Something interesting about this is that according to the research, black students are disfavored on the easier questions, but do fine, or better than white students, on the hard questions. The explanation for that sounded reasonable -- easy questions measure fluency in shared culture, and white students are probably culturally closer to SAT test writers than black students are, while hard questions measure what you've learned in school.
What that left me wondering: doesn't the GRE, these days, feed you different questions depending on how you do on the easy questions to begin with? If you miss early questions, it never gives you the really hard questions, and your score can't be very high? That seems like a real problem if this sort of effect is in operation.
I would bet that the test results show Asian:European results of at least equal magnitude to European:Black.
When states are no longer funding universities generously, so the Universities will not especially need to care about voter sensibilities, but only about alumni donations, will this kind of thing still happen?
http://www.msnbc.msn.com/id/30393117/
Maybe. I expect that there exists detailed demographic assessment of alumni donors, and that this information is very tightly guarded.
Is peer review supposed to be the reason for the high cost of journals? That seems unlikely, since reviewers aren't paid.
What that left me wondering: doesn't the GRE, these days, feed you different questions depending on how you do on the easy questions to begin with? If you miss early questions, it never gives you the really hard questions, and your score can't be very high?
This is why my GRE verbal score is the lowest standardized test result I ever got, since I wasn't paying attention to the directions and chose the word closest to being a synonym instead of an antonym on the first 3 questions, or something like that, and then it proceeded to ask me the dumbest questions imaginable for a long time before deciding I might know something after all. Not sure to what extent these questions tested shared culture, though.
2:I would bet that the test results show Asian:European results of at least equal magnitude to European:Black.
Actually, if the mechanism is what's postulated in the story, I'd expect to see European:Asian results in the same direction as European:Black results -- Asian kids doing worse than their grades would predict on the easy questions, and better on the hard questions.
Anecdotally, [and I've mentioned this here before], when I marked admissions papers here, it was usually second language speakers of English who answered the more difficult, abstract questions in which they were asked to define words correctly. Which would be a similar effect, I presume.
5: Yeah, that kind of story freaks me out -- it seems to make the GRE much more vulnerable to chance factors. I can't see what the advantage is that outweighs the potential for unfairness like that.
Admissions committees for US universities (at least the publicly funded ones) discount asian standardized test results, because otherwise there are too many asians accepted. I don't have an explanation, and many are possible, but this is a fact.
I don't know if the linked study's authors aggregated asian kids to get at the point raised in 1. There is also the possibility that kids with equal problem-solving ability are encouraged to do well in school differently by their families and their peers, so that equal-GPA kids are not equivalent populations across cultures.
9: Yeah, that seems to be clearly true, and clearly a tricky justice problem; one that's been around since the same thing was happening to Jews.
On a tangent: parenting advice involves a whole lot of assuming that kids need to take responsibility for their own academic performance, and that parental nagging/overcontrolling is counterproductive. To stereotype madly, but not, I think, unfairly, doesn't the tendency of Asian kids to perform well in school, combined with the stereotypical highly-academically-pressured Asian upbringing, suggest that the standard parenting advice is kind of bullshit?
doesn't the GRE, these days, feed you different questions depending on how you do on the easy questions to begin with?
You can tell when it's doing this, which is incredibly worry-making while you're taking the thing.
I took the GRE in the last year of its being routinely offered on paper, but they encouraged you to take it on computer. I did so on the first try, and got an abysmal (for me) verbal score. My score went up close to twenty percentile points when I took it on paper.
Another remark about 6: Test-taking is a game. The tricks that Kaplan teaches are pretty simple. Kids who are told to work hard to do their absolute best on tests figure out how to adopt the mindset of the exam writer and grader, or at least try to do so.
Kids who don't think much about tests are at a disadvantage, since tests are a pretty freaky environment for problem-solving.
10. Not obvious BS if you include suicide as a possible outcome
China is the only country in the world where more women than men commit suicide. No magic answer for how much to nag your kid, I think.
To ETS, an SAT question is ideal if it produces a normal distribution of correct answers. (I take this to mean that a sampling of students perform the same on the given question as on the test as a whole.)
This is not the same as producing a question which evaluates whether or not a student is prepared for college. ETS is a total giant racket, and they have made buckets of money off of escalating standardized testing from NCLB. They definitely had a hand in the legislation, as well.
11.last: Me too on the surprisingly poor verbal score. I should have tried to get a paper test, but I didn't think to do it.
To stereotype madly, but not, I think, unfairly, doesn't the tendency of Asian kids to perform well in school, combined with the stereotypical highly-academically-pressured Asian upbringing, suggest that the standard parenting advice is kind of bullshit?
Depends whether the advice is aimed at getting good academic results or, say, a well adjusted young adult. A (non-Asian) friend killed himself in large part because of the intense pressure he felt from his parents - I think they could have done with some of that advice, frankly.
Does 9.1 mean Asians, or Asian-Americans?
At the graduate level there's a real issue with subject-test GREs, where people from China do unreasonably well. I've been told that it's because people compile books of all the previously-asked questions, and there are some sort of camps or summer schools where they memorize all the answers. Frequently the same questions are re-used several years later, or nearly-identical questions are used. Also the letters of recommendation are almost always written by the students themselves. I've been told the only semi-reliable way to decide who to admit is to have someone who personally knows the faculty in China call them and discuss the students.
I wonder if they've done research on how the computer test changes score distributions. Taking three anecdotes as data, the computer test seems to hurt our kind of people -- I wonder who it helps.
16.1: I read it as Asian-Americans.
parenting advice involves a whole lot of assuming that kids need to take responsibility for their own academic performance, and that parental nagging/overcontrolling is counterproductive.
My mom nagged me about homework a lot, and I'd fight her instead of the assignment, and procrastinate to show her that I'd do it on my own schedule.
I'm not exaggerating: it was a huge relief when I went to college and could start assignments early, without feeling like I was losing some battle of principle to my mom.
I wonder if they've done research on how the computer test changes score distributions.
When the computer testing came out, they certainly claimed it had been thoroughly vetted and produced more stable results than paper testing.
I took the GRE on the computer when it was still available on paper and pencil, but it didn't seem to hurt my scores. However, I don't do as well on these tests as the typical Unfogged commenter.
how the computer test changes score distributions
I wanted to know this! There was a lot of encouragement from the GRE people to take the computer version, saying that scores for the same person were "on average" very similar between the paper and computer tests. Argh!
The only way to test 13 for any one question is to give it to very many kids. Does ETS salt test questions into production exams, or do they have test environments? I suspect that thoroughly vetted means verifying that they can stop paying offset press operators and ScanTron.
16. Asian-americans is in the papers, and I know informally about non-US asians from my grad school physics department. High-testing asians are not just Chinese; Koreans told me that cheating there was not common. Xifeng, Hanbin, and Guodi did not need to cheat because they were brilliant. Grad students admitted from China as I was leaving did not seem to be as strong, but small numbers so who knows. None of the Chinese guys my age or older from my U are currently academics.
However, I don't do as well on these tests as the typical Unfogged commenter.
That's what I'm sort of wondering about -- there seems, anecdotally, to be a 'freak testtaker' trait that's overrepresented around here. People who, while generally bright, do even better on standardized tests than their general cleverness would suggest. I wonder if the computer/paper difference somehow cancels that out.
I think when you're taking the exams, one of the sections is a test section, you just don't know which one.
re: 24
Yes, and also people who've been pushed [or chosen] to participate in competitive test taking type events.
I'm very good at essay-based exams. I can produce extremely polished well-argued prose, very quickly, and regurgitate a lot of material from memory. But IQ type tests, or various standard aptitude type tests, I suspect a lot of the 'test freaks' represented here would kick my ass, handily.
I was listening to the radio profile a well-regarded preschool in a poor area with a predominantly Black population. One of the things that they were touting as a great thing that the kids were accomplishing was memorizing the names of all the Presidents. This was considered representative of the type of learning that was most beneficial to building good study habits and thinking patterns later in life.
Meanwhile - and this may assuredly be a case of White privilege - if I found out that my son's White, middle-class preschool was teaching him via that type of rote memorization, I would be very pissed off indeed. Its far more important to me that his education be focused on critical thinking, problem solving, and social development, than on memorizing facts.
Which goes to show, to draw a broad stereotype, that Black communities and White communities have very different notions of what types of education will best serve their offspring later in life. And if that's true, than why wouldn't these differences be reflected on standardized tests?
24. 26: I'm very good at SAT/GRE type tests -- especially compared to my general mediocrity as a student and human being. However, I'm awful at the kind of IQ tests that ask about shapes -- is that called "spatial reasoning"?
25: I was quite cheesed that my extra test was a math one. I would have been a much happier camper taking an extra verbal test.
I think 12/15/20 collectively answer 10. My understanding of the advice has always been that general "nagging" and attempts to be overcontrolling can be counterproductive (and, to the extent you've got a well-adjusted, independent child, are likely to be counterproductive, since no one likes to feel nagged/controlled). It's often possible, however, to boost academic performance with more extreme parental emphasis on academic performance, such that the child's self-worth becomes closely tied to academic performance, but this is going to cut against well-adjustedness and likely diminish the child's overall welfare.
Given that test-freakdom exists, isn't a test that attenuates its effect superior? And, anecdotally, other test freaks I've known have invariably been from UMC/literate backgrounds, so this may be a manifestation of rather than a complement to the OP's Cracker Effect.
31: We could refer to it as the Fancy Cracker Effect.
a 'freak testtaker' trait that's overrepresented around here
I'm one of those. I suspect there's a tight correlation with having been tested a lot as a very young child. As noted above, test taking is a game and one of the best advantages you can have in that game is simply not feeling anxious about playing it.
I'm glad you all are talking about this, but bummed that I can't join in more. I hoped that somebody would be able to explain the study, maybe with some examples. I really don't understand the authors' claims. What is an "easy" question compared to a "difficult" one? It's hard to assess their thesis without seeing a host of examples.
That's why I went looking for the full study. Apparently you can only read it if you are an HER subscriber, or if you are willing to pay $10. In my decade-plus of grousing about the high cost of academic journals for non-academics, people have routinely justified the cost as "Well, peer review is expensive to coordinate, so they have to cost more."
If the journal isn't even peer-reviewed, where on earth is all that money going? The paper gets submitted, the editor decides to publish it or not, somebody has to proofread/lay it out, and it gets printed. How much can we possibly be talking about in terms of production cost?
Nobody trusts me with tests. Harumph.
31: I'm a test freak. (And one who loved the computer test, even. Hooray! I get my scores immediately!) But definitely not UMC or the bookish poor.
I'm closer to bookish poor than puckish boor but I did great on the standardized tests early in life. But as soon as I started reading about how they were created, instead of springing fully fledged from the head of Sophia, I started resenting the whole experience.
"Well, peer review is expensive to coordinate, so they have to cost more."
I essentially did this for a fancy-pants journal. It was neither expensive nor complicated to coordinate. (Who should this go to? Yeah, Professor X. How 'bout Y for the second reader? Sure.) These days you don't even need to pay for stamps on envelopes.
I was always the top test scorer in pretty much everything at school, so in that sense, a moderate freak. But some of the people here have talked about scoring highly in national competitive type maths tests, and the like, which is a very different thing from, "I could join Mensa if I didn't think people who join Mensa were dicks" level test scoring.
What is an "easy" question compared to a "difficult" one?
This is strictly a function of percentage of test-takers who get the question correct.
Maybe that's not what you were asking.
The GRE computer test was fine for me -- at the very least, it saved me the stress of worrying whether I was filling in bubbles correctly.
I'm a very good taker of standardized tests, like many people here, and my recent experience with the LSAT really just highlighted once again what utterly strange things these tests are. I imagine the same test measures different things for people of different backgrounds -- how hard they're willing to study or how much they're willing to pay for prep courses, among other things. For me, besides measuring how good I was at thinking like the people who wrote the questions (and how much time I'd spent practicing the logic games so I could do them very fast), the LSAT was also a measure of how eclectic my background knowledge was -- there was a reading comprehension section on cloud computing, another one on Isamu Noguchi (albeit on his early career, which I was unfamiliar with). Having read the New Yorker and such for many years is apparently a good predictor of success in law school.
having been tested a lot as a very young child
My mom was in college for elementary education when I was in 1st through 4th grade, which put her in contact with a lot of people who needed access to guinea pigs for their IQ-test-giving practice.
Some of these people were very bad at administering IQ tests. I remember one that lasted for hours and hours, way beyond a reasonable time. Even after I had long since failed to be able to put the beads in the correct order, the woman kept giving me pictures of ever longer bead strings to try to reproduce. But I trudged on, motivated in part by duty, in part by the present she had promised me for doing her this favor.
The present turned out to be a pencil. WTF, lady?
Did you stab her with it on the way out?
The present turned out to be a pencil. WTF, lady?
Holy shit, that would have enraged me.
It wasn't sharpened yet! It wasn't even a particularly cool pencil.
Pencils are among the most disappointing presents you can give a child. Right now I'm feeling like I need to go talk to my therapist about pencils.
Huh, in the last day or so I was around some kids politely feigning graciousness over being given pencils as presents. Now I can't place where I was.
