The Prima Donna Rock Star Tester Treatment

I met with her the first time last Sunday a week before the SAT, mother looking on, and the conversation went something like this.

“I want to specialize in one test. Which one should I take?”

“Yeah, okay, back up a bit. You took SAT test prep over the summer, right?”

“Yeah, but I knew everything they told me. It didn’t help.”

“What’s your course load?” (she goes to a 50% Asian school.)

” I’m taking a history honors class now, but it’s my first. Precalc for math.”

“And your GPA? What colleges are you considering? ”

Shrug. “3.8 or so. Colleges, I have no idea. But what I want to know is, should I specialize in the ACT or the SAT? And should I take the old one or the new one?”

“Do you have a target SAT score?”

“2000. What’s the equivalent in ACT? But I really think I should take the old SAT and be done. ”

“Your last practice test was a 1400.” She winced. “Even if all colleges take the old SAT for 2016 admissions–something I find unlikely despite assurances to the contrary–I’m not sure how you can find the time to focus on improvement between now and January, the last sitting of the old test. Besides, why the hurry?”

She waved dismissively. “I want to be done with all this. I hate the SAT. Maybe I should specialize in the ACT. I don’t want to learn the new SAT.”

“Yeah, we’re back to this whole ‘pick a test’ thing. Let’s discuss something touchier. Are you frustrated by the difference between your school performance and your test performance?”

She got very still. “Yes.”

“When I see an academic profile significantly higher than a test score, the student usually mentions it first. I’ve met many kids, a lot of them girls, with a profile like yours. They’ll tell me that they really just want to improve, to get their score into a respectable range, and that they haven’t had good luck with test prep so far. I didn’t hear any of that from you. Instead it’s ‘gotta pick a test’, need a 2000′ despite no college plans, without any acknowledgment of what must be a very disappointing practice history.”

I said all this as delicately as possible, but she was already surreptitiously wiping away tears.

” I don’t see your mom behind this. You’re causing your own pressure but are also very resistant to making more effort or exploring options.”

She started nodding before I finished, and her mom handed her a Kleenex. “I just think I’m wasting my time.”

“So let’s start there. Do you have trouble with school tests? No? How about your state tests? So it’s not a general testing problem, just big standardized tests. Is it nerves?”

She laughed, sadly. “No. My big problem is motivation.”

I snorfed involuntarily, and she looked up in shock. “Sorry. I’m not at all laughing at you. Just the idea that the kid I see in front of me barking orders like an executive suffers from motivation problems.”

The mother demurred here. “Well, her GPA is only a 3.8.”

“Forgive me, but you’re Chinese and prone to distortion on this point.” They’re American enough to laugh. ” I see an articulate, bright, driven girl who appears to have an intellect that I would put conservatively three or four hundred points above this practice score. You are using that intellect in school. I don’t see an obvious motivation issue.”

“No, not in school. Not studying. When I’m testing–you know, like the practice tests? I lose all motivation.”

Well, hey now.

“Tell me if any of this is familiar: The test begins and you’re working away, feeling good. Then you run into a problem that you don’t know how to solve and suddenly, as you try to figure the problem out, everything seems pointless. You give up, make a guess, go on to the next problem. Except now you aren’t sure what to do with this one, either. Suddenly, nothing matters. You simply stop caring. I see by your face that I’m not off-base.”

“How did you know?”

“I’ve seen it before. I describe it as a sort of stress reaction.¹”

” I’m not nervous at all.”

” You should be so lucky. Jitters don’t usually affect performance. You get bored by stress. What happens, best I can tell after hearing many students describe the feeling, is that your brain shuts down to avoid feeling stress.”

My first case was a short, slight blond boy back before the SAT changes, so before 2005. I was going through his practice test explaining the missed problems, and he’d finish my sentences. That is, he knew how to do many of the problems he’d gotten incorrect on the test.

So why the high error count, I asked.

It was after I got bored, he replied. Once the boredom hit, he’d start to randomly bubble. I was aghast. He may as well have told me he sucked dead chickens’ eyeballs for candy, so incomprehensible was his behavior.

“So what you have to start doing, have to understand, is that you are a testing prima donna.”

“A prima donna?”

