Math

Watch Your Back (That’s All I’m Sayin’)

Or "Savor the Flavor," as PWNtheSAT said to me yesterday, as I screamed with rage after being messed with, again (and again and again), by the SAT math section.

I inadvertently struck a nerve a week or two ago when I suggested that you need to know more than just solid math to do well on the math portion of the SAT.

One (anonymous) commenter even left me this message on Psychology Today:

"This idea that the test is full of booby traps is ridiculous. You simply have to READ the question, figure out what they are asking, and then answer accordingly. You need to show that you understand the basic math concepts. The questions aren't tricks. I had read a version of that assessment over and over again, and then took the test again as an adult and easily scored 800. BECAUSE I UNDERSTAND MATH AND CAN READ."

But I'm sticking with my position: Solid math basics are essential, but not sufficient. If you want to ace this test, you need to be prepared not to be messed with by a test that's trying to mess with you.

Take, for example, the following questions, all of which come from just one, lone, College Board practice SAT, and I believe illustrate the point that "solid" math knowledge alone is not enough (at least not while the clock is ticking and you've got about one minute per problem).

Exhibit 1:  

This appeared (to me) to be run of the mill parabola question, so I broke out the "Quadratic Equation" and jotted it down in the margins: y = ax² + bx + c.  Then, I did my very best to turn what they gave me, back into what I knew.

But I couldn't get past that minus sign in between the "a" and the "x²." No idea what that meant.

Well I'll tell you what it meant:

It meant that the "a" referred to in this problem (above) is not the same "a" that I learned about in "math"  -- It's just coincidentally also called "a"  -- just like the one that's usually located in the exact same position.  

But don't be confused. It's not THAT "a."

MEAN....mean mean mean. Makes me scream.

Exhibit 2:

Looked like a 30 60 90 to me.

Wrong!  "Not drawn to scale" = dead giveaway.

And don't let those (a + b)² send you down the "Pythagorean road" that you learned in math class, because it's not that either (go figure).

This would be the fanciest "Sadness Gap" question I ever did see.

(Who would have thunk. Not me, that is for sure.)

 

Exhibit 3:

So (so so so so) proud of myself, and brimming with enthusiasm at the prospect of trying out my newfound Polynomial clarification, I FOILed the thing.

In fact, I probably spent a good 2 minutes down FOIL ROAD -- never arriving at the answer until after the bell, when I went back and looked, and went "dah, I can't believe I did that."

They got me again.

Illustrations by Jennifer Orkin Lewis

 
58 Comments | posted October 19th, 2011
 
 
  • http://sidheag.livejournal.com/ sidheag

    Mmm, you're not going to like this, but your Psych. Today commenter is exactly right. There is nothing tricky about any of those questions.
    - a's just a letter. Why on earth *should* it stand for the same thing it did in some quadratic lesson? You need to think, not start symbol pushing. That quadratic's "upside down", fine, that's because of the - in front of the x^2. What does y = -x^2 look like? Right, a version of what you see here but with the vertex at the origin. So how do you get it to what you see? Add something positive. Right, that was a.
    - sure you can use Pythagoras if you must; a^2 + b^2 = 400 so (a+b)^2 = a^2 + 2ab + b^2 > 400 since a and b are positive so 2ab > 0, done. Or you can use the triangle inequality (which would have worked even if they hadn't been so kind as to make it a right angled triangle).  Or you needn't even know it's called the triangle inequality, and you can just ask yourself, what's the least a+b could possibly be and still make the edges join up? Whichever.
    - seeing that something^2 can only be 0 if something=0 is pretty basic to understanding multiplication! Again, FOILing is an example of symbol pushing instead of thinking.

    I totally respect you for trying to undo what sounds like a travesty of a math education you've met with before, but do understand that what you're trying to do here is undo damage, not learn stuff specifically for SAT. If you've been taught to symbol push before you think, blame your education and STOP IT. Don't blame the SAT writers, they've done nothing unreasonable.

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

      And do you think that the math education today in our country prepares kids for this?

      • Polu66

        sidheag is right....you see...the problem with a lot of students is finding the SAT writers culpable for their performance. The reason students are doing poorly is because they do not have a full grasp on the material the SAT tests. It is not the SAT's fault that you misread that "a"...it is merely due to a student's understanding of the rudiments. 

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

          Well, let's start with A) I agree that it would be great if I had been better educated -- or could somehow manage to learn this now......

          And B) I don't see the schools today doing so much of a better job now than they did with me (there are exceptions).  But they are EXCEPTIONS.

          But I will ask the same question to you that I asked "sidhaeg": Do you honestly think that the schools are preparing kids properly for these types of questions?  Do you have kids who are of SAT age?  And if so, are they "exceptional?"

          Because I can assure you that most kids in school today are absolutely not being prepared properly for these types of questions.  I've been through a few different schools (on the mother end)....and don't see too many kids of the "non extraordinary" sort blowing through these questions with the educations they're receiving today.

