kitchen table math, the sequel: sample SAT

Sunday, December 31, 2006

sample SAT


I think the SAT math test is way harder today than it was back when I took it.

I've just this moment finished the 1st sample test in The Official SAT Study Guide. There were zillions of questions I had never seen before, nearly all of them having to do with functions.

(it wasn't zillions. it seemed like zillions.)

Obviously, I know nothing about functions.


I got 37 correct, 9 incorrect, for a raw score of 35, which translates to a range of 540 - 620.


If I'd been taking the test for real I would have scored somewhere between 600 - 650. I made "careless errors" I wouldn't have made with more adrenalin (and less autism-spiked cortisol) coursing through my system.

I also would have remembered to use my calculator.

Plus I would have used a test-taking strategy or two.

I completely forgot until I reached the 4th section that the plan with the SAT is:

  • do the easy questions first
  • use strategic guess-and-check throughout to eliminate obviously wrong answers

Instead I raced through the test, taking each problem as it came, and attempting to figure out how to solve it if even I'd never seen the thing before.


The good news is that I think it's fair to say I know Algebra 1 cold.

And I'm not bad on simple geometry.

I also know enough math (whatever that means) that I was able to figure out, on the fly, how to do a couple of problem types I'd never done before.

Nevertheless, the only way anyone's getting through this test is by dint of huge practice:

Section 3: 20 questions / 25 minutes
Section 6: 18 questions / 25 minutes (10 of the 18 are "student -produced response" - i.e., not multiple choice)
Section 9: 16 questions / 20 minutes

To do well on the SAT Math, you have to have reached automaticity for virtually every problem you see. There's no time to think or problem-solve; you have to be solving the question one second after you've finished reading the question.

That's an exaggeration, but not by much. I was able to scrape together a few minutes' thinking time left over from problems that took only a few seconds to do. But no more than a few.

Bottom line: the SAT is the exact opposite of everything the NCTM stands for.

Do we know how kids who've been in constructivist curricula in high school are doing on the SAT?


I've always thought SAT tutoring is a waste of money, which it may be (I've got some interesting studies to post).

However, after taking one practice test I can see where SAT tutoring for students who knew algebra 1, algebra 2, and geometry fairly well but hadn't practiced to automaticity could raise scores substantially.

Students definitely need to learn and practice test-taking strategies, too. No question.

That's another thing.

Back when I took the SAT, there were no practice tests. There wasn't even review.

You walked in, sat down, took the test.

I'd bet the ranch that the existence of the test prep industry has changed the tests.


I've completed Lesson 48 in Saxon Algebra 2, which is the second book in the "Saxon Math trilogy":

  • Saxon Algebra 1
  • Saxon Algebra 2
  • Advanced Mathematics
Geometry is integrated throughout the 3 books.

So: I have an SAT score in the low 600s after Saxon Algebra 1.

I think I'll take another sample test midway or perhaps 2/3 of the way through Algebra 2.


College Board list of math topics covered on SAT
sample SAT test
SAT test
get your recentered SAT scores right here


Anonymous said...

"Do we know how kids who've been in constructivist curricula in high school are doing on the SAT?"

I don't know. But I've read that there are no longitudinal studies showing how kids raised on Everyday Math do in rigorous high school math with serious pre-college content.

On the other hand, in New Milford (where they did the Saxon, Singapore, EM experiment), they seemed pretty happy with their SAT scores, and credited EM.

As for me, I'm keeping my kids in Kumon, especially after reading your post. I continue to be amazed at how little practice is built into the EM program. How can anyone develop automaticity this way? Even the strong students need practice ... don't they?

Unknown said...

I hate to admit it, but I don't remember taking the SAT. I vaguely remember taking the GRE -- my administration was the first for the then-new (now dropped) logic section, which was a real pain in the patoot.

LynnG said...

It is so fantastic to see a KTM sequel up! Congratulations, Catherine.

