kitchen table math, the sequel: anonymous on the SAT math learning spike

Sunday, April 17, 2011

anonymous on the SAT math learning spike

anonymous writes:
I am like that with names. At the start of the school year, I need to learn 150 names. For the first week it is slow going and mostly by memory tricks. Then all of a sudden, I know almost every name automatically.

I wonder if your speed has increased because you have become better at instantly categorizing the math questions.

That's a good question!

I'm going to start keeping notes.

I continue to have the "implicit learning" experiences I've mentioned before, where I'll know that an answer is right without knowing why -- or, in some cases, I'll find myself on the path to solving a problem correctly while consciously thinking I'm doing it wrong.

I'll have to check my books on learning and memory to see if it's the case that implicit knowledge shows up before explicit knowledge. (Implicit knowledge is sometimes called the "cognitive unconscious," a term I'm keen on.)

If I had to guess, I'd say anonymous is right: I'm recognizing problems faster. I'm already as fast as I'm going to get at doing the actual calculations, and I don't think I've boosted my speed at setting up word problems (which I need to work on).

Also, my 'number sense,' for want of a better term, isn't especially good. That is, I don't read a problem and think 'the answer has to be in the neighborhood of thus and such because of thus and such.' My math knowledge continues to be fairly inflexible, so I don't take shortcuts doing the problems because the obvious shortcuts aren't obvious to me.

Not unless the problem is super-easy. Here is problem number 2 from yesterday's test:
A machine requires 4 gallons of fuel to operate for 1 day. At this rate, how many gallons of fuel would be required for 16 of these machines to operate for 1/2 day?
I started out setting up unit multipliers and quickly got stuck: I cannot for the life of me make unit multipliers work on an SAT math section. Why? Very frustrating.

So I was sitting there burning time on QUESTION NUMBER 2, the 2nd easiest question I was going to be doing, and finally I just bagged the dimensional analysis, looked at the problem again, and said to myself: "If it's 4 gallons for 1 machine for 1 day, then it's 2 gallons for 1 machine for 1/2 day, so if I've got 16 machines that's 16x2 and that's 32."

I was very happy to see 32 amongst the answer choices.

SAT genre

The other piece of evidence that anonymous is right -- our increase in speed is due to increased recognition (categorization) of what we're looking at -- is the fact that I can now tell a "genuine" SAT math problem apart from an ersatz SAT math problem. (I'm going to try to find out whether C. can tell the difference.)

Interestingly, I could tell the difference between a real SAT reading question and an imitation SAT reading question from the get-go, just about, and of course the reading section is what I'm good at.


Lsquared said...

I wonder if I can do it with dimensional analysis?

4 gal/(machine*day) * (1/2 day) * (16 machines) = 32 gal

(days and machines cancel).

The interesting bit was realizing that the denominator of the unit was machine*day.

Catherine Johnson said...

OK, now I'm going to try!