bubbled in TWO wrong bubbles! On reading for Pete's sake.

How does that happen?

It's not like I'm racing for time; I finish reading sections several minutes early. (And, yes, I do see that the obvious answer is: stop finishing several minutes early. But I thought I had stopped.)

The good news is that I managed to complete every question in Section 8 (Math), Text 6 on page 729-733 of the Blue Book, and I only missed one: number 14. Number 14 is rated "hard" but I missed it because of a dumb mistake, which I think is a good sign.

Number 14  is one of the problems I'm supposed to skip according to my SAT Game Plan.

Anonymous on Professional Learning Communities in Utah

Anonymous left this comment:

Several schools in our school district (Washington County Utah) have started doing this kind of assessment and intervention with individual students. They've had such amazing results that the school district is passing a resolution today requiring all schools and teachers to participate. They call them Professional Learning Communities or PLC's.

From today's newspaper:

"The resolution in support of PLCs would require each educator in the district to participate in the PLC activities, part of a collaborative effort to achieve better results from students by continuously analyzing performance and intervening where necessary with individual students."
School board ponders new background checks
David DeMille • ddemille@thespectrum.com • Published: March 07. 2011 10:29AM

I am a huge fan of "Professional Learning Communities," which I think should probably be seen as an indigenous, American form of Japanese lesson study.

Richard DuFour invented "professional learning communities" at Adlai Stevenson High School in the 1980s, and the school has seen continuous improvement in student achievement since that time. Here's his website: allthingsplc.

The great charter schools use a variant of Richard DuFour's approach, too. Paul Bambrick-Santoyo cites DuFour in his book Driven by Data: A Practical Guide to Improve Instruction which is essentially the companion volume to Doug Lemov's Teaching Like a Champion.

Arne Duncan supports "Gold Star" teachers

Just put up a post at the Parents Forum.

data in schools

“In education, data has traditionally been used for punitive purposes, not for improvement...”
March 7, 2011, 10:05 pm
Coming Together to Give Schools a Boost
By DAVID BORNSTEIN

Reading Bornstein's article over breakfast this morning, I had a revelation.

For years now, a number of us have pressed our school district to assess student learning and adjust instruction accordingly -- i.e., to use formative assessment. We've gotten nowhere, and I've tended to see the district as 'allergic' to measurement in general.

But in fact, my district owns cutting-edge software that tracks disciplinary actions. When a student is sent to the office, the principal can instantly pull up his entire computerized disciplinary record and read out loud all of the bad things the student has done going back for years. I don't know whether the current principal of the middle school actually does this, but his predecessor did. He would fire up his computer and take the student on a little trip down memory lane: all the bad memories, none of the good.

Of course, I doubt the district has used its computerized disciplinary records as a means to monitor improvements in student behavior. The district essentially never sets measurable goals of any kind.

But still.

We have cutting-edge software to track misbehavior and disciplinary actions.

We don't have cutting-edge software to track student learning.

Middle School Mathematics Institute updates

Middle School Mathematics Institute (MSMI) is alive and well with lots of progress.

MSMI's mission is to help teachers, schools, and parents ensure students succeed at school algebra. Focused primarily on elementary and middle school grades 4-8, MSMI offers a variety of services that build the Bridge to Algebra.

We've got a nice new website: www.msmi-mn.org, we are now officially a 501(c)3 non-profit corporation (so donations to MSMI are federally tax deductible), and we're beginning to get some traction in our mission along all of the three prongs--teacher institutes, school curricular services, and parent outreach.

I'll be posting here in the next few days about MSMI 2011 institutes this summer in St. Paul, MN, one on fractions, and another on rational numbers. I'll also be posting about an upcoming event in April here in St. Paul, a workshop on "How to Use the Best Strategies of Singapore Math to Strengthen your Math Instruction." But for now, I'd like to talk about the parent component.

The parent outreach part is just starting to get underway. I gave a talk the other night on the Math on the SAT, Getting to Mastery to a group of parents. Their kids were mostly in elementary and middle school, and that's the time to start helping them understand just what's happening in their students' math curriculum--before it's triage and remediation. The talk highlighted that the SAT reasoning test math portion is a very good test of mathematical maturity, and that maturity simply isn't going to come from the American curricula and textbooks most students see. The talk gave some ideas on just what mastery looks like (both conceptual development and procedural fluency) and how to help students gain that mastery. I was surprised at how well received the talk was, actually, and I hope to do many more on similar topics.