“You know how movie stars always order off-menu? Because they’re just too special for the pre-arranged menu that the rest of us use. Or the ballerinas or opera stars who simply refuse to be rushed, because they are artists. Or rock stars, the kind who make huge demands for their hotel rooms sometimes—Van Halen famously demanded brown M&Ms be removed from the candy bowl (yes, I know they had another reason, but her parents are never going to let her listen to Van Halen, so I’m safe). You need to be a prima donna rock star tester.”

“How?”

“Take two SAT sections daily, from the blue book. Use deadly serious test conditions. No music. No interruptions. No stopping the clock. No laying on the floor or on your bed. Sit at a table, door shut, start the timer.”

“That’s not even an hour.”

“And when the timer starts, I want you to take two minutes, at least, to go through the test and cherrypick. Circle the problems you’ll deign to do.”

“Um. What?”

“In math, pick and choose your problems. Circle the good ones. ‘This one, I shall do. This one, pah!’ Spit upon it. If you don’t instantly vibe to the question, avert your eyes and scratch an X next to that problem, which clearly must be for peasants and other little people. Can you do that?”

She giggled. “Really? What about reading?”

” Skip anything with long paragraphs that looks less desirable than root canal. You like sentence completions?”

“Yes!”

“Do them first, then evaluate each reading passage to determine whether or not Her Majesty–that’s you–is interested. Which part of the writing section do you like best, the paragraph at the end?”

“How do you know this?”

“Do those six questions at the end first. Then go back to the front. The second–I mean the second—you find a long sentence you can’t instantly decipher, that question OFFENDS you. Turn up your nose. Move on.”

“So that’s all I want for the week. Two sections. Vary the subject. Every night. Take them like a rock star looking at candy bowls to make sure there are no…oh, look there’s a brown M&M. Skip it.”

“But I might only want to do four or five questions a section.”

“Great. Do those. Then, oh, hey. You’ve still got 20 minutes to kill. What’ll help pass the time? Let’s look at the other questions to see if they hold any interest. You are a movie star stuck in Podunk, in search of decent dim sum.”

“But the whole thing is a lie. The problems I can’t do aren’t stupid.”

“Sure, but we need to fake out your psyche. You have a fragile testing temperament that must be coddled and swathed in protective coating.”

The mom was a bit stunned, but accepting. “So none of the strategies she learned in test prep?”

“Mom, they didn’t work anyway. But what if I don’t have enough time to go back and do the problems that bored me?”

“Then you will have spent a whole test section working on problems you can do. How is that worse?”

“But if I try to read the long passages, I know I will get bored.”

“Well, I have some ideas for that later, but for now, read the passages that meet with your approval, and do the questions. Then for the rest, amuse yourself with the peasant passages. Do the vocabulary questions. The ones with line numbers. Don’t read them if they bore you. Normally, you understand, I wouldn’t suggest this.”

“So practice that all week. Eat pizza, chocolate, noodles, sesame balls with red bean paste, whatever your favorite food is Friday night. Saturday, have a good breakfast and visualize rejecting all those peasant problems.”

“What if I get bored anyway?”

“That’s a very real possibility. At the first moment you identify boredom, put your pencil down. Take a breath. Remind yourself that while it’s scary, this boredom is a valuable opportunity to practice dealing with it. That it only feels like boredom. Do not give up. Do not let yourself randomly bubble. If you feel done and can’t fight off the boredom, put your head down and take a nap. Otherwise, go back to the test and look for test questions that pique your curiosity.”

“But you said I didn’t have to read the passages.”

“Sure. But don’t randomly bubble, or give up. Estimate. Eliminate known wrong answers. Guess based on the context. But if you can’t kick off the boredom and feel hopeless, take a rest until the next section.”

“And here’s the important part: under no conditions are you to worry about your score. You’re not there for the score. You’re there to practice being a rock star who picks and chooses her projects. We’ll do scores later, if you like.”

“That’s okay. I don’t think I’m going to improve now, so at least I might know why.”

“It’s helpful just to know what the problem is,” her mother agreed.

They actually smiled as I left, both noticeably less anxious than they were when I arrived.

Note: she’s a junior, and has no reason whatsoever to take the SAT in October. I tried to talk the mom out of that, but she was determined to keep the date. Ideally, I wouldn’t send a student to try out this method on a live test, but that was the only option.

