Friday, August 21, 2015

COGAT Question #9

The last question on the COGAT is the mysterious folding question.  It's even more mysterious than you think.

When I took apart the figure analogies, I created questions that can only be described as Hard Core Extreme Diabolical.  I expected them to be way harder than the actual test, in terms of evaluating alterations to shapes, but I became suspicious that the I was heading off in a different direction than the test.  The test, after all, is trying to find kids with promising academic careers in elementary school, not promising academic stints in doctorate programs of Shape Alteration.  If my effort had the intended effect, it was only that I forced my child to think, learn from his mistakes, learn to deal with frustration, and other skills that would be useful for academics.

Regardless, a few months before the test, an opportunity arose in the form of Jury Duty.  Since I live on a block full of police officers, including my upstairs neighbor, it's hard for me to actually sit in a Jury, unless the accused is an obsessive compulsive parent and blog writer, in which case I'd be one of the few peers.

The night before I reported for duty, I organized my objectives for a test of folding questions.  I brought a stack of white paper, a ruler, and a box of sharp pencils.  By the time I was released at the end of the day, I had 100 solid questions on this topic.  These questions were at a brutal level, and after a few grueling weeks of mostly complaining, test prep on this topic was complete.

After the test, the poster child for Test Prep told me the test questions were super easy compared to mine.  I was skeptical.  Kids say that when they miss the whole point of the question and get it wrong.  Then he took some paper and a pencil and started drawing each question and the answer set.  I was stunned.   The questions were easy.   They looked nothing like I expected.

It's worth mentioning that the test takers from the psychology department at IIT give the kids a scented sticker.  When the children emerge from the test, all they remember is the sticker.  It's like a memory wiper-outer.   I'm on to them.  I learned visualization and context in college, and a few minutes later, my kid was back in the test room looking at the test in his memory.  Plus, he had so much test prep, it was quite easy for him to regurgitate the test, scented sticker or not.

So I'm going to walk you through what I did with the folding question without fear of giving anything away from the actual test. Here are the takeaways:

  • The folding question is a fun way to learn multiplication, visually, at a young age, in the same way that the quantitative questions are probably the best way for little kids to learn arithmetic, and the figure analogies are a great way to learn geometry.  There is no downside to spending time doing test prep. I wish our school curriculum looked like this.  More kids would be at 99% in math.
  • Practicing the folding questions are a great way to build working memory which is a tread winding through the whole test.  "Tread" was originally a typo but I think it works better.
  • The folding questions exercise thinking, figuring out, and other great skills.
  • The folding questions break kids of 2 bad habits:  learning by having a parent tell them something, and looking at a question expecting to know the answer immediately.  If your child can break these habits, test prep is 90% finished.
The Analysis

The basic folding question from the test samples and from test prep books is very simple.  Show a folded piece of paper with holes punched into it, and the pictures representing potential versions of the unfolded piece of paper.  Which one answer is correct?

The Test Prep Cowboy just stopped by my computer and picked the 1st choice without thinking.  We went through most of test prep with this bad habit, no matter how many times I demanded that he read all of the answers thoroughly before answering.   Thankfully, test prep identified the problem and corrected it.  Any parent who dismisses test prep is, well, short of adjectives, simply wrong.

The correct answer is the last one.

I'm not going to draw any more of these since they are copyrighted by the test and I have no way of knowing whether or not they actually are going to use one of my permutations, however unlikely.  Fortunately, I don't have to, because you are going to get a stack of paper and a hole puncher and your child for the rest of this article.  I recommend you cut the paper into squares, no more than 12-15 hole widths wide.  The hole I drew above is a bit bigger than I would prefer.

This will be a fun couple of weeks.   You fold and punch holes, and they draw the results.  Then you can compare the original and the drawing, and point out millimeters of incorrectness due to your child's lack of drawing skills.

Level 1 - Multiplication
The first thing you can do is fold the paper once, twice, and three times, and punch 1, 2 3, and 4 holes, for a total of twelve iterations.  That represents an introduction to multiplication.   At least doubling and halving is fair game for the test, so why not overshoot to be on the safe side.  If you are folding the paper only once, there is room for 5 or 6 holes on that paper.  With 3 and 5, you can move the holes around a bit.

Level 2 - Hole Placement
Next, the holes can be on the inside and outside, top or bottom, or a combination of these.  When unfolded, the holes may be on the inside or outside corner,  near the bottom, middle or top.  With one fold and 2 holes, there are a dozen or so different layouts.  Once your child starts to understand placement, he might point out subtle placement errors.

Level 3 - The Trick Folds
Fold a piece of paper in half.  Then take the bottom end and match it to the middle, making another fold. The outside fold only comes half way up.  Then punch holes above or below the fold, or both.  Look at the results.  Many more permutations.

Try diagonal full folds, or diagonal half folds.  A half fold is what I just described where the ends don't meet, but one end meets in the middle.

At this point, I'm not sure what the actual count of permutations is, but even if the a test followed my recipe, you couldn't do them all before the test.  There are many.

