This is amazing.
Some of you may remember our discussing why charter schools do so much better raising math scores than reading scores. (Be sure to read the comments thread.)
Ever since my summer at Morningside Academy, I've suspected that, where reading comprehension is concerned, pretty much everyone is on the wrong track. (Everyone but palisadesk, of course.)
More to the point, I don't really buy the argument that good reading comprehension, or good scores on reading comprehension tests, take years and years to develop because good reading scores are a matter of background knowledge that takes years and years to develop.
Having now taught freshman composition for a few years, and having used as many Morningside techniques as I've been able to, my sense is that struggling readers can improve pretty quickly.
But that's just an impression. I don't have before-and-after scores.
Then there's the SAT, where math scores are widely perceived to be moveable, but reading scores are not. Certainly not quickly.
So guess what?
A month ago Debbie finally took the plunge and created a 28-day "intensive"* course in SAT-type reading ---- and it works!
Students are raising their scores significantly in 28 days.
It's incredible. I thought it would work, and Debbie thought it would work, but then again .... 28 days? That's not a long time, 28 days. I don't think I'm putting words in Debbie's mouth when I say that while we both thought it would work, we were also harboring a sliver of doubt.
But the first batch of scores have come out, and the kids are doing great!
It's incredibly exciting.
If I still had a teenager at home, I would definitely sign him up. (Maybe Andrew, once we get through Katie Beal's GrammarTrainer ---- boy, I would love that ---)
28-day critical reading intensive
* I love "intensive"! I would never have thought of using that word myself & nor would Debbie -- a marketing person told her to call what she was doing "intensive." Brilliant. "28-day intensive" makes me want to take the course.
#28-dayintensive
Showing posts with label SAT prep. Show all posts
Showing posts with label SAT prep. Show all posts
Thursday, February 12, 2015
Monday, December 1, 2014
It's the peers, stupid
I remember being struck, years ago, by Laurence Steinberg's idea that what parents in expensive school districts are really buying isn't good schools but good peers.
Made sense.
From a new NBER paper:
Made sense.
From a new NBER paper:
When effort is observable to peers, students may act to avoid social penalties by conforming to prevailing norms. To test for such behavior, we conducted an experiment in which 11th grade students were offered complimentary access to an online SAT preparatory course. Signup sheets differed randomly across students (within classrooms) only in the extent to which they emphasized that the decision to enroll would be kept private from classmates.
[snip]
When offered the course in a non-honors class, these students were 25 percentage points less likely to sign up if the decision was public rather than private. But if they were offered the course in one of their honors classes, they were 25 percentage points more likely to sign up when the decision was public. Thus, students are highly responsive to who their peers are and what the prevailing norm is when they make decisions.
How Does Peer Pressure Affect Educational Investments?
Leonardo Bursztyn, Robert Jensen
NBER Working Paper No. 20714
Issued in November 2014
Wednesday, March 26, 2014
Debbie at Ed Week!
I edited! (So I'm bemoaning a couple of too-long-for-onscreen-reading sentences...
Seeking the Top Score (Part I)
By Helen Yoshida on March 25, 2014 5:34 PM
Seeking the Top Score (Part I)
By Helen Yoshida on March 25, 2014 5:34 PM
Monday, January 20, 2014
Debbie's book - Today Show - Spreecast !
Debbie's pub date is coming up, and things are getting exciting. She's had incredible response to the book; the blurbs are incredible. So I'm expecting good things.
The biggest news so far is that Debbie and Ethan will be on the Today Show on February 25.
And, on February 12 Debbie will be doing a "Spreecast." (Actually, it's the 2 of us; I'm the interviewer/sidekick).
You can sign up here, and I hope lots of you will---!
The biggest news so far is that Debbie and Ethan will be on the Today Show on February 25.
And, on February 12 Debbie will be doing a "Spreecast." (Actually, it's the 2 of us; I'm the interviewer/sidekick).
You can sign up here, and I hope lots of you will---!
Tuesday, June 19, 2012
all about motivation
For years, I've been wanting to know who is doing the major research on motivation and what I should read.
I think I've found the answer:
Gabrielle Oettingen's homepage
"Mental contrasting" is key: mental contrasting and "implementation intentions."
If you're trying to persuade your kids to study for high-stakes exams, both are probably good to know about.