The talk slides are available on the web site to anyone.

Along with that talk, I hope to develop another talk focused on what is needed to be on a college-prep track in high school, and what is needed for college entrance into a STEM career.

MSMI will also be writing some free pamphlets that help parents understand what's happening in math education. Immediately, I expect to have a pamphlet up explaining "curricula, standards, assessments, and all that" so that parents are familiar with these buzzwords. I hope to also get another pamphlet together talking about the false dichotomy between teaching and learning, a kind of mini-primer on what modern ideas of education mean for their student.

I hope to keep refining MSMI's focus on the parent side to maximize the good it can do. I was surprised after my talk that many parents want to organize to do something to help their students, but simply do not know what to do, and what suggestions on how to get their school to change direction. As you might guess, I didn't have a lot to say on that front; MSMI isn't designed for that kind of advocacy. I think for now, it shouldn't be, but I hope it will facilitate parents coming together to do that for their kids.

Anyway, have a look, download the slides, send suggestions (the web site needs pictures, I know, I know...) and drive traffic to www.msmi-mn.org, please! :)

help desk - questions for management

A friend of ours who sits on the board of a private school watched the Terc Investigations video a couple of weeks ago. Until he saw it, he believed boards should leave curriculum decisions up to school administration. Now he wants to write him a list of questions to ask "management" about the school's math curriculum.

Suggestions?

what is the effect of the Triborough Amendment over the long-term?

I want to check my reasoning with all of you.

Yesterday the Times carried a long editorial on the subject of New York's public sector unions and the state's fiscal crisis, which included these two factoids:

In April 2009, private sector income was down 9%.
In April 2009, public sector employees were given a 4% raise.

and

Average salary for New York’s full-time state employees in 2009 (prior to April raises): $63,382
Average personal income in NY state: $46,957

State Workers and N.Y.’s Fiscal Crisis
New York Times
3/6/2011

I assume these two facts are connected by the Triborough Amendment, a statute that is apparently unique to New York state. Under the Triborough Amendment, when a public sector union contract expires, its terms remain in effect until a new contract is signed.

This means that raises negotiated in good times must be awarded in bad times, which explains the 4% raises paid out in April 2009. It also means that the union has little incentive to negotiate during an economic downturn.

From the Times:

Last April, in the midst of one of the worst financial crises that New York and the nation have ever faced, the state’s unionized workers got a 4 percent pay raise that cost $400 million. It came on top of 3 percent raises in each of the previous three years. These raises were negotiated long before the recession began, by a Legislature that routinely gave in to unions that remain among the biggest political contributors in Albany.

During the same period, many private-sector workers had their pay or hours cut. Private-sector wages in New York dropped nearly 9 percent in 2008. In 2009, Gov. David Paterson pleaded with the unions to give up the raises to help the state out of its crisis. Union leaders attacked him in corrosive television ads, and Mr. Paterson eventually caved, settling for an agreement that reduced pension payments to new employees. The deal wasn’t enough to address New York’s serious fiscal problems.

The Triborough Amendment was adopted in 1972.

Here is the line of reasoning I want to vet with you.

What is the likely effect of the Triborough Amendment over time?

To me, it seems that over time the relative position of public sector to private sector employees would change, with public sector employees moving ahead and private sector employees falling behind.

Over time, the gap between public and private sector income would grow larger. If private sector employees take income cuts while public sector employees receive raises (or, at a minimum, do not take freezes or cuts) -- then each time the economy recovers, hasn't the ratio of public sector to private sector compensation changed?

Then, when the next recession arrives, doesn't the ratio change again?

If so, is that why we see average salary of full-time public sector workers in New York state at $63,382 while average personal income is $46,957?

I realize this comparison isn't apples to apples, but given that public sector employee incomes are presumably included in the $46,957, the actual ratio of public sector to private sector income must be even larger.

What it looks like to me -- and please tell me if I'm not thinking this through correctly -- is a  decades-long redistribution of wealth from one segment of the middle class to another segment.

Or is that wrong?

Do the incomes of private sector workers somehow bounce back up to where they were before each recession while the incomes of public sector workers 'stand still' long enough for the ratio to return to what it was before the downturn?

Magister Green on guerilla teaching

re: memorization is a dirty word, Magister Green offers this advice:

I have found that using "automaticity" in place of "memorization" lets me get around the stigma of the latter word while retaining its basic meaning. And "automaticity" sounds cool, so people don't press.

Guerrilla teaching forever!

Guerrilla teaching or marketing --- !