          • Deborah

            Blaming schools for your SAT? I don't see any justification in that

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

            @92ecdb81ad3e46ae86c57f1e3b650df8:disqus  You misunderstand me!  I obviously didn't say what I wanted to say clearly.
            But I'm too hungry right now to respond properly, so I will be back later with a (hopefully) more thoughtful response that's is ess hunger based than it would be if I answered you right now.

            But thank you for caring enough to comment.  Be back soon....

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

            Ok, I'm back with a question....how do you envision students gaining a proper grasp of the rudiments, if not via the schools?

          • Polu66

            I'm back with a counter question....How do students get home-schooled?

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

            I'm back with a counter counter question ;)  I don't understand the question!  I'm sure there are a million different ways, if I understand the question, depending on the kid, the parents, etc.

            Are you saying it's responsibility of the kids?  The Parents?  I'm confused.

          • Jen

             I'll jump in, late as usual!  I do have kids this age and tutor (very low-key, word of mouth) students this age. 

            Two answers -- they are generally good students who do not expect to be tricked or confused by a math test (or a critical reading test for that matter).  They do have to be pushed to think through an answer rather than just grabbing a calculator.  I can't tell you how many times they'll need to do something like find a tenth of something and grab the calculator.  When the answer pops up, you can see them realize (and usually groan and apologize) how they *knew* that and could have done it in a second if they were just...thinking.

            I'm also not sure that schools should teach SAT tricky type skills in all classes.  A prep class in college board test taking that is NOT skills based, but test-based would likely be very helpful.  But most teachers aren't specialists in the SAT and they'd rather teach skills and that's what those classes end up being.

            My own two who are old enough have done well -- but in part that's because all along I've insisted on things at home that the schools don't insist on -- like memorizing basic addition facts, knowing times tables (must finish that up with 9 year old...), knowing percentages/fractions and what they mean.  Math games, strategy games, and game playing in general helped too, I'm sure.

            My proudest moment though came when oldest told his 3 year younger sibling "just do what mom tells you now so you won't have to take it again!"  I had him convinced that he'd take that damn test until his scores were what I knew they should be.  It only took a second try, though.  Second child did do the practicing I recommended and only took it once.  Both were >700 on all three sections (with one 800, even!) I don't brag "IRL" but here in anonymous land...  ;-D

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

            I love your proudest moment story.  I have a similar one.  My son got off the train after taking the PSAT and he was pumped up and excited (just like his mom).  He had fun -- or at least took it as if it was a sport.  I felt like I truly won with that one!.

          • Jen

             Yes, I like the framing of it as a sport!  It IS a game.  They're crafty and you can match that if you're in the right frame of mind. 

            I confess that I sometimes tell kids that if they come across a problem and see the trick or know that it's one that they've gotten wrong a lot in the past and now they know what to do, that a wee, tiny, breathy little chuckle during the exam is a great way to rejuvenate themselves.

            And it's true, if you can giggle a bit during that thing, it's a huge help in keeping it "fun"!

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

            Great advice.  I'll take it!

        • Jen

           In this exact problem, that might be true.  However, when I tutor, I find that the kids do have a fair grasp on the math skills needed for the SAT -- or with a quick review remember that they do know it.  Most of these kids score between 500-650 on the math (having the money to pay for some SAT tutoring usually goes hand in hand with kids who are scoring at least average).

          I do NOT spend a lot of time on the teaching of those skills, though.  The majority of the time is spent having the kids figure out which of the the things they DO know goes with the oddly worded or strangely drawn (or not to scale) picture.  That's what they need to practice.

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

            Interesting.  When you say "in this exact problem," are you referring to one of the problems above?

            I am definitely of the mind that they are purposely trying to mess with kids on this.  Or, as my friend Catherine says, they are purposely trying to cause Associative Interference.  Here's her post describing the issue: http://kitchentablemath.blogspot.com/2011/10/rat-psych-why-sat-math-is-tricky-redux.html

      • http://sidheag.livejournal.com/ sidheag

        I'm in a different country from you, so no direct experience of math education in the US. What I read about the US is pretty discouraging. I read about children being taught, especially at elementary level, by teachers who themselves don't understand the math they're teaching, so that the only way through is to teach separate "methods" for every conceivable problem type. That seems likely to be the root cause of your trouble, to me. My country is relatively free of state standardised testing and more accepting of same-age children being at different stages; that has to be good, I guess. It would be very interesting to see cross-country comparisons of SAT performance, wonder if it's been done?

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

          Cross-country SAT comparisons would make a great headline, but tell a muddled story. That's because (for the most part -- you didn't mention where you're from) in the US everybody takes it, but in other countries the only people who take the SAT are those who have eyes on US universities. I think it's pretty safe to assume that students aiming to attend university abroad probably skew a little higher than average. 