I think I've found the answer:
Gabrielle Oettingen's homepage
"Mental contrasting" is key: mental contrasting and "implementation intentions."
If you're trying to persuade your kids to study for high-stakes exams, both are probably good to know about.
Sunday, December 4, 2011
prodigy
in the Times today:
Great things were expected of him. His math teacher at Greenwich High School in Connecticut, Stephen Willoughby, now a retiree in Tucson, Ariz., says he was a math prodigy. “I always expected Chris would win a Nobel. I just wasn’t sure what field it would be.”
Mr. Sims’s classmates voted him most likely to succeed. “In a class of intelligent people, he was exceptional,” says Joyce Tracksler, a high school friend who is now a mystery writer in Kittery Point, Me.
His parents were exceptional, too. His father, Albert, was a diplomat, and young Chris lived in Germany a few years as a child. The family later moved to the Washington suburbs before settling in Greenwich. His father became an executive at the Institute of International Education and at the College Entrance Examination Board in New York. During the Kennedy administration, he helped start the Peace Corps.
Because of his father’s College Board connections, Mr. Sims got hold of an old SAT exam, which he and Mr. Willoughby used to conduct a statistical analysis. They found that on multiple-choice questions in English and social studies, the “longer answers tended to be correct.” In math, they determined that the number that was “closest to all of the other numerical choices” was probably the right one. Mr. Willoughby says Mr. Sims got perfect scores on SATs, and his teacher assumed that the young man would later “do something involving math, statistics and probability.”
Good Morning. You're Nobel Laureates by Jeff Sommer | December 3, 2011
Wednesday, November 23, 2011
reading kcab and the SAT
re: answering SAT reading questions without reading the passage
kcab has just provided a terrific example of real-world multiple-choice.
On the original thread, where people were offering their answers to the 1983 SAT question, "The author’s attitude toward children appears to be one of," kcab wrote:
E?
kcab picks E?
I have no idea why I was surprised that kcab picked E. I don't 'know' kcab; we've never emailed off-list, and because I've been somewhat AWOL reading comments for a while now, my conscious perception is that I haven't read enough of kcab's comments to have formed an 'image' of kcab.
Nevertheless, I was surprised. I was surprised, and I felt slightly.... uncertain. I wasn't sure I understood.
My second reaction, which occurred seconds later, was: It's a joke.
"LOL"..."What the heck"...
Funny!
Tonight I find kcab's followup:
And there you have it. A satisfying case of multiple choice in real life: a distinctly SAT-like case in which two conflicting choices both strike you as being possible, and only the author (kcab, in this case) knows for sure.
That is what reading is all about.
At least, I think that's what reading is all about. I've spent essentially zero time reading about reading, so I don't know what reading scientists think reading is all about. I may see things differently once I do.
For now, my sense is that texts often present us with more than one possible interpretation -- and that in deciding which interpretation fits best, readers likely use cues I haven't thought about since graduate school. That is to say, readers don't just read the literal meaning of the text; readers also perceive or construct an 'author' -- an implied author -- who is part of the text but not the text, or not the whole text:
There are other possibilities as well.
kcab has just provided a terrific example of real-world multiple-choice.
On the original thread, where people were offering their answers to the 1983 SAT question, "The author’s attitude toward children appears to be one of," kcab wrote:
LOL, what the heck, I pick E.Seeing this, my immediate reaction was: Really?
E?
kcab picks E?
I have no idea why I was surprised that kcab picked E. I don't 'know' kcab; we've never emailed off-list, and because I've been somewhat AWOL reading comments for a while now, my conscious perception is that I haven't read enough of kcab's comments to have formed an 'image' of kcab.
Nevertheless, I was surprised. I was surprised, and I felt slightly.... uncertain. I wasn't sure I understood.
My second reaction, which occurred seconds later, was: It's a joke.
"LOL"..."What the heck"...
Funny!
Tonight I find kcab's followup:
While I'm commenting, I'm feeling defensive about the answer I gave to the earlier post. I saw that post as a game, one that wasn't quite right. Since I could see that everyone else had picked A, I thought I'd pick anything other than A in the interest of answer diversity. Probably just as well for me that I've never had information about other students' answers on tests.I was tickled to see this because I wasn't sure I picked the right answer. Was kcab joking or not? I had made my bet and bubbled my bubble; now I wanted to know.