As to constructivist SAT prep, I'm not optomistic. It is still too soon to say. We've only had EM for 5 years, so it will still be another 2 to 3 years before we start seeing the effects. Unfortunately, if this town is any indication, we already here the excuses being prepared. Too many kids move to town without the "benefit" of constructivist teaching (these kids must be moving in from the moon, because there are no longer any towns in Connecticut that are not yet using constructivism extensively); the high school curriculum is to blame, certainly not the terrific elementary use of EM, stuff like that. Plus, our SAT scores are stellar to begin with. We average aroung 549 on the math section, but we have a low (86%) participation rate.

Catherine Johnson said...

It's probably worth it for parents to buy a used copy of the College Board book and take the test. The experience was a revelation.

It's crystal clear to me now that we have to be very serious about our Saxon home curriculum. There's just no other way.

Can't remember if I've mentioned this, but Ed and I had a strikingly bad meeting with the math chair a couple of weeks ago, a meeting so bad it surpassed in badness anything we have yet experienced.

We came in thinking we were going to discuss curriculum and pedagogy; the math chair came in thinking she was going to defend Ms. K's latest test.

I have zero interest in discussing Ms. K further, especially now that the union is issuing public threats to sue (hey kids! union intimidation tactics work!)

Actually, I'd lost interest before the union weighed in. We've given up. Christopher is simply not going to learn math in this class, period.

That's why he's doing a separate curriculum at home.

Also, I now see clearly something Rudbeckia Hirta once pointed out, which is that the course content iself is ludicrous. There's far too much of it covered in far too little time.

That's not the teacher's fault.

So back to our meeting. The fact that the union has publicly threatened to sue, at a District meeting no less, produced the unintended consequence that Ed and I now refuse to discuss either Ms. K or our child's performance in her class with District personnel.

We simply state and re-state as necessary the plain fact that "the kids aren't learning" in the "Phase 4 math class."


No good deed goes unpunished.

The math chair told us that she would under no circumstances discuss curriculum and pedagogy with us.

She would only discuss the test.

So we used each and every comment she had to make about the test as a jumping off point to discuss curriculum and pedagogy.

Eventually we managed to tell the chair that the reason kids are doing badly on the tests is that they haven't had enough distributed practic.

Her response?

"If students need more practice, you can find worksheets online."

Catherine Johnson said...

So....the chair of the math department is now on record stating that the school's job is to present content; our job is to get it inside our kids' heads.

I think it's possible the "Phase 3" math track is better.

It's slower, of course, which means more opportunity to practice skills & procedures to mastery.

It's possible the Phase 3 teachers pay more attention to whether students have learned. most respects getting Christopher into the Phase 4 track was a big fat mistake, especially given the fact that the math chair is the calculus teacher.

I have a feeling that calculus-in-high school is going to be a non-starter.

Catherine Johnson said...

I don't know what to think about KUMON, primarily because I don't know whether KUMON's advanced levels correspond to SAT problems.

I do think it's probably time for me to get back to doing my KUMON sheets, just to see whether we need to get Christopher back in the program.

Actually, I need to ask Mr. Liu to show me what the Algebra 2 worksheets look like.

That will tell me what I need to know.


Christopher is not going to be happy to hear that KUMON may be making a reappearance.

Catherine Johnson said...

College Board list of topics covered in SAT Math

Anonymous said...

"Christopher is not going to be happy to hear that KUMON may be making a reappearance."

My kids hate it. Also, it doesn't cover all the math they need to know, so I supplement my son with Singapore and my daughter with Saxon.

But I feel dependent on Kumon. I need a systematic way of ensuring my kids are getting the practice they need in basic math.

The practice and repetition make a huge difference. My "disabled" daughter knows her math facts fluently and automatically. She is confident in her use of the addition and subtraction algorithms (we haven't gotten to multiplication and division yet----Kumon moves very slowly).

By the way, I love Saxon. I agree completely that distributed practice is key.

Anonymous said...

"We've given up. Christopher is simply not going to learn math in this class, period.

That's why he's doing a separate curriculum at home."

We're in the same boat. It's not the teacher's fault; she's required to use the EM program, even for classified kids. The school district is inflexible on this point, although they do allow modifications.

