Math

It’s A “Math Flavored” Test

That's what PWNtheSAT told me after I screamed on the top of my lungs for the umpteenth time because I'd fallen again for some deception in the "Math Section" that wasn't even "math."

"Does that make you mad?" he asked.

"YES," I screamed.

"Good, then don't let them do that to you again."

And then he told me to think of the Math Section like shrimp flavored Ramen Noodles: there could be some shrimp in there, but really it's a lot of other "stuff."*

Not sure if those were the words that inspired my unplanned, last second, impulsive shift in strategy -- but I took SAT #5 in 2011, all in first-serves. I was aggressive. There was not one iota of perseveration in my game that day.

Last Saturday morning, at DeWitt Clinton High School in the Bronx, NY -- I discovered my inner "don't mess with me" self.

No idea what this means for my score, and thank god this doesn't really count for anything. I am very curious though, as to how this "backwards-Debbie" plan worked out, and I'd be lying if I didn't admit that I woke up the next day just a little bit scared.

Here's what I know for sure:

I had a blast and enjoyed every second of the experience. I distinctly remember thinking as I colored in those first bubbles with that deliciously soft and perfectly sharpened #2 pencil, "This feels soooooo good."

I will also say this: Every day I'm less sure about what, exactly, the SAT is testing. More and more it feels like a test of how not to be messed with -- especially the math (and least of all the writing).

And if that be the case (and I do believe that be the case), I'm going to highly recommend a book that I've highly recommended before: PWN the SAT Math Guide.

From the introduction:

"The SAT is not a math test........it's full of booby-traps, misleading diagrams, and intentionally difficult phrasing. Even questions that look a lot like straightforward algebra questions are put there not to see if you can do the algebra, but to see if you can spot the shortcut that lets you avoid the algebra.

.....Taking the SAT like you'd take a regular math test is like bringing a knife to a gun fight......

~~.....The SAT is a test, above all, of how good you are at taking the SAT~~......

UPDATED: One last note: I wrestle a lot with what I think the SAT is really testing, and I don't agree with my own words at the end of the above quote implying that the SAT tests nothing other than how proficient one is at taking the SAT. That's not going to make it to print in the final draft. It's just not where I'm at anymore.**

*"Just to be clear, the fact that the SAT isn't a math test doesn't make it any less challenging. It just makes it different." -- @PWNtheSAT See Full Comment Below for rest of clarification.

**Full comment below.

Illustrations by Jennifer Orkin Lewis

42 Comments

http://blog.pwnthesat.com PWN the SAT

Just to be clear, the fact that the SAT isn't a math test doesn't make it any less challenging. It just makes it different. One of the first things I have to do, as a test prep guy, is convince my students who are very good at math in school that approaching the SAT the same way won't necessarily lead to their best scores. Hence all the appetizing ramen talk. :)

http://www.perfectscoreproject.com Debbie Stier

Clarification added to post. Clarified, I think!
Elise

...and just think, not only are you preparing them for the SAT but you are also getting them ready for college and all the Ramen noodles they will be eating...ha ha.
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

Yay!

I've finally figured out how to post a comment WITH my picture (hope ktm is linked, too - we shall see) ....

PWN writes: "One of the first things I have to do, as a test prep guy, is convince my students who are very good at math in school that approaching the SAT the same way won't necessarily lead to their best scores."

I didn't finally understand - or believe - this until I read the first pages of PWN's book, and this in spite of the fact that Phillip Keller says exactly the same thing. I didn't believe Phillip! Now I get it, though I'm not sure I can explain it coherently myself.

http://www.perfectscoreproject.com Debbie Stier

Comments received!

Elise

I read that statement from PWN's book to my daughter who took the test for the second time on Saturday to see if she agreed and she not only said, "in a sense, yeah" but gave me an example that sort of rattled through my bleary brain...I sort of understood her example but it didn't help that the overwhelming thought in my braggy momma brain was "wow she is really smart!" I couldn't really focus on what she was saying. Hee hee.

http://www.perfectscoreproject.com Debbie Stier

I need to post examples so people understand what I'm saying. Will find those today.