And there you have it. A satisfying case of multiple choice in real life: a distinctly SAT-like case in which two conflicting choices both strike you as being possible, and only the author (kcab, in this case) knows for sure.
That is what reading is all about.
At least, I think that's what reading is all about. I've spent essentially zero time reading about reading, so I don't know what reading scientists think reading is all about. I may see things differently once I do.
For now, my sense is that texts often present us with more than one possible interpretation -- and that in deciding which interpretation fits best, readers likely use cues I haven't thought about since graduate school. That is to say, readers don't just read the literal meaning of the text; readers also perceive or construct an 'author' -- an implied author -- who is part of the text but not the text, or not the whole text:
"[I]t is a curious fact that we have no terms either for this created 'second self' or our relationship with him. None of our terms for various aspects of the narrator is quite accurate. 'Persona,' 'mask,' and 'narrator' are sometimes used, but they more commonly refer to the speaker in the work who is after all only one of the elements created by the implied author and who may be separated from him by large ironies. 'Narrator' is usually taken to mean the 'I' of the work, but the 'I' is seldom if ever identical with the implied image of the artist."I don't know what made me read kcab correctly (or incorrectly), but it strikes me that it may have to do with this second self.
(Wayne Booth, The Rhetoric of Fiction. Univ. of Chicago Press, 1961) - quoted by Richard Nordquis
There are other possibilities as well.
Monday, November 21, 2011
SAT reading question for all you ktm brainiacs
The author’s attitude toward children appears to be one of:What's the answer?
(A) concern for the development of their moral integrity
(B) idealization of their inexperience and vulnerability
(C) contempt for their inability to accept unpleasant facts
(D) exaggerated sympathy for their problems in daily life
(E) envy of their willingness to learn about morality
Sunday, November 20, 2011
bubble this, part 2
wow
I just checked my October SAT scores and discovered that, as Debbie predicted, I apparently failed to answer an entire chunk of questions without knowing it:
Moreover, as Debbie also predicted, the questions I didn't answer were (C. says) on the 2nd Writing Section, which is the last section of the entire 11-Section test.*
Debbie really has become the expert on the actual, real-world SAT: what it's like to study for it, what it's like to take it, and even what your score means before the College Board tells you what your score means. (I didn't believe her! Every time the subject of my Writing score came up, Debbie would say: "Section 10. You didn't answer all the questions." I thought that was nuts! Of course I answered all the questions! I obsessively checked and double-checked to make sure I answered all the questions! Wrong.)
For the record: omitting four questions while checking and double-checking to make sure you haven't omitted any questions is not a "careless" error.
Omitting four questions while checking and double-checking to make sure you haven't omitted any questions is a maxed-out biology error. Omitting 4 questions in the final section of the test is the same phenomenon as a runnerlosing her stride at the end of a real marathon going out way too fast from the gate and falling apart at the end of a real marathon, which Ed says happened to the front-runner in the women's field this year.
By the way, in the run-up to the test, it occurred to me that I needed to start running again. I'm thinking aerobic conditioning would have to help. But I didn't do it.
For parents whose kids will be taking the SAT soon, the bubbling issue is major: it's the reason kids need effective test prep. The SAT is too long and has too many problems jammed into too little time and space** to be considered a test of content knowledge. The SAT tests test prep as well as content knowledge.
High school students need effective test prep for the same reason runners need effective coaching: they need to learn strategy and pacing, especially on the math sections.
I'm a 10
May 4, 2010: mandatory bubbling session
March 8, 2011: bubble this
April 13, 2011: progress report, part 2
May 7, 2011: the return of bubbling errors
* 10 sections that count towards your score plus 1 experimental section that does not count
** Too little space: test font size is too small, white space is too small, desktops in testing centers are too small... I may have left something out.
I just checked my October SAT scores and discovered that, as Debbie predicted, I apparently failed to answer an entire chunk of questions without knowing it:
Moreover, as Debbie also predicted, the questions I didn't answer were (C. says) on the 2nd Writing Section, which is the last section of the entire 11-Section test.*
Debbie really has become the expert on the actual, real-world SAT: what it's like to study for it, what it's like to take it, and even what your score means before the College Board tells you what your score means. (I didn't believe her! Every time the subject of my Writing score came up, Debbie would say: "Section 10. You didn't answer all the questions." I thought that was nuts! Of course I answered all the questions! I obsessively checked and double-checked to make sure I answered all the questions! Wrong.)