40: I'm not being deliberately dense here, but I still can't translate that into an actual example.
It sounds to me like the study results mean "White people are more likely to get a question right if everybody is getting it right, and black people do better on questions that NOT everybody does well on." Why couldn't that just be a function of the fact that a higher percentage of white teenagers take the SAT, compared to the percentage of black teens who take it? In other words, if there are 100,000 eligible white 17-year-olds and 61,000 take it, versus 38,000 of eligible black 17-year-olds....
I dunno. I'm so thoroughly confused by this article and its claims that I feel completely lost. The topic *sounds* interesting, but I have so much skepticism about the axes the authors are grinding (not to mention their critics' axes) that I don't really trust any of the popular interpretations of the study I've seen so far.
I like how Unfogged sprang to life when there was a post about standardized tests.
Why couldn't that just be a function of the fact that a higher percentage of white teenagers take the SAT, compared to the percentage of black teens who take it?
Well, their relative sizes shift. Say an easy question has 75% of all test-takers get it right, and a hard question has 25% get it right. Perhaps within the black test-takers, only 65% get the easy question right, but 35% get the hard question right.
Kids like pencils that are weird shapes in my experience. Star on the end.
Did your pencil at least have a pom-pom?
49: Yeah, if white kids are more likely to take the tests regardless of expected achievement then on average they will do poorer on the hard questions. I haven't read the article, though.
Hey, I have a nagging annoyance that's kind of on topic, almost. So, Sally's in this school that drowns the students, and had to take an admissions test. On the day of the test, she was talking to a boy of her acquaintance, and after they came out they discovered that he hadn't realized one of the parts of the test had questions on both sides of the paper -- he'd answered the questions on the front, but done nothing with the questions on the back.
He wasn't admitted in the first round, but Buck recently ran into his father, and apparently they went in and discussed the kid's error with the school. The school put him on the wait list, and then admitted him as one of the very few waitlisted kids to make it off the list.
This kind of irritates me. No skin off Sally's nose -- she's in the school (we're going to make her wear a lifejacket to class), and we know this kid and he's perfectly reasonably bright, it's not as if he's not an appropriate student for the school. The error's a reasonable mistake. But it burns me that this family can get something like that fixed, where a kid without parents with the social capital to go to the school and be persuasive, for whom attending a good free public school is a much bigger deal, would have been screwed by the same error. Am I just being a jerk, or is this kind of unjust?
Ignore 51. I didn't yet get what Witt was asking.
Witt, if you're interested in the article, I can send you the pdf. Email me at the linked address.
53: That would explain black kids doing better overall -- if nitwitted white kids take the SAT regardless, while nitwitted black kids are more likely not to take it at all, then white kids would be overrepresented among kids who get any of the questions wrong. But the effect reported says that black kids are overrepresented among people who get the easy questions wrong, and underrepresented among people who get the hard questions wrong -- that suggests that there's something going on beyond the black kids being a more picked group.
Did your pencil at least have a pom-pom?
No! It was blue and pretty shiny, but other than that not particularly interesting.
The coolest pencil in my collection was one of those fat little-kid pencils, with a face whittled into the side of it.
27: Rote memorization is a very useful skill. I had some of that in school and the skill has served me fairly well despite my otherwise appalling memory. It would be nice if they'd also teach some of the tricks to extend the ability to memorize things - perhaps they do in some places but I was just given lists of facts. It can't be more than a part of a complete education, but I'd argue that any attempt to educate a child that doesn't include memorization of useful facts is deficient, not just because exercising ones' memory is important but also because you just can't reason without knowledge.
59: I agree with this completely.
I have these drumstick pencils at my desk. They're kind of cute and attract the occasional remark, but they're not really functional as drumsticks. Too light.
It is interesting to see what is actually gettng tested some times. An anecdote from my children is that the one who was quite strong in math but the slowest and most indifferent reader initially tested much lower than would be expected on the Math SAT (and worse than his Verbal score). Through doing some practice tests, we discovered that he was making a lot of "binary" mistakes, "greater than" instead of "less than", "is not" instead of "is" etc.--and the "opposite" answer is almost always conveniently one of the choices. With recognition, he got past that pretty well and ended up with much more expected scores. It was not such a problem for him on the Verbal tests because he was paying attention to just that kind of thing, whereas on the Math ones he was concentrating on the calculation or whatever and was sloppy on the details of the actual words.
Not to belabor the anecdote, but it left me with a couple of takeaways: 1) It highlighted for him a specific cognitive processing problem which although more significant in an artificial setting like the SAT could potentially have real-life consequences so that was good, and 2) It was an instance that showed how "practice" (or having a parent willing and able to dig into what was going on) helped his scores. In some ways a minor example of what LB decries in 54.
Against 30: Asian-americans commit explicit suicide more often, but you don't see them in rehab or as trailer-park middle-aged type II diabetics very often.
Indulging in complete internal apathy rather than keeping up appearances regardless of inner state requires the same well-balanced self confidence that serves a person well when they do have goals. So don't nag, but provide a constant stream of helpful reminders. This normal behavior will itself be a lesson to your kids, and you can hope that they imitate you, since who doesn't want a chirpy, helpful kid?
kick my ass Only be being clever enough to attack from behind when you are drunk or asleep, I expect.
54. Asky dad: If the dad is pushy, his behavior will have many small payoffs until he pisses someone off, when the kid will suffer for the sins of the parent.
50: I feel left out--I haven't taken one in years. I do remember being overly identified with my good (but not test-freak-good) SAT score when I got it back. Theoretically it was like a high school analog to salary--you didn't discuss it. But I was thrilled if anyone asked. Jeez, maybe I'll go take the GMAT or something just so I can feel alive again.
57: Not necessarily, I think, because for smarter children the difference between hard and easy questions is small (eg a student for whom the test is trivial is almost as likely to screw up an "easy" question as a "hard" question).
as soon as I started reading about how they were created . . . I started resenting the whole experience
See, I resented the tests from the word go, and I think that helped. My great ambition was to punish the test-givers for doubting my brilliance by making their questions appear as foolish as possible. Scantron somewhat limited the form this punishment could take.
54: Would anyone here not do the same in those circumstances? Rage against the system, but any specific judgment on the family is quite misplaced in my opinion. For instance, 63.last assumes facts not in evidence.
I've taught test prep, mostly to rich kids, for almost ten years now. During the first math lesson I always make a point to show them how RIDICULOUSLY much having a graphing calculator can boost your math score. They usually make the connection to "Oh. So kids that don't have graphing calculators or aren't trained in all of their tricks are kind of screwed" on their own.
67: Oh, I'm not so much judging the family (and the dad is super charming, so I doubt he's ever going to do anything counterproductive). I'm more judging the school for listening to him. "Admission by objective exam score" is different from "Admission by objective exam score with some flexibility for people with good reasons for having done poorly, just come convince us", and it makes me sad that the UMC kids are operating under the second set of rules while the working class kids get the first set.
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A colleague gave me feedback on a chapter I wrote. She changed "The media does not provide...." to "The media do not provide..."
Is this correct? It sounds so awkward.
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A former colleague once brought me gavel-headed pencils as a souvenir from the Supreme Court. I thought they were pretty cool.
54 and 62 are very common situations in my experience. It's frustrating because a lot of people who loudly oppose "special treatment" for some kids back down and are reasonable enough if you give them the actual example (especially something like 54), but then immediately go back to their assumption of bad faith the next time something similar comes up.
56: Thanks.
During the first math lesson I always make a point to show them how RIDICULOUSLY much having a graphing calculator can boost your math score.
Really? I'm old enough that I don't think we were allowed calculators, much less graphing calculators, on the standardized tests we took. If the tests are designed so that they're helpful, that's shockingly unfair.
To stereotype madly, but not, I think, unfairly, doesn't the tendency of Asian kids to perform well in school, combined with the stereotypical highly-academically-pressured Asian upbringing, suggest that the standard parenting advice is kind of bullshit?
This comes up in Nurtureshock. Their argument is that the standard US parenting advice is pretty much bullshit, and that the highly-academically pressured Asian upbringing is less mean (or, at least, can be less mean) than the stereotype. The authors say that the key (that sterotypical Asian parents have) is to insist that poor results are a failure of hard work that can be reversed by working harder; this increases a certain kind of pressure but also doesn't leave kids thinking that their failure to do well in a particular area is just the result of some inborn and insurmountable personal failing.
My link in 71 was supposed to go here.
And 70: It's not wrong, just British. Therefore pretentious in the US.
70: Either is correct by now (media can be either mass or count). If she's not in charge, keep it your way if you like.
Is this correct? It sounds so awkward.
Yes. "Media" is the plural of "medium."
It's amazing how resistant I am to her editing feedback. I don't want to expand this section or include more examples, because that sounds like work. I like it fine the way it just rolled out, like when I'm blogging.
(LB is more correct than I am -- treating media as plural count noun is an older-fashioned correctness.)
I wonder if one could factor out test-taking skills and find out more about a students abilities by examining how their performance varies with question difficulty: smarter kids having a flatter distribution than better prepared kids.
64: I hear you. Since basically getting me into grad school (I had continued a Heebie-style battle of principle through college, even without an "opponent"), my freak test-taking has been left without outlet, let alone reward.
68, 72: We definitely weren't allowed calculators.
Obviously, I don't do very well on essay tests.
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Kinds of libertarian. Pretty good. Some redundancy, probably just to fill the 4x6 grid. I think there should be more varieties of creepy.
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64/80: I kind of want to take the LSAT. Just to see. Or rather to prove that I am insane.
This kind of irritates me. No skin off Sally's nose -- she's in the school (we're going to make her wear a lifejacket to class), and we know this kid and he's perfectly reasonably bright, it's not as if he's not an appropriate student for the school. The error's a reasonable mistake. But it burns me that this family can get something like that fixed, where a kid without parents with the social capital to go to the school and be persuasive, for whom attending a good free public school is a much bigger deal, would have been screwed by the same error. Am I just being a jerk, or is this kind of unjust?
Sure, it's unjust, but only (I think) in one direction. That is, it's certainly unfair that parents with less social capital would miss out on this fix, but it doesn't seem unfair to me for the school officials to say, "Oh, we don't want to penalize the kid for such a meaningless mistake" in a case where it is pointed out to them.
The sheer existence of Kaplan, for instance, seems much more meaningfully unjust to me.
80.2: I'm sure that's right for the SAT -- I can't quite remember if the APs and the Achievements were "No calculators" or "Sure, bring it, but it won't help."
It's a chapter on Why We Make You Take A Math Class at Heebie U. I think taking a math class is good, but the content provided in your typical one math class is not necessarily going to enrich your life. She wants me to include more stuff about richness of life and competitive job candidates, which I don't really believe.
My five reasons are:
1. Be able to evaluate incoming information (ie journalism, etc.)
2. Be able to communicate numerical info
3. Maybe you'll discover your untapped passion for math
4. Every now and then, life throws you a high-stakes situation involving math, and although you can certainly consult other people, it's nice to be able to understand the math yourself
5. Our society considers mathematical literacy to be part of a well-rounded education.
82: Ahahaha. The "Creepy" one reminds me of that one MRR writer from the 90s.
I don't know about the SAT, but the LSAT is definitely "crackable" in the sense that there are a few test-taking skills that can dramatically increase your score. I tell anyone thinking about law school that it's basically self-malpractice not to take a prep course (not to say that you can't do well without taking a course, but given the importance of LSAT for law school admissions, why not take a class and boost your chances, and you're about to go into debt anyway).
unfair that parents with less social capital would miss out on this fix,
Assumes evidence not presented, or whatever legalism. Pretty big assumption that "other" parents wouldn't know to point out the mistake and at least see what happens. The very fact that the child is testing for the school disproves your theory.
Her reasons are well-encapsulated in your five already, heebie. Maybe she's just tense about wanting a really bite-sized explanation of Why College Can Help You Get a Good Job?
Regardless, irritating.
End of lunch! Maybe this thread will still be going when I get back...?
86: More!
(6) The kind of rigorous detail oriented reasoning you learn in math classes is widely applicable to other sorts of problems.
(7) The brain is a muscle: math class is cross-training for your major.
Her reasons are well-encapsulated in your five already, heebie.
Glad this was your impression as well. The thing is, I really like her as a person, so I am inclined to really buckle over trying to see where she's coming from. But her comments read, well, like standard comments on a Freshman Comp essay assignment. Expand here! Examples, please! Sure, I could...but do I have to?
Our society considers mathematical literacy to be part of a well-rounded education.
O rly? "Math is hard" quoteth the Barbie.
Inumerancy is not on the same plane as illiteracy.
54: For what little it's worth, probably the most fun I had in college was taking the GRE Literature subject test. Not sure if it's up your alley, but it was awesome (especially because scores were discussed and I beat all the people who'd actually taken English classes and whatnot) but that's because I'm a testnerd. Being able to quickly tease out what's being asked was a large part of what made academic team fun for me.
