kitchen table math, the sequel: 2/20/11 - 2/27/11

Saturday, February 26, 2011

tipping point

One pervasive feature of economic life is that men and women do different jobs, and the jobs that women do are less well rewarded, whether it be an agricultural economy where men do the ploughing and women do the weeding or a modern post-industrial economy where women teach elementary school and men work in construction. *

But what is a male job and what is a female job varies in time and space. When I was teaching in Cuba once I casually remarked that, in Canada, most economics professors are male. My students were surprised because, in Cuba, most economics professors are female. A long discussion in Spanish followed, and after some time, the class reached a consensus. The reason for the difference? "In Canada, people listen to economics professors."

Worthwhile Canadian Initiative
Apparently, there is a gender tipping point in occupations:
Not infrequently, jobs "tip", or change from being male dominated to female dominated -- bank tellers, bakers, court reporters, teachers, secretaries. (Female to male shifts are less usual, but do happen, for example, the shift from midwives to obstetricians). In a fascinating paper, Jessica Pan estimates that, for US white collar jobs, the tipping point is somewhere between 30 and 60 percent female. Once that threshold is crossed, men stop entering the profession. At 34% female, the job of "university professor" is ripe for tipping.

Conventional wisdom has it that, when jobs become feminized, wages fall. Typically the reasons suggested for both feminization and falling wages are deskilling, loss of control over important working conditions by members of the occupation, and reduced advancement opportunities. (For a summary that critiques this conventional wisdom, see this Joyce Jacobsen article). (pdf file)

* Not a good example in my neck of the woods, where total compensation for elementary school teachers averages $100K -- and this without taking into consideration the value of pensions and lifetime health care benefits.

Friday, February 25, 2011

Mark Twain on the almost-right word

My favorite saying about writing:
The difference between the almost right word & the right word is really a large matter--it's the difference between the lightning bug and the lightning.
- Letter to George Bainton, 10/15/1888

Steve's SAT reading question - 2nd pass

(fyi: I deleted the first post I wrote on this subject)

I mentioned in the Comments thread that I reliably miss 0 to 1 items on SAT I reading and writing tests. I don't find the tests easy -- I find them taxing -- but I finish the sections five minutes early and never miss more than 1 item.

I don't know why that is, though.

So a couple of minutes ago I tried to analyze why I chose the correct answer to the question Steve posted:
The following line is from an SAT excerpt where the author really(!) dislikes the way science was being taught (in 1939).

(24) "As to the learning of scientific method, the whole thing is palpably a farce."

3. The word ‘palpably’ (line 24) most nearly means
A. empirically
B. obviously
C. tentatively
D. markedly
E. ridiculously

The answer is B.
1st step: I rapidly eliminate and cross out the three obviously wrong answers.

For me, answers a., c., and e. are obviously wrong:

a. empirically
c. tentatively
e. ridiculously

Why are these 3 answers obviously wrong?

a. Empirically is wrong because the author has said nothing explicit about running an experiment or observing actual students who were learning (or attempting to learn) the scientific method. Thus I conclude that the author is voicing an opinion, not describing an empirical observation or experimental result.

This is an example of former SAT tutor LexAequita's advice that to do well on the SAT you'd better start thinking like a 13-year old with Asperger syndrome.

Students should read SAT reading and writing questions the same way they're told to read SAT math diagrams: add nothing to the text that isn't explicitly stated. Easier said than done since reading is all about making inferences, but that's a conundrum for another day.

c. Tentatively is wrong because it's inconsistent with the tone of the passage, which is emphatic, not tentative. Tentative is the opposite of emphatic, so it's wrong.

e. Ridiculously is redundant. The writer says that "the learning of the scientific method is a farce," and farce means ridiculous. So you don't need to add the word ridiculously.

Second step: I choose the "more right" of the two answers that remain.

As far as I can tell, SAT reading and writing questions always come down to two arguably correct answers. Your job is to figure out which answer is more correct and choose that one.

In this case, the two arguably correct answers I'm left with are:

b. obviously
d. markedly

As I tried to reconstruct why the word obviously leapt out as me as the correct answer, it struck me that I may have been influenced by the conventions of idiomatic usage and good writing. If you substitute the word obviously for palpably, the sentence works; if you substitute the word markedly, the sentence doesn't work.