Will it work, this refusal to tolerate brown M&Ms and uninviting questions? Typically, yes, although since I’ve cut back on tutoring I haven’t run into the prima donna tester in several years. The cases I remember always saw an instant boost of 100-150 points the first time they took the test in rock star mode. In every case, they were also mentally exhausted afterwards. They’d never worked the entire test before, having mentally checked out. Prima donnas are fixable. The ones who go into a fugue state, not so much. Fortunately, that’s even rarer.

I started to make a larger point, but it’s too complicated and, since returning this August I’ve vowed to post more. I had too many ideas piling up that just weren’t…perfect, and so I kept putting them off, even though each idea had more than enough for a post. Time for me to limit scope and bite off achievable chunks. Otherwise I’ll think I’m bored and don’t care when really I’m stressed out….hey. Good thing I don’t get like this for tests.

So don’t read too much into this beyond an interesting behavior that I’ve learned to treat. Don’t apply it to policy. Do I think some people underperform their abilities on tests? Yes, I do. Do I think that tests can be gamed by people whose essential intelligence is high on mimicry and memory, giving the impression of skills they don’t actually have? Yes, I do. Do I think tests are mostly accurate? Yes, for most people. It’s a big ol’ world out there. Many cases exist simultaneously.

Meanwhile, I hope all you testers out there did well yesterday. And if you know any fragile testing temperaments, give this strategy a try.

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¹ While writing this piece, I googled and learned that researchers call it stress, too.

Evaluating the New PSAT: Math

Well, after the high drama of writing, the math section is pretty tame. Except the whole oh, my god, are they serious? part. Caveat: I’m assuming that the SAT is still a harder version of the PSAT, and that this is a representative test.

Metric	Old SAT	Old PSAT	ACT	New PSAT
Questions	54  44 MC, 10 grid	38  28 MC, 10 grid	60 MC	48  40 MC, 8 grid
Sections	1: 20 q, 25 m  2: 18 q, 25 m  3: 16 q, 20 m	1: 20 q, 25 m  2: 18 q, 25 m	1: 60 q, 60 m	NC: 17 q, 25 m  Calc: 31 q, 45 m
MPQ	1: 1.25 mpq  2: 1.38 mpq 3: 1.25 mpq	1: 1.25 mpq  2: 1.38 mpq	1 mpq	NC: 1.47 mpq  Calc: 1.45 mpq
Category	Number Operations  Algebra & Functions Geometry & Measurement Data & Statistics	Same	Pre-algebra  Algebra elem & intermed. Geometry coord & plane Trigonometry	1) Heart of Algebra  2) Passport to Advanced Math 3) Probability & 4) Data Analysis Additional Topics in math

It’s going to take me a while to fully process the math section. For my first go-round, I thought I’d point out the instant takeaways, and then discuss the math questions that are going to make any SAT expert sit up and take notice.

Format
The SAT and PSAT always gave an average of 1.25 minutes for multiple choice question sections. On the 18 question section that has 10 grid-ins, giving 1.25 minutes for the 8 multiple choice questions leaves 1.5 minutes for each grid in.

That same conversion doesn’t work on the new PSAT. However, both sections have exactly 4 grid-ins, which makes a nifty linear system. Here you go, boys and girls, check my work.

The math section that doesn’t allow a calculator has 13 multiple choice questions and 4 grid-ins, and a time limit of 25 minutes. The calculator math section has 27 multiple choice questions and 4 grid-ins, and a time limit of 45 minutes.

13x + 4y = 1500
27x + 4y = 2700

Flip them around and subtract for
14x = 1200
x = 85.714 seconds, or 1.42857 minutes. Let’s round it up to 14.3
y = 96.428 seconds, or 1.607 minutes, which I shall round down to 1.6 minutes.

If–and this is a big if–the test is using a fixed average time for multiple choice and another for grid-ins, then each multiple choice question is getting a 14.4% boost in time, and each grid-in a 7% boost. But the test may be using an entirely different parameter.

Question Organization

In the old SAT and ACT, the questions move from easier to more difficult. The SAT and PSAT difficulty level resets for the grid-in questions. The new PSAT does not organize the problems by difficulty. Easy problems (there are only 4) are more likely to be at the beginning, but they are interlaced with medium difficulty problems. I saw only two Hard problems in the non-calculator section, both near but not at the end. The Hard problems in the calculator section are tossed throughout the second half, with the first one showing up at 15. However, the coding is inexplicable, as I’ll discuss later.

