kitchen table math, the sequel: SAT math question

Thursday, March 24, 2011

SAT math question

I have two questions, actually, but I'll post just one for the time being.

Here it is.

For me, SAT math questions are non-routine. They are problems, as opposed to exercises.

Here's my question.

Is that true for kids scoring 700 and 800 on the SAT?

Or is it true for me because my math knowledge is still pretty tenuous?

When I watch Salman Khan work SAT problems, I don't feel like I'm watching a person solve problems.

I feel like I'm watching a person do exercises.

Am I wrong?

29 comments:

gasstationwithoutpumps said...

SAT problems are routine exercises for the most part, unlike the AMC problems, which often are problems.

forty-two said...

I got an 800 on the Math portion of the SAT, and I'd say it was a bit of both, in that a good portion of the problems were novel (I did no prep), but I didn't have much trouble figuring out what to do (and some were pathetically easy - plug 'n' chug with the formula right there on the official test formula sheet). I mostly remember that I had to consciously hoof it on the math parts in order to finish, whereas I naturally finished the verbal sections 10min early.

Also, I hit a mailbox on the way to the exam - spent my spare time worrying about telling my parents than worrying about the exam - did that raise or lower my score ;)? (Missed 5 q's on the verbal section.)

forty-two said...

Definitely agree that the AMC problems were in a completely different level from the SAT problems - I did no competition math outside of taking the test each year (think it was the AMC, anyway), and it was *hard*. Those were definitely non-routine for me, and I was lucky if I could come up with something for half of them.

(Sadly, at the time my math world was so closed that I had *no idea* that people *studied* for those sorts of tests :doh. I thought it was a test of one's inherent mathiness or something :sigh.)

Catherine Johnson said...

mostly remember that I had to consciously hoof it on the math parts in order to finish, whereas I naturally finished the verbal sections 10min early.

True for me, too

What is the AMC test?

Catherine Johnson said...

oh - it's this, right?

American Mathematics Competition

Michael Weiss said...

It's been 20+ years since I took the SAT, but in my memory they were exercises, not problems. I don't remember anything catching me off-guard. And just the past few months I've been working through SAT Math with my teenaged son, and have had the same experience: All routine. (Which is not to say that he has had that experience, but then again, he is only 14.)

forty-two said...

Yep, that looks like what I remember. My only exposure to math beyond the standard school stuff - wish I'd have realized at the time that the high scores had almost certainly actually *done* problems like that before, that they weren't taking the test cold like I was - you know it *never* occurred to me that prepping or studying was even an *option* :sigh, let alone just about necessary to doing well.

Bostonian said...

If you have reviewed the math concepts tested by the SAT, and the questions still seem like problems rather than exercises, I think it may be a matter of math talent, which differs from person to person. Not everyone can be trained to get an math SAT of 700, much less 800. A paper was cited here some time ago finding that SAT prep courses do not increase scores much.

Allison said...

The kids scoring a 700 are two standard deviations from the mean. That's means they are in the 95% of those taking the test. They see these problems as exercises, though occasionally one or two might be interesting. Scoring an 800 puts you 3 standard deviations out: 99.5%. Absolutely these problems are exercises to them.

Your math knowledge is still tenuous, despite all of this work you've done. Isn't it annoying how much more difficult it is to learn things as an adult? Doesn't it make you even more annoyed at the people who waste kids' time when their brains ARE PLASTIC????

lgm said...

I recall that many were exercises; a few were puzzles that were obvious after a few seconds of thought. Some of the number theory and counting I hadn't considered before, so that took a little time.

One problem I see for my sons is that our district didn't cover complex fractions or sequences in either pre-Algebra or Alg I.

An example of a puzzle would be (from 10 Real SATs, 1997, p. 412 #20): The figure above shows parts of two circular gears whose teeth interlock when the gears turn. Gear A has 72 teeth and gear B has 48 teeth. Home many complete revolutions does gear A make when gear B makes 9 complete revolutions? (in pic gear a and gear b look to be the same size, their teeth mesh well and the note is that fig is not drawn to scale).

