kitchen table math, the sequel: 9/26/10 - 10/3/10

Saturday, October 2, 2010

student loans

The privately held Drake College of Business, which trains people to be medical and dental assistants, relied on taxpayers for 87 percent of its revenue in 2007. Almost 5 percent of the student body at its Newark, New Jersey, branch is homeless, says Jean Aoun, director of admissions and student services there. Late in 2008, it began offering a $350 biweekly stipend to students who show up for 80 percent of classes and maintain a “C” average.

“It’s basically known in the community: If you’re homeless, and you need some money, go to Drake,” says Carmella Hutson, a case manager at the Goodwill Rescue Mission in Newark, where about 20 clients have enrolled at Drake in the past two years. “It would put money in my pocket, help me buy a car,” adds Jerome Nickens, 45, who lived at the mission when he talked to a Drake representative but decided not to enroll.

Homeless High School Dropouts Lured by For-Profit Colleges

college tuition

my money blog

[T]uition has been been increasing annually (7.88%) at more than three times the rate of inflation (2.37%) since 1978.

 Carpe Diem

You can't attribute the fantastic increase in college tuition to special education.

Or to unions, for that matter.

This has got to be a big part of it:
The Bankruptcy Abuse Prevention and Consumer Protection Act was enacted in 2005 to include private student loans as one of the 10 debts that can't be forgiven.

Robert Siegel talks with Stephen Burd, senior research fellow in the Education Policy Program at the New America Foundation, who says federal loans had long been included in this list, but private loans were included in 2005 because lenders had been reluctant to take on the risk of student loans.

Now that lenders have no risk, Burd says, student loans have become a very lucrative business.

2005 Law Made Student Loans More Lucrative

algebra I and optics...

Solve for x, given k = x + 1/x and that k is fixed.

This is a reduced and massively rearranged derivation of the lens equation, when the separation distance between an image and object is known, and the focal length of a lens known and fixed at a single value. x = do / di. (Or due to symmetry, it could just as well be the other way round.)

Mathematica kindly pointed out (as it solved the equation for me) that you could write it this way:

k = x + x-1

which resembles a quadratic equation, oooh. kinda. In real life you already know every k (= S/f -2) determines two solutions from experiment, but I was trying to decide how symmetric the ratios theoretically were.

Algebraic equation solvers tell me the solution has approximately the same form as quadratic roots, taking the form p +/- sqrt(q). Kinda. The general solution is x = 0.5 [ k +/- sqrt(k2 -4)]

Unlike most quadratics though, there is a gaping asymptote, and the function y=k rapidly changes from -inf to +inf as x passes from -c to c, where c is a number arbitrarily close to zero. When x is large, k is approximately x; when x is small, k is approximately 1/x.

I puzzle in my head how to solve it algebraically on paper -- this college student who has (up to this point) taken Calc III, linear algebra, and the mess of multiple equilibrium scenarios that tricky chemistry professors throw at you. How do you algebraically solve "inverse-order" polynomials? I mean, this equation should be simple to solve, right?

schoolbook simplification

a. Between 1860 and 1991, American publishers produced readers for the same grade at widely divergent LEX levels (e.g., in 1968, first grade readers were available between -68 and -31).

b. The most difficult readers were generally published before 1918. By modern standards, Professor McGuffy’s pre- and post- Civil War readers were very difficult.

c. After World War I, mean reader LEX levels for all grades were generally simplified.

d. After World War II, mean levels of readers for all grades but third became even simpler. These were the books used by the Baby Boomers and successive cohorts.

e. School publishers in Great Britain did not simplify heir first grade readers after World War II, implying that there was no compelling educational reason for American publishers to further simplify their readers.

f. Today’s mean sixth, seventh, and eighth grade readers are simpler than fifth grade readers were before World War II.

g. Sentences were also shortened, from about 20 words before World War II to about 14 words now in Grades 4—8.

h. Texts for grade x + 1 are typically more difficult (lexically) than those for grade x. When the early readers in a series are simplified by a publisher, so too (generally) are the readers for later grades.

American readers were rewritten after World War II for many reasons: to modernize their content and graphics; to incorporate principles from research in education, psychology and linguistics; to emphasize new kinds of social relations; and to respond to television, which was fast becoming an unprecedented rival for students’ attention. Those considerations required that readers be changed but not that they be simplified. Chall (1967) described the justifications given at the time for simplifying schoolbooks; they were to increase their accessibility for students and raise the level of reading success.

