sleep

What have I learned taking timed SAT math tests?

Apart from how to answer tricky SAT math questions fast?

I have learned once and for all that sleep loss is catastrophic.

I had always been vaguely aware that I "don't function well" on too-little sleep, but it wasn't until I started taking -- and more importantly scoring -- SAT math sections that I realized exactly how not well.

From Permission to Sleep In by Christopher Shea | July 7, 2011, 12:02 PM ET:

Researchers [at Stanford University] measured shooting percentages, sprint and reaction times, and subjective mood for 11 members of the men’s basketball team, for two-to-four weeks during the 2005 and 2008 seasons, as the players followed their ordinary sleep schedules. (Average sleep, according to a motion-detection bracelet: 6.7 hours.)

Then for five to seven weeks the players boosted their sleep time to 10 hours. They were encouraged to take daytime naps when they couldn’t meet that goal.

With the additional pillow time, players dropped their average time on a routine sprinting drill (from the baseline to half court and back, then to the opposite baseline and back) to 15.5 seconds, from 16.2 seconds. Performance on free throws improved to 88%, from 79%. Three-point shots made jumped to 77% from 68%.

Basic reactions, gauged by having players push a button after spotting a stimulus on a screen, improved by 12%, and players were happier.
Source: “The Effects of Sleep Extension on the Athletic Performance of Collegiate Basketball Players,” Cheri D. Mah, Kenneth E. Mah, Eric J. Kezirian and William C. Dement, Sleep (July)

These are young, healthy varsity athletes.

When I take an SAT math section on a good night's sleep (or maybe a good week of good nights' sleep), I miss 0 to 1 questions. Two questions at most.

The other day I took a PSAT math section in a hot room after several nights of going to bed late and getting up early, and I missed 5 questions out of 18, all of them problems I normally get right.

A five-out-of-fifteen miss rate at this stage of the game is, for me, a collapse. Projecting the same percent correct across the 3 math sections of an SAT I, that's a drop from a score in the 700 to 800 range to a score at the bottom of the 600s.

One hundred points. At least.

I'm asking myself what this translates to in terms of lost writing productivity over the years.

working memory in children

[T]he findings from this study indicate that the three main components of the Baddeley and Hitch (1974) model of working memory are in place by 6 years of age. The capacity of each component increases linearly from age 4 to early adolescence.


The Structure of Working Memory From 4 to 15 Years of Age
Susan E. Gathercole
University of Durham Susan J. Pickering, Benjamin Ambridge,
and Hannah Wearing
University of Bristol
Developmental Psychology 2004, Vol. 40, No. 2, 177–190

Children have lower working memory than adults, and lower working memory has ramifications for language learning and some cases of problem solving.

Tiger Mom

Debbie's been telling me for ages how wonderful Battle Hymn of the Tiger Mom is, and I finally bought the book.

She's right. It's incredible.

Here is the first page:

This is a story about a mother, two daughters, and two dogs. It’s also about Mozart and Mendelssohn, the piano and the violin, and how we made it to Carnegie Hall.

This was supposed to be a story of how Chinese parents are better at raising kids than Western ones.

But instead, it’s about a bitter clash of cultures, a fleeting taste of glory, and how I was humbled by a thirteen-year-old.

A lot of parents whose kids are heading off to college will find the book moving, especially parents who've been part of kitchen table math. All the things you wanted to do, and tried to do, and failed to do because your kids had other ideas....your kids and your schools and your culture: all the things you didn't manage to do because no one thought it was a really good idea to spend 4 years of your child's life reteaching math (and spelling) at home so he could be on par with his peers in Europe and Asia.

Hard to sort it all out.

That's what the book is about, though for Amy Chua's kids the contested territory was music, not math.

Battle Hymn of the Tiger Mother is the memoir of a Chinese afterschooler.

Are Schools Preparing Students Well for the SAT?

The College Board's website says in many different places that the best way to prepare for the test is to do well in school:

Keep in mind that the foundation of a student's SAT and college preparation is a rigorous curriculum of English, mathematics, science, history, and other academic subjects. Students should read extensively and develop good writing skills.