...the whole thing is obviously a farce

...the whole thing is markedly a farce


Maybe markedly a farce sounded wrong to me because it's bad writing.

I'm going to start keeping an eye out for how often the right answer is also the better written answer.

Thursday, February 24, 2011


Visiting SUNY Stony Brook today, I found this scrawled inside a stall in the women's restroom:

Eff Twilight.

And eff romantic comedies.

Girls need to stop having such a bad reputation regarding taste in movies.

Harriet Ball: RIP

The EdWeek story quotes from her self-published "Fearless Math" manual. In it, she asserted that most students, particularly those at risk, "learn most naturally and best through play, songs, patterns, movement, imitation, imagination, and rhythm." Her method incorporated all those elements, the story explains. Ball insisted there's nothing wrong with drills—as long as they're presented in a fun and engaging manner. "Drill won't kill," she liked to say. "Boredom is the killer."
Teacher Who Inspired KIPP Schools Dies in Houston

SAT Reading Comprehension Questions

I thought I would start a new thread based on a comment by kcab in the School Boards thread about the SAT reading comprehension section. The question is how much general reading helps versus specific practice. Also, how much won't help at all. I have a lot of difficulty with some of these questions and I wouldn't know how to fix it. Here is an example:

The following line is from a SAT excerpt where the author really(!) dislikes the way science was being taught (in 1939).

(24) "As to the learning of scientific method, the whole thing is palpably a farce."

3. The word ‘palpably’ (line 24) most nearly means

A. empirically
B. obviously
C. tentatively
D. markedly
E. ridiculously

The answer is B.

How do you learn this by just reading? I've always seen papable used by authors to mean much more than "obvious". How would you learn this by studying definitions?

Palpable - Capable of being handled, touched, or felt; tangible

Obviously - unmistakably; clearly apparent

Markedly - in a clearly noticeable manner; conspicuously

In the answer section, they talk about substituting the different words in for palpably, but isn't that different than what they ask for? They wanted to know what it "most nearly means".

I used to teach a SSAT prep class and I would tell students that this sort of reading is unlike anything they've done before. I called it technical reading. Some people do well on these questions. Why?

Wednesday, February 23, 2011

Lifting the Lid on Essay Scoring in Standardized Tests

Our local free weekly rag, the City Pages recently published an "expose" on how the essay scoring sausage gets made on standardized tests. (A lot of the test scoring apparently happens in the Twin Cities.) It's about as you might expect.

I get a feeling I was supposed to come away with the idea that all standardized testing is bad, but I mostly went away with the feeling that standardized test essays were bad news and we should stick with computer scored #2 pencil bubble tests.

Barry's open letter to Deborah Ball

at Out in Left Field

school boards

With the contemporary focus on college and workforce readiness, many may be surprised that 14.1 percent of board members rank preparing students for college as sixth in importance out of six education goals, and 16.4 percent give the same ranking to preparing students for the workforce. When asked what they consider the most important objectives for schooling, the most popular board member responses are to “prepare students for a satisfying and productive life” and to “help students fulfill their potential.”

School Boards in the Age of Accountability
Frederick M. Hess
Olivia Meeks
Here in Irvington, a number of us have been asking the administration to hold itself accountable for student achievement. One parent has been pressing the case for well over a decade.

At this point, two of five board members are also asking the administration to measure the effectiveness of its programs and teaching philosophy.

At last week's board meeting, the interim director of curriculum put up a slide listing 20 "Indicators of Success," and said, "[This] is a new one for us. What indicators do we use to determine if we are being successful?"

Reform Writing

I'm a big fan of sentences. When I edit my work, I'm constantly combining and recombining them, altering the order of phrases, or their depth of embedding, to maximize clarity, flow, and efficiency. Following this, almost in lockstep, is clarifying my message. This works in both directions: the more I play around with sentence syntax, the clearer my thoughts become; when I know exactly what I want to say, the ideal sentence structure comes along for the ride.

