C. and I took another math section of the SAT today, and it looks like I am now definitively finishing math sections. In fact, I'm starting to finish with a minute or two to spare. C. is finishing, too, although he's still not able to do all the problems. He skipped 3 today and probably got everything else right. I skipped none and probably missed 2. (We can't check our answers 'til we enter them online.)
I'm still making dumb mistakes. Typically, I'll miss one of the very first questions on the test, which C. never does but enjoys watching me do. We're starting to have a ritual: I miss question 2 or 3, and C. says, "You always miss the easy one and get the hard ones right."
Today I misread the number 6 on a graph as the number 5. Arrrgh.
The good news: I seem to have stopped making bubbling errors. Thank God. Losing points to bubbling errors when you can't even finish the damn test is uniquely demoralizing.
These days I have enough time to check each page for bubbling errors, but I don't find any when I check. More and more, I think speed is the answer -- whatever speed means, exactly, which is more than simply finishing early.
I'm probably talking about fluency.
As I become more fluent in SAT math, I'm becoming more fluent in bubbling, too.
Next challenge: no more dumb mistakes.
I wish I'd kept better notes about how long we've been working and what we've been doing.
ReplyDeleteI'll have to look through the tests to see if I dated them.
I think we started taking SAT tests in the "Blue Book" fall semester, but I was working so intensely that we probably took them only on weekends.
Not sure.
We definitely picked up the pace as soon as I finished the semester.
We've now taken all the math tests in the Blue Book: 30 sections altogether (10 complete tests). We've also taken 2 sections of Test 1 in the online course and 1 section of the first test in Chung's SAT math.
C. has gone from a math score of 580 to, today, roughly 650.
That's huge.
My lowest score, I am horrified to say, was also a 580 and today I hit roughly 700.
Really felt like I was stuck at 600-ish for eons...
Finishing tests has happened very suddenly - just in the past couple of weeks.
What's the "Blue Book"?
ReplyDeleteStamina, or building "strength", is probably a part of it as well.
ReplyDeleteLast Spring I spent several weeks trying to help my niece prepare for the SAT. Her biggest problem was not the lack of knowledge, but the lack of stamina. She lost concentration and made far more errors in the last sections than in the first. If we tried to do a whole test straight through (simulating the testing day), she simply ran out of gas about 3/4 of the way in. Her scores were always much better on the first couple of sections, no matter what they were.
In addition to the knowledge, fluency, and bubble fluency, the ability to focus for longer periods of time and maintain the same mental sharpness in the last sections is very important.
"Really felt like I was stuck at 600-ish for eons..."
ReplyDeleteWhat broke that wall? What part of the follow-on (100 point!) improvement was test prep and what part of it was something else? How much of the gain was driven by test-focused learning, and how much of it was driven by just picking up a book and reading about the subject?
My experience is that when I want to learn something new, I can never just read about the subject. I have to have a focused and specific goal. You do, however, need a certain amount of background knowledge and skills. If someone is struggling with fractions, I can't imagine that SAT test-driven learning would help much. They need fraction-driven learning first.
And the tests take even longer when you take them for real. All the reading of instructions, etc. It truly does become a test of endurance.
ReplyDeleteIt also shows why some schools go to an all test-prep all the time sort of model. If adults are having problems with bubbling errors, imagine 3rd graders!
Glen - Sorry - should have specified.
ReplyDelete"Blue Book" is the name everyone gives to the CollegeBoard SAT book - the one with 10 tests.
It's blue.
!!!
What broke that wall? What part of the follow-on (100 point!) improvement was test prep and what part of it was something else? How much of the gain was driven by test-focused learning, and how much of it was driven by just picking up a book and reading about the subject?
ReplyDeleteThat's the $40,000 dollar question.
I **think** the answer is practice---BUT practicing SAT math sections is a terrific process because I'm constantly discovering small gaps in my knowledge and/or understanding.
In other words, I'll get an answer wrong on a problem I learned ages ago, have practiced many times, etc. --- and in analyzing my mistake I'll discover a whole facet of the subject that I managed to miss.
I'll try to take notes on this as I go. It's going to be embarrassing, but tant pis.
Often it's not so much that I don't 'know' something as that my knowledge is 'fuzzy' and imprecise. For instance, I have now TWICE missed a Chung question on percent change!
