Quotes

Understanding is Remembering in Disguise

If you're anything like me.....

....E V E R Y T H I N G takes way longer than you think it will.

With regard to the SAT (or I should say, with regard to learning anything, and remembering what you learned), multiply that idea by at least 50.

Thankfully, at this stage in my life, the SAT stakes are about as high as the public humiliation I will have caused myself if I don't improve.

However, if you actually need a good score for a reason more valid than thinking this is a good time, follow this man's advice:

As far as anyone knows, the only way to develop mental facility is to repeat the target process again and again and again.

So, apparently, studying hard doesn't protect against forgetting ... But something else does: continued practice.

Practice is another significant contributor to a good transfer. Working lots of problems of a particular type makes it more likely that you will recognize the underlying structure of the problem, even if you haven't seen this particular version of the problem before.

It is virtually impossible to become proficient at a mental task without extended practice.

Children do differ in intelligence, but intelligence can be changed through sustained hard work.

Intelligence is malleable. It can be improved.

...the amount of information you retain depends on what you already have.

Understanding is remembering in disguise. We understand new ideas by relating them to things we already know.

These are a few of the many many passages I highlighted from Daniel Willingham's book about how we learn.

If you don't believe me, believe him. I promise, he's not wrong.

Illustrations by Jennifer Orkin Lewis

27 Comments | posted August 30th, 2011

Guest

Hi , I believe him, but lets say if you've used an 800 + page Sat book and don't really wanna answer anymore questions after you've answered the whole book; is it a good idea to practice the math sections you've already answered again or just leave them alone and start anew?
- http://www.perfectscoreproject.com Debbie Stier
  
  I'm assuming that 800+ page SAT book is the College Board Blue Book? If not....start all over from the beginning, with that book. Sorry :(
  
  And if it was the blue book, I have a few q's before I say what I think:
  
  1) Are we just talking math?
  
  2) How'd you do? Did you take the sections timed and are you where you want to be?
  
  3) If not -- where are you scoring (you don't have to tell me specifically -- but if you're a high scorer you might want to try Chung -- but not unless your tippy top or you'll be frustrated -- said the one who tried before she was ready).
  
  4) What is your score goal?
  
  Here's the thing with doing the same questions over again (and I speak as someone who has done this, again and again in fact -- and likes doing that, no less because it makes me feel good!) -- BUT, I find that it gives me a false sense of security. I think it's good re-do them until you understand them all deeply -- and then do them again! -- but to really see where you are, you have to test yourself on FRESH material.
  
  I'm always stunned at how poorly I do on fresh material when I'm thinking I'm doing so great by repeating the same material over and over, and getting it right!
  - Guest
    
    Hi, yes it's the Blue Book.
    1, yes.
    2. I think I'm getting there but not yet, about a 500. I haven't used a timer yet, but i think i will to see how i do under pressure.
    3. ok . I barely do well on Sat Math , because it's so different from the real Math. I hope that it don't happen this time.
    4. I'd like to reach a 1900 - or almost 2000.
    That's great advice, thanks. I used to do that with the Little Test Booklets.
    Ps. I'm barely studying now,because i can focus with this weather and i'm also busy with school. If I could I'd hire a tutor to help me end this nightmare once and for all :-)
    - http://www.perfectscoreproject.com Debbie Stier
      
      Ok, this is what I'd do:
      
      I'd get a copy of @pwnthesat:twitter 's BETA access math book and do it cover to cover. It's only $5, and it's fun/funny -- so it shouldn't be too arduous ;) Do a chapter or two every morning before you get distracted by the day. Like brushing your teeth. Just do it b/f you have time to think. Won't take too long.Then, I'd do a few (or more) of those Blue Book sections again, timed. What I do is I put the timer on and do it in pencil -- then (because I'm obsessed), after the timer goes off I see how much I can finish, but I do it after the bell in red pen so I can tell the pre/post bell difference easily when I score it.Then, if you can afford to join the College Board Online course, I think it's worth it to have access to fresh official material. I think it's about $70 and you get 10 more tests.If you do one section a day in the morning before you start your day (say, 25 minutes), then CORRECT IT (key) and make sure you understand all of your mistakes (do you have a solutions book?) -- it shouldn't take tooooo much longer than an hour (depending on how deep you want to go into those solutions). And if you can afford a tutor -- even for a little while -- I think it's could be worth splurging -- just so someone can get you focused. I loooovvve @staceyhowelot:disqusand she uses Skype, so it doesn't matter where you live.I was just saying to someone that the Math is every bit as much a reading section as it is math.
      - Anonymous
        
