anonymous on lefties taking the SAT

Good advice:

Lefties should be particularly vigilant about the chairs/desks. I've heard stories about them having to take long tests on right-handed flip-up deskettes; a true nightmare. I know the registration forms for my grad comps asked lefties to identify themselves, because almost all of the seats in the auditorium had right-hand deskettes. They brought in as many extra lefty ones as they needed. Is there a similar question on SAT registrations?

I have got to find time to write a quick post on working memory.

I believe that the "transmission mechanism" from right-hand desks for left-hand test-takers to reduced performance is working memory blowout.

And see: death by calculator. Death by calculator is a case of working memory blowout.

(The real-world term for working memory blowout problems is cognitive load theory.)

Steve H on SAT math and math prep

from the comments:

SAT math tries to trick students. You could say that the tricks relate directly to whether or not they really understand math. However, when you add in the time constraints, it really relates to preparation. Is preparation the same as mastery? Yes. Mastery of the test. Is this equivalent to mastery of math or whether you will do well in college math? Not necessarily. There are better ways of determining that than with the limited material included on the SAT. Why not just require students to take the Achievement Test? Look at the AP Calculus grade.

What is it about SAT-Math that is so important? They are trying to test something other than just math knowledge. They think that these tricky questions reflect on how well you think on your feet, but what it really does is test preparation and whether you have seen these questions before. The questions don't reflect on whether you have a wide body of knowledge and skills in math.

They create problems where you have to "see" the shortcut. You get problems with hidden 3-4-5 triangles. Add a time constraint and then what do you call those problems? It's not just about math knowledge and skills. The problem has to do with trying to determine the difference between aptitude and preparation. The tricks may have some basis in meaningful math, but that's not what they are trying to test.

It reminds me of questions companies like to ask at job interviews, like "Why is a manhole cover round", and "How many golf courses are there in the US.?" Preparation can make you look like you have a great aptitude. Preparation is directly related to math knowledge, and that is important, but identifying aptitude is an arms race for something like the SAT. That's causing the tricky problems, not any desire to test a breadth and depth of math knowledge.

In Dick Feynman's books, he talks about how he spent a lot of time in high school learning about all sorts of trick, lateral thinking problems. He would challenge people to ask him questions. There is nothing like preparation to make you look like a genius, although he really didn't need help with that. It really annoyed some of his colleagues.

My son will get to calculus in his junior year and he always gets A's. He still has to prepare for SAT-Math. He can't let others, with specific SAT-Math preparation, seem like they have a better aptitude than him.

and:

They try to trick students in most questions....What bothers me the most are the shortcut problems where using standard math techniques cause you to take too much time. This is supposed to identify aptitude, but it really tests preparation for the test.

There are also the problems where using a brute force or direct counting technique works better than any applied math technique. In some cases, there is no math to apply. One question on a sample PSAT test asked for the number of positive integers less than 1000 which don't have a '7' as one of the digits. (notice - "don't have" and positive integer) This simply checks how well you work under time pressure. Nobody expects you to apply any fancy math to this problem. One of the answers was the "have" solution. This tests preparation and practice, not aptitude or math ability. There may be a correlation between the test and aptitude or math ability, but not to the resolution colleges use it to select students. At the top levels, it correlates to preparation. That's not necessarily a bad thing, but there are better ways of figuring that out.

in which I stumble upon a learning style that may actually exist

Barry pointed me to a terrific post by Haim, one of the regulars on Math Teach, who writes:

As it happens, a good friend of mine did his dissertation on learning styles some fifteen years ago. He did his study in the context of math education at the college level. I still clearly remember the frisson when he told me that 30 yrs of scientific literature on the subject was thoroughly consistent: not a shred of (real) evidence to support the hypothesis of learning styles.

His study did not perturb the consistency. At the time, I remember thinking "Gosh, after 30 yrs of nothing maybe it's time to look for another fishing hole."

Since then, of course, I have been deeply impressed by the evident fact that 30 yrs of nothing makes not the slightest impression on the Education Mafia. They carry on, exuberantly, as if learning styles are real.

Just a few days after reading Haim, and quite by accident, I came across the possibility that learning styles may actually exist (!)

Just not the learning styles we've heard so much about for lo these 30 years.

Here is Michael J. Frank on  “Go” and “NoGo” Learning and the Basal Ganglia:

We tested healthy college students who were given low doses of three different drugs: a drug that enhances the release of dopamine, a drug that reduces the release of dopamine, and a placebo; each student was tested in each of the three conditions.

[snip]

We hypothesized that all participants would learn to choose A over B, but that they would do so on different bases, depending on which drug they had been given. When dopamine levels are elevated, we hypothesized, participants should learn to choose symbol A, which had received the most positive feedback (that is, they should learn “Go” to A). But they should be relatively impaired in learning to avoid (NoGo) symbol B....