Daniel Ethier on cognitive load theory

on another thread, Daniel Ethier writes:

Cognitive load theory has much to say about the educational implications of our limited working memory on learning.

As I read various papers on cognitive load theory, I keep having aha moments as I find reasons for things I see in the classroom.

The key to getting around our limited working memory is automaticity. If you know something well enough to not have to think about it, it does not take up working memory. And so you are free to think about the problem you're trying to solve.

Use Google Scholar and read some of the many papers about various aspects of cognitive load theory. Well worth the time.

uh-oh

"when A.P. testing began in 1956, memorization was not yet a dirty word"

Rethinking Advanced Placement
By CHRISTOPHER DREW
Published: January 7, 2011

In theory, the new A.P. courses are going to replace "memorization" with "critical thinking."

In reality, critical thinking depends on memorization: you can't think critically without something to think about, and that something has to be stored in long-term memory. If you're going to think critically, you have to know (i.e. remember) what you're thinking about.

What happens when you try to think critically about a subject without memorizing its terms and concepts first?

What happens is that you can think about 4 items at most. That is the number of new, discrete elements you can hold in conscious, "working memory"^* at one time. Four. And four may be pushing it.

Of course, when it comes to critical thinking, 4 is a tiny number. Experts think critically about far more elements at one time; being able to think about a vast amount of complex material is pretty much the definition of an expert, as a matter of fact:

The sine qua non of skilled cognitive performance is the ability to access large amounts of domain specific information [i.e. knowledge]. For example, it is estimated that chess masters have access to as many as 100,000 familiar configurations of chess pieces (Chase & Simon, 1973). As another example, in order to make sense of what he or she is reading, a reader must have access to information gained from previously read text. This is particularly true when reading complex technical material filled with jargon.
summary of Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
David Zach Hambrick, 1998, gt8781a@prism.gatech.edu

basal ganglia lollapalooza

Here's an example from my own life.

As a nonfiction writer, I'm essentially a permanent student: I am constantly trying to write interesting articles and books (mostly books) about material that may be brand-new to me. My current project involves the basal ganglia, which I knew nothing about going in. The vocabulary alone is overwhelming: nucleus accumbens, orbitofrontal circuit, putamen, striatum --- and that's just for starters.

So here's the question. How exactly am I to (a) understand and (b) think critically about a passage that contains these four terms if I haven't memorized what these terms mean and how they are related to each other first?

The answer is: I can't.

If I don't memorize vocabulary, I have to look up the definitions and then try to hold the definitions in mind while also reading and trying to think about what I'm reading.

It can't be done, and the reason I know it can't be done is that I've spent a lot of time trying to do it. I always make the same mistake with each new project I tackle. Somehow I think I can just look things up (Google!) and remember them while I read a complex study or article.

But I can't. No one can. Looking up four new words and remembering four new meanings maxes out working memory. There's no capacity left to read and understand a text using those four new words and four new meanings, let alone think.

I don't know why this is. Logically speaking, shouldn't it take just as much working memory to hold 4 memorized terms in mind as it does to hold 4 non-memorized terms in mind?

The answer is no: knowledge - content stored in long-term memory - extends working memory.

When you know a lot about a subject - when you have a great deal of knowledge stored in long-term memory - you can think about more than just 4 things at once.


blackboards vs PowerPoints

^* Working memory is essentially consciousness: it's what you're thinking about and/or remembering right now. When you hold a phone number in memory while dialing it, you're using working memory.

contingency budget for NY schools

In another thread, lgm asked about the contingency budget for this year in New York.

The contingency budget is the budget schools can impose by fiat if voters reject the proposed budget.

Here is an explanation by the NYSUT:

the law defines the contingency budget cap as the lesser of 4 percent or 120 percent multiplied by the CPI increase

Assuming I'm reading this right (pdf file), the CPI for 2010 rose by 1.6%.

That would put the contingency budget cap at 1.92%.


(There are various categories that can't be excluded from a contingency budget, such as tax certs. I don't know how those relate to the cap.)

Inflation in one picture
David Leonhardt

corn on the cob

Have been meaning to post this --

A few weeks back David Letterman showed a print ad that reads:

Corn cobs 4 for $1.00
Works out to 25¢ a piece

Kitchen Table Math

So I was just over at Art of Problem Solving cruising their textbooks (I'm loving their Introduction to Counting and Probability, which may be a good example of what Barry calls guided discovery), when I saw a prominent reference to Kitchen Table Math:

How nice! I thought.

