kitchen table math, the sequel: 7/3/11 - 7/10/11

Saturday, July 9, 2011

Friday, July 8, 2011

Rich Beveridge on pre-calculus

Rich Beveridge writes:
I suppose that my experience with Pre-Calculus curriculum began in Steve Patterson’s Pre-Calculus class at Briarcliff High School in the 1981-82 school year. Pre-Calculus always stuck out in my mind because it was the only math course that was completely locally developed. Algebra I, II, and Geometry all had Regents exams and the Calculus course was AP Calculus.

I remember studying Conic Sections, Polynomial Long Division and Synthetic Division, the Rational Roots Theorem (and its proof), elementary Discrete Math (permutations, combinations and binomial probability), Polar Coordinate graphing and hand calculating Riemann Sums at the end of the year. I took the College Board Math Achievement Test II (now the SAT Subject Test Math II) after completing the Pre-Calculus course so I recently looked at some current sample questions and saw these same topics – Analytic Geometry, Permutations & Combinations, Synthetic Division, Functions, Sequences & Series.

During the 1999-2000 school year, I taught Pre-Calculus at Maine Central Institute in Pittsfield, Maine. The school was using the Chicago Series text Functions, Statistics and Trigonometry for their Pre-Calculus course. I know that some teachers like the Chicago Series and FST in particular, but I didn’t really get much use out of the textbook, and began to supplement. Standard textbooks can be supplemented quite easily because the order and difficulty level of the topics is often similar. I found that the Chicago Series was very difficult to supplement and just began to create separate materials for the students. I collected these assignments in a binder and showed this to the University of Maine math department when I was interviewing for an adjunct position the following year (yeah - I didn’t stay at MCI very long – they were sticklers for using the approved textbook). I taught as an adjunct at UMaine for two years before beginning their MA program in Math.
I'm hoping Rich will write more posts for us.

Thursday, July 7, 2011

summer reruns

I just came across this old post by Ken DeRosa!

Apropos in this summer of SAT math prep.

Maybe PWN will tell us what level of difficulty this problem would be rated on the SAT. I'm thinking 3 or possibly 4, and it would be a 4 only because a lot of students haven't taken algebra 2.

Lewis M. Andrews on why suburban schools don't change

How is it that intelligent and motivated parents, many sacrificing financially to afford homes in the most expensive suburbs, end up as uncritical supporters of a public school system...?

IN THEIR HEARTS, says University of Missouri political science professor J. Martin Rochester, many suburban parents know something is wrong. When he interviewed 250 executives of leading corporations for his book on suburban education (Class Warfare: Besieged Schools, Bewildered Parents, Betrayed Kids and the Attack on Excellence), most believed their local schools suffered from programs that are "diluted, distracted, and diffused from the basic mission of education."

The problem, he concluded, is that over decades suburban schools have developed effective techniques for promoting ideas that support the convenience of teachers and administrators, while excluding information and research that would require a change in policies, practices, and personnel.

It starts at the top with boards of education composed largely of busy volunteers, who over-rely on the guidance of superintendents, and goes all the way down to the interactions between teachers and individual parents. When suburbanites join school curriculum committees, for example, they are rarely presented with all sides of an issue and seldom informed of all the relevant research. Critical parents, Professor Rochester found, "end up being demonized as right-wingers or troublemakers."

Other writers who have studied the academic deficiencies of suburban schools reach a similar conclusion. When columnist Barry Garelick examined the inability of three Maryland districts to successfully incorporate a superior math curriculum from Singapore, he found that teachers skillfully used vague technical jargon and inflexible rules to discredit aspects of the program that required them to learn new skills.

As suggested by the title of his book Oversold and Underused: Computers in the Classroom, Stanford professor emeritus Larry Cuban finds suburban educators eager to spend public money on the latest technology to create a "leading edge" aura, yet rarely willing to take advantage of its academic potential. "Curricula, teaching methods, and schedules [could] all be customized to meet the learning styles and life situations of individual students," says Cuban, and "coursework from the most remedial to the most advanced can be made available to everyone...(but educators take) action to prevent technology from transforming American education."

Dr. Armand Fusco, a retired Branford, Connecticut school superintendent who has written and lectured widely on the deficiencies of suburban districts, sees similar problems: "It's one thing for parents to intuit a problem, quite another to do anything about it when educators with advanced degrees flash their credentials and have glib answers for every question."

Superintendents, for example, will always brag that their local public school students perform just as well on state mastery tests as students in neighboring affluent suburbs. What they neglect to mention is that any mediocre suburban school will appear successful, just so long as it is surrounded by other mediocre suburban schools and their average test scores are higher than those of nearby urban districts.