27: I could be wrong here and my dataset is the kids I tutor at our local wacky black lesbian church, but I think you're not accurately discussing what the black community wants but more what this particular set of upwardly-mobile (which really, really isn't the right word here, but you get the drift) parents and administrators are hoping will balance things out for the kids who don't have the kind of homelife your kid has. Your kid might be able to memorize thanks to hearing Good Night, Moon every night for forever or something like that, where a child whose single mother is illiterate (I'm tutoring a few of these) isn't getting that. I grew up (UMC white child of a prof) with a placemat with all the presidents listed on it, but the foster child I've had the most contact with was raised by one parent who was in and out of jail and volatile and one who was blind. It's about evening out different gaps, which is why putting these kids in a pre-K program like your kids had might not be sufficient.
(7) The brain is a muscle: math class is cross-training for your major.
Actually, in the last section on How To Succeed in Your Math Class, I did a big thing on how your brain is a muscle, and you study by getting your brain in shape.
Didn't think about the cross-training angle, however. That's not bad.
Witt @ 49: It sounds to me like the study results mean "White people are more likely to get a question right if everybody is getting it right, and black people do better on questions that NOT everybody does well on."
Did you read the blog post linked to in the linked article? That explanation seemed clearer:
Much of it had to do with a method of test analysis called differential item functioning, or DIF (rhymes with cliff). Psychometricians like Freedle and his colleagues at ETS, which was then managing the SAT, looked at how different ethnicities that were matched at different scoring levels (those who had scored 360 on the SAT verbal test, then those who had scored 380, and so on) did on each item. At each level of ability, but particularly in the lower-scoring groups, white students on average did better than blacks on the easier items, whereas blacks on average did better than whites on the harder ones. (Whites, however, as a group did better overall.)Since they matched by score, (I assume) they just took similarly-sized groups for comparison. That is, they matched 10,000 whites against 10,000 similarly-scoring blacks to find DIFs. After all, once you get to a group as large as 10,000 test-takers, you've got a full statistical universe and you don't really need larger samples.
m, but then again, i may be missing what you're asking
Pretty big assumption that "other" parents wouldn't know to point out the mistake and at least see what happens.
It's an assumption, but it's one I'm comfortable making for at least some, probably most, non-UMC parents. (Actually, I probably wouldn't have gone to the school with that -- with a whole lot of applicants for every spot, little Weatherby is now in the school over someone who got right answers on questions Weatherby never tried to an, under the assumption that he would have done great on that part of the test too if he'd just seen it. That seems kind of straight-up unjust to me, and asking for Weatherby's error to be rectified seems like asking for the school to screw some other kid. I'm not judging the parents too hard, but I probably wouldn't have done it.)
The very fact that the child is testing for the school disproves your theory.
No.
Inumerancy is not on the same plane as illiteracy.
We're talking understanding what percentages mean here, not understanding calculus. If you can't parse a simple percentage during a job interview, you're going to be judged for it, no?
82 is good. There are so many types! I feel like there's one more though, unless it folds into one of those--the kind of libertarian who spends most of his time talking about how things would be if he himself were in charge. (Surprise! Totalitarianism w/ bonus death camps!)
98.2: Probably not. You'd be amazed by how innumerate lawyers will admit being, without any shame in it. I've been a go to math person at every lawyering job I've had, and the hard math I've done has been percentages and present value calculations.
You'd be amazed by how innumerate lawyers will admit being, without any shame in it.
Damn straight!!
Actually, I do have some shame.
59: My problem with rote memorization is that it encourages learning of facts without context, and that knowing facts without context is a very shallow form of learning. I think its much more important to learn the overall context, and then learn how the facts fit into the context, and then to figure out how knowledge can be synthesized based on facts and context.
Especially in an age where fact recall is a task easily outsourced to Google, I think its important that people's brains be optimized for information processing, not data storage.
Thus, while rote memorization is a convenient tool for uploading content into the brain's medium-term knowledge base, I really don't think it should be used for anything more than a very small portion of classroom teaching.
Oh. That's depressing.
Well, this will be mandatory reading for all freshmen, so I'm keeping my lie intact. Be the lie you want to see the world be.
97. Does everyone test for the school, or does this mythical working class parent that goes to the trouble of getting the kid to school for the test suddenly give up when the results are announced? I agree that there certainly is a bunch of social capital at work where on the part of Weatherby's parents to even assume that things can be set right for their precious dunce, but I don't see anyone going meekly into the night once the reported error has been discovered.
Especially in an age where fact recall is a task easily outsourced to Google, I think its important that people's brains be optimized for information processing, not data storage.
This isn't always true. Sometimes you need the facts on quick retrieval in order to move to the next level of abstraction. Having to pause and look things up prevents you from developing a more sophisticated understanding, in these cases.
The coolest pencil in my collection
One of the first things I ever linked as a blogger was this gallery of carved pencils. Some of the links are busted now, but most of it's still there.
104: You don't think there's a huge difference in the amount of social capital/entitlement between 'I think my smart kid has a chance to get into the good school if s/he takes the test and does well', and 'I think my smart kid should be admitted to the good school despite having made a bonehead error and tanking the test'? I do.
Pretty big assumption that "other" parents wouldn't know to point out the mistake and at least see what happens.
Not to speak for LB, but I have personally worked with families on how to speak up on these kinds of issues. There are many, many ways that schools can informally cut off attempts by a parent to explain: 1) Security guards not permitting the parent to enter the school; 2) Secretaries ignoring or purposely giving misinformation about when the principal will be available; 3) Principal feeling free to ignore the parent's request; 4) Student paperwork getting lost.
These can be inadvertent just as much as malicious. If a parent asks "Can I speak to the principal?" and the security guard feels like saying "Not here!" there's no physical way (short of lurking in the parking lot or sneaking in a side door) you can get through. It's not like they list their e-mail addresses publicly.
Probably not. Depends on the level of the interview. You'd be amazed by how innumerate lawyers professionals with high-level of social capital will admit being when they're comfortably beyond the danger of being fired over it.
105: Yes, and I think this is even more important for humanities topics than for the sciences. You need a pretty large corpus of facts to make a solid context for other facts to adhere to.
I agree that there certainly is a bunch of social capital at work where on the part of Weatherby's parents to even assume that things can be set right for their precious dunce
You don't think there's a huge difference in the amount of social capital/entitlement between 'I think my smart kid has a chance to get into the good school if s/he takes the test and does well', and 'I think my smart kid should be admitted to the good school despite having made a bonehead error and tanking the test'
Comity?
I tell anyone thinking about law school that it's basically self-malpractice not to take a prep course (not to say that you can't do well without taking a course, but given the importance of LSAT for law school admissions, why not take a class and boost your chances, and you're about to go into debt anyway).
It's disconcerting to realize I'm going to have to face this with my kids some day (not with the LSAT, I hope, but with the SATs, etc.). I never took a prep course, and have a strong visceral reaction against them (for reasons relating to privilege and social justice, etc.). I view them almost as dishonest--certainly as dishonorable--attempts to better oneself through cheap tricks to game the system rather than through one's own merit.* It strikes me as just one short step from simply buying one's way into college through alumni donations, etc. I don't want to be the sort of person whose children would do that sort of thing. But my sense is that it's become almost an expectation in the UMC set, hasn't it? That most UMC parents would no sooner consider not enrolling their kids in a prep course than they would consider not sending them to college. And I don't want to affirmatively handicap my kids. So I'm torn, and I prefer not to think about it. Fortunately, I shouldn't need to for a dozen more years.
* Yes, of course I know this isn't a fair characterization.
That bit of the sentence, comity, sure, but then I don't understand "but I don't see anyone going meekly into the night once the reported error has been discovered." If it takes social capital to try to fix it, much less successfully fix it, then how are you doubting that there are parents out there who either won't try or won't succeed?
We're talking understanding what percentages mean here, not understanding calculus.
I taught discussion sections for a professor who couldn't do percentages. At ALL. We spent a lot of time in staff meeting talking about what we were going to do, since sections met 9 times yet were worth 10% of the grade. Talk about pulling your hair out! I volunteered several times to share my grading spreadsheet, but no one quite seemed to believe that such a thing could work.
112 to 110.
111: I know how you feel.
I never took a prep course, and have a strong visceral reaction against them (for reasons relating to privilege and social justice, etc.). I view them almost as dishonest--certainly as dishonorable--attempts to better oneself through cheap tricks to game the system rather than through one's own merit.
This reflects a rather charmingly naive view that the system has anything to do with one's "merit" in the first place. Certainly one shouldn't feel bad about trying to game a standardized test that is specifically designed not to test for acheivement but for some kind of supposedly "inherent" ability.
I can't tell if 113 is making me laugh or cry.
Certainly one shouldn't feel bad about trying to game a standardized test that is specifically designed not to test for acheivement but for some kind of supposedly "inherent" ability.
Why shouldn't one feel bad about it? (Given that one knows that the vast majority of students will not have the benefit of such gaming.)
I prefer not to think about it. Fortunately, I shouldn't need to for a dozen more years.
That's because you don't live in New York City.
104. I don't see anyone going meekly into the night once the reported error has been discovered.
How would you see them, if they went meekly into the night? I mean, even assuming you were a school official and not just a reader of an anecdote in a blog comment- if parents (or kids) didn't report the mistake because they thought it wouldn't make a difference (or because they weren't able to navigate the system in order to report it correctly, or because the security guard didn't let them into the building, or because they weren't able to take time off work to personally meet with the principle to request rule-bending) how would you or anyone else ever know about it?
there are parents out there who either won't try
Big assumption on my part, but to my mind any parent who has the gumption to get on the bus with Junior and show up for a special test for admission to a special school would have the gumption to see it through. One of the reason charter schools do better is because of parental involvement, which, chicken: egg. Not to say that if they were actively discouraged, as per Witt, they wouldn't give up because of the lower social capital. And I think the school would be well within its rights to say "tough noogies". Happens all the time. Not being a school administrator, I have no idea what the institutional bias is in this case.
105: I don't disagree that quick retrieval from memory is frequently needed.... my contention is that the it has become significantly less frequent now that quick retrieval on line is available, and that the value of the skill ought to be discounted as such.
In contrast, I think the ability to synthesize new information from a disparate collection of facts is correspondingly more important than it has been in the past, in large part because such a broad array of facts is now available with a few clicks of the mouse. So many more facts are available now that the more important use of mental effort is in figuring out what to do with them, rather than in figuring out how to remember them.
Big assumption on my part, but to my mind any parent who has the gumption to get on the bus with Junior and show up for a special test for admission to a special school would have the gumption to see it through.
Huge, unwarranted assumption. And calling the difference between a parent who assumes asking for special consideration to fix their kid's screwup will work, and a parent who doesn't believe it will, "gumption" is pretty hostile to the latter parent.
102: There is no conflict between processing and storage - in fact improved storage and retrieval improves processing rather than competing with it.
Jeez, maybe I'll go take the GMAT or something just so I can feel alive again.
That's pretty much how I feel about the Professional Engineer exam I'm going to take in October. 'Cept I looked at it, and it is hard! I am outraged. I only like aptitude tests, apparently.
***
I'd bet that a big reason freak test-takers are overrepresented here is that we read fast. Other people read so slowly; it hurts to wait for them. Before we even get to solving, I can read the test in a quarter the time it takes most of my friends. Who else would put up with a text-based chatty blog that doesn't even have nekkid pictures on it?
***
If you don't want to be a high pressure nagging parent about academics but want your kids to feel the same effect, I recommend putting your kids into school with all Asian-Am kids. The peer pressure will drag your kids along, but you can still let them out at night. Win-win!
I just reject the notion that there's anything reflective of "merit" in what the LSAT, SAT, etc. are testing. They are designed to give admissions officers a window into how people might do in (their first year of) school. It's not like you're trying to misrepresent how much you know about Chemistry, or something. So I don't see anything affirmatively bad about trying to game their stupid metrics.
Sure, there's a fairness argument about everyone being on a level playing field. But since this pretty much doesn't exist in any other area of life at all in the United States why make an exception for standardized test prep? It seems to me that treating the standardized tests as in any way either tests of merit or as vehicles for social levelling is just buying into EDS bullshit.
111: Yes, that is where I was (and kind of still am). However as you anticipate, things can look different in the event. My first clearly did not need any prep class, my second was was dead set against them on the principles you describe (which I told her were honorable but probably counterproductive), and my third did take one based on what I described in 62 although we worked out the issue described before he actually started the course. Actual college admission success results (based on my personal infallible expectations-versus-actual-results meter): kid #2, kid #3, kid #1.
Without going in to more detail, my bottom line takeaway for probably the vast majority of the children of people here, don't sweat the SAT, the real issues and opportunities lie elsewhere. Easy to say now, of course.
I think we need to establish first principles here in the issue of what parents do.
A) People with more time and money can do more things.
B) People who have learned from experience that they have no power to do things will not bother to try to do things.
106: I think any one of those pencils would have made me the 8-year-old me die of sheer joy.
How would you see them, if they went meekly into the night
Can't happen. And in my mind precious doesn't rate a spot at the school. Doesn't follow instructions well. FWIW, I don't think I would have asked for special treatment for my kid, given the same circumstances. I would say "Try again next year, dumbass". My wife would camp out on the doorstep of the school until they agreed to a retest, at least. LB and I at least have comity on our outrageous assumptions.
It seems to me that treating the standardized tests as in any way either tests of merit or as vehicles for social levelling is just buying into EDS bullshit.