The extent of this simplification is notable. Apart from one extraordinarily simple text (LEX = -75), most first graders in the Baby Boom era used readers whose LEX levels were between -53 and -65; that is, on average, first grade readers were 12 LEX units less difficult than the readers used by their parents and grandparents between World Wars I and II and 15 LEX less difficult than the texts used by students in the same grade in Britian — where the students were a year younger in age. Since the empirical range for LEX is about 140 units, a 12 LEX simplification represents 9% of the empirical range. Workbooks are also designed by the same publisher as the readers and are used in conjunction with them. Given the workbooks’ format, we cannot measure their LEX levels. It is unlikely the publishers would make the workbooks harder than their own reader for the same grade level.

In simplifying the readers’ patterns of word choice, the publishers also shortened sentence length (Figure 5). From the fourth grade on, the average sentence length was contracted by about 6 words — this is the equivalent of dropping one to two clauses from every sentence. This reduced the students’ experience in working out the meanings of more complex sentences.

Widespread objections from teachers and parents, and media publicity over the simplified, often dull, Dick, Jane, and Spot-like readers, caused most publishers to acknowledge that they had oversimplified their first and second grade readers. In the 1963 —1991 era, the mean LEX levels for those grades was restored to pre-Worid War II levels — and without ill effects. While they made those early texts harder, the publishers made the fourth, fifth, sixth, seventh, and eighth grade readers even easier — to the point where these are now at their lowest level in American history.

Schoolbook Simplification and Its Relation to the Decline in SAT-Verbal Scores
Donald P. Hayes, Loreen T. Wolfer, Michael F. Wolfe
American Educational Research Journal
Summer 1996, Vol. 33, No. 2, pp. 489-508

schoolbook simplification & the 50-point drop in SAT scores

I'm sure I've posted this before, but it bears repeating:
The 50+ point decline in mean SAT-verbal scores between 1963 and 1979 is widely attributed to changes in the composition of the test-takers. Several inconsistencies in that explanation are identified. That explanation also ignores the pervasive decline In the difficulty of schoolbooks found by analyzing the texts of 800 elementary middle, and high school books published between 1919-1991. When this text simplification series is linked to the SAT verbal series, there is a general fit for the three major periods: before, during, and after the decline. Long-term exposure to simpler texts may induce a cumulating deficit in the breadth and depth of domain-specific knowledge, lowering reading comprehension and verbal achievement. The two time series are so sufficiently linked that the cumulating knowledge deficit hypothesis may be a major explanation for the changes in verbal achievement. Only an experiment can establish whether this is causal, so we describe a simple, low-cost experiment schools can use to test how schoolbook difficulty affects their students’ verbal achievement levels.

Schoolbook Simplification and Its Relation to the Decline in SAT-Verbal Scores
Donald P. Hayes, Loreen T. Wolfer, Michael F. Wolfe
American Educational Research Journal
Summer 1996, Vol. 33, No. 2, pp. 489-508

cumulating knowledge deficit...


The perennial issue of foreign language instruction in the early grades is alive once again in my district. I say "perennial" because, where foreign language instruction in the elementary grades is concerned, administrators are perennially against it while parents and interested bystanders are perennially for it.

The question of Mandarin keeps cropping up, too.

Looking for articles on edu-junkets to China, I found this:
Top San Francisco schools officials, who will consider expanding Mandarin language programs later this summer, quietly accepted a free trip to China recently to visit schools and meet with government officials who hope to persuade U.S. educators to expand Chinese curriculum.

Interim Superintendent Gwen Chan, five school board members and four principals made the unannounced trip from June 28 to July 4, spending time in Beijing and visiting schools across several provinces.

A staff member from the district's "multilingual programs department" also joined the entourage, which included about 400 schools officials from across the United States.

"This trip is not costing the school district any money," said Chan, whose first job in the district nearly 40 years ago was teaching Mandarin. "It is a goodwill and educational journey to promote Chinese immersion programs."

The Chinese government picked up the tab as part of its efforts to persuade U.S. schools to teach Mandarin, the official language of China.


The San Francisco contingent -- including board members Mar, Jill Wynns, Dan Kelly, Norman Yee and Eddie Chin -- said they found the trip inspirational.

"I feel it helps us understand a significant portion of our student body,'' said Mar.