I want that for my children.

My question is, are schools really teaching this rigorous academic curriculum that the college board says is the best prep for the test ?

I took my son's 10th grade PSAT the other day, and found myself aghast (again) at how darn hard this test is. I'm not opposed to rigor, by the way; just wondering if our schools are on the same page.

There were passages dealing with Descartes, dualism, genomes, and neuroscience. Students had to compare two passages that were extremely sophisticated, with both authors agreeing on the main point, but from different perspectives, and their distinctions were subtle.

Not easy......

Cross posted on Perfect Score Project

when smart is dumb

Directions:

Make each statement true by moving just one matchstick.

In Choke, Sian Bielock discusses a study in which more than 90% of adults with normal working memory correctly answered the first problem. Roughly the same number of people with damaged working memories also got it right.

Only 43% of normal adults got the answer to the second problem, while 82% of patients with damage to the prefrontal cortex figured it out.

I believe high-functioning people with autism (or a healthy loading of autism genes) will also have a high rate of success on problem number 2, but that's just me.

Better without (lateral) frontal cortex? Insight problems solved by frontal patients
Carlo Reverberi,1,2 Alessio Toraldo,3 Serena D’Agostini4 and Miran Skrap4
Brain (2005), 128, 2882–2890

working memory

Just came across this textbook chapter on working memory and thought I'd share it. Don't know who wrote it.

Bielock writes that "working-memory differences across people account for between 50 percent to 70 percent of individual differences in abstract reasoning ability or fluid intelligence."

Working memory also makes you dumber in some situations.

I'll get to that later.

adults and children - language learning

Age Effect Problems in F.L. Acquisition

• Language is better learned at an earlier age.

• Despite numerous methods of explicit language instruction, older children and adult learners do not reach a native level of language proficiency.

• Adults generally learn the word order and semantic aspects of language more quickly than children but usually never master the grammatical aspects.

The Application of the Less is More Hypothesis in Foreign Language Learning (Powerpoint)
(Simone L. Chin, Alan W. Kersten)
Cognitive Science Program
Kwon Ahram

article:

The Application of the Less is More Hypothesis in Foreign Language Learning
Simone L. Chin (schin2@fau.edu)
Florida Atlantic University, Psychology Department
777 Glades Road, Boca Raton, FL 33431
Alan W. Kersten (akersten@fau.edu)
Florida Atlantic University, Psychology Department
777 Glades Road, Boca Raton, FL 33431

second language learning - the "less is more" hypothesis

I'm reading Choke by Sian Beilock, a terrific book. Mostly it's about why and how people choke under pressure, but I've been surprised at the number of ancillary topics that turn out to be related to choking -- including foreign language learning by grown-ups.

Beilock says that the reason children learn language better than adults is that children have less working memory (pdf file). Less is more.

She has fascinating things to say about math and problem solving, too.

Statement of Research Interests (pdf file)
Alan W. Kersten
This research has been testing one hypothesis for why adults have so much difficulty successfully acquiring a second language, namely the “Less is More” hypothesis of Elissa Newport (1990). According to this hypothesis, the reduced working memory capacity of children relative to adults actually results in better language learningby forcing children to focus on small chunks of language. Adults, on the other hand, can remember larger chunks of language, allowing them to memorize useful expressions in a foreign language (e.g., “Where is the bathroom?”), but making it difficult for them to extract the lower-level meaning elements from which those expressions are constructed. Adults are thus limited to the set of phrases that they have acquired, and are unable to recombine the lower level elements from which those phrases are constructed to express novel meanings. If this hypothesis is correct, one may predict that adults will learn a language better if they are forced to focus on small chunks of language rather than being allowed to learn entire phrases. We have tested this prediction using a miniature artificial language learning paradigm (see Kersten & Earles, 2001). One group of adults was presented immediately with complete “sentences” from this language, whereas a second group was presented initially only with individual words from the language. This second group was subsequently presented with incrementally longer chunks of language until ultimately they were hearing the same sentences that the other group heard all along. The group that was initially forced to focus on small chunks of language showed better ultimate learning of the word meanings and morphology of that language, consistent with the “Less is More” hypothesis. We are currently investigating whether starting small benefits the acquisition of a natural language with more complex grammar, namely French (Chin & Kersten, in press).

update: Less Is Less in Language Acquisition

a company labels its products...

