Math

The Cure For Graph Dyslexia (And It’s Not A Pretty Sight)

I don't want to count any chickens before they hatch, but I do believe I may have cured my "reading functions backwards under pressure" problem. Incidentally, my son told me lots of people have this issue, which made me feel better.

It took me a few tries, and I even double stumped myself -- but here is the most gruesome Function Notation Graph question I could conjure up:

The figure above shows the graphs of the functions f and g. If y = f(x), and f(4) = k, and g(-2) = m, which of the following is closest to f(k) + g(m) - (k/m)² ?

(A) f(-2)

(B) f(2)

(C) g(-3)

(D) g(-6)

(E) g(6)

What do you think? All answers/attempts/questions left in the comments will Make My Day.

By the way, is anyone else having a hard time finding their SAT groove? I feel like there is always something "really important" to do before I can get to my SAT work, and then I never seem to get there ("there" = SAT work).

I'm scheduled to take a full, timed PSAT with my son tomorrow morning -- so hopefully that will be my "get back on the horse" moment.

Illustrations by Jennifer Orkin Lewis

17 Comments | posted October 8th, 2011

Erik

It is great that you are making your own function nightmare problems. Lots of people mix up the input and the output, so this one would be a good mini-test! To make it more like a real SAT problem, the question could be just: "If f(4) = k and g(-2) = m, which of the following is closest in value to f(k) + g(m)?" The answer would then be B instead of A. (The k/m squared is a bit unnecessary since you're really testing function stuff, and the fact that your answers are also functions is nice and makes the problem pretty hard as it is. But this is really a pretty tiny criticism.)
- http://www.perfectscoreproject.com Debbie Stier
  
  Ok, between you and Mr. Keller's feedback, this one's going to be updated...
  
  After I take the FULL TIMED practice PSAT with my son this morning!
Phil Keller

"Don't torture yourselft, Gomez -- that's my job."

Well this is evil. And I can almost hear you cackling all the way here in NJ. But I actually think there is room to make this even more evil. Your f(x) function -- it's a linear function with a slope of 1. So f(3)=3, f(4) =4...you are letting people off the hook! For that function, a kid who doesn't know the difference between an input and an output will still get the problem right. We just can't have that. So if you feel like increasing the torture level, change the slope of that line. Or shift it even 1 unit up or down. Or flip it so that the slope is negative one...
- http://www.perfectscoreproject.com Debbie Stier
  
  wow, you know, that was like a little pebble in my shoe. I knew that was too easy. Flip it so the slop is negative would be very very evil.
  
  I'll see what I can do with that.
  
  But first, a full timed PSAT with my son this morning. He's on his way here now. We are scheduled to begin at 10:30.
SimplyBMW

Is the answer B?
- http://www.perfectscoreproject.com Debbie Stier
  
  no....tell me if you want me to give you the answer.
  
  Or a hint.
anotherSATmom

-2 = f(-2) is (A)
- http://www.perfectscoreproject.com Debbie Stier
  
  Thank you! YES YES YES! Of course you're right. I"m sure it was easy for you too, right?!
  - anotherSATmom
    
    Wouldn't say "easy." (1) The graph is hard to sort through, visually, which is not uncommon on the actual SAT. (2) The two different functions amplify #1! (3) For some reason my mind wants the answer to be the function g(ofsomething), which makes it trickier still. Yes, if you breathe, keep input and output straight, and go step-by-step, I guess it's easy. But most kids don't do that. I'd say it's a fairly evil, spend-way-too-much-time-for-one-raw-point kind of problem... Happy?
    - http://www.perfectscoreproject.com Debbie Stier
      
      yes, very happy. Thank you ;)
      
      In fact, I took a practice PSAT with my son yesterday, and I came upon one of these (though not quite as hard), and I sliced through it like butter. He missed it btw -- and math is his strong subject, so it kind of surprised (and depressed) me.....
      
      .....Though not really, because frankly, he phoned in that whole test and did worse (by far) than he's ever done, and he takes the real PSAT this coming Wed. This was so depressing for me given all the effort the two of us have put into this. Actually, he hasn't put in that much effort (though he thinks he has).
      
      Sometimes I manage to slightly engage him in this process (though I could NEVER get him to write the questions) -- but not yesterday (or really for this whole past week or two). He showed up yesterday morning to take that PSAT with me like he was doing me some big favor -- and he had one foot out the door the entire time, which was making me so anxious; he couldn't wait to be on to his next fun thing (round the clock fun this weekend, apparently).
      
      Which brings me back to square one of this project, and reminds me of something that you said in a comment that still rings in my ears (i.e. something to the effect of, it was more important to you than your daughter).
      
      So here's my question: How do you engage a kid in this process and how do you motive them? I feel like I've done everything I can possibly think of (except for maybe "nothing." I haven't tried just doing NOTHING.)
      
      My kids are decidedly NOT the type A's I always read about (nor are most of their friends) -- and as far as my kids are concerned, they're doing way more than the "other kids" -- which I guess is all relative, because the "other kids" they are referring to are the entitled kids from this upper middle class town who mostly don't work very hard (there are absolutely exceptions). So yes, if you compare my kids to most of the kids they see around here, then yes, they are working harder (slightly). But that bar is low -- and my kids could very well fall squarely into those statistics of lower SAT scores and the dumbing down of America.
      