Dr. Fusco believes that the federal No Child Left Behind law had it right when it sought to measure the performance of individual schools, but it was aimed at demographic groups least able to do anything about the results. "What's needed is data that makes it clear to suburbanites just how badly served their own children really are."
Meet the Suburban Parents

Lewis M. Andrews on suburban schools and tutors

One telling indicator of the low quality of suburban schools is the rise of tutoring. In 2008, PBS's Nightly Business Report estimated professional tutoring to be a $4 billion industry that year, concentrated in the suburbs, with a 10 percent estimated annual growth rate.

Even this figure does not take into account either the common off-the-books arrangements with moonlighting teachers or burgeoning Internet options. With small online providers like Colorado-based e-Tutor seeing revenue jump from $180,000 in 2009 to a quarter million in 2010 despite the recession, the Kaplan online university division of the Washington Post has launched its own reading and math programs for elementary and middle school students.
Meet the Suburban Parents

Mike Petrilli on suburban parents

When I think about my aspirations for my boys (ages 3 and 1), I take as a given that they will do fine academically. Maybe that’s naive, but I just assume that they will end up going to a good college, find interesting work, and so forth. What I want for them is to enjoy the ride along the way: Make close friends, have plenty of time for play, learn to be part of a team (athletic or otherwise), tap into their artistic nature, spend as much time outdoors as possible. These inclinations led my wife and I to pick a Waldorf preschool for their early years. We’re not sure we’ll stick with such an “alternative” approach over the long term. But I surely don’t want my boys anywhere near a “testing factory.”


But with a degree of affluence comes a degree of luxury. Confident that their kids will do OK academically and vocationally, I bet that many upper-middle class parents want to reach for something more: Emotional health, spiritual fulfillment, a sense of social responsibility. And thus the frills that Lewis derides (like all manner of extra-curricular activities) become quite important. And as for the test scores–well, who cares if they are really, really high or just really high?

Understanding upper-middle-class parents
Good enough is good enough.

Mike Petrilli is an Executive Editor of Education Next and an Executive Vice President of the Fordham Foundation.

and see:
decline at the top
nominally high-performing schools

school board member responds to Petrilli

Mike Rose writing at Flypaper: sorta sounds like you’re making a “schools are academically good enough” argument.

I’m a former school board member from an affluent district. We spent – and continue to spend – lavishly on millon dollar artificial turf football fields, band, pottery kilns, and so on. Students take cultural trips to musical events, museums, and plays. The 23 buildings are fairly new, energy efficient, and freshly painted and carpeted. The district spends approximately $1000 per participant on athletics. Overall the kids and parents seem satisfied.

But we have no gifted and talented program. Our AP participation is below other socio-economically similar districts. ACT scores are in the 98th percentile for Michigan public schools, but are not particularly impressive when compared to non-publics, or the International Academy (a public consortium), whose students have similar socio-economic status. The ACT scores of Michigan schools overall are not particularly impressive (I know… an entirely different debate!).

They do very little scholarship counseling.

Our graduates get accepted into good universities, and do get scholarships. However, anecdotally, parents (and graduates) talk of needing to take remedial classes once they get to college. Some bomb out and drop out, heading back to community college for a year or two. It’s anecdotal because the district makes no effort to obtain or analyze matriculation reports.

And the scholarships earned in the district pale by comparison to non-publics and neighboring “high performing” districts.

By the yardstick you’ve offered… I too should be happy because I’m sure my kids will get into a good college, and be in a culturally rich environment, and have friends. But will it be their “first choice” college? What sort of scholarship opportunities will be available to them, and more significantly, what opportunities will NOT be available to them in this competitive world? Will they need to take that now infamous fifth year of college because they weren’t quite ready?

Did they have to take that entry level science class that could’ve been skipped had the school encouraged them to take an AP exam? Did they miss out on the FREE college credit they might’ve earned had the school encouraged them to take that AP exam?

Oftentimes parents don’t realize that their children have lost or diminished opportunities until it’s too late… the child has the diploma, and they find themselves challenged by obstacles that were created years ago by the school.

And how would parents know they’re not getting all they can get? Our district has a full time PR person to toot the horn. “Your kids are getting a top-notch education… just ask us and we’ll tell you!” As you are well aware, education is a complicated topic, and most parents don’t have the time or resources to investigate or challenge school assertions.

Tuesday, July 5, 2011

help desk - fiscal multiplier

We quantify the fiscal multipliers in response to the American Recovery and Reinvestment Act (ARRA) of 2009. We extend the benchmark Smets-Wouters (2007) New Keynesian model, allowing for credit-constrained households, the zero lower bound, government capital and distortionary taxation. The posterior yields modestly positive short-run multipliers around 0.52 and modestly negative long-run multipliers around -0.42. The multiplier is sensitive to the fraction of transfers given to credit-constrained households, the duration of the zero lower bound and the capital. The stimulus results in negative welfare effects for unconstrained agents. The constrained agents gain, if they discount the future substantially.
Fiscal Stimulus and Distortionary Taxation
Thorsten Drautzburg, Harald Uhlig
NBER Working Paper No. 17111
Issued in June 2011
NBER Program(s): EFG
I'm confused about the concept of the fiscal multiplier.