As nearly everyone has mentioned, any evaluation of the questions in the new test doesn’t lead to an easy distinction between “no calc” and “calc”. I didn’t use a calculator more than two or three times at any point in the test. However, the College Board may have knowledge about what questions kids can game with a good calculator. I know that the SAT Math 2c test is a fifteen minute endeavor if you get a series of TI-84 programs. (Note: Not a 15 minute endeavor to get the programs, but a 15 minute endeavor to take the test. And get an 800. Which is my theory as to why the results are so skewed towards 800.) So there may be a good organizing principle behind this breakdown.

That said, I’m doubtful. The only trig question on the test is categorized as “hard”. But the question is simplicity itself if the student knows any right triangle trigonometry, which is taught in geometry. But for students who don’t know any trigonometry, will a calculator help? If the answer is “no”, then why is it in this section? Worse, what if the answer is “yes”? Do not underestimate the ability of people who turned the Math 2c into a 15 minute plug and play to come up with programs to automate checks for this sort of thing.

Categories

Geometry has disappeared. Not just from the categories, either. The geometry formula box has been expanded considerably.

There are only three plane geometry questions on the test. One was actually an algebra question using the perimeter formula Another is a variation question using a trapezoid’s area. Interestingly, neither rectangle perimeter nor trapezoid formula were provided. (To reinforce an earlier point, both of these questions were in the calculator section. I don’t know why; they’re both pure algebra.)

The last geometry question really involves ratios; I simply picked the multiple choice answer that had 7 as a factor.

I could only find one coordinate geometry question, barely. Most of the other xy plane questions were analytic geometry, rather than the basic skills that you usually see regarding midpoint and distance–both of which were completely absent. Nothing on the Pythagorean Theorem, either. Freaky deaky weird.

When I wrote about the Common Core math standards, I mentioned that most of geometry had been pushed down into seventh and eighth grade. In theory, anyway. Apparently the College Board thinks that testing geometry will be too basic for a test on college-level math? Don’t know.

Don’t you love the categories? You can see which ones the makers cared about. Heart of Algebra. Passport to Advanced Math! Meanwhile, geometry and the one trig question are stuck under “Additional Topic in Math”. As opposed to the “Additional Topic in History”, I guess.

Degree of Difficulty;

I worked the new PSAT test while sitting at a Starbucks. Missed three on the no-calculator section, but two of them were careless errors due to clatter and haste. In one case I flipped a negative in a problem I didn’t even bother to write down, in the other I missed a unit conversion (have I mentioned before how measurement issues are the obsessions of petty little minds?)

The one I actually missed was a function notation problem. I’m not fully versed in function algebra and I hadn’t really thought this one through. I think I’ve seen it before on the SAT Math 2c test, which I haven’t looked at in years. Takeaway— if I’m weak on that, so are a lot of kids. I didn’t miss any on the calculator section, and I rarely used a calculator.

But oh, my lord, the problems. They aren’t just difficult. The original, pre-2005 SAT had a lot of tough questions. But those questions relied on logic and intelligence—that is, they sought out aptitude. So a classic “diamond in the rough” who hadn’t had access to advanced math could still score quite well. Meanwhile, on both the pre and post 2005 tests, kids who weren’t terribly advanced in either ability or transcript faced a test that had plenty of familiar material, with or without coaching, because the bulk of the test is arithmetic, algebra I, and geometry.

The new PSAT and, presumably, the SAT, is impossible to do unless the student has taken and understood two years of algebra. Some will push back and say oh, don’t be silly, all the linear systems work is covered in algebra I. Yeah, but kids don’t really get it then. Not even many of the top students. You need two years of algebra even as a strong student, to be able to work these problems with the speed and confidence needed to get most of these answers in the time required.

And this is the PSAT, a test that students take at the beginning of their junior year (or sophomore, in many schools), so the College Board has created a test with material that most students won’t have covered by the time they are expected to take the test. As I mentioned earlier, California alone has nearly a quarter of a million sophomores and juniors in algebra and geometry. Will the new PSAT or the SAT be able to accurately assess their actual math knowledge?

