Merry Christmas - Happy Holidays!

more fun with public schools

Peter Meyer weighs in

if you can't do it, you don't understand it

cross-posted at the Irvington Parents Forum:

Reviewing his son’s grade-school homework in the early 2000s diverted W. Stephen Wilson from his research in algebraic topology to question basic math education. At two well-regarded private schools, Wilson’s son had encountered the most widely used elementary math curricula, Investigations and Everyday Mathematics. Both encourage the use of calculators for multiplication and division, in line with a 1989 report from the National Council of Teachers of Mathematics that downplayed teaching arithmetic with pencil and paper. “What the schools were doing with math was beyond my imagination,” Wilson says. “I knew that my kid’s third-grade math wasn’t going to prepare him for college.”

A professor of mathematics in the Krieger School, Wilson teaches calculus to undergraduates. In 2006, he decided to conduct an experiment with his Johns Hopkins students. His Calculus I for the Biological and Social Sciences class that year bore close resemblance to the 1989 class. Their scores on the SAT math exam were nearly identical, and the two groups contained the same percentage of freshmen. Curious to see how they’d compare on the same exam, he gave the 2006 students the same 77-point final that he’d given the 1989 class. The results, he believes, confirmed his hunch that students were coming out of K–12 schooling less prepared for college math. When he compared scores by the grading scale in use in 1989, 27 percent of the 1989 students received As on the exam and 37 percent scored Bs. Only 6 percent of his 2006 students would have received As, 26 percent Bs.

[snip]

As another experiment, Wilson gave a short test of basic math skills at the start of his Calculus III class in 2007. The results predicted how students later fared on the final exam. Those who could use pencil and paper to do basic multiplication and long division at the beginning of the semester scored better on the final Calc III material. His most startling finding was that 33 out of 236 advanced students didn’t even know how to begin a long division problem.

Wilson says he wouldn’t be so against calculator use if teachers still taught multiplication and division by hand as well, regardless of the fact that few will ever do math that way as adults. “The theory that people should only learn what they are going to use as adults doesn’t make a lot of sense,” he explains. “If you take that to the extreme, there wouldn’t be much left to K–12 education. If someone is going to fly an airplane when they grow up, should we skip all the intermediate steps and just teach them how to fly an airplane when they are 10?”

[snip]

In 2006 he served as senior adviser for mathematics in the U.S. Department of Education, where he helped form the National Mathematics Advisory Panel. Since his return to his Hopkins classes in 2007, Wilson has continued to review K–12 curricula for various states.

Wilson has found that the brightest students work around what he calls their “unnecessary handicap.” In his study of 2007 Calculus III students, for example, the correlation between being “division clueless” and scoring poorly on the final exam wasn’t as strong as he would have guessed; some of those students did just fine. But that seemed true only for the minority. When he followed up on the class two years later in 2009, one-third of the “division-clueless” students were on academic probation.

Wilson doesn’t like the long-term implications of a new generation of engineers and scientists who can’t divide or don’t know their multiplication tables. He compares it to having car mechanics who only know how to fix automatic transmissions. “You might use a calculator if you’re an engineer, but you need to know what it does. If you need mathematics in your career, then it is probably a good idea to really understand it,” he says. “You don’t understand it if you can’t do it.”

Back to Basics for the “division clueless”
By Lisa Watts
December 6, 2010
Johns Hopkins Magazine

pop quiz, part 3

discount

a good school is good for everyone

The report also included a finding that in every country surveyed, girls read better than boys — a gap that has widened since 2000. Also included was a finding that the best school systems are the most equitable — where students do well regardless of social background.
Western Nations React to Poor Education Results
By D.D. GUTTENPLAN
Published: December 8, 2010

I believe it.

Educated parents with the money to hire tutors can go a ways towards mitigating the effects of bad curricula and teaching.

I've seen that for years in my district.