None of my writing instructors ever focused on sentence-level syntax--except to tell us to "vary our sentence structures." But varying structure for the sake of variation alone does not enhance writing; when you structure each sentence for clarity, flow, and efficiency, you will, willy nilly, vary your sentence structures. My focus on syntax comes not from my English teachers, but from my own personal interest in sentence structure (one that ultimately culminated in a doctorate in linguistics). From a young age, I'd constantly scrutinize the variety of structures that undergird effective prose and try to internalize them so they'd become part of my own syntactic repertoire.

So when Catherine recently sent me an article by Robert J Connors on The Erasure of the Sentence, I was astounded to realize that explicit instruction in sentence syntax had been a staple of composition classes (dating back to classical antiquity) until just a few decades ago.

What happened? Here, in a nutshell, is Connors' thesis:
The usefulness of sentence-based rhetorics was never disproved, but a growing wave of anti-formalism, anti-behaviorism, and anti-empiricism within English-based composition studies after 1980 doomed them to a marginality under which they still exist today. The result of this erasure of sentence pedagogies is a culture of writing instruction that has very little to do with or say about the sentence outside of a purely grammatical discourse.
But first, what are these sentence-based rhetorics that have fallen out of favor?

Recent champions of sentence-based rhetorics include Francis Christensen, whose specialty was "sentence combining." In Connors' words, "Sentence-combining in its simplest form is the process of joining two or more short, simple sentences to make one longer sentence, using embedding, deletion, subordination, and coordination."
According to Christensen, you could be a good writer if you could learn to write a good sentence. His pedagogy consisted of short base-level sentences to which students were asked to attach increasingly sophisticated systems of initial and final modifying clauses and phrases-what he called "free modifiers." Effective use of free modifiers would result in effective "cumulative sentences," and Christensen's most famous observation about teaching the cumulative sentence was that he wanted to push his students "to level after level, not just two or there, but four, five, or six, even more, as far as the students' powers of observation will take them. I want them to become sentence acrobats, to dazzle by their syntactic dexterity."
Another "sentence-based rhetoric" was Edward Corbett's "imitation exercises," which involved the "the emulation of the syntax of good prose models." Students would begin by copying a model sentence word for word. Then came "pattern practice," in which students construct new sentences that parallel the grammatical type, number, and order of phrases and clauses of the model sentence, perhaps with the help of a syntactic description of the model sentence's structure. Students might also perform syntactic transformations (informed by Noam Chomsky's Universal Grammar) on the model sentence. In Corbett's words, the aim of such imitation exercises was to "achieve an awareness of the variety of sentence structure of which the English language is capable." Other advocates of imitation exercises noted that student writing "is often stylistically barren because of lack of familiarity with good models of prose style;" the remedy was explicit emulation of good models.

Both Corbett's and Christensen's methods were subject to empirical scrutiny, and studies showed that both methods not only increased the grammatical complexity of student writing, but also improved the overall writing quality (as compared with control groups and as rated by blind raters). In particular, internalizing syntactic structures, even by slavishly copying them, ultimately increased originality and creativity--presumably by giving students a wide repertoire of syntactic tools to choose from and handy ways to play around with them.

But as Connors notes, almost as soon as this sentence-syntax teaching methodology starting showing empirical success, it was shouted down into oblivion by critics who found it philosophically distasteful. After all, these methods involved:

1. textbooks
2. mere exercises, devoid of content and real-world application, with (worse yet!) correct and incorrect answers
3. rote imitation
4. an inorganic, narrow, analytical, reductionist approach that stifles creativity
5. a procedural focus at odds with the authentic writing process in which motivation and communicative intent and self-expression come first and everything else comes along for the ride (including, apparently, grammatically well-formed sentences).

The result of this backlash was that most writing instructors came to believe that "research has shown that sentence combining doesn't work."

Sound familiar?

If not, try substituting "sentence combining" with "traditional math," syntactic transformations with "mere calculation," "imitation exercises" with "drill and kill," and "communicative competence" with "conceptual understanding."

Woops! I thought that by writing about writing I'd be taking a break from math.

(Cross-posted, with a different title, at Out In Left Field)

summer school at Morningside Academy

I have the application sitting on my desk -- !

Tuesday, February 22, 2011

public sector unions & higher education in California

Daniel DiSalvo's The Trouble with Public Sector Unions describes a phenomenon we've seen here in Irvington, which is our unions (we have 3) pressing not just for higher pay and benefits but for a higher absolute number of employees as well -- and this as enrollment is declining.