For the record: omitting four questions while checking and double-checking to make sure you haven't omitted any questions is not a "careless" error.
Omitting four questions while checking and double-checking to make sure you haven't omitted any questions is a maxed-out biology error. Omitting 4 questions in the final section of the test is the same phenomenon as a runner
By the way, in the run-up to the test, it occurred to me that I needed to start running again. I'm thinking aerobic conditioning would have to help. But I didn't do it.
For parents whose kids will be taking the SAT soon, the bubbling issue is major: it's the reason kids need effective test prep. The SAT is too long and has too many problems jammed into too little time and space** to be considered a test of content knowledge. The SAT tests test prep as well as content knowledge.
High school students need effective test prep for the same reason runners need effective coaching: they need to learn strategy and pacing, especially on the math sections.
I'm a 10
May 4, 2010: mandatory bubbling session
March 8, 2011: bubble this
April 13, 2011: progress report, part 2
May 7, 2011: the return of bubbling errors
* 10 sections that count towards your score plus 1 experimental section that does not count
Friday, November 11, 2011
anonymous on lefties taking the SAT
Good advice:
I believe that the "transmission mechanism" from right-hand desks for left-hand test-takers to reduced performance is working memory blowout.
And see: death by calculator. Death by calculator is a case of working memory blowout.
(The real-world term for working memory blowout problems is cognitive load theory.)
Lefties should be particularly vigilant about the chairs/desks. I've heard stories about them having to take long tests on right-handed flip-up deskettes; a true nightmare. I know the registration forms for my grad comps asked lefties to identify themselves, because almost all of the seats in the auditorium had right-hand deskettes. They brought in as many extra lefty ones as they needed. Is there a similar question on SAT registrations?I have got to find time to write a quick post on working memory.
I believe that the "transmission mechanism" from right-hand desks for left-hand test-takers to reduced performance is working memory blowout.
And see: death by calculator. Death by calculator is a case of working memory blowout.
(The real-world term for working memory blowout problems is cognitive load theory.)
Tuesday, November 1, 2011
math professor's experience coaching the SAT
The Effectiveness of SAT Coaching on Math SAT Scores
(pdf file) by Jack Kaplan
Chance Magazine | Volume 18, Number 2, 2005
Comment: Jack Kaplan's "A New Study of SAT Coaching"" (pdf file)
By Derek C. Briggs
Here's the Fairtest write-up of Kaplan's coaching results:
(pdf file) by Jack Kaplan
Chance Magazine | Volume 18, Number 2, 2005
Comment: Jack Kaplan's "A New Study of SAT Coaching"" (pdf file)
By Derek C. Briggs
Here's the Fairtest write-up of Kaplan's coaching results:
Kaplan's course includes 20 hours of classroom instruction and seven to 12 hours of individual tutoring. Of the 34 previously uncoached students he worked with over six summers, 21 increased their Math scores by more than 80 points from a baseline SAT administration with 11 going up by 100 points or more. Average score increases were higher for students with lower initial scores. In a control group Kaplan studied, average scores increased by only 15 points during the same period. Thus, he concludes that "the estimated coaching effect was 63 points" on the Math component of the SAT.Kaplan was coaching the SAT math test being given prior to the 2006 changes.
the writing test and the math test
Chemprof (and others, I'm sure) pointed out in Comments that math/science professors value the SAT math test for the same reason I value the SAT writing test: both exams test standard mistakes that college students make.
Btw -- this is something I haven't gotten around to putting inside a post -- when I mention "the main errors student writers make," I'm referring to the Connor and Lunsford list of errors compiled in 1988, which is pretty close to the SAT list.
The Connor-Lunsford list is close to the SAT list except for the fact that Connor and Lunsford did not see ginormous numbers of parallel structure problems in the student papers they read, apparently. I find that hard to fathom. I personally do see ginormous numbers of non-parallel structures in the student writing that comes my way.
Faulty comparison, tested on the SAT, does not make the Connor-Lunsford list, either. (I'm not surprised by that.)