In a world where the EDS bullshit wasn't conventional wisdom, I'd agree with you. But it is -- more people than not believe that the kid with the better SAT scores is a smarter kid, with more academic potential, than the kid with the worse scores. To the extent that people believe that, or act as if they did, test prep is a kind of fraud.
I don't know what to do about this, because we're stuck in the system where other people are taking prep classes. But there's something very unseemly going on.
I can't tell if 113 is making me laugh or cry.
It was an oddly useful experience for me, in that it helped push me over into the mindset of Wow, the academy is truly fucked up if this guy can be a full professor at Harvard.
Can't happen. And in my mind precious doesn't rate a spot at the school. Doesn't follow instructions well
Okay, I don't think I understand what you're talking about any more. What can't happen?
I thought at first you were saying that you didn't think any parents failed to report mistakes like the one above, and were offering as proof that you "didn't see" them.
Now it seems like you're saying you do think there are parents who wouldn't report things like this (including yourself?) and that anyway kids who make dumb mistakes "don't follow instructions well and therefore don't deserve a spot in the school."
But that has nothing to do with the fact that given the dumb mistake, kids with more-clout-y parents will get in to the school, and kids whose parents don't/can't get the rules bent, won't.
hm. I missed a tag there. Whoops.
Also, off to the doctor!
132.last: But there's something very unseemly going on
Yes, at some level it is all one small part of a neo-feudalism/Mandarin trend in US and the world. And you also happen live right in the heart of a place that leads that trend (not judging, it just is because it is the leader in so many things--many other places in the US are close behind--but in Manahattan/Brookylhattan it is especially intense in my experience).
128 is encouraging. For some reason I'd developed the idea that it had become something that more or less "everyone" automatically did.
*By "everyone", I mean everyone whose families (1) assumed without questioning that they were going to college, and (2) had the financial resources to pay for the courses, which of course isn't really anything close to everyone, which is the whole problem.
doesn't even have nekkid pictures on it?
??? Are you using an old browser or something?
Regarding the justice of asking for special treatment- I guess that I don't see that much advantage to a marginally better school for kids with books at home, safety issues excepted. So I basically see test prep anguish as much ado about very little. If a few points make a big difference, then squeaky wheels etc.
But why would capable parents choose to live in a place that worked that badly? They'd be better off moving to a different zip code where there was more than one OK school.
But why would capable parents choose to live in a place that worked that badly?
Please don't make me use your IP address to find you and hurt you.
I thought only Megan swaggered.
No really, the falloff in school quality is that steep?
But why would capable parents choose to live in a place that worked that badly?
Probably because they're stupid, and they hate freedom.
They'd be better off moving to a different zip code where there was more than one OK school.
And thus were born a million suburbanites.
132 -- I think the current standardized test system is completely fucked up, as is the current distribution of wealth, but I just can't get mad about folks trying to game a fucked up system. "I got this SAT score on my own merits!" doesn't seem like a particularly boast-worthy event.
And the prep courses will (hopefully) spell the end of the ETS/standardized testing regime, and get us to a system that actually tests for knowledge, acheivement, and accomplishment instead of "potential." It's not like I know the world of college admissions well, but my sense is that this is already happening.
140: Are you doubting that there can be big differences between the quality of public schools, or wondering why 'capable' parents would be located someplace where poor public schools were a possibility? If the first, why, yes -- turns out public schools are very variable. If the latter, um, there are many constraints on where people live other than whether or not they're 'capable'.
Sorry about the swaggering -- I'm unlikely actually to hurt a fly, not so much because I'm too nice but because I'm just not all that physically imposing. But what you said was pretty bizarre.
But why would capable parents choose to live in a place that worked that badly?
Some of us live here for the weather and the beaches.
OT: I'm in the middle of grading a paper written in bizarrely colloquial English. See, these poems are both about guys who are all into scoring, but because they are total dicks, they end up cock-blocked by their own ego shit.
142: And that was written by someone who said "I don't see that much advantage to a marginally better school for kids with books at home, safety issues excepted." two sentences earlier.
134. Let me first say that if the error goes unreported, either by the test taker to the parent or by the parent to the school nothing can happen. There is no way in God's green earth that a school administrator is going to recognize that Johnny forgot to turn the paper over rather than ran out of time, didn't know the answer or whatever. Further that it takes some "guts" otherwise known as "social capital" to try to rectify the situation. My disagreement with LB is with her assumption that it was only a UMC parent that would have the social capital to argue for admission. It is absolutely true that is a hell of a lot easier for a UMC person to have the wherewithal to make it happen. Given a finite number of places at the school, not everyone can attend. Is this unjust? Probably. I'll give the school administrator the benefit of the doubt on this one, not knowing anything other than the story as related here.
Further that it takes some "guts" otherwise known as "social capital"
What a screwy equivalence to draw.
But why would capable parents choose to live in a place that worked that badly?
Bagels and pizza, right?
I'd bet that a big reason freak test-takers are overrepresented here is that we read fast.
Actually I read exceedingly slowly, but did very well on standardized tests back when I had to take them. Part of why I read very slowly, though, is that I read very carefully.
Yes, that means that I waste more time than you do by commenting on this blog the same amount of time.
What a screwy equivalence to draw
Guts, hutzpah, hubris. All words trying to describe fighting city hall, upsetting the apple cart, sticking it to the Man. Social capital, white skin privilege, institutional racism, etc trying to describe advantages of some over others. They are not equivalent. We regret the error.
I was actually thinking about people who change countries, who are pretty numerous. If the schools really are disastrous except for one hard-to-test-into beacon, why not leave and find a place where they are better? There are no internal passports in the US; Either it's not worth moving, or the school choice crisis is not that serious, or people are stuck against their will and also disinterested in change-- other possibilities? By capable, I meant capable of moving, not necessarily a moral judgement.
Barring danger to students (yes, a real concern), I don't think the concern with average test scores between schools is all that meaningful, more often driven by competition between parents than by meaningful difference in outcome for kids. This is what I saw where I grew up, and this is what I see where I live now (where my elementary school is great, totally above expectations). Manhattan may well be different, I'm honestly not trying to be insulting.
why not leave and find a place where they are better
Maybe cuz your job isn't anywhere near this Utopia?
why not leave and find a place where they are better?
Because you have a job where you are, and you don't have money to move?
I think you're trying to say that well-off people with lots of options fret too much about minor differences in schools, which is probably true. But the way you're saying it sounds like you're including poor people, with many fewer options, who are more likely to be in a position where their default school is genuinely bad (not always, but sometimes). People in the latter position should be forgiven worrying about whether their kids are in the better of the available schools, and may not have the money to move to someplace where the default school is excellent.
Those were both me -- don't know where my name went.
157: Ah, but you had the gumption social capital to post an explanatory follow-up.
72: Calculators are allowed on the ACT and SAT but not on the GRE (which is one of the reasons why GRE math is actually easier than SAT math). For the ACT/SAT I've heard rumors that proctors go around and make students clear their calculators' memory, but this has never happened to any of my students, which means they all were able to use formulas/programs that they had stored in there.
Graphing calculators also allow you to:
* find the roots of an equation automatically by plugging it in, hitting "graph," and then getting the coordinates
* quickly plug the answers into certain questions by hitting "store" and "recall"
* convert decimals to fractions and vice versa
All three of those, but especially first, give students with graphing calcs and the skill to use them a huge advantage in terms of time and accuracy. It's disgusting.
OK, I see that I've pissed people off, no harm intended. I don't imagine that I live in utopia, but there are hundreds of square miles here where the schools are pretty good. From what I can tell, the same is true just outside most American cities. I know lots of people who have in fact moved because of dissatisfaction with a school.
As for being poor and moving, people did it here in large numbers in the thirties and again after WWII. All the people who used to live in Detroit, Cleveland, and St Louis went somewhere. My folks and I came to the US with the proverbial cardboard suitcase, in part because I would not have gone to university otherwise. Moving costs less than a used car-- that's a pretty low threshold. Work ties matter for specialized occupations much more than otherwise. When things are bad enough, people move or they change things. Is it possible that people living in bad school districts are not that upset about it?
Yes I have watched the education season of The Wire. It's fiction, but the remark that there are kids in the terrible schools who are at their best on Wednesday because it's farthest from the weekend, if that's a valid observation, that says a lot.
146: When the content is good, I love papers which use that style. It actually winds up sounding a lot like Unfogged.
161: I can wholeheartedly agree that regardless of your situation, you are in that situation only because you don't perceive it as being bad enough to make it necessary to do what it takes to change it.
The beautiful thing is that this observation is absolutely universal. There's always something you can do if you have enough willpower.
163: I guess I must just lack willpower.
They can't keep you from holding your breath.
Excellent, I love aphorisms and that's a good one. I will stop procrastinating now, though.
A bit more about what is actually getting tested with these things, it is interesting that per essear's 5 and my 62 that most people would naturally assume (and it is generally true) that if you are asking for the antonym the synonym is one of the choices, or that the most common misreading of a math problem (less than for great then etc.) is one of the choices. In the first instance are they actually trying to knock off people who have those two concepts confused? Surely not. And in the second is that really what they mean to test for rather than an understanding of the math concepts? I can construct arguments that they are legitimate things to differentiate, but it contributes to giving the tests a game-y, "avoid the common gotchas" feel. Maybe that is what they want to test, but it seems more appropriate for a newspaper puzzler than a test with potential life consequences. But a small nit compared to the overall asshattery of the system.
167: Yuck, too much whitespace at the end of that comment, -10 points and 4 percentiles.
167: Huh. That's a real point, and one that I hadn't ever quite formulated.
I don't think there's a defense in the math context, but for synonym/antonym I could imagine a hypothetical testtaker who had a vague acquaintance with the word, so as to know sort of the general subject matter of its meaning, but not to know it well enough to pick the meaning out from the reverse. ("Alacrity? THat's something to do with speed, but does it mean fast or slow?")
But mostly I'd think you're right.
167, 169: If the wrong choices shouldn't include common gotchas, what should they consist of? Don't they need to be the results of mistakes someone might plausibly make in solving the problem, rather than just random numbers? Also, real-life misreadings of, e.g., whether a number is positive or negative can have serious consequences and are not just "gotchas".
170: I'd need a real problem to look at, but don't you think there's a distinction between conceptual misunderstandings and sign errors? A kid who subtracts 1/4 from 3/8 and gets 5/8 has made a mistake, but she knows how fractions work. A kid who gets 2/4 as her answer to the same problem doesn't. It'd make it harder to design the problems if you left out the non-conceptual gotchas, but there's a fair argument that it'd be a better test.
Also, if the wrong answers are mostly that sort of gotcha, it makes it possible for the savvy testtaker to get the right answer as the one that's one step away from each of the others, if you see what I mean.
Also, real-life misreadings of, e.g., whether a number is positive or negative can have serious consequences and are not just "gotchas".
No one disputes this, but that's a very different thing than "mathematical aptitude". What are we supposed to be testing?
As for your first question ("If the wrong choices shouldn't include common gotchas, what should they consist of?"), this is a real problem with multiple choice questions, and to some extent is unavoidable. You don't want the wrong answeres to be implausible. But one could imagine them actually screening and removing answers that would be the results of common "gotcha" mistakes (reversed sign, missed negative, etc.). Then someone who knew how to do the problem but made such a mistake would not see an answer choice that matched their result, and would know they messed something up and could recheck the problem for their error. Whereas someone who just doesn't know how to do the problem would still be left clueless.
It would even be fair game, I'd say, to include answers that are the results of common conceptual mistakes, and just remove those that are the results of common calculation mistakes. Then you wouldn't have implausible answers, and would trip up plenty of people--just not the people who clearly understood the mathetmatical concepts involved.
I wonder if there's any way to make Scantron readable open answers to math problems. Like, there's a grid that gets used for digital readouts -- two squares on top of each other with diagonal lines, and depending on which segments are lit, the different digits display. Could they give you a several-digit blank grid, and tell you to fill in the segments to show the digits of the answer?
There are probably too many ways for it to go wrong, but it'd be interesting.
This not something I have thought much about, it really just occurred to me reading this thread with essear's story in 5 in conjunction with writing up my son's experience and noting that in both cases my thinking "of course that would be one of the wrong choices". And then thinking, "Why do I think that?"
I wonder if there's any way to make Scantron readable open answers to math problems.
You can certainly make computer tests free-answer without too much trouble.
I mean, computerized math tests.
177: If that's a solved problem, then it seems just wrong that there are any multiple choice math tests out there.
I'm sure there's a ginormous literature on all this, almost none of which I've read, but I have read this old book, which isn't actually a great book IMO, but does cover a lot of this ground.
179: We've got software we use for some classes where they do homework online, and some of the problems are open answer. They get frustrated at first because this program is strict with answer formats. But I don't think this is the smartest program ever. I'm pretty sure in general it's a solved problem.
Here, kids have two weeks of testing at the beginning, middle, and end of the school year. I can't imagine anything duller than taking standardized tests for two fucking weeks straight.
181: Oh, do you mean that each kid has to sit at a terminal? I was thinking of machine-readable paper.
The SAT is already exclusively given on computers, isn't it?