          • http://sidheag.livejournal.com/ sidheag

            Oh, of course; I had in mind taking a properly balanced sample from each country and asking them to take the SAT for the study. I had a quick look, but didn't find such a study reported.

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

          I was thinking the same thing.  Where ARE you from? 

          • http://sidheag.livejournal.com/ sidheag

            Scotland.

          • http://sidheag.livejournal.com/ sidheag

            I should make clear that I'm not claiming that kids in Scotland would do better on the SAT-M than those in the US; I don't know. I did find this report which is quite interesting:
             http://www.nuffieldfoundation.org/values-and-variables-mathematics-education-high-performing-countries

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

            Thanks for that link.  Fascinating.

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

            Agreed...fantastic link. My favorite points:

            There is no link between achievement and enjoyment in maths education. Pupils in countries that perform well in international surveys do not necessarily enjoy maths more than those from countries which perform less well.Pupils from high-performing countries often have low confidence in maths.

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

            That should be my epitaph.

  • The SATs are fun!

    Sorry this is going to be a lengthy comment and I hope I don't offend anyone who struggles with the SAT or math or sound like I'm bragging though with how its written that's hardly avoidable. Math was just always a subject I enjoyed.

    I just came upon this blog yesterday and started reading it because it seems like an interesting project. It brought back some memories of watching everyone take very different approaches to how they prepare.

    For the record I scored a 790 on the math section when I took it in 2006 (i think anyway, it was the first year the writing section was available so while I did that one it wasn't taken into account by colleges or anyone else yet). I was actually upset I missed that one question. The only prep I did for the SAT was taking the PSAT and doing a single practice test the day before.

    Thus, I have to admit I have some agreement with regards to the person saying that an understanding of math and common sense is enough for a perfect score. Most of my friends scored between a 750-800 and thought all the questions were relatively simple. I don't mean that to sound insulting in any way to those who struggle with it, but let me explain. I don't think any of us did that well because of all the SAT test prep courses, though. In fact, one of my friends is applying back to a school for another degree after getting his bachelors. The school is making him retake the SAT 4 years after his last math class and he got an 800 on the math portion of his first or second practice test.

    In math, concepts build upon each other. However, the concepts on the SAT are hardly the peak of the math taught in high school. While my high school may be a bit of an exception the path of classes in high school consisted of:
    9th grade: Geometry
    10th grade: Trigonometry
    11th grade: Pre-Calculus
    12th grade: AP Calculus BC

    That meant at the time of taking the SAT in my junior year we were already being introduced to calculus. Calculus requires a good understanding of any of the content required on the SAT and then some. So while some people panicked over the SAT math section the difficulty of my next pre-calc test seemed much harder in comparison.

    I say this all as a precursor so that I can type anonymously on the internet from my soapbox to say that school's should not be teaching to a test, and scoring well on a standardized test should be 2nd to actually learning the material.

    To quote the person that complained "You need to show that you understand the basic math concepts." However, what is on the SAT for many people are not basic math concepts, but the height of their knowledge of mathematics. If you just learned how to foil and encounter a problem that looks like it might use it, that is hardly a basic skill. However, you are taking calculus and foiling becomes a single step in a larger problem rather then the problem itself.

    I don't know if a single comment on your blog would convince you to try a suggestion for an alternative method of preparation, but I would be interested to see if it would make a difference.

    If you can find some spare time or maybe use a little of the time spent studying the SAT, go and try to study math more advanced than what is used on the SAT. Go take an intro to calculus course. You don't have to stop studying for the SAT, but try taking it alongside. The extra wrinkles added into equations will hopefully make the SAT ones easier because rather than looking for shortcuts for what to do with an equation you'll see easier forms of questions you encountered in your class.

    I imagine a type of cross training would help with the other parts too as I remember my Latin teachers always claiming that students that took Latin did better on the
    reading and grammar sections of the SAT.

    Thanks!
    Good luck with your quest.

    PS: Answers and explanations on why those problems shouldn't seem as confusing as they are at first glance. Though with my luck I'll still screw up those answers and cause more skepticism to anything I've said here. Oh well, I'll take my chances when it comes to math.

    ===============================

    Exhibit 1:
    The equation is given in the form of f(x)=ax^2+bx+c you just need to learn how to recognize the coefficients and not try to memorize it based off of a preset formula.
    That equation could easily be written as f(x)=ix^2+jx+k or even f(a)=xa^2+ya+z

    While that may initially seem confusing variables should be thought of as representing any number rational, irrational, or imaginary. Any time a variable is used multiple times, for example x, it simply means that the value is constant throughout the equation.