      The thing they've got going for them is that they go to great schools that are filling them with an amazing body of knowledge, whether they like it or not (and my son does like it, to a degree).
      
      I've been trying to put my finger on exactly what it is that motivates a kid to push through the hard stuff and engage and work hard -- and maybe you're born with a perseverance gene, and maybe there's some parenting gene I'm missing that instills it. I'm just not sure -- but that is the $64000 question as far as I'm concerned.
      
      I know the culture we live in is at odds with me, that's for sure.
      
      And I've come to believe that there's this unfortunate paradox: it turns out the more I give (on any level), the less they do on their own and the worse they behave.
      - anotherSATmom
        
        You know, I think you're right about the paradox. And about the $64,000 question. And I do not know the answer. I think the motivation has to come from them.
        
        I knew, growing up, that a scholarship was the only way I was going to college. And I only knew that because Jane Hobson brought a news clipping about her sister's scholarship awards to school. I didn't know anything about loans and the guidance counselors didn't guide. So, I set out, from eighth grade to build my resume. "Driven" would be an understatement.
        
        My kids, on the other hand, have always know n that they will go to some college and that we will pay for it (we will require that they borrow the max allowed without our co-signing, but that isn't a lot).
        
        I think that's made them a lot more relaxed and a good deal lazier. They're also a lot more savvy than I was at the same age. They know that high school counts less than college counts less than grad school. They also know the world is not really meritocratic. That insight, whether entirely accurate, takes a lot of pressure off of things like the SAT. I don't know whether that's an entirely bad thing.
        
        By the way, my son (10th grader, the one who scored 2100 on the SAT last June so he could take the math course online) is taking the PSAT. Too late, I noticed he forgot his lunch...
        
        I think your dad is right about raising them well and letting them fly -- how did he put it?
      - http://www.perfectscoreproject.com Debbie Stier
        
        I think I've also decided that the further we get from the "hungry/striver" generation, the less motivated we become.
        
        All that said, I *think* that my son did put in more effort today on that PSAT than he would have had I not stood on my head on a tightrope blowing him kisses while waving flags -- to get his attention.
        
        Considering where we live and the vast majority of the kids he's in contact with, and that he's extremely social kid (not necessarily a bad thing, but at odds with "studying" for sure), I do believe he put in a pretty decent effort beforehand, and he showed up today, took it seriously, focused, and did well enough to egg him on for the next thing (SAT in Jan?).
        
        (BTW, I just overheard him saying to his dad on the phone "it was fun" - and I'm pretty sure he was referring to the PSAT. That's pretty good, right?! I will take FULL credit for any fun he found in this experience!).
        
        Did your son survive sans lunch? I actually went out and bought my son breakfast this morning because it's pretty slim pickings at my house and I wanted him to show up on a full belly and not the seeds and berries we usually eat at 6 am.
        
        I also packed him two bars of very dark chocolate (75% cocoa), because I've found that's the most effective food to eat during those 5 minute breaks. He said "it worked" -- so I don't think it's just me.
        
        He also said that taking that full timed PSAT on Sunday (referred to above), during which he drove me crazy with his inattention, was helpful in terms of stamina and timing.
        
        All in all, I'd say one little baby step forward.
        
        How was your son's experience?
      - anotherSATmom
        
        I know you would have liked your son to take the practice PSAT more seriously, but less than full bore has some benefit and seems to have helped. I'm glad he had fun.
        
        As for my boy genius, they fed him at school (although no great dark chocolate snacks)! This test was a "preview" for next year. Boy, is ETS raking in the bucks! Every tenth grader was urged to take it.
        
        Anyway, he listened to a little of what I told him: when I picked him up from school (how does a 2-1/2 hour test turn into 4 hours?), he told me about the last math problem on a section and how he changed his answer at the very last second after an oops/aha moment when he realized the answer he chose was too easy (hard problem) and checked his thinking (I can't get him to write down his steps - arghhhh). The answer he changed to was right (if he described the problem to me correctly).
        
        Little by little, it drips into their brains.
        
        Maybe.
      - http://www.perfectscoreproject.com Debbie Stier
        
        I agree. Having fun with this is high on the list of priorities.
        
        Oh, was that problem your son was describing the one where they had to make equation with variables out of a word problem about men and the letter k was involved? My son was describing that one to me on way home and I have NO idea what the right answer is. (note to self: Write some questions like those.)
        I've been working on "property of numbers" questions. Didn't realize A) how little I knew about property of numbers, and B) how much you need to know.
        
        And on a related note, I took a full, timed practice SAT today (from CB online course), and I found a College Board mistake!
        
        Not sure if this makes me feel better about my own mistakes, or worse that the line just moved.
        
        Mistake attached.
      - anotherSATmom
        
        The problem my son was talking about was a cylinder, really straightforward I thought, except for one very intentional ETS-inflicted hiccup, which he caught at the very last second. I'll ask him about the one you describe when he gets home.
        
        Yes, ETS is big on definitions. HUGE.
        I love that you screen-captured the boo-boo. A good share of their practice tests were never actually administered, at least not in toto. I would bet real money that the line on the actual tests you will take didn't move. Here's hoping, anyway!
  - anotherSATmom
    
    OK, Phil Keller is right, but he must live to torture children! ;-)
    - Phil Keller
      
      It's more like a hobby...