When Unfogged was strictly a paper and pencil operation?
186: Unf and Ogged passed back and forth little pieces of paper during philosophy class.
It looks like I'm wrong. I just assumed since the GRE was in the process of converting to computers back in 1999, that the SAT must have, too.
The SAT is given on computers now!? I'm appalled.
I always wondered to what extent people graded essay-based exams on whether they made good arguments, and to what extent it was based on length, diction, and rigid adherence to the five-paragraph essay format. My impression is it was mostly the latter, more superficial things. In principle I like the idea of standardized tests with essays more than pure multiple-choice, but in practice I'm not sure it's an improvement.
to what extent people graded essay-based exams on whether they made good arguments, and to what extent it was based on length, diction, and rigid adherence to the five-paragraph essay format
My impression is that either of those would be an improvement over how many people grade them, which is basically skimming for the key words or phrases they're wanting to see parroted in answers, and awarding points based mostly on how many of those key words or phrases appear.
I always wondered to what extent people graded essay-based exams on whether they made good arguments, and to what extent it was based on length, diction, and rigid adherence to the five-paragraph essay format.
I'm sure that the English people here have much more experience than me. But this past spring I graded those essays from kids (ostensibly high-achieving) who were applying for scholarships from us. All I was looking for was decent grammar, trajectory, and coherence. Actually having a good argument blew everyone else out of the water.
I'm writing multiple choice questions right now, and I do include things that might be called "gotchas" in the incorrect answer list. The situation is a little different, because I am mostly testing comprehension of the arguments in the reading, but there is a fair amount of technical vocabulary learning and sometimes factual knowledge as well.
One thing I will do is have several answers that are in the basic range of the right answer, and one answer that isn't even close if you have been paying attention, but might seem close if you are guessing on your general background knowledge. The ones that are in the right range get you partial credit.
For instance, I just graded a medical ethics test with a question that asked what went on in the Tuskegee Syphilis study. A wrong answer that gets a lot of partial credit (70%) says that people in Tuskegee AL were intentionally infected with syphilis spirochetes. The totally wrong answer talks about the Tuskegee airmen.
If it was given on computers you could just have Word assess the grade level.
This thread brought back memories.
I wrote about this poem http://www.atmos.umd.edu/~dankd/adrienne.html
in my AP English test. I quoted Bob Dylan in my essay. I got a 5. Ah, the petty triumphs of my life!
That was 30 years ago.
The things I remember.
The things I forget.
I had a perverse love for AP testing week. IIRC they were held at the local university and I got to take nearly the whole day off, only a few hours of which were actually exam hours, because my high school was overly lenient about the transit time (ten-minute walk) and the lunch break. Though the days when I took two successive exams were a bit rough.
I'm not sure I've ever heard of awarding partial credit for less-incorrect multiple-choice exam answers. I can't really think of anything wrong with it, though.
Sure you have, Brock. All those lifestyle mags have questionnaires with different points awarded for different answers. For all answer B, award 2 points. Add up total.
80-100 dump him!, 60-80, One night stand. 40-60, keep your eye out for another. 20- 40 bring him home to momma. You know the drill.
Momma needs her one night stands, too?
198: I get that reaction from students all the time. Generally, if they chose a partial credit answer, they are happy with the system, and if they chose a no credit answer, they think I have violated The Rules for multiple choice tests.
In general, writing multiple choice tests is really very hard. They have a bad reputation because most people write very poor multiple choice tests.
I have been shocked this semester by how many papers I've graded in which students assigned random centuries to various books and poems. It's not just the standard "1900's means 19th century, right" stuff, but also saying a 1650 text and an 1895 text are both "eighteenth century." I mean, yes, it's a notoriously long century, but Jesus Christ. Why mention the century at all if you know nothing about history, not even what the numbers refer to?
"18th century" is just a figure of speech, right? It just means "old".
||
I just got some Barnes&Nobles spam for their Nook reader, and it included the sentence "Easy to read in bright sunlight!"
It took me a minute to figure out how that wasn't a drawback.
|>
This person thinks it is just a statistical quirk:
Momma needs her one night stands, too?
Your personal life is your own business, Heebie. If Jammies is cool with it, who am I to judge. But if you are asking permission, the answer is no. I am a traditionalist.
I guess, if you call being propositioned "asking permission". But I'll seek elsewhere.
BLUSH.
Ahem. I am at the moment, geographically undesirable. I think it was Chris Rock who said that men are only as faithful as their opportunities.
failing the bar exam was a paradigm changing shocks to my belif in freakish test taking cleverness
This not something I have thought much about, it really just occurred to me reading this thread with essear's story in 5 in conjunction with writing up my son's experience and noting that in both cases my thinking "of course that would be one of the wrong choices". And then thinking, "Why do I think that?"
Because you're the sort of person who comments here.
Because marking schedules tend to give out marks a lot more than they take them away, so there's more sense in guessing and failing than not guessing.
That's what I think is going on.
96: Did you read the blog post linked to in the linked article? That explanation seemed clearer....
Yeah, it's funny. I can read each individual sentence of that, and they all make sense. I put them together and try to understand the thesis and I'm stuck again.
Maybe I'm stumbling over their terminology, or maybe I just can't think at the level of abstraction they're working at. I have now skimmed the entire underlying article (thanks, Blume!) and I still don't get whether the authors' explanation holds water.
I don't mean to hold the thread hostage to my personal denseness on this question, but if I'm grasping the argument correctly, it goes like this:
- All students taking the SAT have a basic background level of literacy, and many of them are likely to have formally studied even more to get ready for the test
- The test designers assume that most people will be able to answer the easy questions (that's actually how they're defined as easy; lots of people get them right) and that fewer will get the questions right as the test gets progressively more difficult
- But when you look at the underlying scores,* even of students who scored the same on the verbal portion of the test overall, white students get more "easy" questions right and black students get more "difficult" ones right.
- The authors claim that this is because the "easy" questions are actually measuring a kind of cultural background noise that white students are more likely to be in an environment to absorb, while the "difficult" questions are ones that all students typically have to formally study to learn. Therefore, the test is biased against black students.
And this is where I go all cock-eyed again. What ARE those blasted "easy" questions? What do they contain? Are they measuring whether you know the word "regatta" or have they been scrubbed of any known class signifiers? How can it be that people who are studying for the test, and getting the "difficult" ones right, are not getting them? Do SAT study guides just deliberately leave them out because "everybody knows" them?
Are they causing a sophisticated version of stereotype threat, in which students freeze up when faced with literature or celebrity questions referring to those not of their own ethnic background? (Footnote #5 to the study seems to suggest that black students do fine on questions involving so-called black literature and celebrities.)
It's confusing, and all the more so because I want to understand, and I hate feeling like I can't.
*Which the article discloses took two years and great effort to acquire -- such fact alone should condemn the ETS to the eternal fires.
['oh, and: welcome back, max']
Darn it, 213 was me.
And there was one part of the article that blew me away. The authors suggest that ETS should conduct "think-alouds" with students to study their cognitive processes when reading and responding to the test.
They don't do this already? A powerful monopoly controls a massive international test with billions of dollars riding on the results, and they don't do this?
That SAT question about calculating the average blending speed of a stand mixer seems like it may be culturally biased.
213: ['oh, and: welcome back, max']
Hi! Thanks!
It's confusing, and all the more so because I want to understand, and I hate feeling like I can't.
The explanation you laid out has got it as far as I can tell. In theory, the only reasons the DIFs stand out is because on the easy ones white students did significantly better than blacks, and vice versa on the hard ones. It's pure numbers. I don't know what the identified DIF questions consist of and, in fact, the researchers may not know why blacks score worse and whites score better on those questions. But they are arguing test bias because of the scoring system rating those easy questions very highly.
You should also read the article lemmy linked to in 205, although that woman is apparently a fan of Johm Stossel. She is, of course, a total skeptic. But then, being a right-winger, she would be, wouldn't she?
m, i haven't paid the ten bucks to read the paper
I don't understand your confusion, Witt. The authors explicitly avoid trying to make any interpretation about the cause of the DIF. All they're pointing out are that there are questions that are not answered identically by black and white students who otherwise perform in the same way on the entire test, and that the direction of this difference is correlated with the fraction of all test takers who answer the question correctly. As far as I can tell, they explicitly do not claim that this is due to some sort of cultural background, although they mention that previous studies have suggested this.
213
But when you look at the underlying scores,* even of students who scored the same on the verbal portion of the test overall, white students get more "easy" questions right and black students get more "difficult" ones right.
This appears to be the effect you would expect from regession to the mean. A student's score on the test is a combination of ability and luck. So if you give the test again (not exactly the same test but a similar one) a student who scored above average the first time will probably score a little worse the second time and a student who scored below average the first time will probably score a bit better. This is because a student who scored well the first time most likely was a bit lucky and a student who scored poorly was most likely a bit unlucky. So with average luck the second time the scores move (regress) towards the mean.
What does this have to do with blacks and whites? Because the mean ability (in terms of what the SAT is measuring) is lower for blacks than whites this means a black student who scores the same as a white student was probably a bit luckier while the white student had a bit more ability. So the black student will on average score a bit better on the questions most influenced by luck while the white student on average will score a bit better on questions least influenced by luck. It seems probable that luck will be more important on the harder questions as the students are more likely to be guessing.
54
... Am I just being a jerk, or is this kind of unjust?
I think you are being a bit of jerk although this depends on whether the test was actually defective or the kid just wasn't paying attention. If the test was actually defective than it is good that this was brought to the schools attention and it is reasonable to admit the kid as an incentive to report this sort of problem. Perhaps if the school had more pushy obnoxious upper middle class parents it wouldn't drowning kids. Which would be good for everybody.
Since the main difference between "good" schools and "bad" schools is that good schools have more students from UMC families it seems a bit strange to be complaining about such students having an admissions advantage. The more such students the school admits the better the education it will provide its the students.
Guidelines for authors for the HER. Looks like there's a bit more than general editorial work for some types of articles, just not full-fledged peer review. Other articles appear to be fluff accepted or rejected with minimal changes.
I've never heard people say peer review is why an article costs whatever it costs. Peer review probably is included in editorial costs or management costs when people talk about them as part of the cost of producing articles.
However, the explanation I heard, years ago, and which might even be true, is that the non-subscriber individual article/issue market is heavily weighted towards companies rather than individuals, and those companies tend to be willing to pay a bunch of money for an article rather than pay the cost of sending someone, likely a para-professional making more than article cost/hour, to the library to make photocopies every time someone wants an article.
Oh, and of course that money isn't tied to costs under that explanation. $10/article actually sounds cheap compared to some of the individual article costs you see come up in searches. I've heard the that for-profit presses charger more than the non-profit university presses for both articles and subscriptions. They probably make pretty large profits too.
Obligatory: I'm not defending the pricing of $10. I've just seen prices listed as $29.74 or whatever on Ingenta or wherever.
People should stop publishing in journals.
Especially scientists, whose journals are by far, far the most expensive.
I try to do my part to convince other people to shun Elsevier. Too bad they own most of the important papers of the late 70s and the 80s in my field.
8
Yeah, that kind of story freaks me out -- it seems to make the GRE much more vulnerable to chance factors. I can't see what the advantage is that outweighs the potential for unfairness like that.
The advantage is that in theory it should give a more accurate score for students who follow directions as they will get fewer questions that are too easy or too hard and which don't give much information about their ability. Of course it is possible it was implemented poorly. I vaguely recall a horror story about students failing an interactive exam although they had no incorrect answers because the questions got so hard they were unable to answer a minimum required number of questions in the time allowed.
24
That's what I'm sort of wondering about -- there seems, anecdotally, to be a 'freak testtaker' trait that's overrepresented around here. People who, while generally bright, do even better on standardized tests than their general cleverness would suggest. ...
I think this is actually the bright but lazy trait.
I'd be thrilled to stop publishing in Elsevier journals. Unfortunately until I get tenure I don't think I have that luxury.
Regression to the mean seems to explain too much. There was no difs on the math seCtion between the hard and easy questions. I think it Was probably a fluke.
You should also read the article lemmy linked to in 205
Hm. Once you get beyond the political biases (and I actually agree with her that those biases exist quite strongly on the left, too) and the general ignorance (even I know that using a sample of students who were admitted to the University of California is not evidence that their sample was "not representative" enough), I can't see she has very much there.
Her argument mostly seems to be: "The College Board says there is a mainstream consensus that there is no racism in the SAT and why don't you believe this totally unbiased source? YOU'RE BIASED!!!111 ELEVENTY!"
Which, you know, probably.
Except I still want to know. Because if it's true, the question should be: How do we fix it?
I'm still boggling over the fact that ETS et al. apparently don't do internal studies of what students are thinking when they read the test. Why on earth would you not want to know?
(And I'm full agreement with Stormcrow et al's reaction to tricky wrong answers, I forgot to say. Insofar as resentful fury is my major reaction to standardized tests, that's part of why. Tricking people for the sake of tricking them is a lousy thing to do, and I'm reluctant to believe that "You should read questions carefully" is such a critical skill that it should be tested on every question.)
230
Regression to the mean seems to explain too much. There was no difs on the math seCtion between the hard and easy questions. I think it Was probably a fluke.