It annoys me greatly that NY does require districts to offer an accel course (i.e. high school level, for high school credit) in the 8th grade, but does not force districts to offer honors math. It bothers me greatly as a citizen that these people have so much power that they have been able to greatly restrict the opportunity for students to learn both arithmetic and math.

Anonymous said...

lgm's example "puzzle" is a simple ratio problem (although it requires being familiar with the term "gear ratio" - Wikipedia has a whole page dedicated to it). Because the gears are meshed, the total number of "teeth" moved will be the same for each gear, but the total rotations will be different.

rotations = teeth moved/number of teeth
rotations (A) = rotations(B) * teeth(B) / teeth(A)
rotations(A) = 9 r *48 t / 72 t
rotations(A) = 6 r

-- Andy

lgm said...

The distraction on that one is the gear pic..some people may spend too much time wondering why the gears look the same if the # of teeth/gear is so different. Of course some people may not have considered gears before so the pic is an aide to them.

The fast way to solve it is to think one revolution in terms of teeth is a 72:48 ratio, so 9 rev Gear A :x Rev Gear B. x is obviously 6 since the ratio must stay fixed.

Anonymous said...

"The fast way to solve it is to think one revolution in terms of teeth is a 72:48 ratio, so 9 rev Gear A :x Rev Gear B. x is obviously 6 since the ratio must stay fixed."

Assuming one has a calculator, I think it is simpler (and no slower) to count teeth:

48×9 = small-teeth.
small-teeth = big-teeth
big-gear = big-teeth/72

-Mark Roulo

lgm said...

Shrug. YMMV. This is a typical sixth grade problem (here) to solve for x without a calculator when one sees 72:48 is 9:x. Should be no trouble at all on the SAT to solve quickly mentally without writing down a thing rather than setting up all that you've written and then using the calc. I'll agree to disagree as it doesn't matter to me how you school your child.

Catherine Johnson said...

My problem on SAT isn't brain plasticity; it's that I've never taken algebra 2. (I thought I did, but algebra 2 in my high school turns out to have been algebra 1 in any other high school.)

I was never taught counting; I had never heard of counting until a year or so ago.

I'm completely self-taught, and I haven't done daily study of math for many months.

Catherine Johnson said...

If you have reviewed the math concepts tested by the SAT, and the questions still seem like problems rather than exercises

Review isn't the issue.

Practice is the issue -- practice to the point of automaticity.

You can review 'til the cows come home; that doesn't make you fast.

I can do all the SAT problems; the issue is that I can't do them fast.

Kumon is a practice program, not a math review program.

Catherine Johnson said...

I'll have to post the intro to the Chung SAT book--it's funny from a U.S. perspective.

Americans typically believe in innate qualities; Asian culture tends to believe in effort.

As I recall, that comes from Stigler & Stevenson's work -- and I think perhaps Nisbett, too, but I'm not sure.

In any event, you can see it in the Chung introduction.

Actually, I can see the difference in my collection of SAT books.

The books written by Asian authors have a gazillion practice problems.

The books written by Americans have a huge amount of review.

Catherine Johnson said...

One problem I see for my sons is that our district didn't cover complex fractions or sequences in either pre-Algebra or Alg I.

Astonishingly enough, I did learn complex fractions in high school.

Nothing about series or sequences.

Catherine Johnson said...

It bothers me greatly as a citizen that these people have so much power that they have been able to greatly restrict the opportunity for students to learn both arithmetic and math.

You said it.

I find it incredible that administrators here feel free - and in fact are free, since the BOE approves everything they do - to dump Open Court (which we taxpayers paid for) and adopt Fountas and Pinnell (which we taxpayers also pay for).

Now we taxpayers are paying "reading specialists" to teach phonics to kids who don't learn to read using balanced literacy.

I suspect we taxpayers are also paying to "train" teachers to teach phonics ---- at least, the word "training" has been bandied about by our administrators.

Teachers are being "trained."

Whenever the word "training" or "trained" or "train" crops up in discussion, you should assume stipends are involved.

Catherine Johnson said...

And just the past few months I've been working through SAT Math with my teenaged son, and have had the same experience: All routine.