My daughter is quite capable of learning math using Saxon and Kumon. I'm sure there are many other children like her. They could learn with an appropriate program. It's sad that the district doesn't see this.

Tex said...

Catherine & Robyn –

You guys are not making me feel too good right now about starting Kumon with my 4th grade daughter this month. She has already told me many times that she does not want to go. I took her once last spring for a look see, and she decided she hates it. I think it’s just the idea that she has to go somewhere and do extra school work.

Like Robyn, I also need a systematic way to handle the gaps. I am optimistic that Kumon will do the job for my daughter. And I want to enroll her in the reading program also. But, we will not do both at the same time.

I don’t want to have to drag her to Kumon kicking and screaming (more likely pouting and whining). But if that’s the only way it’ll happen then that’s the way it’ll be.

Anonymous said...


Try bribery. Promise a reward after she passes each level, or after she completes a certain number of worksheets. It sort of works.

Anonymous said...

"So....the chair of the math department is now on record stating that the school's job is to present content; our job is to get it inside our kids' heads."

The schools aren't teaching, they're sorting. That's what Englemann says.

Catherine Johnson said...

I need a systematic way of ensuring my kids are getting the practice they need in basic math.

It works.


Catherine Johnson said...


I might not do the reading program if I were you (though I can't remember what you've said about your kids).

It's somewhat in the "how to" category of reading.....

I think.

I would concentrate on increasing background knowledge (probably using the Hirsch series) & vocabulary (Vocabulary Workshop).

Then I'd give my kids a standardized reading test at least once a year to make sure they're progressing at least one year every 12 months.

Catherine Johnson said...

otoh, KUMON reading does teach summarizing, but it takes quite awhile to get to that point.

Tex said...

"otoh, KUMON reading does teach summarizing, but it takes quite awhile to get to that point."

That’s one of the areas where she’s having difficulty. Summarizing, getting the main idea, incorporating details.

In two weeks NY fourth graders are taking the state ELA tests, and a big part of the test is “extended answer” essay writing. The way they are teaching is to start with a planning page. (Back when I was in school we were taught to do outlines. They don’t teach that anymore. They use diagrams with circles & lines. Whatever happened to outlines? But I digress.)

Anyway, for my daughter, she is very slow to complete her planning page. So I think she needs to gain proficiency by going back to single sentences and taking baby steps so she masters each level.

It seems so much like last year when she was struggling with long division because she wasn’t fluent with math facts. Once she nailed her math facts, long division was a breeze.

I don’t know if it’s truly similar to learning math. The Kumon worksheets I saw did seem to systematically teach writing step by step. I’m going to look at the Hirsch series. Any other ideas would be welcome.

Catherine Johnson said...

I'll think about it....

Take a look at KUMON. I decided against it (we did it for awhile) because of Hirsch on "how to" approaches to reading.

The passages were good, though.

KathyIggy said...

We're dropping reason is increased cost and another the hassle of getting across town, interfering with other activities, etc. But Megan did become a lot faster on her math facts. I also agree the reading passages are very good and really held Megan's interest, and we went to the library and checked out some of the complete books. Megan started at Reading A1 a year ago and will end up finishing C2. I did notice some improvement in answering wh- questions. We stopped math halfway through Level C. Another reason we stopped is I was wondering if some of the worksheet repetitions were not needed--Megan already knew her multiplication facts very well, and finished the sheets well within the time, yet they were assigned over and over and she was getting bored. We'll pick up Saxon Math 54 again and also keep going with Wordly Wise too.

Catherine Johnson said...

I suspect the KUMON sheets are overkill....

KUMON isn't "precision teaching"; it isn't built to give kids the exact amount of practice they need and no more.

I still think it's a terrific program, and I may pick it up again myself (and perhaps for Christopher).

But once you get off track - once you're not doing 5 sheets a day - it's expensive.

We'll see.

RSydnor55 said...

I found a nice site that provides great information on the SAT and interesting strategies.

Catherine Johnson said...