And yay for your daughter. I've become convinced that some people have the right kind of smart for this test. My son took to the math section like a duck to water. And he LOVES it.

http://twitter.com/akilbello Akil Bello

the circle question from saturday is a good one. any plug in. any solve for x that ask for 4x is a good one to post

Elise

As a follow-up to Elizabeth and satverbaltutor's comments below I will add something else that my daughter said...although you may not always have to use certain parts of math to answer a problem, a person who does not know how to do math to begin with will not be able to answer the questions...at least that is what my daughter said. I think that is why she had said "in a sense, yeah" when I told her about this post - she said this doesn't mean that you don't have to know the math, it's just that you didn't always use what you knew in a direct way.

http://blog.pwnthesat.com PWN the SAT

Perhaps we should go with an old philosophical cliche: the math is necessary but not sufficient.

http://www.perfectscoreproject.com Debbie Stier

What he and she said.....

http://www.perfectscoreproject.com Debbie Stier

Agreed. It's like jazz: you still have to know how to play music to be able to improvise.

http://elizabethkingcoaching.com Elizabeth King

Mornin'! I just want to go on the record at this opportunity and say that I am totally against this philosophical approach. Anything, including a mental stance [which, by creating, you are acknowledging to yourself that you find this thing confusing, which propagates the idea in your subconscious], that turns this test into more of a confusing soup than it already is bad for test taking.

There is **rarely** a reason to worry about getting around just solving the problem on the test. If you're a student who's already scoring in high 600s or 700s, yes, we can talk about workarounds on the rare puzzler problem, but if you're a student who is missing a solid math foundation (and, unfortunately, many many students, even from our premier private schools, are), then spending time learning and understanding algebra is a far more beneficial way to spend your prep time than finding ways to not do the math.

Not Doing The Math is how the Princeton Review has become the billion dollar, largely ineffectual company that it is. Same with Kaplan. It's so enticing to consider that there are ways to "do better" on this test without actually having to buckle down and do the math, which what those brands ultimately latched on to and grew on.

...which is why they don't work.

This is a dangerous road. I don't like to get into the fray around here, but the only reason anyone makes a mistake on the SAT is because s/he is missing a fundamental or s/he didn't understand the way the question was asked. Ninety-nine point nine percent of the time it is *not* because s/he missed the workaround.

~Elizabeth King
author: Outsmarting the SAT
President, Elizabeth King Coaching

http://twitter.com/akilbello Akil Bello

I agree that for kids the esoteric what is the sat has limited value for us testing nerds it loads of fun and pointless debate.
Anonymous

Thank you for saying that Elizabeth; you took the words out of my mouth pretty much verbatim.

The SAT measures a person's grasp of the *skills* tested on the SAT. It's a mathematical and vocabulary-based reasoning test, one that requires test-takers to have a absolutely thorough grasp of basic math and English skills in order to apply those skills to unfamiliar situations. Just because the English that people do in school doesn't necessary resemble the English that shows up on the SAT doesn't make certain skills that are tested any less "English."

For example, many students consistently miss sentence completion questions not only because they don't know the words but because they 1) can't figure out the logical relationship between the words, and 2) lack the fundamental knowledge (e.g. roots) that would allow them to make logical conjectures about the meanings of unknown words. Just because they haven't studied those exact skills in English class doesn't make them somehow inapplicable to anything outside the SAT.

Even though I don't tutor the Math section (with good reason!), I imagine that it works pretty much the same way. If the only thing the SAT tested were the ability to take the SAT, then it follows that really top Math students would also have trouble with it -- and I've frankly never seen that happen. What I have seen is kids who are pretty good at Math but have a fairly over-inflated idea of their abilities (mostly based on the fact that they take advanced math at fill-in-the-blank NYC private school) stumble when they take the test. But the ones who are really and truly mathematically gifted? Never.

Anonymous

Just wanted to add that the reason many kids seem to need SAT tutoring is not that they lack the actual skills being tested, but rather the ability (not to mention the willingness) to think things through logically and systematically and precisely. In that sense, yes, the only thing that the SAT tests is their ability to take the SAT -- most of them have probably never encountered a school-based situation where they were required to do that, at least not from what I've read of their papers...
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

satverbaltutor wrote: "absolutely thorough grasp of basic math and English skills in order to apply those skills to unfamiliar situations"

Right!