Fewer students, higher pay, more employees. That is the formula. Per pupil spending currently stands at roughly $30K, and negotiations have been at impasse since last school year. So, under the Triborough Amendment, the district must continue to award raises that were negotiated during boom times.

Here's DiSalvo:
[A]s economist Richard Freeman has written, "public sector unions can be viewed as using their political power to raise demand for public services, as well as using their bargaining power to fight for higher wages."


For a case study in how public-sector unions manipulate both supply and demand, consider the example of the California Correctional Peace Officers Association. Throughout the 1980s and '90s, the CCPOA lobbied the state government to increase California's prison facilities — since more prisons would obviously mean more jobs for corrections officers. And between 1980 and 2000, the Golden State constructed 22 new prisons for adults (before 1980, California had only 12 such facilities). The CCPOA also pushed for the 1994 "three strikes" sentencing law, which imposed stiff penalties on repeat offenders. The prison population exploded — and, as intended, the new prisoners required more guards. The CCPOA has been no less successful in increasing members' compensation: In 2006, the average union member made $70,000 a year, and more than $100,000 with overtime. Corrections officers can also retire with 90% of their salaries as early as age 50. Today, an amazing 11% of the state budget — more than what is spent on higher education — goes to the penal system.

In 2009, the New York Times reported on cuts to the UC system:
As the University of California struggles to absorb its sharpest drop in state financing since the Great Depression, every professor, administrator and clerical worker has been put on furlough amounting to an average pay cut of 8 percent.


And on Thursday, to top it all off, the Board of Regents voted to increase undergraduate fees — the equivalent of tuition — by 32 percent next fall, to more than $10,000. The university will cost about three times as much as it did a decade ago, and what was once an educational bargain will be one of the nation’s higher-priced public universities.

A Crown Jewel of Education Struggles with Cuts
Published: November 19, 2009

Spittleless Politicians, Apathetic Constituents and Collective Bargaining

A new post on Throwing Curves.

There is plenty of blame to throw around, but Rosemary takes an unexpected approach in her latest blog post. Comments on the site are always welcome (and they so encourage us!).

have iPad apps solved the page riffling problem?

A friend bought me an iPad a couple of weeks ago, and it is amazing.

I've been skeptical of 'technology' in education, mostly because nothing I've tried (online learning, educational software, educational CDs & DVDs, educational audio CDs for the car, the Kindle) has worked well for me. ALEKS came closest, but I would only use ALEKS for review, and I probably wouldn't do that, either. I found the need to look back and forth from the computer screen to my paper-and-pencil notebook tedious.

The iPad is the first form of technology that I can imagine changing the way people read and study.

First off, the 'content' apps I've looked at so far (Wall Street Journal & The Economist) format articles so that video and interviews really are "integrated" in a way that CDs tucked unto the backs of textbooks can't be.

More importantly - and this is a fantastic innovation -- the graphic design of the content apps potentially gives readers a workable substitute for page riffling.

The inability to riffle pages is the huge drawback of reading on a Kindle; I would never buy a Kindle edition of a textbook or a cookbook for that reason. On Kindle, reading is a strictly linear affair.

The iPad apps potentially change that. The mobile versions of WSJ and The Economist places content inside two rectangles: a big rectangle containing the article you're reading, and a much smaller, scrollable rectangle containing all the article titles in that section of the paper or magazine.

This would be a terrific feature in a textbook, where you need to grasp the structure of the subject, not just the content on the page you're reading. Each chapter could (and should) have a scrollable list of all the chapter's subject headings flanking the page you're reading.

Having all of the subheads directly at hand would let you riffle. For example, I'm working my way through Greg Mankiw's economics textbook, and I need to constantly flip back to previous sections to remind myself, say, why the aggregate demand curve slopes downward. Doing that on the Kindle is next to impossible. Yes, you can use the search function to find content elsewhere in the text, but it takes forever, and gives you too many hits. If I could read the Mankiw text formatted like the WSJ app, I would be able to click on "The Downward Slope of the Aggregate-Demand Curve" and instantly be where I need to be.