In any event, while musing about chemprof's observation (which I agree with, btw), an essential difference between the two tests, one that I hadn't focused on, suddenly leapt out at me: where SAT Math tests content and procedures students have been seeing in school for years,* SAT Writing tests content students have never seen or even heard tell of unless their Spanish teacher happened to explain what a gerund is in Spanish class.
(I use that example because I asked C. this week whether he knew what a gerund was, and he said he did because he'd learned it in Spanish. I myself had no idea what a gerund was until this semester. Public schools don't teach formal grammar today and haven't taught formal grammar in decades.)
So....when you think about it....isn't the Writing Test a bit of an odd concept?
Students have never been taught grammar, and now they're being tested on grammar?
And why would I be in favor of testing students on content the schools don't teach?
Now I'm thinking: well, maybe I'm not!
Mulling over chemprof's comment, I realize that what I value about the writing test is almost exclusively the test prep kids do for the writing test. The fact of the writing test, the fact that that the writing test exists and students have to take it, gives parents an excuse to insist their kids learn some formal grammar before they graduate high school.
And that's pretty much it; that's what I value about the test.
So, since high scores on writing come entirely from test prep (at least in my experience), what does a high score on the writing test actually mean? Does a high score on the writing section tell us anything about the student's writing?
I don't know the answer to that, and I don't have a good guess.
Basically, I think it's a good thing for a student to recognize a comma splice in an SAT sentence regardless of whether he recognizes a comma splice in his own writing, and effective SAT prep can make that happen. This is a statement of value: I value knowledge of comma splices, and I want my kid to possess it.
* Most of the content anyway. That's a subject for another post: these days the SAT now features counting problems, and students taking traditional algebra classes don't seem to have counting "units" in their courses (although chapters on counting units are included in traditional texts). Ditto for the algebra 2 material on the SAT if a student has not taken algebra 2.
Btw -- this is something I haven't gotten around to putting inside a post -- when I mention "the main errors student writers make," I'm referring to the Connor and Lunsford list of errors compiled in 1988, which is pretty close to the SAT list.
The Connor-Lunsford list is close to the SAT list except for the fact that Connor and Lunsford did not see ginormous numbers of parallel structure problems in the student papers they read, apparently. I find that hard to fathom. I personally do see ginormous numbers of non-parallel structures in the student writing that comes my way.
Faulty comparison, tested on the SAT, does not make the Connor-Lunsford list, either. (I'm not surprised by that.)
In any event, while musing about chemprof's observation (which I agree with, btw), an essential difference between the two tests, one that I hadn't focused on, suddenly leapt out at me: where SAT Math tests content and procedures students have been seeing in school for years,* SAT Writing tests content students have never seen or even heard tell of unless their Spanish teacher happened to explain what a gerund is in Spanish class.
(I use that example because I asked C. this week whether he knew what a gerund was, and he said he did because he'd learned it in Spanish. I myself had no idea what a gerund was until this semester. Public schools don't teach formal grammar today and haven't taught formal grammar in decades.)
So....when you think about it....isn't the Writing Test a bit of an odd concept?
Students have never been taught grammar, and now they're being tested on grammar?
And why would I be in favor of testing students on content the schools don't teach?
Now I'm thinking: well, maybe I'm not!
Mulling over chemprof's comment, I realize that what I value about the writing test is almost exclusively the test prep kids do for the writing test. The fact of the writing test, the fact that that the writing test exists and students have to take it, gives parents an excuse to insist their kids learn some formal grammar before they graduate high school.
And that's pretty much it; that's what I value about the test.
So, since high scores on writing come entirely from test prep (at least in my experience), what does a high score on the writing test actually mean? Does a high score on the writing section tell us anything about the student's writing?
I don't know the answer to that, and I don't have a good guess.
Basically, I think it's a good thing for a student to recognize a comma splice in an SAT sentence regardless of whether he recognizes a comma splice in his own writing, and effective SAT prep can make that happen. This is a statement of value: I value knowledge of comma splices, and I want my kid to possess it.
* Most of the content anyway. That's a subject for another post: these days the SAT now features counting problems, and students taking traditional algebra classes don't seem to have counting "units" in their courses (although chapters on counting units are included in traditional texts). Ditto for the algebra 2 material on the SAT if a student has not taken algebra 2.