I don't have access to the paper. According to the second hand accounts the paper is claiming that blacks were hurt relative to whites of equal ability because they lost more on the easy questions than they gained on the hard questions. This means they weren't comparing whites and blacks with equal scores. So it is unclear what they were doing or why they thought they were comparing groups of equal ability. If the groups really were of equal ability in math than regression to the mean would not apply. But if you compared groups with equal scores then I would expect this pattern (blacks doing relatively better on hard questions).
68, 160: Jenny: I've been doing math tutoring, including some SAT/ACT prep, for the last year, and I don't buy that using a graphing calculator (as opposed to a decent scientific calculator) makes that much difference, particularly on the reasoning test. I just took a quick look through the math sections of the first practice test in the College Board's The Official SAT Study Guide, and I found only two questions out of forty four where numerical root finding might be useful to a kid who was otherwise stuck. In both cases, a kid with only a scientific calculator could have gotten the same result just by plugging the five choices into the original equation and seeing which one worked. Sure, maybe the kid with the graphing calculator could have done that a little faster (as per your second point), but it doesn't strike me as a huge advantage. In both cases, a kid who actually understood the math could have gotten the right answer quickly without using a calculator at all.
For the record, the first question is #9 in section 3: if 2^(2x) = 8^(x-1), what is the value of x? (Using ^ to represent "raised to the power" here.) Choices are: 2, 3, 4, 5, or 6. The second question is #1 in section 6: If x + 2/x = 5 + 2/5, then x can equal which of the following? Choices are 1/5, 4/5, 1, 5/2, and 5.
Even if the kid with the graphing calculator got both these questions right, and the kid without couldn't solve either, two extra points of raw score is worth maybe 20-30 points on the math section (out of 800; perhaps worth a bit more at the extreme upper end of the scale). And that seems to be around the upper limit of the effect here, considering that you don't actually need a calculator to answer either question.
Now the Math Level II Subject test is much more calculator intensive - you don't want to attempt it without at least a halfway decent scientific calculator. I still recommended to my son that he stick with the scientific calculator that he had been using all year rather than borrowing my graphing calculator and trying to familiarize himself with it in the last couple of days before the exam. He did fine. The one place where I think the graphing calculator has a significant advantage is a question about finding the limits of a function. For those types of questions, if he couldn't solve it algebraically, I just advised him to evaluate the function moderately close to the limit. If they ask about the limit of a function as x approaches 3, try evaluating it at 2.99 and 3.01. If they want the limit as x goes to plus (or minus) infinity, try evaluating at a moderately big positive (negative) number like 10,000 (-10,000). That will normally be enough to pick the right answer out of a list of five. I did warn him about taking this too far: evaluating at 3.00000001 or 1e+20 risks having the right answer swamped by roundoff errors.
Oh, and those two questions from the reasoning test? If you remember that 8=2^3 and the rules for exponent manipulation (raising a power to a power multiplies the exponents), the first question reduces to solving 2x = 3x - 3, which gives you x=3. The second question can be answered without any calculation at all by noticing that the left hand side of the equation has the same pattern as the right, which allows you to see that x=5 is a solution while the kid with the fancy graphing calculator is still punching the equation into the calculator. (If you don't see that right away, multiplying through by x gives you a quadratic equation that can be solved for both roots of x=5 and x=2/5. That's easily handled by a scientific calculator, provided you remember the quadratic formula. And if you don't, there's always the approach of trying all five answers in the original equation.)
For those types of questions, if he couldn't solve it algebraically, I just advised him to evaluate the function moderately close to the limit.
I see this, and wonder why they allow calculators at all. Isn't the point that they're supposed to be able to solve the problems algebraically?
I see this, and wonder why they allow calculators at all. Isn't the point that they're supposed to be able to solve the problems algebraically?
The problem is with multiple choice, surely. You could use the same brute force method in your head - it would just take longer.
it would just take longer.
But a lot longer -- the kid who doesn't know how to do the problem algebraically does worse on the rest of the test because she's using up her time doing calculations. The calculator seems to flatten the distinction between two very different students.
Are SATs particularly time constrained? I finished my maths GCSE half an hour early and a) I wasn't all that good at maths compared to my peers and b) it wasn't multiple choice. A-Level was more time constrained, it's true.
I only have vague memories of doing a mock SAT when my parents wanted me to apply to US universities but I don't recall feeling pressed for time.
Regardless, my point is that the surest way to distinguish between differently able students is to get them to show their working.
Are SATs particularly time constrained?
While it seems weird to me too, my understanding is that time is a real issue for most students.
237.last: Are you my old geometry teacher?
re: 237.last
Yeah, definitely. I used to be able to do a lot of simpler maths questions just by mental iteration. Pick results either side of where you think the answer roughly lies and do rapid mental arithmetic until you hit the right answer. But you could (rightly) never use that method in exams because there was no working to show.
"I just guessed until the answer came out right" doesn't go down well.
I don't buy 233. Specifically: I still recommended to my son that he stick with the scientific calculator that he had been using all year rather than borrowing my graphing calculator and trying to familiarize himself with it in the last couple of days before the exam.
Totally agree that trying to learn a new graphing calculator a few days before the exam is a bad idea. But that doesn't erase the advantage that someone who is fluent with the graphing calc has over someone who is using the old scientific calc.
And, more fundamentally, I think you're drastically underestimating the advantage a graphing calculator gives to the mediocre students. You're right that it's not that significant an advantage to someone who fully understands all the mathematics involved in all the questions, since the questions are designed to be solveable without a graphing calculator. But for someone with only a half-assed understanding of the concepts (i.e., most students), it can make a world of difference.
In your two examples, the student who remembers (A) that 8=2^3, and (B) the rules for exponent manipulation, and (C-1) notices that the left hand side of the equation in the second problem has the same pattern as the right (or, alternatively, (C-2A)realizes that multiplying through by x gives you a quadratic equation, and (C-2B) remembers the quadratic formula), can do the problems easily with only a scientific calculator. A student with a graphing calculator can solve them both without knowing anything other than how his calculator works.
My general recollection from both types of calculators (which included using a scientific calc. through all the pre-calc and trig, up through calculus--i.e., the stuff tested on the SAT) was that you could usually solve things with a scientific calc, but getting the problem in a position for you to do so usually required more manipulation (and assocuiated conceptual understanding). Whereas a graphing calc. really was often able to do the heavy lifting all on its own.
Our high school maths exams weren't multiple choice, and you did have to show your working and/or proofs. Calculators were allowed in the maths exams, but not in the GCSE-equivalent Arithmetic paper, which, afaik, no longer exists.
To restate and shorten, basing your analysis on "a kid who actually understood the math" is pretty misleading, except for students at the very top of the distribution.
Seriously, I want someone to explain to me what the benefit is of allowing calculators at all. You can test the math just fine without them, and did until fairly recently (and while I sympathize with the person with a deep conceptual understanding of the math who nonetheless makes dumb calculation mistakes, and I've been that person, I don't think it's a major problem if you write exams where the numbers work out fairly easily.) Calculators are great, useful tools, but not on math tests.
I have a bee in my bonnet about this, because I blame the availability of calculators even in Samoa for holding my students back -- they never did arithmetic, which meant that they couldn't do it, which meant that they had a hell of time understanding anything. (Of course, I also blame my own utter incompetence as a teacher, but all the calculators didn't help.)
244: I don't think we ever used calculators on tests, even in college. There was a time when I could multiply in my head very well. Now that I'm old, I have trouble figuring a tip, but I used to be able to give you 6.2 * 456 without a pen.
I want someone to explain to me what the benefit is of allowing calculators at all
IMO there's no (good) theoretical justification. I suspect the only real "benefit" to allowing them is avoidance of the fact that too many kids would bomb the tests without them, even if you write exams where the numbers work out fairly easily.
Practice is amazing for mental arithmetic. It wore off after a couple of years, but teaching math (making up problems that'd work out cleanly, having to work stuff out fast up at the blackboard so as not to have to slow down while teaching) left me with blinding calculation speed for a while. I'm back to needing to say stuff out loud to hold it in my memory between steps, though, and have been since about the end of law school.
Calculators are great, useful tools, but not on math tests.
My arch-nemesis in the math department will debate you on how kids need to be able to use a TI-89 in their future jobs, and their bosses will mock them if they are used to doing everything in their head. He'll say it really sneeringly, too, in a way that pretends to capitalize on our life experience gap, he being the older and wiser.
I used to love exams set by teachers who wanted the numbers to work out fairly easily. If you got 1.3546 for an answer, you knew you made an error somewhere and could go fix it.
246: I suppose it might be a recognition that while you can ban them on the tests, you can't successfully ban them in schools, so the population of students you're testing is already crippled by having relied on them for so long, and can't fairly be tested without their crutches. Somehow, it seems as if there's a better solution.
248: Grrr. You can console yourself by remembering that he'll die sooner.
248: Laugh a cold yet polite-sounding laugh, and tell him that the only calculational tool used in the average workplace is Excel.
I suppose one justification for using calculators is you can test a wider range of material, in a set length of exam. And banning calculator use really would widen the bell curve a lot. I had school mates who conceptually understood the maths -- well enough to get very high marks -- but weren't anywhere near as quick at mental calculation as I was. If we start factoring in arithmetic ability it's going to get pretty savage.
As I said above, in 'olden dayes' Scotland they were tested as different exams, and in the arithmetic exam all calculator use was banned.
Or roll your eyes, and say "TI-89? We might as well teach them to use slide rules."
Interesting items from Wikipedia:
Calculator Use
With the recent changes to the content of the SAT math section, the need to save time while maintaining accuracy of calculations has led some to use calculator programs during the test. These programs allow students to complete problems faster than would normally be possible when making calculations manually.
The use of a graphing calculator is sometimes preferred, especially for geometry problems and questions involving multiple calculations. According to research conducted by the CollegeBoard, performance on the math sections of the exam is associated with the extent of calculator use, with those using calculators on about a third to a half of the items averaging higher scores than those using calculators less frequently [8]. The use of a graphing calculator in mathematics courses, and also becoming familiar with the calculator outside of the classroom, is known to have a positive effect on the performance of students using a graphing calculator during the exam.
The point about "programs" confused me, until I read this:
An SAT calculator program is a software application that resides on a calculator which is used in helping to answer SAT questions. The programs themselves are different from SAT preparation books and classes in that they are actually used during the SAT test, and contain programs to answer questions with common SAT math formulas or simply answer common SAT questions.
But, sure, a scientific calculator is just as good...
IMO there's no (good) theoretical justification.
The standard math pedagogy says:
1. the more avenues along which you can present the material, the better. So the graphing calculator allows the kid to easily graph each problem, which gives them more than one way to see the material.
2. it saves time
I don't let kids use calculators whatsoever, and I don't put much stock in these reasons. My belief is that the real reason is:
3. I was given a bunch of students who can't do fractions or deal with equations, and I'm supposed to build on that knowledge, so I'd better let them use calculators or else I'm going to spend all year re-teaching the old stuff.
I think this is misguided as well, because they'll only internalize the fraction rules and equation techniques when they're forced to apply them to the new, harder setting. They act like they don't remember the material, but it is actually in a state of suspended animation in their brains.
Practice is amazing for mental arithmetic.
The way to get fast is to work a cash register or a farmers' market booth.
'Course, I'm now the person who has to come up with the weights to put on the bar, which takes a little figuring out and double checking.
254: On Halloween, my calc professor came to class dressed as himself in 1960 whatever when he was a student. He had a slide rule on his belt like Nerd Aragorn.
I suppose it might be a recognition that while you can ban them on the tests, you can't successfully ban them in schools, so the population of students you're testing is already crippled by having relied on them for so long, and can't fairly be tested without their crutches.
Given how much "teaching to the test" occurs, you don't think banning calculators on the SAT (and other national performance tests) would lead a lot of schools to ban them in the classroom, or at least routinely require kids to solve problems without them?
the only calculational tool used in the average workplace is Excel.
So, so true.
250. Except that if you ban calculators in tests, schools, which want their students to pass the tests (or awkward questions will be asked) will take measures to ensure that the students can do the tests with their brains.
256 more or les elaborates on the parenthetical "good" in my comment that it quotes. I do understand that theoretical justifications are made; I just don't really buy them.
253: I suppose one justification for using calculators is you can test a wider range of material, in a set length of exam.
Mmmmmaybe. It should be possible to design questions that test concepts without involving brutally difficult calculation. I guess I'd want to look at a modern test, and a circa 1960 test of the same subject, and see if the modern test really does address a wider range of material.
So the graphing calculator allows the kid to easily graph each problem, which gives them more than one way to see the material.
Aarrrgh! Whatever happened to learning to sketch curves with the intercepts and the derivatives and the inflection points and so forth? (And thank you for being a math teacher who appears to teach in accordance with all my crochety prejudices; I feel warm and comfortable knowing that there are kids in Texas being taught properly.)
256: I was given a bunch of students who can't do fractions or deal with equations...
Seriously? Maybe I just had a very good primary school teacher, but how do you get to college without being able to work with fractions? I never understood why equations were hard either, but I knew people who did, but fractions are intuitively comprehensible.