    The only time you should assume that a variable will be fixed for a particular thing is for a given value like ? or e or if you are doing physics

    If it helps change the formula into something more recognizable for you.
    f(x)=a-x^2
    becomes
    f(x)=(-1)x^2 + (0)x + a

    All that is really inconsequential though. Regardless of all this your job is to find a.
    This means you want to correlate a point on the graph to the equation and the only* one it gives you the nice simple one of if x=0 then f(x)>0
    When x=0 the equation becomes f(x)=a
    So look on the graph at where x=0. You see that the point is positive so that means a>0

    *technically you also know that when f(x)=0 then x=[a,-a]

    Exhibit 2:
    I'll give you that this question tries to throw you off by giving you one angle as 90 degrees, but even if it was drawn to scale you shouldn't be assuming the the other angles are 60 and 30 unless you are measuring with a protractor.

    Start with information that you can get from the picture and find one that you can use to get to (a+b)^2 (what you are trying to find based on the available answers)
    a^2+b2^=400
    a+b>20
    0<a<20
    0<b20
    (a+b)^2>20^2
    (a+b)^2>400

    (technically even answer E is incorrect too because it can't be equal otherwise you'd have 2 lines on top of each other without any angle)

    Exhibit 3:
    I'm not entirely sure what to say about this one. If you can solve for a variable, just solve for it.
    (w-2)^2=0
    w-2=0
    w=2

    (2+3)(2+4)=(5)(6)=30

    Since you mentioned the FOIL method you should probably be aware that the first thing you do when trying to deal with or graph more advanced polynomials is reverse-foil because it can easily give you what a variable is equal to when all other variables are 0.
    And this problem is already given in the exact form you want for a reverse foil.
    http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm

    • The SATs are fun!

      Guess I can't edit my post.
      *technically you also know that when f(x)=0 then x=[a,-a]

      This was a bad choice of variable name. x is equal to some value and that same value multiplied by -1. I used 'a' because it was the first variable that came to mind forgetting there was already an 'a' in the equation.

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

        It was an intentionally bad choice of variable name.  And they do it all the time.  Which is why I love/hate the test.  More I love it though (but then, the stakes aren't that high for me).  This is more of a science experiment than anything else.

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

        Just going through all of my emails, and found one that's relevant about the purposeful associative interference, written to me by a bestselling writer who has a Ph.D. and studies cog. science.:
        Absolutely – there is no question they are doing it intentionallyI can say that just as a writer (and a teacher): I CONSTANTLY rewrite (and re-speak) in order to GET RID OF associative interference. As a writer, you’re constantly aware that what you say may sound like one thing inside your head but quite another inside someone else’s head; you’re constantly making bets about how other people ‘hear.’When you say or write something you think other people will interpret differently from the way you mean it, you change your language.They are deliberately choosing variables they know students have powerful associations to — and I bet they know that people are **more** likely to go with their pre-fab solve-for-x associations when they’re under stress. If they don’t know it consciously, they know it unconsciously. (I don’t usually make assumptions about other people’s motives, but in this case I have Noooo problem doing it!)

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

      Math is a beautiful thing, and I wish that EVERYONE learned it as well as it seems that you have. But as someone who has A) studied very advanced math and B) been in the SAT prep business for a while now, I have to disagree with you that more advanced math study necessarily leads to higher SAT scores. 

      Exceptional SAT scores come from intimate knowledge of the test's favorite tricks, and a wake-up-at-3-AM-with-a-gun-to-your-head-and-you-have-to-be-perfect comfort with the concepts of basic algebra and geometry.

      Don't look at the SAT from your own perspective as a student who is able to perform quite admirably on it. Look at it from the perspective of the test writer. Why, on that right triangle question, did he or she include square the a + b term? Why did he make that triangle a right triangle when it didn't need to be? 

      For most kids, it's important to be aware of the techniques the SAT writers will turn to in order to shake a few extra kids off a question. Since they have a fairly limited scope in the concepts they can test, they'll often try to increase the number of careless errors. It's not necessarily evil of them, but it does necessitate added vigilance on the part of the test taker. 

      I agree with you. The SATs are fun. But to call them easy is to insult the 99% (or so) of people who don't just waltz in there and score 790s like you do. 

      • The SATs are fun

        I'll agree with you that the test makers do add unnecessary wrinkles to problems and design them in such a way that the problems look like the most common mistakes are the method they should use (and lead to one of the listed answers).

        While I can't agree with the way a lot of the questions are designed (not a fan of standardized testing in general despite doing well on them), I can't believe that somebody with an understanding of the topic shouldn't be able to solve it. When you take the equation outside of a math formula and put it in a physics problem you might know its a right angle and you might in fact be about the term (a+b)^2 because its representative of a different characteristic.

        Sure you can say that the questions are worded differently than a math test, but at the college level that can quickly become your joke of choice for the difference between a mathematician, physicist, engineer, and computer scientist. (really just wanted an excuse to include this link)
        http://www.phy.ilstu.edu/~rfm/107f07/epmjokes.html

        I just think that when actually mastering the material, the "tricks" on the SAT cease to look like tricks and become more sidenotes to the problem.
        f(x)=a-x^2 is written in that manner for the deliberate confusion of identifying the y-intercept and coefficient of x^2
        Someone shown the formula y=ax^2+bx+c and told to match the terms is likely to have some confusion while somebody who tries to understand what impact each part of the equation has without needing to revert to the formula is going to be fine.
        Don't get me wrong, the formula is a great and useful introduction and still useful later, but the mastery needs to come from understanding why the equation is in that form and what each part of it represents.