Wynns said there was great value in seeing another society, "especially one from which so many of our students have come.''

The trip included excursions to the Great Wall of China and Tiananmen Square in addition to a speech by the Chinese minister of education in the Great Hall of the People.

Even though five elected school board members traveled together without a public announcement, Wynns said the trip did not violate California's open-meeting law known as the Ralph M. Brown Act because no official business was discussed.

Kelly put an even finer polish on the point:

"You could say it was a junket," he said. "Totally a junket. We did no real work at all."

China trip for top schools officials
- Jill Tucker, Nanette Asimov, Chronicle Staff Writers
Thursday, July 13, 2006

A: The point of junkets is to get junketeers to spend money. There is no free junket.

B: Open Meetings law applies to any gathering of a majority of the board. A special exception for junkets does not exist.

Tuesday, September 28, 2010

Audacious Idea #2: Placement by mastery, not age

My apologies to Gas Station Without Pumps -- I forgot a direct link to the post Placement by Achievement, which is

Somehow I got from Megan Golding's audacious idea (see here) to the blog Gas Station Without Pumps's discussion of eliminating age-based grade level instruction in math, and instituting placement by achievement.

This approach to placing kids has long been popular with parents of gifted children (though for some reason not with school teachers and administrators). It has gone by many names (subject acceleration, readiness grouping, grouping by ability or skill or mastery, … ). I prefer the name placement by achievement, since we are not accelerating students but letting them move at whatever velocity best suits them, and we can’t measure “readiness” but only what has already been achieved. Ability is not the point, achievement is. I guess that “grouping by mastery” is ok, but “mastery” seems to me a more cumbersome word than “achievement” and “mastering” a subject seems to me appropriate for post-baccalaureate studies.

Personally I prefer "placement by mastery", but reasonable people may differ.

In another post, GSWP discusses the recent article by Bill Evers and Ze'ev Wurman, advancing the idea that the California state math standards are superior to the proposed Common Core standards. (I believe California adopted the Common Core standards -- if Evers and Wurman are correct, look out, afterschooling! -- but I digress).

GSWP goes on:

My opinion is that the whole notion of age-based grade levels is wrong and twiddling with the standards won’t fix that. There is value to having standards that all schools and curricula must meet, but I wish that the standards were not labeled with grade levels. There are students ready for algebra long before 8th grade, and students who are barely ready for it by the end of high school. Having students progress through the standards based on mastery, rather than age, would be greatly helped by not labeling the standards with grade levels.

One specific criticism of the Common Core that Evers and Wurman raise, that there is a big jump at 8th grade because the K–7 standards are too weak to provide sufficient support for the 8th grade algebra standards, is probably a valid one and should certainly be considered by the State Board.

Discussions on the Common Core:

Audacious Idea #1: Illustrate Every Math Standard

Megan Golding is a 10th grade math teacher in Georgia. She has come up with an audacious idea:

I have a simple, if huge, goal: I want to publish a podcast for every single [Georgia Performance Standard] standard and element.

Sure, I’ve seen Khan Academy. It’s great! My addition is real state standards correlation (most of what I’ve seen that’s supposedly correlated to Georgia’s math standards is of shallow, if at all, relevance).

I’ve found that in math, my students want me to repeat the same explanation several times until that light bulb comes on. The podcast allows me to put an explanation in a kid’s hands and let him rewind & replay as much as he needs. Build in a little practice, and you have a nice little remediation tool.

Go look at her first post & do leave comments there.

Wouldn't it be great if every state had a video library like that?

[Cross published at Academic Remediation]

Monday, September 27, 2010

Eight O'Clock Class

Three times a week this small assembly meets, With drooping eyelids and half-hidden yawn,
To hear, incredulous, how Shelley, Keats,
And Wordsworth rose to write before the dawn.

Richard Armour

Source: College English, Vol. 21, No. 7 (Apr., 1960), p. 383

Sunday, September 26, 2010

Big "Aha!" moment from the MSMI2010 follow-up day

Saturday 9/25 - late afternoon:

My notes from Wu discussing the teaching of division with remainder:

Actually, this was a big "Duh!" moment.

Prior posts from MSMI2010.

Homeschooling by the Numbers

Via Pat'sBlog who saw it at Maria Miller's "Homeschool Math Blog.

(Click to enlarge)
Homeschooling by the Numbers [Infographic]

Any thoughts on the accuracy of these figures?