AA2

A company labels its product with a three-character code. Each code consists of two letters (not necessarily different) from the 26 letters of the English alphabet, followed by one digit, as shown above. What is the total number of such codes that are available for labeling the company's product?

I'll post the answer in the comments thread later.

My answer is wrong, and I don't understand why.

David Sedaris on language lessons

Ah, grammar. How dry. How boring. Right up there with those tedious times tables and those soul-sapping algorithms of arithmetic.

But then here's David Sedaris in the latest New Yorker reflecting on the Pimsleur language program:

Thanks to Japanese I and II, I’m able to buy train tickets, count to nine hundred and ninety-nine thousand, and say, whenever someone is giving me change, “Now you are giving me change.” I can manage in a restaurant, take a cab, and even make small talk with the driver. “Do you have children?” I ask. “Will you take a vacation this year?” “Where to?” When he turns it around, as Japanese cabdrivers are inclined to do, I tell him that I have three children, a big boy and two little girls. If Pimsleur included “I am a middle-aged homosexual and thus make do with a niece I never see and a very small godson,” I’d say that. In the meantime, I work with what I have.

The problem is that Pimsleur is all about mimicry:

Pimsleur's a big help when it comes to pronunciation. The actors are native speakers, and they don't slow down for your benefit. The drawbacks are that they never explain anything or teach you to think for yourself. Instead of being provided with building-blocks which would allow you to construct a sentence of your own, you're left using the hundreds or thousands of sentences you have memorized. That means waiting for a particular situation to arise in order to comment on it; either that or becoming one of those weird non-sequitur people, the kind who, when asked a question about paint color, answer, "There is a bank in front of the train station,"or, "Mrs. Yamada Ito has been playing tennis for fifteen years."

What are those "building-blocks which would allow you to construct a sentence of your own," and, equally importantly, the rules that tell you how to put those building blocks together? That dry, tedious, soul-sapping entity known (or sort of known) as Grammar.

However tedious and soul-sapping it is to do so, mastering a language's grammar rules is the only way to move beyond mimicry and use the language creatively: the only way to move from  "I have three children, a big boy and two little girls" to “I am a middle-aged homosexual and thus make do with a niece I never see and a very small godson.”

Pimsleur isn't alone in presuming that you can master a language without learning its grammar; the biggest seller of this fiction is Rosetta Stone (whose slogan, ironically, is "More than Words. Understanding.") Other grammar-denialists (as I discuss here) are k12 foreign language curriculum developers, as well as (as I discuss here) autism therapists and the general American public. It's a vicious cycle that worsens with each succeeding generation of mis-educated students, more of whom need to spend time attempting to converse with Japanese cabbies before foisting their language lessons on the rest of us. Thank you, David Sedaris, for yours!

(Cross-posted at Out in Left Field)

The Learning Part is Easy; It's the Remembering That's Hard

A commenter pointed me to this Wired article about Piotr Wozniak and SuperMemo. Has anyone tried SuperMemo?

These quotes from the article describe how I feel, to a tee.

Learning things is easy. But remembering them — this is where a certain hopelessness sets in.

Wozniak felt that his ability to rationally control his life was slipping away. "There were 80 phone calls per day to handle. There was no time for learning, no time for programming, no time for sleep...."

Our capacity to learn is amazingly large. But optimal learning demands a kind of rational control over ourselves that does not come easily. Even the basic demand for regularity can be daunting.

(cross posted on Perfect Score Project)

how the SAT changed in 2006

I'm tossing old papers, or trying to, and in my rummaging came across this Times article from 2005.