Now, percent change is something I think of myself as knowing more or less cold.
And yet I missed the same question twice.
Turned out I wasn't distinguishing between time (in rate x time = distance) and distance. I was (correctly) finding the percent change in time rather than rate.
Now, in fact, I **do** know the difference between time and rate when I work an ordinary problem...but I didn't 'see' it in the Chung problem...and then, as I thought about it, I realized that the difference between 'time' and 'rate' is actually confusing to me because rate includes a measure of time.
I can't explain it any better than that at the moment.
At this point, I think studying for SAT math is fantastically valuable -- to the point that I think SAT math problems should be part of high school homework.
I am constantly discovering some new implication of the h.s. math I know via the mechanism of taking SAT math tests and analyzing my mistakes.
btw, this jump is quite new, so I'm still asking myself whether it's a fluke or real.
ReplyDeleteHowever, at this point, given that I've easily finished 3 math sections in a row - and given the fact that C. is doing the same thing - I'm inclined to think we've both had some kind of sudden 'gelling' of our ability to do SAT math tests.
Last but not least, I spend a lot of time reteaching myself the problems I got wrong --- and then I teach Chris what he's gotten wrong & make him re-do the problem OR just write out the steps with me if he absolutely doesn't know it.
ReplyDeleteBasically, I write out a worked example and make him write the steps along with me.
So at least for C. he's doing quite a lot of practice AND he has a 'peer tutor' (he's ahead of me in math at this point, but not on SAT math) who explains things.
Barry has been teaching me some of the problems -- and so have all of you.
Thanks!
If someone is struggling with fractions, I can't imagine that SAT test-driven learning would help much. They need fraction-driven learning first.
ReplyDeleteoh, lord
Chung had a fraction problem that was a revelation to me.
I'll have to post it.
My difficulty with that problem was an H. Wu moment: I was never taught to see fractions as numbers on the number line.
I see fractions as being more like an "operator" or, in language, a "modifier."
A fraction in a word problem is an adjective or an adverb, not a noun.
btw, yesterday's '700' (projected from my score on 1 section) isn't what I would score on a real test or even on a bunch of math sections taken here at home.
ReplyDeleteRealistically, I'm probably approaching a reliable 650 -- and so is C.
That's major progress, and it makes me think that a 700 for him (& for me - ) is a realistic goal.
In addition to the knowledge, fluency, and bubble fluency, the ability to focus for longer periods of time and maintain the same mental sharpness in the last sections is very important.
ReplyDeleteRight.
We haven't even dealt with that.
C. seems to have terrific stamina, though. (Not sure why I say that...AP tests, I guess.)
Not sure that stamina is a big issue for me because the reading & writing multiple choice is 'easy.'
That said, the reading and writing sections are fantastically taxing in spite of being easy. It's the tiny, tiny little font size and the massive amount of print on each page, and the flipping back and forth from question to text, and the massive demands on working memory...
Still and all, I assume I spend less mental energy doing the reading & writing sections than a high school kid does.
fyi: so far every adult I've known (or read about) who took the test as an adult did significantly better on reading than they did as a kid.
They don't do better on math, though they don't necessarily do worse.
One last thing: the reason to shoot for as high a score as possible on math is that there's a difference in the difficulty of the problems -- and I want C. to be able to do the hardest ones.
ReplyDeleteOn critical reading, I just don't see a big difference between an 800 and a 700...there's no pattern of C. getting hard questions wrong and easy questions right.
With writing, I am horrified to say that he is consistently missing comma splices.
More on that later.
fyi: so far every adult I've known (or read about) who took the test as an adult did significantly better on reading than they did as a kid.
ReplyDeleteThat's interesting, because I do believe that part of the explanation for why math is shortchanged in so many schools is that the teachers prefer teaching subjects where their expertise is strong. People who don't study much of anything can still be experts, relative to kids, in one subject: the native language they've used every day for decades longer than the kids have used it.
Like being able to reach higher or being able to glue things to cardboard, your native language is a default expertise you get, relative to kids, by just being an adult who grew up in the same culture. Other subjects, like math, require specific subject training, and if you don't feel like bothering with all that, you can still be The Expert by keeping the class focused on Language Arts and gluing things to cardboard.