Seriously, I want someone to explain to me what the benefit is of allowing calculators at all.
It saves people carrying around trigonometric tables?
259, 261: Well, some schools would and some wouldn't -- there might be a big weird factor in test success depending on whether your high school had managed to pull its head out of its ass.
265: On tests. For a test, you can hand out the little booklets.
265: You just give the values you need (or a very reduced table) in the question on the exam.
Is 266 pure devil's advocacy or a real argument? I don't really want to take the time to address it, unless you're serious.
266. At which point awkward questions should be asked. You can't design your educational system around the Platonic form of the worst imaginable teacher.
I'm very sympathetic to the point of view that in the modern world (where integrals.com exists and google itself can tell you the answer to log(37)^2 * pi) that we should be moving away from an emphasis on performing computations in math classes and towards more conceptual things that allow students to use those tools. However, what doesn't make sense at all is having stupid straightforward computational questions and letting the students use calculators. Fine let people use calculators or mathematica or google or whatever, but then you have to have much more challenging questions that test material not just calculation.
He had a slide rule on his belt like Nerd Aragorn.
Whereas people who dress up as Aragorn aren't nerds at all...
(I should say that I still think of my HP 12C with immoderate fondness, and think that it deserved half of my freshman Chemistry/Materials Science grade. A well designed calculator is a wonderful thing, and I'm sure I'd feel the same thing about graphing calculators if I'd ever used one. Just not in math class.)
Whatever happened to learning to sketch curves with the intercepts and the derivatives and the inflection points and so forth?
Well, these arguments are applying more to lower level classes - algebra, trig. But it's still complete nonsense. You're always introduced to the functions you're expected to be fluent in, within a course. So a typical Precal course has a day on our "Library of Functions" where you review lines, parabolas, square root functions, cubics, abs. value, etc. Then you're expected to acquire new functions as the semester progresses. It can be done easily without a calculator.
The harder problem is if you're given a textbook that is designed to be taught with a calculator, and you don't have the freedom to choose your own book. (Which you usually wouldn't, because you're one of a dozen people teaching College Algebra, and everyone else likes the book.)
If a book is designed to be used with a calculator, then it is really hard to disentangle it. None of the instructions for the homework problems work without substantial modification, and when you're already taxing kids mathematically, you don't want to pile on that. And the problems generally get super messy by hand, even if you tried to sort them out.
I was able to stomp my feet loudly enough that we've gotten rid of all books that necessitate calculator use. But I'm just one gal down in Texas.
270, 271: I'm serious that I think it might be an issue. I don't think it's a good enough reason to justify allowing calculators, but there are enough shitty math teachers out there that I think there'd be a risk of people not getting that they were hurting their students by not expecting them to learn to calculate.
I'm completely shocked that they allow calculators on the SATs. Did they always allow them, and I just don't remember?
I actually sort-of think that teaching how to sketch curves with inflection points, etc. is kinda useless, and you're better off graphing it on a computer.
Maybe I just had a very good primary school teacher, but how do you get to college without being able to work with fractions?
BECAUSE YOU USED A CALCULATOR FOR THE PAST 12 !@#!@ YEARS AND IT CONVERTED EVERYTHING TO A DECIMAL.
Am I being trolled?
277: wikipedia says they started allowing them in 1994.
I actually sort-of think that teaching how to sketch curves with inflection points, etc. is kinda useless, and you're better off graphing it on a computer.
Well, it helps you understand what the first and second derivative tell you about the function. If a function is simple enough, and I need a quick graph, I'm certainly going to go this route before I haul out a computer.
278: No, I was serious. I've never encountered not being able to deal with basic fractions. I had no idea it was common. Perhaps my experience has not been typical. I had tough nuns teaching primary school math, a strict high school math teacher, honors calc in college, etc.
272: I'm not really sure why, but allowing calculators too early causes some sort of brain damage, where you become completely helpless in the face of anything you can't instantly punch into the machine. If you reach for your calculator when you need to multiply by 1, you've completely lost the ability to think when confronted with a mathematical problem.
re: 257
Not so much use for trigonometric calculations, or logs, or working out nth roots of long numbers.
280: Right. If you learn how to do it, it's helpful for developing a ballpark sense of what a function is going to look like just by looking at the expression. If you want something exact, sure, the computer is your friend.
I actually sort-of think that teaching how to sketch curves with inflection points, etc. is kinda useless, and you're better off graphing it on a computer.
I think this is certainly true once you know how to do it (i.e., in higher-level courses), but learning the process teaches you a lot about what functions are and how they work (not to mention the cartesian plane, etc.).
281: Well, seriously, it's because you were taught without calculators. Calculators convert everything to decimals. Kids raised on calculators don't think of fractions as a ratio.
It completely hobbles their intuition on slope and on derivatives.
286: Plus, I had to walk home from school, so I'm only overweight and not obese.
Excel
Send him a large detailed dataset just before a meeting and ask a basic question that can only be answered with a pivot table or by loading the data into a server.
One problem with calculators or other automated tools and basic understanding is that the sense "this can't be right" may never develop, because the user never actually thinks about the question being asked, but just transcribes it.
http://www.skytopia.com/project/fractal/mandelbulb.html
Not so much use for trigonometric calculations
You can do a lot of ballpark trig by remembering the values at the easy angles, π/6 and so on, and interpolating. If you want something exact, you're stuck, but if you never have to estimate, then you don't know how to catch your errors.
The extra physical dexterity really helps when chasing kids out of my lawn.
Not so much use for trigonometric calculations, or logs, or working out nth roots of long numbers.
There's absolutely no reason that the kid can't just keep the expression 5^{1/19} or cos(3pi/11) in their answer, unsimplified further.
Again, reliance on calculators prevent them from first checking logically how you might simplify 2^(2/5)*2^(3/5). They just automatically plug it in a calculator.
FWIW, although we did use calculators at school we were only allowed to use them from 3rd year of high school onwards, iirc. Before that they were banned. And we were taught to use slide rules, log tables, trig tables, and all that.
In conclusion, get off my lawn.
280: That's a good point. But isn't is sufficient to go the other way, and say, "Here's a graph. What's the inflection point? Where is the first derivative positive or negative." Back when I taught calculus, the actual whole process of sketching the graph based on the derivatives seemed incredibly time-consuming for the level of payoff.
But isn't is sufficient to go the other way, and say, "Here's a graph. What's the inflection point? Where is the first derivative positive or negative."
It's sufficient for strong students. I think the weaker students get a real payoff from successfully navigating those 8-step problems where no single step is too difficult, and then they synthesize it all together into a single coherent graph.
Maybe I just liked the graph sketching because it was fun -- you could get a complicated graph out of not very difficult to acquire information. But I think it was conceptually valuable seeing the picture emerge from the numbers, at least for me.
As near as I can recall, the only truly useless thing I learned in a math class is imaginary numbers. I cannot recall why we learned that or what it was supposed to be for.
I didn't just call LB a weaker student.
Complex numbers come up a lot in physics.
Wait, hold on--I must be misunderstanding something. Please tell me that elementary students aren't using calculators in their math courses. Please. I thought the point of those courses was to learn how to do simple arithmetic, and learn fractions and ratios, etc. I actually hadn't even considered the possibility that students would be using calculators earlier than algebra, at the very earliest (which I would still think of as too early). What exactly would a third-grader be supposed to be learning, if they're allowed to use a calculator?
296: So that eventually, when you get to a Complex Variables class, you will realize that Euler's Formula actually makes perfect sense and isn't arbitrary at all, and your mind will be totally blown.
297: No worries. I don't think I would have suffered much in understanding if I'd never done that sort of graphing, but it was something that make me feel the concepts clicking solidly into place.
298: That probably explains it. But, I spent a great deal of time trying to get my head around it before deciding that it was like being able to parallel park. Somebody has to know how to do it well, but I only need to be able to half-ass it.
Euler's Formula
Euler. Euler. Euler....
Sorry. That was much funnier in 1989.
Complex numbers make 98% of trigonometry trivially easy. Deriving something like the formula for cos(2x) takes about 30 seconds.
Plus the basic laws of the universe (quantum mechanics) require complex numbers to even write down.
What exactly would a third-grader be supposed to be learning, if they're allowed to use a calculator?
They are learning how to use a calculator -- probably the only math they will ever know.
Also, I parallel park by driving straight into the spot, and then multiplying by i to rotate my car.
Please tell me that elementary students aren't using calculators in their math courses....What exactly would a third-grader be supposed to be learning, if they're allowed to use a calculator?
I don't know the degree to which calculators are used in elementary school. I bet there's a fair amount of hands on manipulatives, and calculators at most come out on special days. But I bet in middle schools, they're pretty pervasive.
I'm meeting with a Math Ed person this afternoon, actually, so maybe I'll ask.
My kids didn't use calculators in elementary school. I'll be interested to see what happens in Sally's middle/high school, which has an STEM focus -- are they good geeks, who understand the perverse effects of overuse of calculators, or bad geeks who are in love with gadgets even when they're harmful?
Okay. So people actually do learn fractions at some point, they just forget much about them after they get used to using their calculators reflexively.
When I realized that you said "12 !@#!@ YEARS" in 278, I got a little worried that maybe they were being introduced in first grade these days.
309 to 307, although it would work fine to 308 as well, except I'd have to replace the "you" with a "heebie".
Can we blame NYSE (for stopping the 'down 1/8th') and the decline of horse racing for kids not learning fractions anymore?
308: My bet is that the kids are sharp enough that the teachers can afford to nurture good geeks. That the other track gets pulled out on middling to weaker students.
I had to have a scientific calculator in middle school (1990-93) and a graphing calculator in high school. My parents complained about the expense but the teachers insisted. The main thing I did with my graphing calculator was type lots and lots of rows of dots and lines and spaces, and then scroll back through it so it made a swirly pattern of the spaces moving back and forth across the page.
Then I had to give the calculator to my sister after my junior year, and I never took another math class because Reed lets you take French instead.
Reed has curious beliefs about fungibility.
That sounds like a line from Strongbad's children's book.
And the picture would have mushrooms, probably.
No two mushrooms are not psychedelicized.
Re: standardized tests (167-170 in particular, but also in general), I agree. I used one simple assumption: each incorrect answer is one mistake away from the correct answer, with maybe one completely-out-of-left-field option thrown in to trip up people who are trying to get too clever. To apply that principle to the sample test questions in 233, I'm not sure whether or not it would produce the right answer to the first question, but I could make a good argument that it does produce the correct answer to the second. (Every answer has a "5" in it except for "1", and in a question like this "1" is actually sort of out of left field.)
275
I was able to stomp my feet loudly enough that we've gotten rid of all books that necessitate calculator use. But I'm just one gal down in Texas.
On the plus side, as I understand it, Texas is responsible for the school textbooks used around the country.
Reed's curiosity about fungibility resulted in a trip to the psych ward.
But if you compared groups with equal scores then I would expect this pattern (blacks doing relatively better on hard questions).
This pattern occurred for 1 out of 4 of the verbal tests and for none of the math tests.
I can confirm what Heebie's saying: Calculus students at Berkeley have a lot of trouble with fractions. In fact I'd say the only thing they're worse at than fractions is taking cases. If a problem requires splitting into two cases, then only one or two people in the class can do it correctly.
So that eventually, when you get to a Complex Variables class, you will realize that Euler's Formula actually makes perfect sense and isn't arbitrary at all, and your mind will be totally blown.
So true. That was probably the coolest moment of my maths "career", and one of the few I can remember.
I'm trying to figure out in what context someone would have been introduced to Euler's Formula in a way that made it seem potentially "arbitrary". I think Calc II was when I first saw it, in connection with infinite sequences. Do most people see if earlier, in some other context?
I was vaguely familiar with it as a neat math object from sometime in high school, but didn't know what I was supposed to do with it. But even encountering it in a class, didn't it seem "Wow, that's weird and unlikely that that should be true" rather than, after you're exposed to the complex trig functions and so on, "It's as self-evidently necessary as 2+2=4"?
(Sadly, it'd take me weeks with a textbook to get back to where I actually understood the latter statement again -- I sort of remember the shape of it, but I'd have to relearn everything to get it back.)
One problem with calculators or other automated tools and basic understanding is that the sense "this can't be right" may never develop
Which is unfortunate, as that may be one of the most important skills of all time in hiring people. It continues to astound me that so many people can make it to adulthood without developing it. At least I don't have to hire them.
Sorry, s/b one of the most important skills to look fro when hiring people. As in, you want them to have it.
317 made me laugh.
I don't really understand why calculators even exist anymore. The need for a distinct tool to do calculations seems kind of irrelevant now that computers are everywhere. This goes especially for the fancy overpowered graphing calculators; give the kids a laptop with a computer algebra system instead.
I don't really understand why calculators even exist anymore. The need for a distinct tool to do calculations seems kind of irrelevant now that computers are everywhere.
This is crazy. What if, for example...you aren't using a computer, and yet you need to do a calculation. This may seem unlikely but it occurs a lot in my experience.
It's possible to not be using a computer?
Some people stand up and walk around occasionally.