        I hate to even suggest it since it causes a shudder in all but the most hardcore mathematicians, but writing out proofs is actually a good way to prove to yourself that you know what you are doing. Not feasible for time constraints on the SAT but definitely viable when practicing and struggling with a problem.

        In writing that I think I've also realized that a programming background has made me a little spoiled when it comes to variables. CS tends to make a focus on variables easier, though intro programming isn't needed enough to actually require it as a class as much as I wish people would take it.

        Anyway, I'm rambling. The reason I suggest more advanced math isn't because I believe that more advanced math will give a better test score. Its that one of the beauties of math is how it builds upon itself. Learning more advanced math should force people to look back at their previous knowledge and know they've mastered it. Lacking understanding of a previous concept causes problems with the next concept. To me it seems like a way to force somebody to prove they've mastered it by reducing it to a step, though there are ways around that.

        Mileage may very but looking at where a more advanced problem is being screwed up is a good way to tell what skills weren't mastered as well as they should have been. There's that old adage "you learn more from your mistakes" since you could do a problem right 100 using a shortcut, but mix up the problem on something more advanced where the shortcut no longer works and you need to start from scratch. I'd rather screw up the 1 had problem and see where I'm struggling than get 100 right and never know it.

        And I'm sorry if saying that the SAT math felt easy for me is insulting to many of the people that struggle with it. I can't really help how I personally felt about them. But if it will make that 99% feel better and can guarantee they can all sing better than me. :D

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

          oh blah blah blah. show off ;) (kidding)  I don't know anything at this point -- except for I LOVE THE MATH the most (by far), and I did great on the writing, which I worked the least on.  

          About to post a video of my scores from Oct. SAT, which I just got back.It's a good thing I'm making a living with words and not numbers -- that's all I know.  Reminds me of image attached.THANKS FOR YOUR COMMENTS!!

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

          I agree with you that a math whiz should have no problem solving any of these. Remember though that it's not ONLY ability, but also speed and accuracy that eventually contribute to a score. That's why the hairpin turns are so dangerous. If you're going at breakneck speed and you don't see them coming, you'll fly right off the cliff. 

      • Elise

        I hate to say it but to say that he/she was able to waltz in there and score a 790 is an insult as well.  I'm sure that there were years of hard work throughout high school behind that 790.  It seems that all they were trying to say is IF someone has the ability, maybe they could try learning higher level math and MAYBE that would help.  I did not think that they were being insulting.  As an example, I think what they were saying was sort of like saying for a kindergartener learning the ABC's is difficult but once the same kid learns to read, the ABC's are a piece of cake.  

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

          Point taken. For the record, I was a waltzer-inner in high school, too. My point, I guess, is that since time travel isn't an option, it's not practical advice to someone who's currently embroiled in SAT prep to tell them they should have learned basic math better years prior. I think the issue here is the conflict between the ideal situation (that test prep would be completely unnecessary because of solid fundamentals and an immunity to test-writer trickery) and the situation on the ground for many students, (that there are a few holes that need patching up, and exposure to the writing style of the test can teach some valuable lessons as well).

          Put more concisely, I don't begrudge anyone an un-prepped high SAT score. You're right that it reflects years of hard work, and I'd add that it also reflects exceptional intelligence. I just want to show my support to students who don't get super high scores right out of the gate, but aspire to improve.

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

            I keep meaning to say something to the effect of what you just said.....but maybe more that I don't believe that schools should teaching to any test -- or "test prep" (as a few people over the months have suggested that I might believe).

            I think kids should be properly educated with a solid foundation of basics in literature, grammar, math, science, etc. -- and then ideally, all they'd have to do is layer on some test taking techniques to get ready for the SAT.

            Unfortunately, that "solid high school education" was not my personal experience (I will take a lot of the responsibility for not working hard enough, though no one from the school seemed to care too much if and what I was learning, as long as I was cruising along on Bs) -- and my impression is that most schools today don't prepare the vast majority of kids well enough either (thus the inexorable decline in SAT scores) .... and so what you're left with is exactly what you say above (i.e. test prep that will hopefully fill in some fundamental gaps along the the way) -- because what other alternative do you have if you haven't been one of those high achieving outliers?