I was tickled to see that one of the problem types added to the revised test was the absolute value inequality word problem, a category I had never seen or imagined until I encountered one in Dr. Chung's SAT Math:

For pumpkin carving, Mr. Sephera will not use pumpkins that weigh less than 2 pounds or more than 10 pounds. If x represents the weight of a pumpkin, in pounds, he will not use, which of the following inequalities represents all possible values of x?
a. | x - 2 | > 10
b. | x - 4 | > 6
c. | x - 5 | > 5
d. | x - 6 | > 4
e. | x - 10 | > 4

Pop Quiz; New and (Maybe) Improved
Published: November 7, 2004

Talk about inflexible knowledge. Somehow I had concluded that absolute value inequality calculations were just that: calculations. Arithmetic. I was stunned to discover that you could have an absolute value inequality word problem.

Wonders never cease.

Elizabeth King's explanation of these problems is excellent.

 

Algebra Review: Laying the Groundwork for Pre-Calculus

I've been using Michael Sullivan's Algebra and Trigonometry textbook for the last few years to teach College Algebra/Pre-Calculus/Trigonometry on the quarter system, but we're switching to John Coburn's Algebra and Trigonometry next year. They're both pretty good textbooks.

In building Pre-Calculus curriculum I've drawn mainly from four textbooks:

Mary Dolciani - Modern Introductory Analysis (original copyright 1964, my edition is from 1986)

Richard Brown/David Robbins - Advanced Mathematics (this copyright is from 1984, a newer edition of this book is here)

Paul Foerster - Pre-Calculus with Trigonometry (copyright 1987)

Max Sobel/Norbert Lerner - Pre-Calculus Mathematics (copyright 1995)

I had thought about using the Sobel/Lerner book for the Pre-Calculus course I developed for Clatsop Community College, and even e-mailed Max Sobel asking him about a new edition of that text, but he very kindly replied that he had retired (I also have the Harper & Row Algebra I and II textbooks from his series with Evan Maletsky and like these as well).

One of the things I liked about the Sobel/Lerner textbook was the coverage of rational expressions that several of the other books I had considered didn't have. I like rational expressions because this topic requires a firm grasp of many of the most important concepts from algebra – factoring and multiplying of bi- and trinomials, simplifying complex expressions, and combining like terms in the context of manipulating algebraic fractions. If students understand numerical fractions it helps a lot.

When I teach College Algebra courses at Clatsop CC, I often begin with exercises like (x+7)(2x-3) – (x+1)(x+5) to address these topics and prepare the students for when they see this again in working with rational expressions. Another good example is (x+6)(3x+1) – (x+2)^2, to get them used to seeing the squared binomial. ( I make the squared binomial a regular visitor in most of my algebra classes). These expressions often appear as the numerator of a combined fraction in a problem like (x+7)/(x+1) – (x+5)/(2x-3).

Here is a link to a collection of problems I often assign for this topic.

I recently began to reacquaint myself with the College Board Math II Subject Test which I had taken after taking Pre-Calculus in the spring of 1982. The first question on the sample test I looked at was intriguing, and an understanding of rational expressions is really useful in finding a quick solution:

If 3x+6=(k/4)(x+2), then k=

a) ¼

b) 3

c) 4

d) 12

e) 24

In this problem, dividing through by (x+2) so that 3=k/4 (and 12=k) gives the almost instantaneous answer we need for a timed test. This is an interesting problem because it really gets at the concepts involved in working with factors in an equation.

In the Sobel/Lerner textbook, Sections 1.7, 1.8 and 1.9 cover the algebra review (multiplying polynomials, combining like terms, factoring polynomials and rational expressions) necessary to move on. This is where it is important to illustrate these topics with problems, because when I say “combining like terms,” I don't mean 2x+5x. While this type of problem could be appropriate when first teaching the concept, in the context of review for Pre-Calculus, a problem from the Sobel/Lerner text like (x^3-2x+1)(2x)+(x^2-2)(3x^2-2) is better practice for using these skills together.

This is something that I consider extremely important and that textbooks and assessments often don't include enough of – using the skills together. Learning skills in isolation is useful to grasp each skill individually, but to really DO MATH, a student must be able to make decisions about what to do and when. Something that I like about the Pre-Calculus curriculum is that it lends itself well to the type of problem in which the tools of algebra must be applied in a variety of situations.