That is what I'm concluding.

SAT questions that used to be problems for me are now routine --

So the goal with C. is to get him to the point where LOTS of the problems are routine.

Crimson Wife said...

I didn't find the SAT math problems tricky so much as I ran out of time.

I wish I could find the reference, but I read one time that offering an untimed version of the SAT significantly raised girls' math scores but had little impact on boys' scores. This article alludes to it in passing but does not name the author or provide any other info.

Catherine Johnson said...

oh my gosh - that reminds me of a fabulous story C. told me

a friend of his has a sister who took the SAT in a 'tough' ghetto school, and the proctor, after handing out the tests, disappeared

the kids had all the time they wanted, and she **still** did crummy

C. was cracking up when he told that story and so was I

Catherine Johnson said...

I took an SAT math section today, finished the whole thing, and missed two - which one of my books says is around a 700

hah!

One of the questions I missed was a fantastically simple question concerning a median test score. I started the question by not grokking the fact I'd been asked for median, so I spent a lot of time adding up a gazillion scores and finding a mean....then, after figuring out that the letters m-e-d-i-a-n do not speal 'mean,' I managed not to count to 8 correctly.

pathetic

I missed the other question because I couldn't understand what it was asking.

After I'd scored my test and re-read the question, it seemed a lot more clear.

Jo in OKC said...

I asked my daughter today. She took the SAT this fall and got a score in the range you mention.

She said the questions are all routine exercises.

She would agree the AMC questions and AIME questions are problems.

One of her favorite areas of math is counting. :-) I remember covering permutations and combinations in high school math. However, what I learned was just a small fraction of what's covered in Art of Problem Solving's Intro to Counting & Probability course or book.

lgm said...

I learned the basics of counting in Dolciani PreAlgebra. It was picked up again in a more absract form in Alg II at the end of the year. Haven't seen a test prep question that requires more than what was covered in prealgebra.
NY moved what I had in preAlg to the end of Alg I, but the course my son took resorted to only teaching how to punch in perms and combo on the calculator. Poor lady didn't get the other topics across.

lgm said...

>>Now we taxpayers are paying "reading specialists" to teach phonics to kids who don't learn to read using balanced literacy

We've had these for years. The beef now is that their program -Reading Recovery- has been cancelled and they fall under rTi in terms of paying for resources needed.

We are paying for a few other hidden things too..for ex. master's degrees for teachers and pHDs for principals who we then award raises to - the rationale seems to be since some large profitable companies reimburse employees to advance their education, the school district should too.

Then there is the 'pay students to come to school'. It uses Gates Foundation money and pays $5/day to those in alternative. We also make it possible for older students who are babysitting in the a.m. to attend alternative school on elementary school hours so they can get home around the time the elementary bus brings their siblings home.

Catherine Johnson said...

The last I checked, Reading Recovery was the single most expensive program on the market AND it is whole-language based.

They've added just enough quasi-phonics to the program that it's now somewhat effective -- and still fantastically expensive.

Catherine Johnson said...

Jo in OK -- hi!

Favorite topic is counting!

Wow!

I'm fascinated by counting, but it is HARD.

On the other hand, I'm starting to get questions right. (Using Art of Problem Solving book)

I'm also starting to get questions right by a different means than the solution manual employed - and to be able to understand why the Solution Manual used the approach it did.

I still find multiplication mystifying in some core way, though.

I 'see' that if you have 5 houses and inside those 5 houses you have 2 bathrooms and that makes 10 bathrooms in all....but I don't like it.

Anno's factorial book came in the mail today, and I don't like it, either.

SiouxGeonz said...

For me teh SAT was a mix of figuring out what the problem was asking for and then figuring out what kind of exercises got the right answer. It always amused me that I did better in math than verbal, since I'm much,much more verbal -- but I applied the verbal skills to the math and there just aren't as many kinds of math problems as there are words.
In working with adults, an awful lot of them have very poor basic number sense. (See http://engagingideas.net/frcc-student-learning/math/ ) Procedure-based teaching is liberating for the teacher -- hey, you don't have to worry about whether anybody understands stuff or not!