Sunday, October 30, 2011
Susan S on her son's experience with competition math
re: the question of whether middle school competition math prepares students for ACT math:
C. and I both learned a tremendous amount prepping for SAT math. We learned a tremendous amount about algebra 1, geometry, and arithmetic, and we learned a tremendous amount about what we didn't know we didn't know.
I only have an anecdotal story concerning math contests and the ACT. When my son was taking the ACT in middle school at the beginning of the year, I hired a genius kid to tutor him on some of the things he had never experienced, like algebra 2 and some trig stuff. The tutor thought he would break 30, but he actually was in the middle 20s. Still not bad for a 13 yr. old.If I had it to do over again, I would have had C. doing middle school competition math problems from the get-go -- and not just because SAT math is so closely related to middle school competition math.
As the year went on he made the Mathcounts team and had to practice the problems every week for a few months. He usually only finished half of them since we couldn't really help him. I signed him up for the actual Midwest Talent Search at the end of the year, but I didn't prep him this time or hire a tutor. His math score jumped to a 29 which placed him in the 99th percentile of the MTS, or Midwest Talent Search, kids and earned him a high scorer medal from Northwestern.
I have no idea if that means anything, but I thought it was interesting. He was only in accelerated algebra 1 at the time. Competition math just may help out in some way. It was the only thing I could think of at the time to explain the jump in scores.
C. and I both learned a tremendous amount prepping for SAT math. We learned a tremendous amount about algebra 1, geometry, and arithmetic, and we learned a tremendous amount about what we didn't know we didn't know.
puzzle math - from the comments
in an earlier Comments thread about SAT Math, gasstationwithoutpumps writes:
My son did no prep for the SAT when he took it in 6th grade and got a 720 on the math part. I'm quite sure that he'll do better on it when he takes it as high schooler next year without doing any SAT prep. The math questions just aren't all that hard.to which SteveH responds:
He had all of the material on the SAT by 6th grade? You are using this as normal?gswp's reply:
No, he had not had all the SAT math. He'd had a very feeble algebra series in school (The Key to Algebra) and had self-taught geometry from a good book (he'd gotten through about half of Art of Problem Solving Geometry). The SAT supposedly tests much more than he had had at that point, but the questions are more like simple puzzles than testing content knowledge.Gswp is exactly right! Setting aside the issue of the SAT using core features of cognitive function to produce error, which it does, SAT math is middle school puzzle math.
Saturday, October 29, 2011
an SAT math tutor on seeing the 'trick'
A friend forwarded me an email from a parent whose high school age child rapidly sussed out SAT math and scored somewhere in the neighborhood of 800 with minimal test prep. The dad said his child has what he sees as a kind of "insight." After reading through some SAT math tests, the child could instantly see the 'trick' involved in the questions (trick used in the nonpejorative sense of the word). The dad said, too, that he believes this form of insight isn't necessarily present in students earning physics degrees from Columbia.
An SAT math tutor I know agreed and, when I asked why, wrote this response and gave me permission to post:
An SAT math tutor I know agreed and, when I asked why, wrote this response and gave me permission to post:
I've interviewed LOTS of math/physics/computer science majors from NYU and Columbia for potential teaching gigs who couldn't make sense of relatively simple SAT problems. Almost universally, the issue is that they WAY overcomplicate things.Steve H mentioned Richard Feynman's hobby practicing "divergent thinking" problems. I think that's probably what this dad (and this tutor) are talking about.
Sunday, October 23, 2011
summer boarding school and SAT prep
I talked to some friends I hadn't seen in awhile last night. They told me that over the summer they sent one of their kids to a summer boarding program where he prepared for the SAT.
His mom said he gained 60 points on reading, 90 points on writing, and 180 points on math.
I'm pretty sure this is the program: Wolfeboro The Summer Boarding School.
His mom said he gained 60 points on reading, 90 points on writing, and 180 points on math.
I'm pretty sure this is the program: Wolfeboro The Summer Boarding School.