The Brown/Robbins text covers complex numbers and the quadratic formula in Chapter 1 (1-4, 1-5) and then the solution of equations involving rational expressions in Section 2-2. Chapter 2 goes on to examine the graphing of quadratic and polynomial curves and finishes with material on finding rational roots.

The Sullivan book covers polynomials and algebra in sections R.4, R.5 and R.7, Coburn covers this in sections R.3, R.4 and R.5.

The Foerster and Dolciani texts don't really cover much algebra review at all, but, as a result, they explore a number of topics the other books don't. I'll probably follow a path similar to the Brown/Robbins book and talk about rational roots next.

practice in school

Hey everyone - I'm back from IL (didn't get to see Susan S - darn!) - and have just read a brilliant comment left by Lynne Dilligent on Joanne Jacobs' blog. Lynne's comment sums up a core frustration I've felt with the schools forever, re: the need for the school, not the parents, to be in charge of providing and overseeing the practice children need to learn what they're supposed to be learning.

Must go do "SAT work" with C. -- back in a little bit.

(Thanks to Barry for sending the link.)

Competing Memory Issue

Six months into this SAT project, and I've repeatedly experienced that learning something new only sticks, until I learn something else new. Very frustrating.

Reminds me of my daughter who tells me that it's very hard for her to get good grades in every subject at the same time. (I get it now, deeply.)

There's a new study from Beth Israel researchers about this competing memory issue:

For the last 100 years, it has been appreciated that trying to learn facts and skills in quick succession can be a frustrating exercise,” explains Edwin Robertson, MD, DPhil, an Associate Professor of Neurology at Harvard Medical School and BIDMC. “Because no sooner has a new memory been acquired than its retention is jeopardized by learning another fact or skill.

....and a possible new solution:

TMS is a noninvasive technique that uses a magnetic simulator to generate a magnetic field that can create a flow of current in the brain......They discovered that by applying TMS to specific brain areas, they were able to reduce the interference and competition between the motor skill and word-list tasks and both memories remained intact.

On a related note, I have started working with a Cognitive Psychologist on my working memory. Yesterday's appointment: IQ test.

(Cross Posted on Perfect Score Project)

Practice Makes Perfect (But only Briefly)

Sustained practice makes the kind of perfect I'm looking for.

More inspiration from Daniel Willingham:

When we refer to "practice," it is important to be clear that it differs from play (which is done purely for one's own pleasure), performance (which is done for the pleasure of others), and work (which is done for compensation). Practice is done for the sake of improvement. Practice, therefore, requires concentration and requires feedback about whether or not progress is being made. Plainly put, practice is not easy. It requires a student's time and effort, and it is, therefore, worth considering when it is appropriate.

(cross-posted on Perfect Score Project)

Throwing Curves: New Posts

While Catherine is away, check out new posts at Throwing Curves.

gone fishing

I'm in Chicago 'til next Wednesday - see you then!

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.

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 EducationNews.org 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.”

[snip]

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:

...it 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.

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?

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.

and:

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.

off-topic - vegetables make you thin

Seriously.

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.

[snip]

“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
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.

Students will make and investigate mathematical conjectures

from New York state Education Department Geometry standards (pdf standards):

Now that Jeanette has finished inventing the rule to find the measure of an angle in a regular n-gon, maybe she'll have time to invent the wheel.

help desk - variables and expressions

from Glencoe Algebra 1 Skills Practice (pdf file):

the difference of 17 and 5 times a number

How do you write this?

17 - 5n

I don't think I've seen a number problem worded that way.

do students learn to read from beginning to end?

from the math and reading thread, EM reports:

I have in fact encountered quite a few SAT students who quite literally don't understand what it is that they're reading.

It has nothing to do with them not producing a particular answer that a teacher has arbitrarily deemed "correct" but rather is a result of their inability to unpack complex syntax, infer meanings that aren't literally spelled out for them, and, astonishingly (at least I was astonished the first time it happened - now I've been desensitized), to read an entire sentence from beginning to end, paying attention to every word, rather than "skimming" it in such a way that they only pick up random words that bear no apparent relationship to one another. If asked to summarize the gist of a reading in their own words, they're often completely lost.