I'm curious about the reading gap in countries with highly phonetic languages.

leaning tower of PISA, part 2

“Germany has improved its status from ‘horrendous’ to ‘average’ — we are at least satisfied with that upward trend,” Ulla Burchardt, chairwoman of the German government’s education committee, said in a radio interview.
Western Nationsl React to Poor Education Results
By D.D. GUTTENPLAN
Published: December 8, 2010

leaning tower of PISA

In Britain, where results showed students falling behind peers in Estonia and Slovenia, Education Minister Michael Gove promised to overhaul the examination system to make it tougher, using tests from China and South Korea as benchmarks. Britain will “explicitly borrow from these education tiger nations,” Mr. Gove said.
Western Nations React to Poor Education Results
By D.D. GUTTENPLAN
Published: December 8, 2010

Estonia and Slovenia?

it isn't the culture, stupid

Barry G on the new international comparisons

The news last week that Shanghai students achieved the top scores in math on the international PISA exam was for some of us not exactly a wake-up call (as Secretary of Education Arne Duncan characterized it) or a Sputnik moment (as President Obama called it).

We've seen this result before. We've seen the reactions and the theories and the excuses that purport to explain why the US does so poorly in math. In fact, there are three main variations used to explain why Chinese/Asian students do so well in international exams:

Version 1: They are taught using rote learning and then regurgitate the results on exams that test how well they memorize the procedures of how to solve specific problems.

Version 2: They are taught using the reform methods of a "problem based approach" that doesn't rely on drills, and instills critical thinking and higher order thinking skills

Version 3: The teacher or the culture produces the proper conditions for learning

This argument is based on the observation that the education-valued culture manifests itself in ways that are unlikely to happen here: long school days, after-school math “clubs” in which math facts and procedures are drilled (pointed to by some as evidence that students in China are engaging in rote learning), long hours studying and teachers who know the subject matter extremely well. . . . The “culture argument” also paints a picture of U.S. culture as totally oblivious to educational values and ignores the subcultures that place a value equal to that seen in China and other countries. Those are the students whose goals are to enter the top universities in the US, who work very hard and take AP classes and exams. Some of the parents of those students have protested against the adoption of substandard math programs such as Investigations in Number, Data and Space, and Everyday Math. These are the parents who have been told by school boards that the traditional method of teaching math may have worked for some, but not for all. Those are the parents who have discovered that the traditional methods of teaching math (in the 50’s and 60’s) work very well indeed, and are similar in some respects to how it is taught overseas.

decline at the top

Speaking of our best students, the other reaction to mediocre U.S. performance on international tests I've seen -- which shows up in the comments to Barry's article -- is the claim that our best students are doing as well as the best students elsewhere. This is a variant of the 'culture' argument: American  slackers are bringing down the mean.

Not true.

Here's a passage from the Baltimore Curriculum Project video. In this section, William Schmidt, who headed one of the TIMSS studies, is talking about the best American students:

8:05 Schmidt: This system of ours has failed the elite kids, too. This is a little known fact because it wasn't emphasized very much, but in the early TIMSS study there was a high school specialist exam for those kids that were the AP physics kids and those that were the AP calculus kids. Those kids were last among their counterparts in the rest of the world. That is, if you took the elite track in the French system that was leading to math and science, these [American] kids were at the bottom. So we're failing those kids just as much as we're failing the kids on the other spectrum.

William Schmidt Baltimore Curriculum Project
Dr. William H. Schmidt of Michigan State University
Leading Minds K-12 Math Education Forum, April 24, 2008 in Baltimore.
U.S. TIMSS NATIONAL RESEARCH COORDINATOR
MICHIGAN STATE UNIVERSITY
12th grade

wake me when it's over

cross-posted to the Irvington Parents Forum:

I attended a meeting on the Race to the Top teacher evaluation protocols up in Bedford, and the new regs are a horror.

I’m completely off the boat with RTTT. If even half of what I heard the other night is true, schools are going to become a compliance nightmare beyond imagining as every teacher in the state receives annual ratings of “highly effective” and all probationary teachers are granted the right to years of appeals when they don’t get tenure. This is the ultimate bad law.

I talked to a number of school board members coming out of the meeting as well as one assistant superintendent. They were reeling.

Preview of coming attractions: under the new law, a school with 40 teachers could have ALL FORTY TEACHERS appeal their RTTT-mandated evaluations AT THE SAME TIME, and the principal would be required to respond to all 40 appeals on deadline and with multiple documents and timelines and rationales and data sets and god knows what else in order.

Schools will have to hire armies of administrators to process all the appeals. More likely, everyone will be rated Highly Effective forever.

Tsunami.