That is precisely the cognitive function that disappears under pressure.

One of them anyway.

Phil Keller

Oh, I think we are going to have to agree to disagree on this one. There are MANY kids out there who just don't have a good grip on the whole abstraction we call algebra. And I can't fix that in any reasonable amount of time. But the "work-arounds" work. They allow kids to read, think and play their way to a solution. To say that those kids would just be better off being better at algebra completely denies the facts on the ground. And I am talking about kids with 400s and 500s. But even the 600 - 700 kids do well to learn the tricks. For them, it gives them multiple ways to attack a problem.

As for Princeton Review, its biggest weakness is that it has grown so much that you cannot be sure that the instructor you get will know how to effectively communicate the program. But the claim that these methods (and this philosophy) don't work is contradicted by what I have observed in the (oh lord) 27 years I have been doing this.

http://www.perfectscoreproject.com Debbie Stier

"multiple ways to attack a problem" is the operative phrase for me here. There are many ways to skin a cat -- and I want to know them all -- especially the faster ones.
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

Phil writes: "But the "work-arounds" work."

I can attest to this.

I have never completed Algebra II. (I'm at the end of Saxon's 3-book series, which I abandoned a couple of years ago in order to take the ALEKS geometry course & do other things.)

When I confronted the SAT Math section, I had **very** limited ability to deal with parabolas and the more difficult function problems (although I had studied both. Nevertheless, I simply don't have the knowledge base and basic ease with the topic that would allow me to do SAT parabola problems.)

Phil's section on functions -- and, in particular, his section on 'shifts' -- was all I needed to do every function-shift problem I've encountered since. Same for C.

His book is worth the money for that chapter alone.

http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

oops - sorry, what I meant to say is that I'm at the end of the 2nd book of Saxon's 3-book series

http://blog.pwnthesat.com PWN the SAT

Yikes. OK. Deep breath.

Math tests, in today's high schools, are not generally multiple choice. They often award partial credit if it's clear that a student understood the basic concept, if not the full execution. And for the kids I work with who are usually in precalculus or higher, they don't usually involve remainders, or the number of members of the ski club who are also members of the chess club. Systems of equations, on school math tests, don't generally resolve directly to the solution with a single addition or subtraction step.

When I tell students that the SAT is not a math test, it's usually because I catch them trying to solve a triangle question with the law of sines, or trying to solve a system of equations with matrices. And freakin' logs, man. I see a lot of logs. When students treat the SAT like they would a math test in school, they're not testing optimally, and there's an opportunity for score improvement. So I tell them the SAT is not a math test, because it's a snappy phrase, and it drives home a point that this test can (and maybe should) be done differently. This reminds me of a blog I regularly enjoy called "Stay Out of School" -- a title that, when taken out of context, might sound like dangerous advice.

When I spot a hole in the fundamental knowledge of one of my students, I don't try to patch it with duct tape. If a student doesn't know the exponent rules, I teach the exponent rules. If a student isn't comfortable with function notation, I make sure she becomes comfortable with function notation. But to stop there and call it a day is to send a soldier into battle unprepared. Period.

Standardized tests are, by nature, susceptible to nuanced strategy and pattern recognition. This is especially true of the SAT, which is why one might choose to write and market a book about pwning it, (or indeed, about "outsmarting" it). My students have math teachers 5 days a week in school (and I suspect that, much like the math teachers I had in high school, they are quite skilled). They come to me to learn a skill that, while related, is different.

---
One last note: I wrestle a lot with what I think the SAT is really testing, and I don't agree with my own words at the end of the above quote that the SAT tests nothing other than how proficient one is at taking the SAT. That's not going to make it to print in the final draft. It's just not where I'm at anymore.

http://elizabethkingcoaching.com Elizabeth King

"But to stop there and call it a day is to send a soldier into battle unprepared. Period." <--Right. Exactly.

But, I don't like the hype. I should, theoretically, love the hype, because the hype is what sells books.

All I teach is What You Need To Know and How They Ask The Questions. It would appear that, at the heart of it, you do too. This forum, though, is an interesting place in that *many* of us having the conversation here know each other and are in the profession of preparing students (and, notably, selling books). My concern is that this will all be dug up by students (or parents) who may end up more flummoxed than anything.