Did I mention that some of these kids have attended elite Manhattan private schools since kindergarten?

At least from what I've seen, the problem isn't as bad as most people think. It's actually a lot worse.

I assume some of the problem can be attributed to balanced literacy reading instruction, which teaches students to move their eyes around the text as they seek clues to help them decipher unknown words. But I don't know, of course.

Thoughts?

Must get palisadesk on the case---!

Here is Arthur Whimbey making the same observation.

'the most important fact about IQ'

Garret Jones slides (pdf file) 
National IQ and National Productivity:
The Hive Mind Across Asia (pdf file)
Garett Jones
Center for Study of Public Choice
Department of Economics
George Mason University
January 2011
[Published in Asian Development Review, June 2011]

sitters

Susan Cain's op-ed in today's Times reminds me of Katharine's book:

But shyness and introversion share an undervalued status in a world that prizes extroversion. Children’s classroom desks are now often arranged in pods, because group participation supposedly leads to better learning; in one school I visited, a sign announcing “Rules for Group Work” included, “You can’t ask a teacher for help unless everyone in your group has the same question.” Many adults work for organizations that now assign work in teams, in offices without walls, for supervisors who value “people skills” above all. As a society, we prefer action to contemplation, risk-taking to heed-taking, certainty to doubt. Studies show that we rank fast and frequent talkers as more competent, likable and even smarter than slow ones. As the psychologists William Hart and Dolores Albarracin point out, phrases like “get active,” “get moving,” “do something” and similar calls to action surface repeatedly in recent books.

Yet shy and introverted people have been part of our species for a very long time, often in leadership positions. We find them in the Bible (“Who am I, that I should go unto Pharaoh?" asked Moses, whom the Book of Numbers describes as “very meek, above all the men which were upon the face of the earth.”) We find them in recent history, in figures like Charles Darwin, Marcel Proust and Albert Einstein, and, in contemporary times: think of Google’s Larry Page, or Harry Potter’s creator, J. K. Rowling.

In the science journalist Winifred Gallagher’s words: “The glory of the disposition that stops to consider stimuli rather than rushing to engage with them is its long association with intellectual and artistic achievement. Neither E=mc2 nor ‘Paradise Lost’ was dashed off by a party animal.”

We even find “introverts” in the animal kingdom, where 15 percent to 20 percent of many species are watchful, slow-to-warm-up types who stick to the sidelines (sometimes called “sitters”) while the other 80 percent are “rovers” who sally forth without paying much attention to their surroundings. Sitters and rovers favor different survival strategies, which could be summed up as the sitter’s “Look before you leap” versus the rover’s inclination to “Just do it!” Each strategy reaps different rewards.

IN an illustrative experiment, David Sloan Wilson, a Binghamton evolutionary biologist, dropped metal traps into a pond of pumpkinseed sunfish. The “rover” fish couldn’t help but investigate — and were immediately caught. But the “sitter” fish stayed back, making it impossible for Professor Wilson to capture them.

[snip]

Next, Professor Wilson used fishing nets to catch both types of fish; when he carried them back to his lab, he noted that the rovers quickly acclimated to their new environment and started eating a full five days earlier than their sitter brethren. In this situation, the rovers were the likely survivors. “There is no single best ... [animal] personality,” Professor Wilson concludes in his book, “Evolution for Everyone,” “but rather a diversity of personalities maintained by natural selection.”

[snip]