          • Elise

             PWN the SAT you are making me work way too hard (ha ha)....I had to reread the comments by "The SATs are fun" because I didn't remember him/her saying that Debbie's problem was that she should have learned basic math better years prior.  I thought I had maybe missed something.  I felt that if anything, he/she had assumed Debbie had indeed learned the basic math (maybe not in the past but she seems to be learning it pretty well now)  It seems that "SATs are Fun" is actually suggesting to move on to more difficult math in conjunction with SAT prep/trick learning.  I couldn't find anything in either of his/her comments about Debbie having a poor foundation in math.  And I think it is key that he wasn't suggesting that she should stop SAT prep but just that trying more difficult math might be helpful in addition to the SAT prep.  I wonder if you maybe blurred the line between his comment and sidheag and Polu66's comments below.

            I think that the only thing that "SATs are Fun" may be guilty of is having more confidence in Debbie than she has in herself.  I think he/she was actually assuming Debbie is pretty good at the basics.  If anything they were suggesting she move ahead not travel back in time.  He/she seemed to be saying she might want to try something even harder and when she mastered that, the tricks won't seem so tricky.  Maybe he/she is wrong in that theory but I really can see some logic in it.

             

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

            Clearly anyone who thinks I've mastered the basics isn't employing critical reading skills (kidding).

            I will be breaking out my Dr. Chung book again to give it a whirl  http://www.amazon.com/Dr-John-Chungs-SAT-Math/dp/1439234973/ref=sr_1_1?ie=UTF8&qid=1319156375&sr=8-1

            It's like the SAT, but HARDER.  Last time I tried, I got 5/20 on a section.  Ouch.  I put it away for when I improved....which I seem not to do on "tests," (though I still maintain that I KNOW MORE MATH) but, no time like the present to try try again. The reviewers on Amazon swear by it.

            Well, maybe not the present.  The present is pizza on the couch -- and tomorrow is full timed test (again).  Maybe Saturday ;)

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

            I think 'The SATs are fun!' is completely well-intentioned, and clearly very smart. I hope he or she doesn't feel misrepresented by my comments.

      • Jen

         "Since they have a fairly limited scope in the concepts they can test,
        they'll often try to increase the number of careless errors. It's not
        necessarily evil of them, but it does necessitate added vigilance on the
        part of the test taker. "

        Yup.  And actually, when I tutor?  I do tell them they're pretty evil.  And that it's even more evil that you pay to take the SAT and then one of those earlier, while you're fresher sections is experimental and you're doing their experimenting for free while paying for the test.  Also quite evil. 

        Honestly?  My lack of memory of higher math and my enjoyment of basic math and puzzles and games is what makes me able to tutor kids to higher scores.  I can teach them the basics of algebra and geometry if needed and I'm really good at explaining the wily ways of the College Board.  If you needed a Trig or Calculus tutor to get you through a year of math?  I'm so NOT your person! 

        And that all says to me that this can be both a test of basic HS math skills AND a tricky test.

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

          I'm in a similar boat, actually. I won math awards in high school and took some sort of advanced math every year of undergrad, but years out of academia and in decidedly non-mathy jobs left me without much of a memory of calculus, trig, etc. by the time I started doing test prep. While I did well (99th percentile, but not 800) on the SAT in high school with brute-force math and no technique, I get 800s now. It helps to have a mind that has always enjoyed (and approached confidently) a challenge, but I also credit some of my success to my knowledge of how few math tools are actually required to solve all these problems. 

          Many of my students know math that I knew well once but have long since forgotten. They sometimes need my help getting out of their own ways. 

          • Jen

            Exactly.  They're so concerned with getting it exactly right and looking good while doing it that my vague and basic questions are usually enough to get them to step back and look at the big picture and realize they know what to do. 

            My son taking calculus now asks me to help him with a homework problem about once every week or so.  My value there lies in 1) having him explain briefly what they're doing right now 2) having him show me a similar problem he did understand and then 3) looking at what he did and noting where it either looks funky in the algebra or very different from what he's told me.  Or I actually look at the textbook!

            Usually though, his trying to dumb it down to explain quickly and easily to me is enough for him to find his mistake or think of a new thing to try. 

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

          When @PWNtheSAT and I were going over my test last week, we were taking note of the fact that when we'd come to one of their evil tricks, it's as if they know that they'll shave a few people's score down off with that one little tweak/twist.  

      • Neyaney

        I have to agree here. I'm 27 and just now taking the SAT's. I never took anything beyond algebra 1. However, I had no problem reasoning my way through SAT problems that had quadratics among other questions where I did not know the math/concept. Yet I got them right %99 of the time, especially when paired with a graph.
        Interestingly, once I learned the concept I'd sometimes make a mistake factoring the quadratic down, waste time, and might get it wrong.The SAT problems that get in the way of me achieving a 700+? The ones I see as "solvable", the ones I grind the numbers. Why? Because I get lost/time crunched/distracted in solving for "X" instead of 2x. Taking a step back and using reasoning instead of grinding the math has been far more productive in raising my score.Just a note, I started at a baseline of M 520, within a SINGLE weekend I was consistently scoring M 670-690. Later that week I scored M 770 on an official previous exam.Unfortunately, during the actual exam, I panicked and really messed up on a few of the easy questions. C'est la vie.
        Easy? For me, no way! Not because the concepts are hard but because I felt like I was watching for landmines, running a race, with a lion chasing me. I wish I had the money/resources to continue on and try again.