Key point: The SAT and the ACT’s ability to reflect a full range of abilities is an unacknowledged attribute of these tests. Many colleges use these tests as placement proxies, including many, if not most or all, of the public university systems.

The difficulty level I see in this new PSAT makes me wonder what the hell the organization is up to. How can the test will reveal anything meaningful about kids who a) haven’t yet taken algebra 2 or b) have taken algebra 2 but didn’t really understand it? And if David Coleman’s answer is “Those testers aren’t ready for college so they shouldn’t be taking the test” then I have deep doubts that David Coleman understands the market for college admissions tests.

Of course, it’s also possible that the SAT will yield the same range of scores and abilities despite being considerably harder. I don’t do psychometrics.

Examples:

Here’s the function question I missed. I think I get it now. I don’t generally cover this degree of complexity in Precalc, much less algebra 2. I suspect this type of question will be the sort covered in new SAT test prep courses.

These two are fairly complicated quadratic questions. The question on the left reveals that the SAT is moving into new territory; previously, SAT never expected testers to factor a quadratic unless a=1. Notice too how it uses the term “divisible by x” rather than the more common term, “x is a factor”. While all students know that “2 is a factor of 6” is the same as “6 is divisible by 2”, it’s not a completely intuitive leap to think of variable factors in the same way. That’s why we cover the concept–usually in late algebra 2, but much more likely in pre-calc. That’s when synthetic division/substitution is covered–as I write in that piece, I’m considered unusual for introducing “division” of this form so early in the math cycle.

The question on the right is a harder version of an SAT classic misdirection. The test question doesn’t appear to give enough information, until you realize it’s not asking you to identify the equation and solve for a, b, and c–just plug in the point and yield a new relationship between the variables. But these questions always used to show up in linear equations, not quadratics.

That’s the big news: the new PSAT is pushing quadratic fluency in a big way.

Here, the student is expected to find the factors of 1890:

This is a quadratic system. I don’t usually teach these until Pre-Calc, but then my algebra 2 classes are basically algebra one on steroids. I’m not alone in this.

No doubt there’s a way to game this problem with the answer choices that I’m missing, but to solve this in the forward fashion you either have to use the quadratic formula or, as I said, find all the factors of 1890, which is exactly what the answer document suggests. I know of no standardized test that requires knowledge of the quadratic formula. The old school GRE never did; the new one might (I don’t coach it anymore). The GMAT does not require knowledge of the quadratic formula. It’s possible that the CATs push a quadratic formula question to differentiate at the 800 level, but I’ve never heard of it. The ACT has not ever required knowledge of the quadratic formula. I’ve taught for Kaplan and other test prep companies, and the quadratic formula is not covered in most test prep curricula.

Here’s one of the inexplicable difficulty codings I mentioned–this is coded as of Medium difficulty.

As big a deal as that is, this one’s even more of a shock: a quadratic and linear system.

The answer document suggests putting the quadratic into vertex form, then plugging in the point and solving for a. I solved it with a linear system. Either way, after solving the quadratic you find the equation of the line and set them equal to each other to solve. I am….stunned. Notice it’s not a multiple choice question, so no plug and play.

Then, a negative 16 problem–except it uses meters, not feet. That’s just plain mean.

Notice that the problem gives three complicated equations. However, those who know the basic algorithm (h(t)=-4.9t² + v₀ + s₀) can completely ignore the equations and solve a fairly easy problem. Those who don’t know the basic algorithm will have to figure out how to coordinate the equations to solve the problem, which is much more difficult. So this problem represents dramatically different levels of difficulty based on whether or not the student has been taught the algorithm. And in that case, the problem is quite straightforward, so should be coded as of Medium difficulty. But no, it’s tagged as Hard. As is this extremely simple graph interpretation problem. I’m confused.

Recall: if the College Board keeps the traditional practice, the SAT will be more difficult.

So this piece is long enough. I have some thoughts–rather, questions–on what on earth the College Board’s intentions are, but that’s for another test.

tl;dr Testers will get a little more time to work much harder problems. Geometry has disappeared almost entirely. Quadratics beefed up to the point of requiring a steroids test. Inexplicable “calc/no calc” categorization. College Board didn’t rip off the ACT math section. If the new PSAT is any indication, I do not see how the SAT can be used by the same population for the same purpose unless the CB does very clever things with the grading scale.