...sitter children are careful and astute, and tend to learn by observing instead of by acting. They notice scary things more than other children do, but they also notice more things in general. Studies dating all the way back to the 1960’s by the psychologists Jerome Kagan and Ellen Siegelman found that cautious, solitary children playing matching games spent more time considering all the alternatives than impulsive children did, actually using more eye movements to make decisions. Recent studies by a group of scientists at Stony Brook University and at Chinese universities using functional M.R.I. technology echoed this research, finding that adults with sitter-like temperaments looked longer at pairs of photos with subtle differences and showed more activity in brain regions that make associations between the photos and other stored information in the brain.
Once they reach school age, many sitter children use such traits to great effect. Introverts, who tend to digest information thoroughly, stay on task, and work accurately, earn disproportionate numbers of National Merit Scholarship finalist positions and Phi Beta Kappa keys, according to the Center for Applications of Psychological Type, a research arm for the Myers-Briggs personality type indicator — even though their I.Q. scores are no higher than those of extroverts. Another study, by the psychologists Eric Rolfhus and Philip Ackerman, tested 141 college students’ knowledge of 20 different subjects, from art to astronomy to statistics, and found that the introverts knew more than the extroverts about 19 subjects — presumably, the researchers concluded, because the more time people spend socializing, the less time they have for learning.

THE psychologist Gregory Feist found that many of the most creative people in a range of fields are introverts who are comfortable working in solitary conditions in which they can focus attention inward. Steve Wozniak, the engineer who founded Apple with Steve Jobs, is a prime example: Mr. Wozniak describes his creative process as an exercise in solitude. “Most inventors and engineers I’ve met are like me,” he writes in “iWoz,” his autobiography. “They’re shy and they live in their heads. They’re almost like artists. In fact, the very best of them are artists. And artists work best alone ... Not on a committee. Not on a team.”
Shyness: Evolutionary Tactic?
By SUSAN CAIN
Published: June 25, 2011

Quiet: The Power of Introverts in a World That Can't Stop Talking




Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School

Susan Cain's blog

Bonnie on college student reading skills

from the Headsprouts thread:

Reading comprehension is a huge problem for my college students. The introductory CS textbooks are written using vocabulary and a sentence complexity that is way beyond them. I wish I had a better sense of their actual reading skills so I could do some vocabulary work with them. The gasstationwithoupumps blog has posted links to some excellent material on teaching students how to read technical material that I think I may use next semester.

"people love pizza"

Math lovers of the world unite

Envision or Math in Focus?

query from Peter Meyer

Any thoughts?

Newhart

Headsprouts reading comprehension program

abstract:
Teaching learners how to comprehend text remains a largely unsuccessful attempt in our school system. Drawing from the fields of learning sciences, education, instructional design, and performance improvement, we designed, tested, revised, and released to schools and homes an interactive online program that reliably teaches flexible, widely applicable reading comprehension strategies to children. This article describes the analysis and design processes involved in the development of such a program.
Comprehension by Design: Teaching Young Learners How to Comprehend What They Read (pdf file)
Marta Leon, PhD; Victoria Ford Hirofumi Shimizu, PhD; April Heimlich Stretz Jay Thompson Melinda Sota; Janet S. Twyman, PhD T. V. Joe Layng, PhD

Reading this tonight!

More Connected Math Woes, This Time in Pennsylvania

The Riverview School District enrolls about 1,100 k-12 students in Oakmont and Verona Boroughs, Pennsylvania.

From an online news blog, the Plum-Oakmont Patch

The Riverview School Board meeting on Monday had the largest attendance in years, according to school board members. Parents filled the high school library, and in a citizen comment session that lasted two hours, they discussed their concerns about the middle school Connected Mathematics 2 program.

The parents had a lot of familiar things to say:

Among the parents' concerns were the group work involved, the participation aspect of the class, the frequency of testing and the combination of students at different math levels in the same classroom.

Parent Joseph Knapp said his son struggled in the class because of the way it was structured.

"I, unfortunately, found the Connected Math program to be an unorthodox way of teaching students," he said. "It seemed like the students taught themselves, in theory.

"They have groups where they figure out problems and are encouraged to come up with the ideas on their own. I thought that was ridiculous. In sixth and seventh grades, you need instruction."

Parent Tim Lazor said his son usually did very well in math class until he took the class this year. Lazor said he doesn't think the program has the support of the students or the teachers who are teaching it.

"I don't think the teachers bought into this," he said. "That's a critical component.

Eight years to find a new curriculum?

Superintendent Charles Erdeljac said district officials had been looking for a way to improve the math curriculum for about eight years. He said to participate in the Math and Science Partnership of Southwest Pennsylvania, the district would have to implement Connected Math 2 or MathScape—the only two programs with the National Science Foundation's "stamp of approval."