Steve H on SAT math and math prep
from the comments:
SAT math tries to trick students. You could say that the tricks relate directly to whether or not they really understand math. However, when you add in the time constraints, it really relates to preparation. Is preparation the same as mastery? Yes. Mastery of the test. Is this equivalent to mastery of math or whether you will do well in college math? Not necessarily. There are better ways of determining that than with the limited material included on the SAT. Why not just require students to take the Achievement Test? Look at the AP Calculus grade.and:
What is it about SAT-Math that is so important? They are trying to test something other than just math knowledge. They think that these tricky questions reflect on how well you think on your feet, but what it really does is test preparation and whether you have seen these questions before. The questions don't reflect on whether you have a wide body of knowledge and skills in math.
They create problems where you have to "see" the shortcut. You get problems with hidden 3-4-5 triangles. Add a time constraint and then what do you call those problems? It's not just about math knowledge and skills. The problem has to do with trying to determine the difference between aptitude and preparation. The tricks may have some basis in meaningful math, but that's not what they are trying to test.
It reminds me of questions companies like to ask at job interviews, like "Why is a manhole cover round", and "How many golf courses are there in the US.?" Preparation can make you look like you have a great aptitude. Preparation is directly related to math knowledge, and that is important, but identifying aptitude is an arms race for something like the SAT. That's causing the tricky problems, not any desire to test a breadth and depth of math knowledge.
In Dick Feynman's books, he talks about how he spent a lot of time in high school learning about all sorts of trick, lateral thinking problems. He would challenge people to ask him questions. There is nothing like preparation to make you look like a genius, although he really didn't need help with that. It really annoyed some of his colleagues.
My son will get to calculus in his junior year and he always gets A's. He still has to prepare for SAT-Math. He can't let others, with specific SAT-Math preparation, seem like they have a better aptitude than him.
They try to trick students in most questions....What bothers me the most are the shortcut problems where using standard math techniques cause you to take too much time. This is supposed to identify aptitude, but it really tests preparation for the test.
There are also the problems where using a brute force or direct counting technique works better than any applied math technique. In some cases, there is no math to apply. One question on a sample PSAT test asked for the number of positive integers less than 1000 which don't have a '7' as one of the digits. (notice - "don't have" and positive integer) This simply checks how well you work under time pressure. Nobody expects you to apply any fancy math to this problem. One of the answers was the "have" solution. This tests preparation and practice, not aptitude or math ability. There may be a correlation between the test and aptitude or math ability, but not to the resolution colleges use it to select students. At the top levels, it correlates to preparation. That's not necessarily a bad thing, but there are better ways of figuring that out.
rat psych - what to do about SAT math (part 3)
Your typical high school student, I presume, has spent several years setting up equations and solving for x. At least, let's hope so. I certainly did.
The SAT uses this fact to elicit many wrong answers from test-takers who have worked a problem correctly. The student gets the solution right but the answer wrong because the answer isn't x. The answer is 3x, say, or xy. I seem to recall a problem or two where the answer was -x, for god's sake, but I might be making that up.
Other times the test will give you a value for x + y, say, and you're supposed to see that you should simply insert that value some place else in the problem, et voilĂ : the answer they're looking for pops up.
Here's a typical problem, medium difficulty (according to the College Board):
For what it's worth, I think using x + y as the value, instead of x or y alone, is an interesting and instructive way to write a problem. (I'm curious what math people think). It seems to me that writing problems in which x + y is the salient unit may be a way of teaching what Ron Aharoni calls the fifth fundamental operation of arithmetic:
Still, there is no doubt in my mind that these questions elicit wrong answers from test takers who know the math involved, can do the math involved, and have a reasonable understanding of the math involved. Students who have spent years of their lives solving for x aren't going to break the Solve for x habit for the first time ever when they're working at breakneck speed and their eyes are bleeding from the Ella Baker passage.
Which brings me back to extinction learning. Test prep for SAT math involves spending a fair amount of time building new habits that conflict with ingrained old habits. You've been conditioned to solve for x; now you have to condition yourself not to solve for x. Also, you have to build as much speed as possible at not solving for x because you are never going to forget solve-for-x. The two impulses are inside your head, competing with each other, and the competition takes time (and probably eats up some precious working memory resources to boot).
Funny thing: during the time we spent doing SAT math prep around here, I overlearned don't solve for x to the degree that a couple of weeks before taking the real test I came across a practice problem that did ask the test-taker to solve for x. I was so surprised that I wasted several seconds reading and re-reading and re-reading again to make sure I hadn't misunderstood. You can't win.