[Side note for In The Biz]: I find it interesting that you have students solving systems of equations with matrices. In nearly ten years, teaching students from all across the US and from at least 3 different countries, I have never seen that happen *a single time*. Logs mights surface once every two or three years. Isn't that fascinating? I wonder if Akil has ever had that happen. Do you see students from a few particular schools doing that?

Anyway, we can talk in circles all day and we'll never arrive anywhere. Point is, let's keep it simple and differentiate ourselves by not propagating the nerve-wracking mystical hype around the SAT and how "esoteric" its math section is. It's all learnable. Doing the Algebra is a very legitimate solution. Practicing/reviewing fundamentals and getting students to revert back to their 12-year-old mathematician selves is usually the best way to go.

http://twitter.com/akilbello Akil Bello

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

I will not be sucked into an online debate about the esoteric merits of the SAT. I. WILL. NOT.

Ok maybe later when i have more time i will..

but I agree with Elizabeth. and Mike. and Phil too.

Phil Keller

And I agree with YOU -- don't want to get sucked in...and yet...

http://xkcd.com/386/

But seriously, It seems we agree more than we disagree. And yes, a lot of us (jeez, nearly all of us) would like to sell books. But the books do help kids (of all ages) through this very stressful event, and that's not hype. Still, I'd rather have written the great American novel. I'll get back to you all on that...

Phil
http://www.perfectscoreproject.com Debbie Stier

Ok, that's hilarious. i.e. http://xkcd.com/386/ And the story of my life. I call it "the lock."

My new rule (which I break all the time), is NO COMPUTER after 10 pm. None. It goes away. And only paper books allowed in my bedroom. And if I'm really good, I try to be upstairs by 11. I'm usually not that good though.

College Confidential is a KILLER for me though. I can get sucked into that for hours. I'm almost afraid of going there at this point.
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

oh you know you want to!!!!!!

http://www.perfectscoreproject.com Debbie Stier

Oh shoot. I just typed up a whole long comment and then lost it b/f I saved.

Anyhoo, here's the short version because I'm rushing now:I agree, basics are GREAT and the more you know the better off you are for a whole variety of reasons. I WANT BASICS! I committed to Kumon for godsakes.

HOWEVER, 12 year old math basics will get me about mid-way through any given SAT math section, and personally, I want my pocket full of options on test day. I want to be fast on my feet and know how to MacGuyver it, if/when necessary.

Attached is an archetypal, SAT "Don't Mess With Me" problem, as far as I'm concerned. I started collecting them from the math section about a month ago and I have at least 50. Coincidentally, my friend Catherine started the same type of collection at about the same time. We have overlap. And by the way, we both started this thinking that it's about the basics. Now we both have a pile of "how not to be messed with" cards.

Also, I'm referring to the math section only here. I think there is a degree of this type of thing in the reading and writing sections too, but MUCH less.

And I think there is a huge distinction to be made between the sophistry of some test prep companies -- and tutors and books such as Erica Meltzer's (which teaches basics, but also notes in her book the "tip-offs" to their "tricks") or Philip Keller's "Back Door Trick in Grid-In Section" from The New Math SAT Game Plan.

I could write a whole blog post about the distinctions, but I don't have time right now (sick son just called my cell phone and said "can you please come upstairs...")....

And as an aside, I love YOUR book and it was one of the very first that I bought. I'd say it was #3. BB, then Barrons, then yours. I swear. And I refer to it often.
http://blog.pwnthesat.com PWN the SAT

I think, at the end of the day, we've all spent a lot of time thinking about the test and I bet if you put us all in the same room to take one, we'd all approach it ourselves in mostly similar ways. And probably, if we all watched each other in a classroom or tutoring session, we'd all see things we really liked about each others' styles. That I believe with great conviction. All I do, when I teach, is try to twist and turn my own insights until I've presented them at the right angle for the student I'm with to see them clearly. It's different almost every time.