Scores declined?

When asked by parents about Pennsylvania System of School Assessment Scores, principal Jay Moser said the scores of last school year's seventh graders dropped by 9 percent, according to primary figures from the state department of education.

Hmmn I guess math is different in small-town Pennsylvania.

Erdeljac said district officials are going to continue to monitor the program and data associated with it to ensure it is a good fit for students.

"On the one hand, we have to have fidelity to the program as it's intended to be taught, but on the other hand, we're Riverview," he said. "We need to find out how this program can be most successful here at Riverview…we're still in the process of making this program Riverview's Connected Math program."

gaps

From the reading and math, math and reading comments thread:

Erica writes:

You can tell C. that I beat him: 220 point gap between CR and math (800/580), and I actually knew a couple of people with even larger gaps (800/560, 800/490!).

Independent George wrote:

I scored a 420 on my Writing achievement test (waaaay back in 1994). I had a 720 on the SAT-Verbal, and a 5 on the AP English test, but I scored 420 on the writing test.

C. has a friend who got an 800 on reading and a 550 on math.

He's still only at 670 on writing, which is equally ridiculous! (Ridiculous because he's losing his points on the grammar section.) Erica's going to shape him up.

reading and math, math and reading

via Marginal Revolution:

To an economist, the most important fact to know about mental abilities is that across large populations, different mental abilities are positively correlated.1 In other words, people who are above average in arithmetic tend to perform above average in vocabulary tests, block puzzles, as well as in memorizing lists of numbers and then repeating them in reverse order. This positive correlation conflicts with the commonsense view that abilities are negatively correlated, that for instance while some people are good in math, others are good in verbal tasks.

This positive correlation is at the heart of the psychological concept of intelligence. Quantitatively, it is at the heart of psychometric methods that extract a principal component from a broad variety of mental ability subtests. This principal component is formally called g, or the g factor. Lay persons, and most routine psychological research, refer to IQ instead of g, but it is worth keeping the concept of g in mind. Across thousands of studies on the correlation across mental abilities across populations, no one has yet found a reliable negative correlation.

This fact should strengthen our priors when we come across new mental tasks and we ask ourselves, “Will high IQ groups be better than average at this new mental task?” For every mental task so far that involves any level of sophistication, the answer has been yes.
National IQ and National Productivity: The Hive Mind Across Asia
Garett Jones
January 2011
[Published in Asian Development Review, June 2011]

Serendipity!

Since last Thursday, I've been trying to explain to C. that a 190-point gap between your reading score & your math score is ridiculous. Ridiculous because a 190-point gap between a reading score & a math score is not consistent with the way a person's brain is built. On IQ tests, everything goes with everything; if you're good on one task, you're good on another.

C's math scores, I keep telling him, like my math scores when I was his age, are a measure of the math teaching and math curriculum he's had, not of his innate ability to do math. His math tutor told him the same thing this morning, but C. claimed later not to have heard. So I was in need of fresh ammunition, and now here it is.

I love the internet.

SAT grammar rules from Erica Meltzer

Complete SAT Grammar Rules

If we didn't have the SAT to prep for, C would never have learned what terms like pronoun case or pronoun antecedent meant. I'm convinced C. is going to develop more quickly as a writer because of it.

Hack the SAT on the writing section

Hack the SAT on tutoring the writing section:

The grammar portions [of the SAT writing test are far more important [than the essay]. And they're very easy to prepare for. In fact, there are only a handful of grammar rules that the SAT loves to test, and they repeat them over and over. So if you can just memorize the rules that we'll lay out in this section, you'll find that the actual test won't be that much of a challenge. During test prep, scores on the writing section tend to increase most reliably, and by the most number of points.
Hack the SAT by Eliot Schrefer
p. 159

I believe it.

Last week I skimmed an SAT roster for our high school from a couple of years back. I saw no 800s on math, one 800 on reading, and four 800s on writing. (Not sure how many students in that group -- perhaps 125?)

I think that's consistent with Schrefer's observation that the writing section is easiest to coach.