For parents: your child needs to spend enough time not solving for x that he or she gets to be really, really fast at not solving for x.
Then he should be on the lookout for problems that say Solve for -x.
I'm a 10
rat psych: what to do about SAT math (part 1)
rat psych: what to do about SAT math (part 2)
rat psych: what to do about SAT math (part 3)
rat psych: careless reading errors on the SAT
The SAT uses this fact to elicit many wrong answers from test-takers who have worked a problem correctly. The student gets the solution right but the answer wrong because the answer isn't x. The answer is 3x, say, or xy. I seem to recall a problem or two where the answer was -x, for god's sake, but I might be making that up.
Other times the test will give you a value for x + y, say, and you're supposed to see that you should simply insert that value some place else in the problem, et voilĂ : the answer they're looking for pops up.
Here's a typical problem, medium difficulty (according to the College Board):
If 4(x + y)(x - y) = 40 and (x - y) = 20, what is the value of x + y?A kid who's had no test prep at all will likely miss this question -- either miss it outright or take too much time spotting the solution, thus leaving him too little time to finish the test and increasing the likelihood he'll make "careless errors" on the questions he does get to because now he's working too fast trying to make up for the time he lost on the x + y problem.
For what it's worth, I think using x + y as the value, instead of x or y alone, is an interesting and instructive way to write a problem. (I'm curious what math people think). It seems to me that writing problems in which x + y is the salient unit may be a way of teaching what Ron Aharoni calls the fifth fundamental operation of arithmetic:
In addition to the four classical operations, there is a fifth one that is even more fundamental and important. That is, forming a unit, taking a part of the world and declaring it to be the “whole.” This operation is at the base of much of the mathematics of elementary school. First of all, in counting, when you have another such unit you say you have “two,” and so on. The operation of multiplication is based on taking a set, declaring that this is the unit, and repeating it. The concept of a fraction starts from having a whole, from which parts are taken. The decimal system is based on gathering tens of objects into one unit called a “10,” then recursively repeating it.Maybe I'm wrong, but it seems to me that the x+y questions test math as opposed to obedience under pressure, which is what the Find xy questions test.
The forming of a unit, and the assigning of a name to it, is something that has to be learned and stressed explicitly. I met children who, in fifth grade, knew how to find a quarter of a class of 20, but had difficulty understanding how to find “three-quarters” of the class, having missed the stage of the corresponding process of repeating a unit in multiplication. What I Learned in Elementary School by Ron Aharoni
Still, there is no doubt in my mind that these questions elicit wrong answers from test takers who know the math involved, can do the math involved, and have a reasonable understanding of the math involved. Students who have spent years of their lives solving for x aren't going to break the Solve for x habit for the first time ever when they're working at breakneck speed and their eyes are bleeding from the Ella Baker passage.
Which brings me back to extinction learning. Test prep for SAT math involves spending a fair amount of time building new habits that conflict with ingrained old habits. You've been conditioned to solve for x; now you have to condition yourself not to solve for x. Also, you have to build as much speed as possible at not solving for x because you are never going to forget solve-for-x. The two impulses are inside your head, competing with each other, and the competition takes time (and probably eats up some precious working memory resources to boot).
Funny thing: during the time we spent doing SAT math prep around here, I overlearned don't solve for x to the degree that a couple of weeks before taking the real test I came across a practice problem that did ask the test-taker to solve for x. I was so surprised that I wasted several seconds reading and re-reading and re-reading again to make sure I hadn't misunderstood. You can't win.
For parents: your child needs to spend enough time not solving for x that he or she gets to be really, really fast at not solving for x.
Then he should be on the lookout for problems that say Solve for -x.
I'm a 10
rat psych: what to do about SAT math (part 1)
rat psych: what to do about SAT math (part 2)
rat psych: what to do about SAT math (part 3)
rat psych: careless reading errors on the SAT
Thursday, October 20, 2011
I'm a 10
I probably used too many semicolons.
update: I left out the last 4 grammar questions. Probably failed to transfer my answers from the test booklet to the bubble sheet.
I'm a 10
rat psych: what to do about SAT math (part 1)
rat psych: what to do about SAT math (part 2)
rat psych: what to do about SAT math (part 3)
rat psych: careless reading errors on the SAT
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