Then, after re-reading the material on AG, I would be able to click on the subject heading of the section I had been working on before I returned to the AG section.

(It would also be incredibly helpful to be able to ask the book to give me the numbered explanations of the graphs illustrating long-term-vs-short-term effects in sequence instead of having all of the "Point As" and "Point Bs" and "Point Cs" visible at all times.)

I doubt any textbooks have adopted this structure as yet, but they should.

Ed is writing a textbook for Oxford, and I'm telling him they need to include author interviews -- interviews, not lectures -- in the electronic edition. I'm going to push the idea of a scrollable column of subsection heads, too.

new Regents diplomas - survey

from lgm:
If any NYers would like to give the Regents feedback on College & Career Readiness, their survey is here

Several questions ask about the various diplomas and there is plenty of room for comments.


"War is God's way of teaching Americans geography."
- Ambrose Bierce
True of me, sad to say.

This morning, studying the Wall Street Journal's map of the Middle East, I noticed for the first time that Sudan is directly south of Egypt.

Also, Libya is next door.


Monday, February 21, 2011

I remember everything

So now we have our public schools setting no-recall standards.

Meanwhile, back on planet Earth, the rest of us are trying to remember where we put our car keys, one of the few remaining factoids you can't find on Google.*

Which probably accounts for the appearance in the Sunday Magazine of a 6000-word book excerpt on the World Memory Championships.


Oh, look!

The world memory champion is from China!

* Speaking of where I put my car keys, the iPad has a finder! I need a finder-for-everything, and I'm often amazed that a finder-for-everything doesn't exist and can't be purchased on Amazon. The Sharper Image had a finder-for-everything gadget out a few years back (actually a finder-for-four-things-of-your-choosing), but the one I ordered didn't work.

I remember nothing

ms-teacher on history & science

re: I remember nothing

As a result of NCLB, many school districts have chosen to focus on reading & math, meaning that emphasis is placed on test skills that will ensure higher test scores.

This has meant that in school districts such as where I teach, elementary schools have virtually eliminated both history & science. When students enter middle school, those who continue to score below basic or far below basic usually have a semester of science & a semester of history, where they are expected to read from on grade level (or above) expository text.

It is no surprise to me that our students are not performing well in history. Until we start emphasizing the value of all subject matters, even when they are not tested, you can expect that schools will continue to deemphasize those subjects that they don't believe boost their test scores.

Teachers hate it & yet, our hands are tied.

Sunday, February 20, 2011

I remember nothing

in The Economist:
History teaching is far from the biggest crisis in American education. But it is a problem nevertheless, and a neglected one. A broad effort to create voluntary national standards does not include history. No Child Left Behind, George Bush’s education law, tests pupils on maths, reading and science. On February 14th Barack Obama stressed the importance of teaching science, technology and 21st-century skills. Meanwhile America’s schoolchildren score even more poorly in history than in maths: 64% of high-school seniors scored “basic” on a national maths test in 2009, but only 47% reached that level on the most recent national history test.

One problem, a new report argues, is that states have pathetic standards for what history should be taught...A study from Fordham, published on February 16th, grades each state for the quality of its history standards. Twenty-eight states received a “D” or an “F”.

Many states emphasise abstract concepts rather than history itself. In Delaware, for example, pupils “will not be expected to recall any specific event or person in history”.

Don't know much about history
The dismal state of a vital subject
Teaching standards
Feb 17th 2011 | CHICAGO | from PRINT EDITION
 Will not recall any specific event or person in history ----

Is that a standard?

thank you Susan S -

Off-topic, but I have to write a public post about this.

Susan S, who has been part of kitchen table math from the very beginning (right?) babysat Andrew while Ed, Chris, Jimmy & I attended my mom's funeral.

She was shaking in her boots, having read the tales here for lo these many years, but she did it. I told her she was starting at the top.

That is one of the most generous things anyone has ever done for me.

Thank you, Susan.

I owe you.

Investigations Math in action: crashing and burning with large numbers

A third grade girl attempts, unsuccessfully, to add several large numbers using an Investigations Math strategy. She then adds them successfully using traditional "stacking" (disallowed at school) in a fraction of the time the Investigations method took her:

Filmed and edited by a fellow concerned parent who is a specialist in math remediation.