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

      Well, I wish it was as easy as you make it seem -- and I certainly started out thinking all it would take was a little elbow grease -- but unfortunately, it's been a harder mountain to climb than I ever expected.  

      At this point, I'd say it's probably a lack of a great rock solid math foundation from the time I was a little kid, more than anything else. I even had my IQ tested, thinking "maybe I'm not smart enough" (but it wasn't that ;))You did inspire me though to break out Dr. Chung's book again.  I haven't tried it in months (it's harder than actual SAT math -- and last time I did it I got about 5/20 right -- so maybe it' time to check it out again.In a word, I think you're one of the lucky outliers.P.S. I also think it's fun. despite my less than perfect scores.P.S.S.  Scores for my Oct. SAT are due.....ANY SECOND.  I'm on pins and needles.

      • elise

        I think maybe you are being too sensitive when you are reading the comments by "The SATs are fun".  I think it may be making you miss his or her's point.  In part of the comment he/she wrote:

        "I don't know if a single comment on your blog would convince you to try a suggestion for an alternative method of preparation, but I would be interested to see if it would make a difference.If you can find some spare time or maybe use a little of the time spent studying the SAT, go and try to study math more advanced than what is used on the SAT. Go take an intro to calculus course. You don't have to stop studying for the SAT, but try taking it alongside. The extra wrinkles added into equations will hopefully make the SAT ones easier because rather than looking for shortcuts for what to do with an equation you'll see easier forms of questions you encountered in your class."

        I think he/she is just trying to suggest that MAYBE you could try this and he/she even said it would be interesting just to see if it made a difference.  They were not saying that you weren't smart, in fact they seem to think you are smart and that you enjoy math just like they do so maybe what worked for them would work for you.  I think that one of their big points was that math knowledge builds on itself so a good way of practicing easier concepts is to use them while doing more difficult concepts.  I don't think he/she would have made this point if they didn't think you were smart enough to learn more difficult concepts.  I think that he/she also acknowledged that you might not be able to find the spare time to even try out their idea of studying more difficult math but would find it interesting if you did try it. 

        In fact, if he/she is one of the "lucky outliers", by making their thoughtful comment, they probably feel as if you share their company and are an outlier as well.  Why would they waste their time commenting to a dummy?

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

          ohhhhhh, so much can be lost in "tone" on email and in comments.  

          I didn't mean to come off as being offended or overly sensitive by "The SATs are fun." (thus my wink back in the reply).  And in fact I did appreciate the comment immensely -- and "got it" -- which is why I said I'd pick up Dr. Chung (thus taking commenter's advice).  

          And how can I not LOVE a commenter who signs in with "The SATs are fun"?  That's ABSOLUTELY my kind of person.

          Sometimes I'm moving way too quickly and should probably slooowwww down and make sure my tone is clear.

          And really.....Someone thinks I'm a lucky outlier?  That is the craziest thing I've ever heard....though I'm honored if that is the case.  I see myself as much more the middle of the road work hard and pick yourself up by your bootstraps type of person.  From where I sit, it seems like these tests come a lot more easily to people who have a different kind of brain than mine.

          I'm not saying I don't have anything going for me (I'm "creative" ;)) -- but, I *feel* like these tests come more easily to others (thus, my Bennington education).

          • Elise

            I guess I still don't understand why you think that other people are "lucky outliers" and you are different.  You started your SAT prep on February 1, 2011 and you managed to get an 800 on the writing and 740 on the reading.  Doesn't that make you an outlier?  Do you think that other people who get 800s on ANY of the sections of the SATs "prepare" for such a short time?  My son "prepared" the entire time he was in school.  I think if you are able to continue to take SAT prep and get 800 on math by the end of your year then you are more of an outlier than most people.  If not, it really doesn't mean that the test was more easy for others than for you, it means that they have spent more time learning than you.  You just can't call them luckier than you.  

            If what you say is true and you slacked off in school, you should expect that you should have put the same time in as the other people who didn't slack off and got the 800s.  I'm sort of guessing that between 7th grade and11th grade a good student who always paid attention (like my son) may spend at least 900 solid hours working on math.  I actually calculated that using one hour a day for 180 school days a year times five years.  Anyway, that's over 22 forty hour weeks.  So I feel that you can only say others are more lucky and have it easier than you after you have put in that amount of time and still don't get an 800. However, I have a feeling since you have pulled it off with writing and are almost there with reading, you will also pull it off with math.  Sorry Debbie, that makes you a lucky outlier as well:)  Probably even more so than the others you have put into that category.....hmm I still can't see why you wouldn't think your most recent scores put you in the lucky outlier category.    