Mythologies

One way to win a debate is to make sure you're in on developing the question, for it is the nature of the question that frames the debate. The question is the fence around the playing field and when the question is, for example, "What should our standards be?", or "How will we measure success?", you can't discuss, "What are our standards for?", or "How will we act on our measurements?".

In public education much of the debate has been co-opted by this time tested debating technique. While people argue about curriculum, pedagogy, and standards, two mythologies, central to the field are left outside the fence. One myth is that all children have the same abilities (child as widget) and its partner is that public education can be designed as a singular (widget factory) assembly line, replicated across towns, states, and country. Much of the flailing in evidence today is about how to come up with this mythical process for our mythical widgets.

First, child as widget. I don't buy it. Without addressing why or how children arrive at their various capabilities, it is demonstrably true that any age based cross section of kids will produce a vast range of abilities. These can be athletic, academic, maturity, or any other measure you can think of. Kids exhibit huge differences in any category you can think of.

Unfortunately, many (most?) of the education establishment does buy into the child as widget meme. It's understandable since this is both politically and emotionally correct. Who wants to admit an inconvenient truth after all? If you buy the myth while being charged with developing widget factories, then your first task as a designer is to come up with a device that supports your mythological fantasies.

This is the root of subjective standards. With subjective standards one can disguise differences. It allows for the substitution of exposure for mastery. It facilitates social promotion. It pretends that there are no dependent stages to building an educated widget. It eliminates the need for expectations. Subjective standards remove the scoreboard from the game.

The second myth, the widget factory, is only made possible by instituting the first. It would be absurd to design a singular assembly line if your raw materials were not being delivered to the line meeting some minimum level of specification. Fuzzy specifications clear this problem. Subjective standards that support the 'child as widget' myth are a precondition for the widget factory. Fuzzy subjective standards create the necessary illusion that permits the universal solution.

So if you find yourself arguing text books, teachers, pedagogy, and expectations, lift your head out of the weeds to see if there is greener grass over the hill. You might be surprised at what you see.

half and half

Geek Optimism

Love it!

Revolutionizing Math at the School of the Future

(Cross-posted at Out in Left Field)

A front page article in Monday's Local News section of the Philadelphia Inquirer profiles a math class at Philadelphia's Microsoft-funded High School of the Future, whose teacher, Thomas Gaffey, placed second in Microsoft's U.S. Innovative Education Forum and was a semi-finalist in its Worldwide Innovative Education Forum. In Gaffey's ninth-grade algebra class there are:

No textbooks, no paper, no chalk, no desks, and no assigned seats.

Instead, students use laptops while sitting in rolling chairs at trapezoidal tables spaced out in hexagonal classrooms.

Just how newsworthy this sounds to you depends on whether you think chair mobility and table shape have a big influence on learning, on whether you've been following current trends in education over the last 50 years, and on how unusual you think it is for a teacher to "encourage his students to find answers to their own questions" and engage with them in exchanges like these:

"Is this an obtuse triangle?" one student asks.

"Well, what can you tell me about an obtuse triangle?" Gaffey replies.

"One of the angles has to be more than 90 degrees," the student answers.

"Are any of the angles here like that?"

"Yeah. Oh, I get it now!"

As the Inquirer explains:

This snippet of student-driven discussion is a glimpse of the style and approach that have earned Gaffey national and international recognition.

Student-driven? Who's asking most of the questions? But I'm splitting hairs here. What I should be asking is: Why does this kind of exchange warrant international recognition?

To fair, it wasn't this, specifically, that earned Gaffey his honors. Rather:

Les Foltos, one of the judges who reviewed Gaffey's work, was impressed by his emphasis on "actively engaging students in solving real-world problems." As Gaffey puts it, "If we want to teach math to learners, we should teach math how it is actually used. It doesn't matter how much you know. It matters what you can do."

Ah yes, "real world problems." Again, only if you've been out of touch with the last half century of educational reform, and with today's Reform Math in particular, will this strike you as revolutionary. Here is Gaffy's version of real world math:

In his classroom on a recent Tuesday, Gaffey's challenge to his "learners" - as students in the Parkside public school are called - was to estimate Earth's land area.

To solve the problem, the class first covered basic concepts about area and polygons - shapes with three or more straight sides.

Gaffey then asked, "If a shape has four sides, is it always a polygon?"