I've read explanations characterizing the multiplier as a simple multiple: if the multiplier is 1.5 and the government spends $1 million, then the net spending beyond that $1 million is $500,000.

1.5 x 1,000,000 = 1,500,000

But that's not right, is it?

What does a multiplier of .52 actually mean in terms of what the public spends beyond the amount the government spent?

Monday, July 4, 2011

highly selective colleges redux

[O]btaining unbiased estimates of the return to college quality is difficult due to unobserved characteristics that affect both a student’s attendance at a highly selective college and their later earnings. In particular, the same characteristics (such as ambition) that lead students to apply to highly selective colleges may also be rewarded in the labor market. Likewise, the attributes that admissions officers are looking for when selecting students for college may be similar to the attributes that employers are seeking when hiring and promoting workers.

Early research attempted to overcome this omitted-variable bias by controlling for observed student characteristics, such as high school grades, standardized test scores, and parental background (see, for example, Monks 2000 and Brewer and Ehrenberg 1996). More recent research has tried to overcome the bias created by unobserved variables through a variety of techniques. Hoekstra (2009) uses a regression discontinuity design that compares the earnings of students who were just above the admissions cutoff for a state university to those that were just below it. He finds that attending the flagship state university results in 20 percent higher earnings five to ten years after graduation for white men, but he does not find an effect on earnings for white women.
Estimating the Return to College Selectivity over the Career Using Administrative Earnings Data
Stacy Dale, Alan B. Krueger
NBER Working Paper No. 17159
Issued in June 2011
I'm not sure how Dale and Krueger interpret the finding of 20% higher earnings five to ten years after graduation in (white male) students who just made the cut-off versus students who just missed it.

I assume they would expect to find that the students who made the cut-off applied to a more selective group of colleges than the students who just missed the cut-off, but I don't know.

highly selective colleges and lifetime earnings

following up on Who gains from attending a highly selective college? :
...[T]he average SAT score of schools that rejected a student is more than twice as strong a predictor of the student’s subsequent earnings as the average SAT score of the school the student attended...

Estimating the Return to College Selectivity over the Career Using Administrative Earnings Data
Stacy Dale, Alan B. Krueger
NBER Working Paper No. 17159
Issued in June 2011
Assuming I'm following the argument, Dale and Krueger are saying that when you account for unmeasured factors such as a student's level of ambition, the selectivity of a school has no effect on the earnings of white children raised by educated parents. In other words, more ambitious students file more ambitious applications; they apply to more highly selective schools than do students who are less ambitious. Same SAT scores, different set of college applications.

I think.

I can email a copy of the article to anyone who'd like to read.

also from the paper:
The high selectivity of the colleges within the C&B [College and Beyond Survey] database make it particularly well-suited for this analysis, because the majority of students that attend selective colleges submit multiple applications, which is necessary for our identification strategy. In contrast, many students who attend less selective colleges submit only one application, because many less selective colleges accept all students who apply. For example, according to data from the National Longitudinal Study of the High School Class of 1972, only 46 percent of students who attended college applied to more than one school.
Nearly two-thirds of the 1976 cohort and 71 percent of the 1989 cohort submitted at least one additional application (in addition to the school they attended). For both cohorts, of those students submitting at least one additional application, over half applied to a school with a higher average SAT score than that of the college they attended, and nearly 90 percent of students were accepted to at least one additional school. Of those accepted to more than one school, about 35 percent were accepted to a more selective school than the one they ended up attending. The data for black and Hispanic students (shown in columns 2 and 4) are similar, though blacks and Hispanics were somewhat more likely than students in the full sample to be accepted to at least one additional school, and to be accepted to a more selective school than the one they attended.

who gains from attending a highly selective college?

Is the Ivy League Worth It?
July 1, 2011, 12:13 PM ET
Christopher Shea | WSJ

Estimating the Return to College Selectivity over the Career Using Administrative Earnings Data (pdf file)
Stacy Dale, Alan B. Krueger
NBER Working Paper No. 17159
Issued in June 2011

from the abstract:
We find that the return to college selectivity is sizeable for both cohorts in regression models that control for variables commonly observed by researchers, such as student high school GPA and SAT scores. However, when we adjust for unobserved student ability by controlling for the average SAT score of the colleges that students applied to, our estimates of the return to college selectivity fall substantially and are generally indistinguishable from zero.
Not having read the paper, I don't understand how controlling for average SAT score of the colleges students applied to, as opposed to simply controlling for SAT scores of the students, makes a difference.