Hey Glen - I think that's right **except** that I'm not sure how much better you get at reading just by reading...unless you're pushing yourself to read difficult texts.
ReplyDeleteHowever, the few people I've read about (or know) who took the SAT as adults probably **were** reading fairly difficult material.
I've got to find the posts I wrote about the kids who scored 800 on reading & math. Their defining feature was that they had done lots of assigned reading, guided by teachers.
They did lots of reading on their own - but the author clearly felt that the source of their 800s was reading they were 'taught.'
The problem with math is there are about 5 decent math teachers on the planet.
ReplyDeleteSeriously.
I pretty often think that's the issue.
I say that because the parents I know who've had kids at private schools have had TERRIBLE math teaching experiences.
And....I know we've all talked about this before, but there's a HUGE problem with knowledge gaps. There's NO subject (as far as I know) that is so unforgiving of gaps.
Since schools (all schools) have essentially no well-oiled way to diagnose gaps and close them, students just get worse as they go along --- and eventually a h.s. teacher is facing a whole room full of kids with different blind spots.
Different multiple blind spots.
Hey Glen - I think that's right **except** that I'm not sure how much better you get at reading just by reading...unless you're pushing yourself to read difficult texts.
ReplyDeleteI agree with you, but where do you plateau? If it's true that popular checkout stand "literature" such as People Magazine and Cosmo are written at about an 8th grade reading level (not by 8th grade standards but by measured average proficiency of 8th graders, and I think this is approximately right), then someone who reads People for twenty years won't plateau until reaching at least the average 8th grade level, which is above the average K-5 level of the kids.
And, as you say, background knowledge contributes a lot to your reading level, so just LIVING in the same culture decades longer, accumulating general background knowledge from People, TV news, and so on, should make the teacher the Big Kid in reading just by virtue of having lived longer.
You don't just accumulate math by default.
Just imagine paying $25,000 for the privilege of going to your neighborhood used car lot and being assigned a random used car.
ReplyDeleteThis is how we get math teachers for our kids. Whether there are five great math teachers in the world or a few more, your chances of winning one in the school lottery are small.
This is why I've always considered it crucial to be able to learn from books. This is a case where "teaching kids how to learn" can actually mean something. There aren't many great teachers in any field, but one of the great ones often writes a great book. If your kids can join the apparently few people who are able to learn from a textbook with no live teacher, they can have their pick of the best teachers in every field.
Otherwise, good luck winning the lottery.
And, as you say, background knowledge contributes a lot to your reading level, so just LIVING in the same culture decades longer, accumulating general background knowledge from People, TV news, and so on, should make the teacher the Big Kid in reading just by virtue of having lived longer.
ReplyDeleteYou don't just accumulate math by default.
Good point!
I bet accumulated background knowledge is the reason you see adults go up in critical reading.
I think you've just put into words the reason why I don't think it 'matters' that C. is getting roughly a 700 on reading as opposed to an 800.
I've been having the word "maturity" pop into my head as the explanation for why I don't care that he at age 60 is in the 700 as opposed to the 750 to 800 range---but I think you've just explained to me what I mean by that: I mean that at age 16 he's got 'X' amount of background knowledge.
I'm amazed at how well he reads -- how quickly (he's as fast as I am) and with a very high level of comprehension.
I'll make some notes on the kinds of things he gets and doesn't get...I don't think I've seen him make a 'dumb' mistake...I think he typically picks the other plausible answer (but I'll look).
long story short: a 700 on critical reading seems fantastic to me in a way that a 700 on math does not.
(Don't get me wrong - a 700 on math seems AMAZING to me! All I'm saying is that a 700 on critical reading is more amazing vis a vis reading comprehension than a 700 on math is vis a vis math.)
This is how we get math teachers for our kids. Whether there are five great math teachers in the world or a few more, your chances of winning one in the school lottery are small.
ReplyDeleteabsolutely
While I've been skeptical of the Khan videos, THIS is the area where I am deeply grateful to him for doing them.
I don't think the Khan videos will work as the primary teacher --- but as the back-up teacher they may be indispensable.
And I'm guessing parents may be able to use them to reteach themselves content they're going to have to be reteaching.