Learners who answered yes (the wrong answer) were asked to redefine what a polygon is, while those who answered no were asked to draw a four-sided shape that was not a polygon on the class "smart board."

Gaffey drew a shape with three straight sides and one curved side.

"Is this a polygon?" he asked.

"No," the class responded.
...

The class drew lines through each of the continents, chopping them up into complex polygons, then simple polygons.

The final phase was to derive formulas for the areas of the simple polygons, and add up the areas.

This sort of problem is not particularly new, as a quick survey through now-standard textbooks like Everyday Math and the Interactive Math Program makes clear. And it's been around long enough to have garnered some serious criticism--specifically in what Barry Garelick calls its "just in time" approach to teaching.

Among other things, "just in time" often means serious delay. For example, one would hope that students would already know the formulas for the areas of simple polygons, and how to derive them, well before they hit 9th grade.

But because so many students are so far behind where they should be, there is one thing in which I and Gaffey are in whole-hearted agreement. In Gaffey's words, as cited by the Inquirer:

"Math education, more than any other subject, is in need of drastic reform."

Your Child Left Behind

I think Mark Roulo left a link to the new article on Hanushek's research in the Atlantic.

I've posted a list of pulls on the Irvington Parents Forum.

the real world

Speaking of ditching the daily lesson plan, Allison wrote:

For those so enamored with preparing kids for the real world, why do they want school at all? Wouldn't child labor better? That would integrate everything.

Let's not and say we did, part 2

Ditch the daily lesson plan

If you think about the “real world” that we’re preparing kids for, how often is the “real world” day broken up into science moments, math moments, writing moments, etc?

I don't know about you, but for me the "real world" day gets broken up into science moments, math moments, writing moments, etc. any time I happen to be doing science, math, writing, and 'etc' all on the same day.

Say I'm studying math for the SAT.

I just study math. Without any science or writing at all. (Also, if I can find a decent worksheet, I do a worksheet.)

Or say I'm writing a book proposal or an article for the local paper.

I just write!

I don't do any math or science to speak of, unless I happen to be writing about math or science. And even then, I don't do math or science. Writing about math or science isn't the same thing as doing math or science.

...science moments, math moments, writing moments, etc? We engage all of these things at all times.

No we don't.

Also, it’s not like integrated units are anything innovative…

True.

Kids don’t need a six-week unit on mastering quotation marks; they need to learn to master the quotation marks piece in the screenplay they write collaboratively about the people of Iceland solving problems around a catastrophic tectonic event that includes the gathering and analysis of quantitative data.

oh, man

Speaking as a person who is finishing up a semester teaching English composition to college freshmen, I would have a very hard time convincing my students that what they really need isn't to learn when and where to use a comma but to write collaboratively about the people of Iceland solving problems around a catastrophic tectonic event that includes the gathering and analysis of quantitative data.

I'd get some stony looks on that one.

Real stony.

let's not and say we did
let's not and say we did, part 2
let's not and say we did, part 3

WordSmart Software

Does anyone have any comments on a product called "WordSmart High School Excellence"? I got a call out of the blue based on something my son filled out at school, although he doesn't know what that was. The implication is that this product is recommended by our school and that we can get a big discount because of that. To get the discount, they have to arrange a time to call me back. I'm trying to find out whether his high school really recommends the product or not. When I read the guidance dept. info on the school site, they talk of putting together an IEP for each child and that the parent plays an integral role. Right now, I don't feel integral.

Race to the Average

Our state will get Race To The Top money, so our town is putting together a plan that is based on the state test. The goal is:

"90% of students entering the 4th and 8th grades will be proficient in reading and math on our state assessment"

This is really a Race To The Average. Do most parents think that state proficiency levels are good enough for their own kids? I don't think so, but do they think the money will help their kids? I haven't seen our (58 page!) proposal yet, but I can't imagine that there is anything more than a guess and check approach to increasing the numbers.

wrong again

a letter to the Times:

Middle-class American children attending well-financed schools outscore nearly all other countries. But our overall scores are unspectacular because we have such a high percentage of children living in poverty.

Rich schools are good schools: the very assumption that led me to overspend on a house in an overspending town.

Maybe I should write a letter to the editor.