        Thanks for the shout out Debbie! Also you can find explanations to the blue book questions on the collegeboard site at http://www.collegeboard.com/satstudyguide.
      - Guest
        
        Is it free ?
      - Anonymous
        
        Yes - the explanations to The Official SAT Study Guide, 2nd edition are free on the college board website
      - Guest
        
        Damn it , I have the old version, isn't there another way??
      - Anonymous
        
        It will work with either edition. (Look for the link for the 1st edition after you log in) The second edition is available on Amazon for $9 - it offers 3 more practice tests in addition to 7 from the first edition
      - Phil Keller
        
        One more free resource: GOOGLE! Take the key phrase from any problem in either edition of the blue book and search for it in google. You will find explanations, often from yahoo answers or collegeconfidential. These questions have been picked over so many times by so many students that you can almost always find multiple explanations. And unlike the college board site, the explanations will include the "sneaky" solutions. The collegeboard always seems to point you at the formal-algebra way of doing things. If that were going to work for you, it would already be working!
      - http://www.perfectscoreproject.com Debbie Stier
        
        The Google machine. How could I forget!!!
      - http://www.perfectscoreproject.com Debbie Stier
        
        The Google machine. How could I forget!!!
      - Guest
        
        I've just searched for that book on Amazon.com and it doesn't appear. but if it's really going to help then i'd like to order it. But when you are answering the math questions timed, you won't have time to solve them the long way right? i'd be to choose the answer you think is right. Now that you mention it, I think that i may purchase the $ 70 college course online. By Solutions book, do you mean the Guide book that comes with all the answers? or the regular blue book?
        I'll think a bout it :)
        How so? I mean those sections aren't as difficult as the mathematics section; but it can be equally as tedious.
      - http://www.perfectscoreproject.com Debbie Stier
        
        For @PWNtheSAT:twitter Math book, you need a Google Account, and you can get it here: http://blog.pwnthesat.com/p/pwn-sat-math-guide-beta-access.html Sorry I thought I put link before.
        
        Re a solutions book -- The College Board link that Stacey put up above is FREE -- but, I can't make sense of their solutions for the life of me.
        
        For the math, I like to use Tutor Ted's book http://www.amazon.com/Tutor-Teds-SAT-Solutions-Manual/dp/1450516505/ref=sr_1_1?ie=UTF8&qid=1314830365&sr=8-1 I think it's worth it because if you don't understand your mistakes you're not going to make progress.
        
        Khan Academy has video solutions for free too -- but I can never find the right place in the video easily, so I spent a ton of time navigating. (arrggg)
        
        Also, if you don't understand something, @PWNtheSAT:disqus will explain in great detail here: http://qa.pwnthesat.com/ask (FREE)
        
        AND, here are more FREE solutions: http://bbb.ttprep.com/2011/06/practice-problem-14-page-340.html
      - Guest
        
        I can't understand, in the College board website when they explain the answer of a math problem, it tends to look like a very long essay; thus waisting the readers time.
        
        Thank again for the help!! I've seen the Sat Solution book on amazon , but i think that 's only for the second ed of the blue book. I use khan Academy the most, but I don't like him and the way he explains he's exercises…. he does a lot of strange things that end up confusing me even more.
        I also like using Pwnthesat's tumblr to ask questions about the exercises that stump me the most, because I want to know why I got the answer wrong or right.
      - http://www.perfectscoreproject.com Debbie Stier
        
        I agree! College Board explanations make my eyes glaze over, and Khan confuses me as often as he helps me! I actually don't even use either anymore.
        
        And I agree with Stacey that Keller's book is excellent too.
      - Guest
        
        Great ! and have you ever used Sat Math For Dummies ?
      - http://www.perfectscoreproject.com Debbie Stier
        
        Nope. But I've never had luck with those Dummies books :( So I'm disinclined.
      - Guest
        
        good, because it's really not good.
      - Anonymous
        
        I would recommend a tutor over the $70 online course. The online course *is* great for additional practice. But I think you need to focus on learning *how* to answer the questions. Debbie's list of resources is excellent. I'd add Keller's SAT Math Game Plan to the list
      - http://www.perfectscoreproject.com Debbie Stier
        
        I agree.
    - Anonymous
      
      If you are starting at a 500 untimed, I'd recommend hiring a tutor ASAP.
      
