kitchen table math, the sequel: not your father's SAT

## Saturday, October 15, 2011

I've been amazed by the difficulty of SAT math in its current incarnation; I remember SAT math as being pretty easy. Now it's hard.

I'd been wishing I could look at an old test -- and I seem to have misplaced the email Akil sent me that included an old test (must find email...) when I raised this issue before --

Anyway, long story short, I've carried on being mystified over the question of what has or has not happened to SAT math.

Suddenly, the other day, it hit me: 10 Real SATs! The book was published before CollegeBoard changed the test in 2005 (2006?) It has real SAT tests -- 10 of them! -- with real prior-to-2006 SAT math.

So I ordered it.

And ----- wow.

The math on the earlier tests is so much easier. Easier at the level of: I found myself doing the final, hardest problem in a section in my head, in bed, in a state of sleep deprivation, and after drinking a glass of wine.

I'll have to sit down and take a timed section and see what happens.

gasstationwithoutpumps said...

Since I last took the SAT in 1970, maybe I need to retake it to see if it is any different now. I remember it as pretty trivial, but it may be that it has changed.

Crimson Wife said...

The math was easier because the College Board didn't allow the use of calculators. Once calculators were permitted, the "trickiness" factor had to be increased since everyone could do straightforward calculations by brainlessly punching in numbers.

Catherine Johnson said...

Crimson Wife - interesting.

Many, many, many of the problems are tricky. "Tricky" seems to be the whole point of the problems at times.

I'm going to check to see how many geometry questions they have on the old tests. The geometry questions now are very difficult because they require you to override what you see ("not drawn to scale") with logic -- then hold that override in working memory while you try to find a solution -- those problems are testing Presence of Autism Genes (a plus) and/or Field Independence (a major plus).

Autism genes and field independence may correlate with math achievement (I'm guessing autism genes do), but they're not math & they're not what CollegeBoard says it's testing.

Molly said...

I'd agree with Crimson Wife. I scored a 750 on the SAT in the early 80s - no calculators allowed. I can't remember whether we were allowed to use calculators on the AP Calculus exams, but even if we were, graphing calculators were not available to students.

(I was incredulous when my 8th grade daughter told me she needed a \$90 graphing calculator for her algebra 1 class. How is it I managed to get through AP Calculus, a semester of differential equations and a semester of linear algebra without one?)

Grace said...

In a presentation to parents last week, our high school guidance counselor repeated the "SAT is trickier than the ACT" warning.

Grace said...

The calculator explanation does make sense.

SteveH said...

"In a presentation to parents last week, our high school guidance counselor repeated the "SAT is trickier than the ACT" warning."

At the top level, it is. The ACT might have trig problems, but they are trivial.

I don't buy the calculator reason either. I think it has more to do with the fact that college demand has gone way up and that many more kids are preparing for the SAT. In the old days, many kids (myself included) never prepared one tiny little bit for the PSAT or the SAT. The PSAT was the preparation. If you don't prepare now, you will get killed!

Since the SAT has a limited amount of material that can be tested, the questions have to become more tricky. This may not be much of an issue in the <600 score range, but all it takes are a few missed tricks to drop down to a score of <700.

My son took the PSAT yesterday and I did manage to get him to prepare a little (20 minutes!) and take a timed practice test. It's was easy for him to see that some questions go out of their way to trick you. It doesn't matter whether you are caught by the trick or if you really don't know what you are doing. It's wrong.

One question on the PSAT gave two of three sides of a triangle and asked you for a possible length of the third side given some relationship to an equilateral triangle - I forgot the relationship. You had to know what the relationship was and to test out each answer. The trick was that one seemingly correct answer would not work because the sum of the two short sides would be less than the length of the long side.

This doesn't test some critical thinking ability. It only tests whether you have prepared properly for the test. The need to spot this three sides of a triangle relationship is as important as quickly seeing common right triangles, like 3-4-5. There are many things like this. The SAT might think that it's testing critical thinking, but it's really testing preparation.

Catherine Johnson said...

I don't buy the calculator reason either. I think it has more to do with the fact that college demand has gone way up and that many more kids are preparing for the SAT.

Ed says he thinks it's like the war between the Chinese govt and the Chinese hackers.

The Chinese hackers hack into the govt's sites; the govt fireproofs them; then the hackers come up with new hacks, and so it goes.

He thinks the tutors keep hacking the test, and the SAT problem writers keep coming up with new versions of problems the tutors haven't thought of.

That certainly describes the October test I took: it was different from all of the prep tests I took -- and I've taken them all.

Literally. I've taken every single math section in the Blue Book & every single math section in the online tests. The October SAT math section was not the SAT math section I prepared for.

I'm more convinced than ever that everyone aiming for a score in the 700-800 range should be using Chung's book & probably also the two middle school math competition books.

Catherine Johnson said...

In a presentation to parents last week, our high school guidance counselor repeated the "SAT is trickier than the ACT" warning.