I'm going to download and take a look.

Sunday, July 3, 2011

off-topic - vegetables make you thin


They do.

Vegetables make you thin.

I'm starting to see fruits and vegetables (and legumes) the way people used to see diet pills back when it was legal for housewives to take amphetamines to lose weight: eat your vegetables, fruits, and beans, and you can eat anything else you want and still stay thin.

The reason you can eat anything else you want and still stay thin is that you don't want to eat as much as you do when you're not eating beaucoup fruits, vegetables, and legumes. Fruits, vegetables, and legumes are natural appetite suppressants.*

Here's more evidence:
[R]esearchers from Penn State gave 20 men and 21 women casseroles made with varying amounts of purée — a strategy popularized by the cookbook author Jessica Seinfeld, who has encouraged parents to sneak vegetables into foods like spaghetti.

But in the Penn State study, the goal wasn’t to trick people into eating vegetables. Adding the purée bulked up the dish and resulted in fewer calories per serving. (You can see two of the recipes developed by the researchers here.)

In a macaroni and cheese recipe from the researchers, for instance, the cheese sauce is made with skim milk, reduced-fat cheese and one cup each of puréed cauliflower and puréed summer squash.

The diners were fed the casseroles during different visits. They ate pretty much the same amount of food during each visit and reported no differences in flavor or enjoyment. But when they were served the casseroles made with puréed vegetables, they ate 200 to 350 fewer calories a meal.

“We’ve been able to change recipes a lot, even baked goods, and we’ve been doing it for preschool kids and adults,” said Barbara Rolls, director of Penn State’s laboratory for the study of human ingestive behavior. “We had a huge effect on energy intake. We’re adding cups of veggies to recipes and people don’t even notice.”

Other research by Dr. Rolls, author of the popular diet series Volumetrics has shown that eating soup or salads before a meal can also curb the appetite and result in eating fewer calories over all.

But the stealth-vegetable approach allows diners to eat the same amount of favorite foods without ingesting as many calories.


“We offered a Tex-Mex casserole, and we could get away with adding the vegetables much more easily,” she said. “Once you put in those spicy flavors, they mask other changes in calorie density and vegetable content. The people were totally unaware we were adding lots and lots of veggies.”

While the best option is to purée vegetables and add them to home-cooked meals, Dr. Rolls said she hoped the food industry would respond by offering more convenient canned and frozen vegetable purées and more foods bulked up with vegetables
Adding Food and Subtracting Calories
by Tara Parker-Pope
May 2, 2011, 5:03 pm
my rules:
animal fat makes you eat more
plant foods make you eat less

The Sneaky Chef: Simple Strategies for Hiding Healthy Foods in Kids' Favorite Meals

The Sneaky Chef: Simple Strategies for Hiding Healthy Foods in Kids' Favorite Meals
by Missy Chase Lapine

* I'm not sure plant foods are natural appetite suppressants; it's a 'working hypothesis.' I'm 99% certain palmitic acid makes you eat more.

Richard I and Orange Math on Jeanette, or Jeannette, as the case may be

Richard I says:
My eyes were attracted to the fact that her name is spelt in two different ways. Maybe all this innnvennnntinnnng is goinnnnng to her head?

Of course maybe the n-gon to her head instead?
And here's Orange Math:
I guess I'll cite Jeanette whenever I use that formula. The rule really helps. I tried using a protractor.
Steve H has some questions, too.

Errors on Report Card?

We just got my son's report card and there are numbers on it that don't match up. Our high school uses i-Parent so that parents can get immediate feedback. I like it. We can see and validate all of the homework and test scores. I see no errors in those numbers, and grades are calculated to many decimal digits. However, there seems to be some sort of problem translating those numbers into whatever computer system our high school uses for reporting grades. Interestingly, his final course grades look correct, but some are mathematically incompatible with the quarter grades on his report card, and they don't match i-Parent. Of course, the final grades are rounded off so there is a limit to what correct means. I-Parent just records the grades for each quarter. It does not include the midterm and final tests or try to calculate a semester or yearly final grade. However, the formula for semester grades is simple; 40% for each quarter and 20% for the midterm or final. Semester 1 and 2 grades are averaged to get the final grade for the course.

Have others run into grading calculation or reporting issues? I'm paranoid now because I see numbers that don't match or add up. Final grades are rounded so I can't check to see if they agree with my calculations, and the class rank is based on a weighting scheme that might use rounded grades rather than the the real numbers. They did not include a weighted rank number on the report card, so I couldn't check that. I sent off an email to the guidance department, but I don't know if anyone is there during the summer.