  • a-none-e-mouse

    It seems that the optimal solutions to these problems involve maybe one or two steps?

    For problem 7, you can plug 0 into f(x) = a - x^2 and realize that a is positive. 

    For problem 8, note that (a + b)^2 = a^2 + 2ab +b^2 >/= a^ + b^2 = 400. Which means 
    (a + b)^2 >/= 400 (by >/= I mean "greater than or equal to")

    For problem 13, (w - 2)^2 = 0 implies w = 2 and you can solve from there.

    Sure enough, the SAT tricksters are up their usual tricks. However, when I took these exams, if I ever found myself spending 2 minutes writing 20+ lines of calculations, I would go back and make sure I'm not misreading the question or falling into one of the the trickster's traps. Take that for what it's worth

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

      I will take that for what it's worth.  Thank you!

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

      if I ever found myself spending 2 minutes writing 20+ lines of calculations, I would go back

      I've been telling Debbie that's my ONE significant advantage taking SAT math.

      Being old enough to forget names, I've learned that if I want to remember a name I can't remember at the moment, I have to stop trying to remember. Stopping is key. (There's actually an identified reason for this, as I recall, but...I've forgotten it. sigh)

      I do remember that it was my mom who first pointed this out to me: stop trying to remember & you'll remember.

      I managed to generalize that tactic to SAT math pretty quickly, but even so I'm pretty sure I lost points on the October test because I got sucked into a protracted bout of calculator-ing.

      With SAT math, I'm pretty sure the issue has to do with 'cognitive set': you're focused on Potential Solution A, and you need to get off that in order to think of Potential Solution B, but breaking set is difficult under the best of circumstances and close to impossible under stress.

      Dumping the problem, moving on, and solving other problems is a way of erasing the slate.

      Very often, when I return to the original problem, the correct solution "pops."

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

        My mom used to say "if it's important, you'll remember."  (I hated that!)

        I'm thinking I'm going to try something like the inner game of tennis for this next one.  Ordering book now....

        AND, I'm breaking out Dr. Chung.  I think it's time to try again.

      • Anonymous

        Hi Catherine - 
        Sian Beilock in http://www.amazon.com/Choke-Secrets-Brain-Reveal-Getting/dp/B004KAB2W6/ref=sr_1_2?ie=UTF8&qid=1319139647&sr=8-2 says that "stalling" strategies help: "..pausing in the middle of a challenge can prevent you from going down the wrong solution track....giving your cognitive horsepower time to percolate can be beneficial.."

        Debbie - I try and teach my brightest students to take a few seconds and "notice" things about the problem before jumping in and solving immediately. (They are trained in school to solve problems that look like X in Y way - whenever they see anything that looks like a nail, they grab their hammer - I guess schools don't spend much time "disguising" questions)

        You have quite an array of skills to bring to bear - pause for a second to think about which ones you are going to use on a problem.  And remember that the SAT is fabulous at disguising screws to look like nails!

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

          oooohhhhhh "take a few minutes"  (or even a few seconds, for that matter) is scary for me, because time is such an "issue."  I've been doing the "run like the wind.  Run debbie run" school of SAT.

          I actually haven't been perseverating as of late; if I can't get it, I run like the wind to the next one.

          That said, I RARELY have time to double back for a second look to see if I can get it on a second try.

          • Anonymous

            SECONDS!  Take a few seconds - like 5 - to see what they are asking, note the obvious traps, a choose a path to try. 

            Like Catherine, :-), I can't remember where I read this but I saw somewhere that experts aren't wedded to any particular path to solving a problem as much as beginners are.  I think that is b/c of the whole "if I only have a hammer, I'm going to hammer the crap out of this screw and make it work like a nail" thing :-)

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

            Ok, noted ;)  Will employ tomorrow.

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

    SAT math questions use the phenomenon of associative interference against the test taker. That's what makes the questions tricky: each of the problems above is designed to activate the wrong associations inside your mind. Why else choose the variable 'a' in question #7? If your goal as a problem writer were to avoid associative interference, you would deliberately choose another letter to serve as the variable.

    Add to the College Board's question-writing formula the high-stakes, time-pressured, and mentally grueling nature of the entire 4-hour ordeal, and you radically increase the odds that test-takers with high working memory will take the bait. (I'm thinking of Sian Beilock's research in particular.)

    As for the small number of people who breeze through the test racking up correct answers, I would be interested to see how they fare on find-the-missing-figure puzzles. I'm guessing many of them would do well. (I don't know whether aptitude for missing figure tests is associated with aptitude for math.)

    For the rest of us, it is simply not possible to "break set" in the heat of the moment: breaking set in the heat of the moment is precisely what our brains are built not to do.

    For the rest of us, the answer is "extinction learning," which is a critical component of SAT math test prep.

    I think I'll finish this up over at ktm.

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