WAY trickier ---

I use the analogies of misdirection and optical illusion to try to convey what I mean.

btw, that's what makes SAT math fun: it's a challenge -- it's a game.

You're trying to beat the test, not 'ace' the test.

Catherine Johnson said...

The trick was that one seemingly correct answer would not work because the sum of the two short sides would be less than the length of the long side.

PWN calls this the "sadness gap"!

There are MANY questions testing the ability to instantly see that they're asking whether the sum of each set of two sides is greater than the length of the 3rd side.

I think Steve is right: there's basically an arms race between the test writers and the test tutors.

The reading test isn't tutorable. (Again, I know that people like Erica are in fact tutoring the reading test --- but Erica is teaching reading and grammar over a fairly long period of time ---- what she does isn't 'test prep' in the sense that the math prep is test prep. Erica - if you're around & I've put this wrong, please correct!)

Basically, the reading test can't be tutored. Not the way the math test can be tutored.

I'm going to be interested to see what happens with the writing test, which can be tutored.

Will we see the same arms race -- the same escalation of super-tricky grammar questions?

We might.

Catherine Johnson said...

I was talking to Debbie about the writing test this morning.

C's SAT tutor, who is a triple-threat kind of guy, tutored C. on the writing test, too, last summer. C's score on writing was 680; we all wanted him to break 700.

AND: Ed and I wanted him to break 700 because SAT writing is testing REAL STUFF. SAT writing tests the EXACT errors college students make in their writing -- and it was clear that C. really couldn't spot those errors & didn't know what they were.

C., who is an excellent reader, was going entirely 'by ear' on the writing.

You can do grammar by ear ---- BUT he wasn't seeing comma splices; he wasn't seeing faulty parallelism; he wasn't seeing faulty comparisons --- these are core concepts in formal written expression.

I'm expecting his writing score to be in the 700s this go-round -- but even if it isn't, the tutoring he had this summer has had a huge pay-off in his writing. The first little essays he wrote for school had essentially NO grammatical errors at all (though he had a whopper of a dangling participle in his college essay).

But talking to Debbie, I realized that for most kids SAT grammar tutoring probably won't transfer to actual writing.

That's the nature of all learning; it doesn't transfer easily or quickly at all.

I think the tutoring transferred in C's case because he's already had a lot of experience writing and was ready to 'get' these things....

SteveH said...

I've seen arms races in various areas. The more important the test or race or whatever, the more money that gets fed into beating it. In the case of SAT-math, there is a limited domain of material that can be tested. The testers have to go out of their way to find problems that supposedly test one's mathematical thinking ability. It's a war between both sides, and the advantage always goes to the money and preparation side. I suspect that the questions reflect the development of new math competition questions.

"The October SAT math section was not the SAT math section I prepared for."

Do you remember the details of a question that surprised you? I suppose there are web sites where people write down all of the problems they can remember from the test.

Catherine Johnson said...

Do you remember the details of a question that surprised you?

absolutely - it's the one I posted:

What is the lowest value for r^2 when r^2 is a multiple of 24 and of 10?

I don't have the expertise to explain why that question is different BUT I think it may be right to say that I've never seen a somewhat complicated factoring problem before.

If I were an SAT math tutor, I would assume that the SAT is now going to have lots of tricky factoring problems.

A second problem I couldn't begin to do (and I can now do all the problems on the available tests): this was a 'hard' problem at the very end of one of the sections.

It was an exponent problem....oh heck. I don't remember it well. It was an exponent problem with, I think, functions embedded inside the exponents.

When I get a copy of the test I'll let everyone know.

If I've said that correctly, then SAT math tutors (and parents) need to start prepping their kids for function problems embedded inside exponent problems.

And remember everyone: kids are taking this test under extreme pressure AND MENTAL FATIGUE.

You really can't overestimate the level of mental exhaustion. The test goes on FOREVER, and the reading sections are GRUELING.

Kids who are good at math come to the math sections after exhausting themselves dealing with the reading and writing sections.

One last thing: there is no way to make the reading and writing sections less taxing. None.

I am a very good reader & a very good writer (or, rather, a very good taker-of-the-SAT-grammar-test), and I find both tests grueling.

The reading and writing sections are "easy" for me, and they are also exhausting and deeply depleting.

That's the deal.

SteveH said...

"What is the lowest value for r^2 when r^2 is a multiple of 24 and of 10?"

Do you mean the lowest integer value of r, not r^2?

Anonymous said...

Actually, you just have to look for multiples of 120 because that is the lowest number dividable by 24 and 10 and then take the square root to find the correct integer for r. When this is done, it is found that the lowest integer with these properties that also has an integer square root is 3600 meaning that r is 60.

lgm said...

It's even easier. Since 10 is a factor, and anything multiplied by 10 ends in a zero, r must also end in zero. All you need to do is whip out the handy dandy calculator and check 20 squared, 30 squared etc for divisibility by 24. Probably just as fast as solving it the 'right' way.