So I clicked on the link.

LIFO -- Connecticut Considers a Change

A new post on Throwing Curves considers the possible defenses of what the popular media has already decided must go -- LIFO rules. The system everyone loves to hate. I got that. It's easy to think that getting rid of LIFO solves the problem. But I've tried to dig deeper into the issue and spark a broader debate.

palisadesk on psychopaths in schools

re: Snakes in Suits, palisadesk writes:

*I* know how you came across this book -- I recommended it to you (about 2 years ago I think). I still recommend it. Robert Hare's first book, which has been revised a few times, is a don't-miss one: Without Conscience: The Disturbing World of the Psychopaths Among Us.

We tend to think of psychopaths as serial killers like Ted Bundy, but in fact the defining characteristic of psychopaths is a total lack of conscience. They are all about me, me, me and have no empathy for others, nor any scruples about exploiting or cheating others. Since they are totally focused on their own needs and goals, they usually are not criminals; however, they are often cunning manipulators, narcissistic power-trippers, and they wreak emotional havoc wherever they go. Snakes in Suits deals with such charmers in the workplace.

Robert Hare is a world-reknowned authority on the topic, and a lucid writer who gives insight into how to deal with such individuals. A rather high percentage of the population (something like 5% IIRC) has psychopathic tendencies, so we are all bound to encounter them.

They are less attracted to the "helping professions" than to other venues for their talents, but I have known more than one in public education, and these individuals taught very briefly before rising through the management ranks where they could do ever more damage on a wider scale.

Hare does share some useful strategies, as well as cautions against courses of action that are known to backfire badly. Counter-intuitively, therapy and counselling makes these individuals worse and more dangerous, since it enables them to con people even more effectively. They often fool mental health professionals.

True story.

A long ways back, I was trying to decide whether to sign with a particular agent.

I had some concerns, so after lunch with my possible new agent, I stopped in a bookstore and skimmed Without Conscience to see if he/she fit the profile for psychopathy.

I must have spent at least an hour with the book, finally reaching the conclusion that, no, my potential agent was not a psychopath.

The significance of the fact that I had just spent an hour of my life researching the question escaped me at the time.






Suffering Souls: The Search for the Roots of Psychopathy
by John Seabrook
The New Yorker | November 10, 2008

way off-topic: ALERTS TO TERROR THREATS IN 2011 EUROPE

Ed and I are sitting here guffawing, reading this.

Starts slow, then hits warp speed in paragraph 4, with the Scots.

Of course, I love anything to do with the Scots and their bloody-mindedness.^*



Born Fighting: How the Scots-Irish Shaped America


^* I'm probably using that term incorrectly. Good thing it's not likely to appear on the SAT.

the choice

in my district

Snakes in Suits

No idea how I came across this book --- but I may have to read it.

Robert Hare is a major researcher in the field.

for writers & writing

The Mumpsimus

I'm a huge fan of Scrivener's.

Have just ordered a copy of Patterns of English.

Downloading Bean next.

decline at the top - the best students fared worst

Back in 1977, having watched SAT scores fall for 15 years, the College Board, which developed and administers the SAT, engaged a panel to try to identify the underlying causes of the decline. A first hypothesis to be checked was whether the test had somehow become more demanding. But, no, to the contrary, indications were that scoring had become more lenient. A second prominent hypothesis was that the decline was due to changes in the demographics of the test takers. Analyses shows this hypothesis to be largely correct, but only for a brief while. Over the early 1960s, changes in the composition of the tested population accounted for as much as three-quarters of the test score decline—and, no wonder, for during this period the number of students taking the SAT tripled. Over the 1970s, however, though the test-taking population stabilized, the scores did not. Instead, the decline continued, even steeper than before, while the extent to which it could be ascribed to demographic shifts shrank to 30 percent at most. Furthermore, the scores that dropped most were those of the strongest students, the students in the top 10 percent of their class; the scores of students toward the bottom of the distribution held steady or even increased.

Advancing Our Students' Language and Literacy: The Challenge of Complex Texts
by Marilyn Jager Adams
American Educator | Winter 2010 - 2011

answer key - Glencoe Algebra 2 - Chapter 12

online (pdf file)

how many different groups of 4?

A school librarian would like to buy subscriptions to 7 new magazines. His budget, however, will allow him to buy only 4 new subscriptions. How many different groups of 4 magazines can he choose?

Counting Principle, Combinations, and Permutations Worksheet (pdf file)