Here are Hanushek, Peterson, and Woessmann:

White students. The overall news is sobering. Some might try to comfort themselves by saying the [achievement] problem is limited to large numbers of students from immigrant families, or to African American students and others who have suffered from discrimination....

...[L]et us consider the performance of white students for whom the case of discrimination cannot easily be made. Twenty-four countries have a larger percentage of highly accomplished students than the 8 percent achieving at that level among the U.S. white student population in the Class of 2009. Looking at just white students places the U.S. at a level equivalent to what all students are achieving in the United Kingdom, Hungary, and Poland. Seven percent of California’s white students are advanced, roughly the percentage for all Lithuanian students.

Children of parents with college degrees. Another possibility is that schools help students reach levels of high accomplishment if parents are providing the necessary support. To explore this possibility, we assumed that students who reported that at least one parent had graduated from college were likely to be given the kind of support that is needed for many to reach high levels of achievement. Approximately 45 percent of all U.S. students reported that at least one parent had a college degree.

The portion of students in the Class of 2009 with a college-graduate parent who are performing at the advanced level is 10.3 percent. When compared to all students in the other PISA countries, this advantaged segment of the U.S. population was outranked by students in 16 other countries. Nine percent of Illinois students with a college-educated parent scored at the advanced level, a percentage comparable to all students in France and the United Kingdom. The percentage of highly accomplished students from college-educated families in Rhode Island is just short of 6 percent, the same percentage for all students in Spain, Italy, and Latvia.

The Previous Rosy Gloss

Many casual observers may be surprised by our findings, as two previous, highly publicized studies have suggested that—even though improvement was possible—the U.S. was doing all right. This was the picture from two reports issued by Gary Phillips of the American Institutes for Research, who compared the average performance in math of 8th-grade students in each of the 50 states with the average scores of 8th-grade students in other countries. These comparisons used methods that are similar to ours to relate 2007 NAEP performance for U.S. students to both TIMSS 2003 and TIMSS 2007. His findings are more favorable to the United States than those shown by our analyses. While our study using the PISA data shows U.S. student performance in math to be below 30 other countries, Phillips found the average U.S. student to be performing better than all but 14 other countries in his 2007 report and all but 8 countries in his 2009 report. (Oddly, the 2007 report takes a much more buoyant perspective than the 2009 report, though the data suggest otherwise.) Phillips also finds that individual states do much better vis-à-vis other countries than we report.

Why do two studies that seem to be employing generally similar methodologies produce such strikingly different results?

The answer to that puzzle is actually quite simple and has little to do with the fact that Phillips compares average student performance while our study focuses on advanced students: many OECD countries, including those that had a high percentage of high-achieving students, participated in PISA 2006 (upon which our analysis is based) but did not participate in either TIMSS 2003 or TIMSS 2007, the two surveys included in the Phillips studies. In fact, 19 countries that outscored the U.S. on the PISA 2006 test did not participate in TIMSS 2003, and 22 higher-scoring countries did not participate in TIMSS 2007. As a report by the U.S. National Center for Education Statistics has explained, “Differences in the set of countries that participate in an assessment can affect how well the United States appears to do internationally when results are released.”

Put starkly, if one drops from a survey countries such as Canada, Denmark, Finland, France, Germany, and New Zealand, and includes instead such countries as Botswana, Ghana, Iran, and Lebanon, the average international performance will drop, and the United States will look better relative to the countries with which it is being compared.

Teaching Math to the Talented
Eric A. Hanushek, Paul E. Peterson and Ludger Woessmann
Winter 2011 / Vol. 11, No. 1

what does Google want?

A friend of mine (ok, it was Debbie S.) talked to a person at Google about what they look for in job candidates.

He gave her a typical problem a candidate might be asked to solve during the interview. 

As I recall, it was a permutation problem.

A hard one.

So here's Tom Friedman on the three basic skills:

There are three basic skills that students need if they want to thrive in a knowledge economy: the ability to do critical thinking and problem-solving; the ability to communicate effectively; and the ability to collaborate.

Teaching for America
By THOMAS L. FRIEDMAN
Published: November 20, 2010

I guess Google-level math knowledge falls under 'problem-solving.'

equation

Economists' Grail: A Post-Crash Model
By Mark Whitehouse
Wall Street Journal November 10, 2010

I love this.