      In one hour with a tutor, he or she can figure out where your weaknesses are and give you pointers on math strategies which can use to directly increase your score. For example, at the moment you shouldn't answer the last 3-4 questions per section because they are the hardest ones. Focus on mastering the easy and medium questions before trying to tackle the hard ones.
      
      SAT Math *is* real math with logic thrown in. You don't need to know how to calculate the answer, but you do need to know how to find the answer and they are two different things. A tutor can show you how to avoid a lot of the traps on the test - like medium questions do not have easy answers.
      
      Many tutors offer a sliding scale of rates so you should be able to find someone to help you out. Also tutors can point you to terrific resource that can help you study on your own.
      - http://www.perfectscoreproject.com Debbie Stier
        
        Our responses crossed in the air.
        
        I recommended YOU as you were writing this!!
      - Alex Jacobson
        
        You see a lot of advice about gaming the test.
        
        This is bad advice.
        
        Valuable time is wasted by the student trying to study tricks, and during the exam, trying to outsmart the problem writer when the student panics at a hard problem.
        
        Put all effort into understanding. In particular, in math, if you know your stuff, you have time to calculate each answer, and the hard ones in two ways. Most will not get to this level. But strive for it.
        
        But at least spare us the gaming approach: "You don't need to know how to calculate the answer, but you do need to know how to find the answer and they are two different things."
        
        Baloney.
      - Anonymous
        
        I don't advise students to game the test - in fact, I don't think it can be gamed.
        
        Many students approach a math problem only one way. And if they don't know how to do it the "right" way, they stop and turn off their brains. Or they solve it out the "right" way and it takes too much time and they can't finish the math section.
        
        The SAT rewards students who can find the right answer *in the shortest amount of time*. The College Board doesn't care *how* you arrive at the answer (whereas in school you often must show your work of solving the question correctly in order to get full credit)
        
        One of the best examples of this is spring problem - Test 5, Section 2, Question 5 in the Blue Book. "The force required to stretch a spring beyond it's natural length is proportional to how far the spring is being stretched. If a force of 15 pounds stretches a spring 8 centimeters beyond its natural length, what force is needed to stretch the spring 20 centimeters?" Answer choices are A) 23, B) 27, C) 30.5, D) 35, E) 37.5
        
        If you know how to do the algebra, you just set up the proportion and solve it. 15 lbs/8 cm = x lbs/20 cm. x = 37.5 lbs.
        
        But for some reason a lot of my students struggle with this problem. So I ask them to *draw* the problem ("Trick" number one.)
        
        If that doesn't spark an insight, I ask them what would happen if they doubled the force - "poke" the problem. ("Trick" number two.) (I work with a lot of math phobic students)
        
        If you applied 30 lbs, the spring would stretch 16 cm. Hmm. Not far enough. But they can eliminate answers A-C.
        
        From here they can guess or backsolve with the two remaining answer choices, set up the proportion and solve it directly, or poke it again.
        
        If you increase the force by 15 more lbs the spring would stretch to 24 cm. Hmm. Too far. But halve that - increase by 7.5 lbs and the spring would stretch to 20 cm. So 30 lbs + 7.5 lbs is 37.5.
        
        So there you go - can can solve problems the algebraic, "math" way or you can mess around with the problem and see if you can find the answer that way. You must be able to *find* the right answer, but you don't necessarily have to know how to "calculate" the answer.
Alex Jacobson