"Wow, that's weird and unlikely that that should be true"
Oh, I guess, although I'd replace "weird and unlikely" with "amazing". I thought you meant something else by "arbitrary", more like "just a fluke coincidence resulting from how we've chosen to define these various terms"*, instead of something both useful and fundamentally true.
*Which, of course, is actually true, in a trivial sense.
You know who didn't use a computer? Stalin.
But really I do mostly mean the fancier calculators -- I can see why some people might want a pocket calculator to do basic arithmetic (although, yes, a phone works for that these days, or there's always paper and pencil in a pinch). But if you need to graph some functions, or solve equations, or do some numerical integration, are you really ever in a situation where a laptop is hopelessly inconvenient but a TI-89 isn't?
I'm with 331. Ned: In what common scenario do you (1) need to do a complex calculation, (2) have access to a calculator, but (3) not have access to a computer?
You kids stay the hell away from my 12C.
Or furthermore, if you are the field engineer who comes across those situations regularly, surely you can purchase and read the manual to your TI-4Billion.
One problem with calculators or other automated tools and basic understanding is that the sense "this can't be right" may never develop
God, yes, and is it ever jaw-dropping. I expect we're seeing the same thing with spelling-fu. As more people become dependent on that wiggly red line under a misspelled word, the "that doesn't look right" sense is increasingly absent. Boo.
332: Some people stand up and walk around occasionally.
This made me laugh.
I ahve a 12C that I use daily. But that's because I first learned to do things with it, not with excel. Almost all of my use of the 12C occurs while sitting at my computer. I suspect if I'd learned with excel first, I'd be just as quick with it, and I'd have no use for a 12C.
336: You're an urban high school student and neither your parents nor your school has the budget to provide you a laptop?
I don't share the suspicion in 340.last, but that may just mean that I'm turning into my dad.
341 is fair, although the price difference between, say, an EeePC and a TI-89 is not all that dramatically different. It won't be long before a laptop is more-or-less equally cheap, and they're far more useful. School systems really should have the budget to provide them....
Working through what the derivative of a complex function is cleared up a lot about continuous functions for me, got me out of thinking about derivatives as just the limiting cases of a discrete process.
Also, understanding what the fundamental theorem of Algebra says is important.
341 is fair ... except insofar as ned sounded like he was talking from personal experience, and I don't think this experience is his.
I'm with 331. Ned: In what common scenario do you (1) need to do a complex calculation, (2) have access to a calculator, but (3) not have access to a computer?
What "complex calculation"? How about if I want to add 1 + 4 + 4 + 5 + 4.25 + 4.75 + 0.125 + 13.625 + 15 + 28.65 or something, as happens every day in a lab.
I expect we're seeing the same thing with spelling-fu
Grrrr. If I hear "How do you spell...?" one more time I will kick the dog. And I like the dog. Did the Devil finally get Webster? Don't you people know how to use a dictionary? There is one on the net you know.
241: In your two examples, the student who remembers (A) that 8=2^3, and (B) the rules for exponent manipulation, and (C-1) notices that the left hand side of the equation in the second problem has the same pattern as the right (or, alternatively, (C-2A)realizes that multiplying through by x gives you a quadratic equation, and (C-2B) remembers the quadratic formula), can do the problems easily with only a scientific calculator. A student with a graphing calculator can solve them both without knowing anything other than how his calculator works.
Yeah, but the kid with the scientific calculator can also solve the problems by plugging the 5 answers into the equation without knowing anything other than how his calculator works, too. And either kid who can't do the algebraic manipulations will be at a serious disadvantage on the other 42 questions that don't ask for a simple numerical root finding. A good symbolic algebra package, on the other hand, could be a serious advantage to the kid who has it, if any of the allowed calculators offer it as a standard option.
Following the link in your 255, I'd say that SAT calculator programs like this look evil. I was thinking of graphing calculators off the shelf, not what you might be able to cram into their memory with negligent proctoring.
Still, I'm not overly impressed with how long it takes the guy to solve that particular problem. Given that question, if I wasn't up to finding the full prime factorization, I would just toss any answer that wasn't a prime, and start checking prime answers for divisibility from the biggest on down. Even without Dave's handy rules for testing divisibility by small numbers (for 11, you form the alternating sum and difference of the digits and see if the result is divisible by 11: 2-4+2 = 0, so 242 is divisible by 11), how long does it take to try 242/11 on your calculator and see that the result is an integer?
Or figure out how many grams of something with molecular weight of 146.7 I need to get 40 milliliters of a 1.5 molar solution.
346, 349: right, as I said, I can see wanting a pocket calculator for that sort of thing, although a phone can suffice.
This is not the kind of calculator students are being taught to use. I just don't see a role for the calculator that does more than arithmetic but infinitely less than a real computer.
spelling-fu
When I write in languages that I'm not fluent in, I routinely google uncertain phrases to see whether they are grammatical. Le singe est sur la branche and all.
As more people become dependent on that wiggly red line under a misspelled word, the "that doesn't look right" sense is increasingly absent.
I'd be glad of that, to be honest. My brain seems to produce an awful lot of false positive "that doesn't look right" signals when I'm typing correctly.
350. It is a piece of hardware that does not require administration, cannot be used to enjoy porn in the classroom, and its work functions cannot be corrupted by viruses from Sendspace.
cannot be used to enjoy porn in the classroom
Someone just isn't trying hard enough, then.
OT: By the way, it looks likely that I'm going to be in New York the first week of August. Any chance of a meetup then? I need to figure out my travel dates in the next few days. Something midweekish to maybe Friday would probably work best for me.
Generally, sure, although specific planning should probably wait a couple of weeks.
Don't you people know how to use a dictionary?
TLL. If your radar doesn't even go off that something doesn't look right, you're not going to think to turn to the dictionary; and of course, even if you do, you'll have trouble knowing to which page to turn.
Googling can actually be helpful in such a case, as lw notes (providing that "did you mean [blah]?") helper. You need the radar in the first place, though.
(providing that "did you mean [blah]?") helper.
I really wish they also included a "no" answer, though. No I did NOT mean that! I put it in quotes and everything, you stupid Google!
If your radar doesn't even go off that something doesn't look right, you're not going to think to turn to the dictionary
Different problem. I was complaining about being the "shout out" dictionary. Look it up yourself, lazy bad spelling person!
This is not the kind of calculator students are being taught to use. I just don't see a role for the calculator that does more than arithmetic but infinitely less than a real computer.
A calculator that generates a basic quadratic equation is quite useful in the lab as well. A lot of the time we use a series of limiting dilutions for something, and then we need to calculate the concentration at which, theoretically, 50% of the spots would have changed color, or something.
But yeah, I usually only find it essential for artimetic.
339: But really I do mostly mean the fancier calculators -- I can see why some people might want a pocket calculator to do basic arithmetic (although, yes, a phone works for that these days, or there's always paper and pencil in a pinch). But if you need to graph some functions, or solve equations, or do some numerical integration, are you really ever in a situation where a laptop is hopelessly inconvenient but a TI-89 isn't?
Having worked with a bunch of statistics students this past year, I'd say that for many practical statistics calculations, the TI-89 has it all over Excel (which is not to say that there isn't a better statistics program for the PC out there). Excel's built-in statistics functions are just far too limited for a bunch of the calculations you want to do. Even calculating the standard deviation of a non-uniformly distributed random variable is a royal pain in the ass in Excel, and the only good way to do it is to break the calculation down into its components and calculate them separately. I had one student who was taking an Excel-based course in statistics, and so much of that course for her was building specialized spreadsheets to do the calculations that are built into the TI-89.
I was complaining about being the "shout out" dictionary.
Ah. I see. Like people at home and/or in office asking, "How do you spell ..."? I might get a little passive aggressive about that after a while: "Gee, I don't know. Here's a dictionary! Let's look that up! Together!"
This would strictly be in order to avoid kicking the dog.
361: You mean like finding the standard deviation by numerically integrating the PDF?
50% of the spots would have changed color, or something.
Are you making acne medication?
361: Excel is teh suck for many common statistical functions. But most working statisticians don't use Excel for any but the simplest calculations. I use it for making tables, but the numbers that go into the tables are from SAS or Stata.
Excel is a godawful piece of shit, and shouldn't even be part of the discussion.
Oh please. All managers use excel, will send you data in Excel, expect to receive summaries in excel. For many simple tasks, it's a huge labor saver. It's not a database or statistical system, but can look like one for small datasets and simple tasks.
The biggest problem with spreadsheets in practice is cache-coherence, everybody has a local copy of the relevant data, or even better, many local copies from various sources and times.
Another problem with Excel is people who put information in by color-highlighting cells instead of using some way of marking information that doesn't require the analyst going through the whole fucking thing to create an actual useful field.
367: But I thought we were talking about what to teach people to use in math classes. Excel is not designed to do the things that calculators do; it can do some of them, but only painfully.
Excel came up first in the context of how students will likely do any calculating that they need to do in their eventual jobs.
366 is correct. Not only a godawful piece of shit, but one that has established piece-of-shitness as the standard for spreadsheets.
363: I was thinking more of discrete distributions, like trying to find the standard deviation of the total of two fair dice. In Excel, if you want to use the built-in functions, you need to enter the data so that each variable occurs as many times as it does in the overall distribution (so one 2, two 3s, three 4s, etc., for 36 separate numbers). The TI-89 allows you to enter a second list that has the frequency of occurrence of each element in the first list, though it's not quite as good as I remembered it (it requires that the frequencies be integers, and it only calculates the sample standard deviation, so you need to correct to get the population s.d.). It still beats what you have to do in Excel.
You want to compute the exact standard deviation of a discrete distribution in Excel? That's just a weighted sum of numbers, which is easy in Excel.
Also, if someone encodes data by color coding, you can convert the color coding into real data by using a macro.
Basically Excel is perfect in every way.
Excel doesn't do statistics, statistics do Excel.
Also, if someone encodes data by color coding, you can convert the color coding into real data by using a macro.
Now you tell me.
I miss my HP32.
This brings up one of my more nerd-pride moments from high school; I was taking a test in a physics class, which (reasonably) expected you to have and know how to use a scientific calculator. However, I discovered that I'd forgotten my calculator at home when I tripped across the first problem that needed it, something with computing forces in various directions, involving trig. Instead of doing something reasonable, like ask the teacher if he had a spare calculator, I proceeded to evaluate the first few terms of the Taylor series for the function on my four-function watch calculator, and merrily went on with the test.
I am awed by your nerdly competence.
373: You want to compute the exact standard deviation of a discrete distribution in Excel? That's just a weighted sum of numbers, which is easy in Excel.
Well, that's basically what I meant by breaking the calculation down into its components, but it's a little tricky to call "easy." You use the population variance definition, Var(X) = E(X^2) - E(X)^2. Basically, you put the frequencies in column A, the associated values in column B, and compute the squares of those values in column C. Then you use SUMPRODUCT on columns A and B to get E(X) (dividing by the SUM of column A in case the numbers represent counts or relative frequencies and don't sum to 1), and likewise use SUMPRODUCT on columns A and C, dividing by SUM(A) to get E(X^2). Then take the square of the first SUMPRODUCT and subtract from the second to get the variance, and take the square root of that to get the population standard deviation. If you want sample variance and standard deviation instead, assuming that column A represents counts rather than absolute frequencies, then you divide by SUM(A)-1 rather than SUM(A) in the two divisions.
It's certainly possible to "roll your own" this way if you know and are fully comfortable with that variance formula. Lots of my students' statistics texts don't present it in that form, but in another equivalent form that would need to be massaged in order to get it into that form (or that would take more work to implement directly in Excel). I think that's a bit much to ask for students who are struggling to understand statistics in the first place and not too familiar with Excel. Given that Excel has supplied something like six different built-in functions to compute standard deviations, is it too much to ask that at least one of them allows for non-uniform frequencies? Apparently so.
234: (Me): For those types of questions, if he couldn't solve it algebraically, I just advised him to evaluate the function moderately close to the limit.
LB:I see this, and wonder why they allow calculators at all. Isn't the point that they're supposed to be able to solve the problems algebraically?
Well, the specific question was #31 from the first Level II practice test (in the specific Math level I & II study guide): What value does (ln x)/(x-1) approach as x approaches 1? The choices are: 0, 0.43, 1, 2, and "It does not approach a unique value." The College Board-approved solution basically says "use a graphing calculator for this one."
Now if I had to solve this elsewhere, I would use l'Hôpital's rule, but the test isn't supposed to require calculus (it expects math up through Precalculus). Or if you knew the series expansion for ln(1+x) = x - x^2/2 +x^3/3 - x^4/4 +..., you could transform the problem into the limit as x goes to 0 of ln(1+x)/x, and then the answer is pretty clear. But that's not supposed to be required for the exam, either. It seems they just expect the kids to look at the graph around x=1 and figure it out, unless there's some elementary method I'm missing here. So my advice for my son with the non-graphing calculator was just to calculate ln(.99)/-.01=1.005 and ln(1.01)/.01 = .995, which is enough to suggest strongly that the answer is 1, and answer the question and move on. It's only one question, and I didn't want him either conceding the point unnecessarily or wasting a lot of time on it.
320
This pattern occurred for 1 out of 4 of the verbal tests and for none of the math tests.
Are you getting this from the paper? How did they match groups of equal ability?