And again, a lot of my "it's a math-flavored test" talk has as its aim the same thing you're talking about when you talk about "getting students to revert back to their 12-year-old mathematician selves." And honestly, it's informed by memories I have of my own 12th grade SAT experience. I took a derivative. I know the dark realms of the mind from whence such ideas creep. I have traveled there, done battle with the demons, and lived to tell the tale.

I wouldn't say the students who try logs, trig laws, and matrices (rare, but happened more than once) come from one or two particular schools, but they're almost always kids who'd be knocking on the door of 800s if they'd only resist the urge to overcomplicate. Phil, I'm sure you've come across a few kids like this given all the time you spend on College Confidential. :) I was one of them. One of my motivations in starting this crazy project was to provide a service that I would have benefited from when I was 17.
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

C. once solved an SAT triangle problem using sine & cosine.

I was sitting next to him at the time thinking, "I need to finish Algebra 2."
http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

Elizabeth wrote: "racticing/reviewing fundamentals and getting students to revert back to their 12-year-old mathematician selves is usually the best way to go."

I disagree pretty strongly with this observation.

If C. were to revert to the skills he had at age 12, he would score .... perhaps somewhere in the 400 range. Possibly even lower (I haven't looked at raw scores at that level.)

I tend to think - I'm interested to hear from people who know more about this than I do - that SAT math is a cousin of middle school competition math. I'm thinking of the Art of Problem Solving books on middle school competition math in particular (and I'm hoping to find time to write a post about the math question that cost my son a higher score this round & stumped me, too: turns out the solution to that question is explicitly taught in the Art of Problem Solving book.)

I've been wondering for a year whether middle school competition math books might be the way to go if you don't have the money for a tutor.

http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

PWN writes: "They often award partial credit if it's clear that a student understood the basic concept, if not the full execution."

Right.

I have now taken many timed sections as practice.

I routinely miss the easy problems while getting the difficult problems correct. In the last month, that has been happening to C, too.

For instance, I recently divided 18 by 6 and came up with 6 as my answer.

The SAT is a high-stakes, high-pressure, timed test, and under those circumstances human performance typically deteriorates. People who are interested in the "performance" aspect of the SAT should take a look at Sian Beilock's book CHOKE, which contains a large section on the SAT. Here's her page: http://psychology.uchicago.edu/people/faculty/sbeilock.shtml

Beilock is a sports psychologist among other things, and she has some fascinating data on free-throw percentages. I'm not going to take the time to look it up now, but percentages drop significantly when players are under pressure. As I recall, their percentages are always higher in practice - **and** their percentages decline even further when the outcome of a game depends upon making the shot.

This is a universal phenomenon that has nothing to do with math.

http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

hmmm....I don't think that's what Debbie is saying, is it?

I've never heard Debbie say you can do well on the SAT without knowing the math. She's saying that knowing the math isn't (nearly) enough. Haven't read PWN's or Phil's comments yet ----

http://www.perfectscoreproject.com Debbie Stier

Exactly. You need Math+ Seasoning.

Guest

That is true, the Sat kind of is like a Shrimp Ramen Noodle soup, but the Sat is even more disgusting and complex. You can eat the shrimp flavoured noodle soup/ not like it ; and rinse the flavour out of your mouth or throw rest away. but with the SAT's it's a whole other thing, you can Take the exam and pass it , but not be satisfied with score and take it until you are. This bothersome process can take multiple tries.
I don't know if my examples make sense; but that is how I see this Sat Ramen noodle Problem :-)

Guest

That is true, the Sat is kind of like a Shrimp Ramen Noodle soup, but it's even more disgusting and complex. You can eat the shrimp flavoured noodle soup/ not like it ; and rinse the flavour out of your mouth or throw the rest away. but with the SAT's it's a whole other thing, you can Take the exam and pass it , but not be satisfied with score and take it until you are. This bothersome process can take multiple tries.I don't know if my examples make sense; but that is how I see this Sat Ramen noodle Problem :-)

http://kitchentablemath.blogspot.com/ Catherine

test -
Catherine Johnson

test

http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

trying to get my photo in here

http://www.facebook.com/people/Catherine-Johnson/100001040094552 Catherine Johnson

btw, Elizabeth's section on absolute value inequalities is fantastic. Absolutely fantastic. I made C. read it, and he had the same reaction.
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