kitchen table math, the sequel: another reason to teach to mastery

Thursday, August 30, 2007

another reason to teach to mastery

With results that will hardly put to rest the controversy over the merits of the SAT, scores for the high-school class of 2007 are in -- and they're down.

The point drop in the average math score for the latest year was the biggest in more than three decades, reported the College Board, the New York nonprofit that administers the college-admissions test. Math scores declined three points, to 515, from the previous year's 518 out of a possible 800. Critical reading -- formerly called "verbal" -- also dropped, to 502 from 503, marking the lowest score since 1994. Scores for the writing section slipped to 494 from 497 the previous year -- the first time the new section's scores were released. Taken together, the scores are the lowest of the decade so far.

Class of 2007 Logs Slide In SAT Scores
by Anne Marie Chaker WSJ 8-29-2007; Page D1


I'm not sure anyone knows what's going on, if anything.

However, it does sound as if the test has gotten harder, and we know for a fact that it's longer:

"The new test was designed to be more challenging," says Seppy Basili, senior vice president at Kaplan Inc., the test prep concern owned by Washington Post Co. The inclusion of material from advanced algebra is "a serious concern for some students," he says, some of whom don't reach the material until their junior year.

Level of Attention

The revisions to the test also added 45 minutes to the length. "It is a problem," says Scott White, director of guidance at Montclair High School, Montclair, N.J. "There is no way on earth a kid can test for nearly four hours and have the same level of attention and acuity as with a three-hour test."

Andrew Bennett-Jackson, a senior at Montclair, says he found his "focus really go down" toward the end of the exam, which he took over the summer. He scored a 1610 out of a possible 2400. He plans on trying the ACT, a rival admissions test accepted by a growing number of schools, in the fall. One big plus: The ACT's writing section is optional, which makes it shorter for students who just want to retake the other two sections. "It just makes the test a little bit easier," Mr. Bennett-Jackson says.


I don't need a statistical analysis to tell me that your best shot at a high score on a nearly-four-hour test is going to be knowing algebra & geometry to automaticity. The whole point of automaticity (well, one of the points) is that your brain uses far less energy to work with "automatic" material than it does with material you're shaky on. The reason a well-learned subject seems "easier" is probably that it is easier. You use fewer resources.

I still remember how sad I felt the day I saw research showing that mentally retarded children's brains are far more "active" on brain scans than normal children's. I didn't know as much about scans & brain metabolism then, and the sudden realization that mentally retarded children were working very hard to understand and remember things typical children could do while barely lighting up a CT-scan was heartbreaking.

The brain is an expensive organ:

The calculations presented in this paper show that the energy metabolism of the brain may account for about 50 percent of the BMR in the new-born. As indicated by our calculations the proportion of BMR accounted for by the energy metabolism of the brain decreases with age, but it still accounts for about 30 percent of the BMR at age 12 years.

Energy metabolism of the brain in children


This is cool. Numbers Guy says there probably is a change in test population. That's the Sun's take (I'm not going to link; no chance the editorial will be free). The Sun says that the decline in NYC SATs happened because more black students took the SAT, which is good. More black students are in the running.


another reason to teach to mastery
why SATs predict college success
more stats from 2007 SAT

3 comments:

le radical galoisien said...

Focus isn't so much the issue. Additional time is always a plus, not a minus. Plus in Singapore, in secondary school especially, every semester you have an exam week. Your teachers don't simply give you midyears or final exams -- you're all coralled into a giant exam hall, take a formalised exam with hundreds of other students in your level, and may take two 2-hour exams in the same day, and rinse and repeat for a week or even two. This is for the O-levels.

For the PSLE (that 12 year olds take), each language subject (and it's compulsory for people take two -- English and an L2) has an oral examination, a listening comprehension examination, a paper 1 (composed of two sections -- a functional composition and a narrative) and a paper 2 (section A abd section B), for 200 marks and 4 hours total, not counting the time spent waiting in the oral exam hall room.

So when my American teachers tell their groaning classes the reason they're giving final exams is to prepare us for the rigours of college and to know what a heavily-weighted end of year exam is like, I have to stop myself from bursting out laughing because that is nothing compared to what us Singaporean students experience.

So anyway, on the subject of SATs, my biggest grievance was the time given. For Math, some of the questions were interesting, and you wanted to spend time thinking about related concepts, (like hmm! What are the implications of this, if my algorithm is correct!), but they give you no time to *enjoy* doing the problem.

To me, enjoyment is the biggest issue. The biggest reason why I loathe standardised examinations is that while you can have the time to further test the implications of your idea in your homework for example, you don't have time to explore a problem with the SAT.

Again, with some of the harder problems you discover relationships which are pretty interesting, and you always want to go back and check your relationships again to see if your method was fallacious. Sometimes you just want to double-check why that works.

Call it sour grapes if you will, but I ran out of time at each of the math sections and didn't get to answer around five math questions, as well as double-check tentative ones. (And thus it was my lowest section, with a 660.) Each problem was doable.

Also, standardised exams call for a "skip a problem if you can't solve it immediately" approach, I totally hate. If you're encountering difficulty, you have the urge not to abandon it ... because that just seems wrong to you.

Catherine Johnson said...

Call it sour grapes if you will, but I ran out of time at each of the math sections and didn't get to answer around five math questions, as well as double-check tentative ones. (And thus it was my lowest section, with a 660.) Each problem was doable.

oh my gosh

I know you!

this happens with little kids, too -- I remember a friend from graduate school who had been a real bright little kid.

She'd get tangled up in IQ tests because to her the multiple choice answers had nuances!

Unknown said...

Without looking at the data -- because I don't have the data -- it looks suspiciously as if the drop in scores isn't statistically significant.