Let's do this one by one:
As far as anyone knows, the only way to develop mental facility is to repeat the target process again and again and again.Pretty true, unless you get it the first time. Everyone has something they get the first time.So, apparently, studying hard doesn't protect against forgetting ... That's right. If you don't understand, you will forget. Evidently, understanding is key.But something else does: continued practice. Absolutely, provided the practice leads to understanding.Practice is another significant contributor to a good transfer. Working lots of problems of a particular type makes it more likely that you will recognize the underlying structure of the problem, even if you haven't seen this particular version of the problem before.Very well put.It is virtually impossible to become proficient at a mental task without extended practice.I agree.Children do differ in intelligence, but intelligence can be changed through sustained hard work. I disagree. Performance can be improved. Intelligence, talent, is innate, whether or not it is developed.Intelligence is malleable. It can be improved.Nope. Not anymore than height, beauty, or natural athletic talent....the amount of information you retain depends on what you already have.Yes, but only in the context of understanding. When you understand something, you can use the underlying pattern to more easily understand other things, and also to order facts.Understanding is remembering in disguise. We understand new ideas by relating them to things we already know.An utterly false statement. Unfortunately, you do not have a clear understanding of what understanding is.Understanding is creating neuronal patterns that involve cause and effect, that relate one group of concepts or objects to another. Without those intuitive neural patterns, no understanding, no ability to make quick, currect judgments without even thinking, no ability to immediately begin to solve a problem.Remembering is just that. I remember, for instance, that Khloe is married to Lamar. But what understanding is that?Mathematics, physics and chemistry involve understanding. In people with limited aptitude in these areas, the doing of many problems will increase understanding and performance, but only to a limit. The same thing, by the way, operates in a basketball jump shot, or the playing of a musical instrument. In virtually all intellectual activities, we are limited by innate aptitude, and also, by the finite amount of time we can afford to devote to developing that aptitude.In junior high, I had a friend named Hyman Chansky. He was tall and wiry. He was a good student, good in math, but not quite as good as me. But he was a much faster runner, and after typing class, he could type 60 wpm whereas I could barely manage 20 and I practiced and practiced. You learn a little something about aptitude when you really try to do something, and when you are acquainted with people who have aptitude.
- Alex Jacobson
  
  I'm sorry to repost below. But the software ruined all my layout. So it was unreadable.
  
  Let's do this one by one:
  As far as anyone knows, the only way to develop mental facility is to repeat the target process again and again and again.
  
  Pretty true, unless you get it the first time. Everyone has something they get the first time.
  
  So, apparently, studying hard doesn't protect against forgetting ...
  
  That's right. If you don't understand, you will forget. Evidently, understanding is key
  
  .But something else does: continued practice.
  
  Absolutely, provided the practice leads to understanding.
  
  Practice is another significant contributor to a good transfer. Working lots of problems of a particular type makes it more likely that you will recognize the underlying structure of the problem, even if you haven't seen this particular version of the problem before
  
  Very well put.
  
  It is virtually impossible to become proficient at a mental task without extended practice.
  
  I agree.
  
  Children do differ in intelligence, but intelligence can be changed through sustained hard work.
  
  I disagree. Performance can be improved. Intelligence, talent, is innate, whether or not it is developed.
  
  Intelligence is malleable. It can be improved.
  
  Nope. Not anymore than height, beauty, or natural athletic talent
  
  ....the amount of information you retain depends on what you already have.
  
  Yes, but only in the context of understanding. When you understand something, you can use the underlying pattern to more easily understand other things, and also to order facts
  
  .Understanding is remembering in disguise. We understand new ideas by relating them to things we already know.
  
  An utterly false statement. Unfortunately, you do not have a clear understanding of what understanding is.
  
  Understanding is creating neuronal patterns that involve cause and effect, that relate one group of concepts or objects to another. Without those intuitive neural patterns, no understanding, no ability to make quick, correct judgments without even thinking, no ability to immediately begin to solve a problem.
  
  Remembering is just that.
  
  I remember, for instance, that Khloe is married to Lamar. But what understanding is that?
  
  Mathematics, physics and chemistry involve understanding. In people with limited aptitude in these areas, the doing of many problems will increase understanding and performance, but only to a limit. The same thing, by the way, operates in a basketball jump shot, or the playing of a musical instrument. In virtually all intellectual activities, we are limited by innate aptitude, and also, by the finite amount of time we can afford to devote to developing that aptitude.
  
  In junior high, I had a friend named Hyman Chansky. He was tall and wiry. He was a good student, good in math, but not quite as good as me. But he was a much faster runner, and after typing class, he could type 60 wpm whereas I could barely manage 20 and I practiced and practiced. You learn a little something about aptitude when you really try to do something, and when you are acquainted with people who have aptitude.