[snip]

We found a striking effect of the different dopamine medications on this positive versus negative learning bias....While on placebo, participants performed equally well at choose-A and avoid-B test choices. But when their dopamine levels were increased, they were more successful at choosing the most positive symbol A and less successful at avoiding B. Conversely, lowered dopamine levels were associated with the opposite pattern: worse choose-A performance but more-reliable avoid-B choices. Thus the dopamine medications caused participants to learn more or less from positive versus negative outcomes of their decisions.

These research discoveries raise the intriguing question of whether individual differences in learning from positive versus negative outcomes of decisions can be found even in nonmedicated healthy people. Indeed, although on average our study participants taking the placebo showed roughly equal choose-A and avoid-B performance, individual participants still performed better at one or the other; we refer to these subgroups as positive or negative learners....[A] mutation in another gene previously shown to control the density of (NoGo) D2 receptors in the basal ganglia predicted the extent to which participants learned from negative decision outcomes. Together, these results provide more-specific confirmation of our model’s suggestion that Go and NoGo learning depends on the D1 and D2 receptors.

I am gobsmacked.

Until the moment I read Michael Frank's research, I believed that positive reinforcement was better than negative. Always. Turns out the truth of the matter may be it depends.

Choose A or Avoid B.

The lady or the tiger.

The opposition

The Wall Street Journal has an op ed on Race to Nowhere today:

Directed by parent and first-time filmmaker Vicki Abeles, "Race to Nowhere" is marketed through a kind of partnership with local schools. The film suggests that if there are problems in American education, they are largely due to standardized tests, overambitious parents, insufficient funding, and George W. Bush. It also offers possible solutions, which include abandoning testing and grading and giving teachers more autonomy. 

[snip]

Parents in New Jersey suburbs have received numerous emails about the film and its upcoming show times from parent-teacher associations. Ms. Abeles and the schools split the revenue from ticket sales, but the director told the crowd in Bergen County that she is holding off on a DVD retail release while she explores a possible broadcast on PBS. She also said she is moving full speed ahead to hire companies in Washington to lobby for policy changes suggested in the film.

[snip]

Ms. Abeles argues that U.S. education is focused too much on giving kids "things to memorize and regurgitate," instead of developing the critical thinking skills that will be most useful in solving problems and thriving later in life.

Jeanne Allen, who leads the Center for Education Reform in Washington, reports that her sister back in Bergen County is one of those Jersey parents receiving a blizzard of email pitches to see the movie. Ms. Allen says that if U.S. tests are flawed it is because they demand that kids memorize too few facts, not too many. "You can't teach critical thinking," she says. She argues that kids cannot possibly develop problem-solving skills without a base of knowledge. How can one analyze a piece of literature, she asks, without knowing any vocabulary? Can students solve math problems without being able to multiply and divide?

Whether Ms. Abeles is ultimately advocating necessary reform or simply the latest educational fad, anything that changes the subject from unfunded pension liabilities is probably good news for the New Jersey teachers union. But that doesn't mean all the state's teachers will be thrilled if Ms. Abeles is successful.

Some of the most passionate advocates for rote memorization of critical facts can be found among the faculty in New Jersey public schools, a state that has traditionally scored highly on the standardized tests that may be going out of fashion. To put it another way, New Jersey may have more to lose from another nationwide shift in educational policy than states that are consistently ranked near the bottom.

Do American Students Study Too Hard?
By JAMES FREEMAN
APRIL 30, 2011

...she is moving full speed ahead to hire companies in Washington to lobby for policy changes suggested in the film...

Well, more power to her - but what about parents and teachers who like memorization and standardized tests?

We're out of luck.

For me, this is further evidence that we simply must have choice. Let the teachers and parents who want critical thinking without memorization have critical thinking without memorization.

Let the teachers and parents who want memorization and knowledge have memorization and knowledge.


critical thinking without content

In a recent comments thread, I mentioned visiting a Cambridge Pre-U Global Perspectives class at a local high school. The teacher and principal told us proudly that the class was "not content-rich." That was the selling point. Not content-rich.

All of the other courses the school offered, they said, were content-rich. This was a bad thing. In the content-rich classes, they said, students memorized but did not think. In Global Perspectives, students engaged in "critical thinking" and did not memorize.

So what happens in a class that is content-poor?

Students Google op-eds and feature stories and look for "bias."

For me, the idea of spending a year and a half (the course consumed 3 semesters and replaced English) Googling op-eds and looking for bias is almost unspeakably drear: not enough to keep the mind alive.

But the principal loved it, and the two team teachers loved it, and the other parent in our group loved it.

So let them create and attend the schools they believe in, and let the rest of us create and attend the schools we believe in.

Live and let live.


Critical Thinking: Why Is It So Hard to Teach? (pdf file)
Dan Willingham

Daniel Ethier on cognitive load theory

on another thread, Daniel Ethier writes:

Cognitive load theory has much to say about the educational implications of our limited working memory on learning.

As I read various papers on cognitive load theory, I keep having aha moments as I find reasons for things I see in the classroom.

The key to getting around our limited working memory is automaticity. If you know something well enough to not have to think about it, it does not take up working memory. And so you are free to think about the problem you're trying to solve.

Use Google Scholar and read some of the many papers about various aspects of cognitive load theory. Well worth the time.