Level 4 - Direction
Instead of a circular hold punch, get something that punches a different shape, like a triangle or dove.  If you are ambitious, you can buy a shape hole puncher by Friskars or Martha Stewart.   I recommend just using a sharp pen and pressing really hard so you have evidence to win the ensuing argument with your argumentative child.

Arrows can point in all directions, multiplying the thousands of permutations we have so far by a big number.

The Focus
Your child does not need to be an expert at folding and punching, and there is no way you will do enough to practice the actual test questions.  As I mentioned, the test goes off into some Level 2a Bizarro World of folding questions that I don't cover here so it's pointless to try anyway.  If you hit level 4, you'll be beyond the difficulty of the test (at least for 1st grade), so instead you need to focus on best practices.

Best Practices for Kids
1.  Spend time thinking about the problem.   The corollary best practice for parents is to NOT help the child. Give them 20 minutes or more to consider the problem and instead of undermining their progress by helping, offer helpful guidance like 'Stop looking at your shoe and look at the problem again."

2.  Spend time thinking about the answer set.   The method I outlined above doesn't have answer sets, so you'll have to address it the easy way.  Make 20 squares, pick 20 folding patterns, punch holes and open them.  Then draw what you see.  This will cut down on your own mistakes which will confuse the child.  Lay out all 20 squares in front of your child, and then refold a blank piece of paper, and substitute the punched one.  She can pick from the 20.  She'll have to look at all 20 every time.  And you'll have to repeat the whole exercise for 20 straight days for a total of 400 practice questions.  Or not.

3.  If your child gets the wrong answer on the first try, ask them to prove it.  If you say "wrong", they'll just point to the next answer and look at you.  If they have to prove it, then they have to check their work, which is the point.  Once it a while ask them to "prove it" when they got it correct so they'll never know if they are right or wrong.  Until they check, which is, again, the point.

4.  Discuss mistakes.   When the child is totally lost, describe in words what your mental ruler sees.  Before the final answer, the child is only allowed to see the folded pieces of paper with the holes in it.  After they answer, they can slowly unfold the paper to see how the holes move.

Feel free to have a child who answers most problems incorrectly.  You will be in good company.  This is called learning and it's a great thing.  Any time my children are getting less than 50% wrong, I raise the bar, and I then lower when they get too many wrong.

I think I covered 5 questions types.  They all deserve to be covered in more depth, except the vocabulary questions which just need lots of talking in big sentences and lots of reading.


  1. How did you prep your boys for COGAT? There are a few different types of questions and we have a year to prep at this point. More than anything I want my kids to be familiar with questions types and what each question asks. Do you recommend working on practice questions by types of questions (for example, a couple of days or a week each to work on figure analogies and then train patterns) or mixed.

    1. We did math first because we are always ahead in math. Next, we did the verbal very slowly, straight through. I discovered lots of problems and bad habits to correct, especially with classification questions. We did all of the figure questions next. I spent as long as I could on each question because there is so little material available. Then I saved 1 of the 4 test prep books to do a full practice test in the last few weeks - which was a total disaster.

      This part of test prep is absolutely essential for catching mistakes but absolutely useless for teaching cognitive skills. I'm working to fix it but my material is insane and I think my market is limited to the 10 parents who are desperate to go from 65% to 99.9% in 3 months.

  2. Can you PLEASE upload any sample question on paper folding that would cover the different types ? I have been working withy child on this topic and ...honestly's driving me crazy...:(

    1. OK, that's a really good idea. Give me some time to prepare and I'll create a follow up article. Sometimes I forget that not every one of my readers are engineers and mathematicians and spent 7 years in graduate school.

  3. You INSPIRE me to be a better parent ... The amount of time and effort you put into teaching your kids is amazing...i read your blog everyday ....helps me be a better parent.

    1. Good to here. I've been putting my kids through a 20 to 30 minute daily routine focused on thinking and working hard, and the results are stunning.

  4. I need your help, once again! The test is in one month from now. We went full steam ahead in Summer, but now that school has reopened, I find that the 6+ yr old is very low on stamina when he comes home.

    I fear if the revisions go at the speed that they have dwindled to over the past three days (after school reopened), we will not have enough time to review the strategies - Fig Classification & Matrices etc.

    I have started one hour session in the morning before he leaves for school. That way at least I can get him to take a few tests etc.

    I do have a copy of your 'gospel' at his desk - #1 Skill for CoGAT (and feel that we may have to rely on pt. 2 a good bit - "Have you seen something like this before")....

    How would you suggest we schedule our test prep for the next month to make sure that he is ready.

    1. I had the same problem. First, we did 1 or 2 sessions after dinner during the week. If this won't work, feed him a really big snack (this will ruin dinner) after school. Give him at least 45 minutes between getting home and starting the training.

      Plan on 1 or 2 days during the week, and then Saturday and Sunday mornings. That would be 4 days, which I found is about the max.

      Go slow with the material, looking for mistakes in how he approaches the questions. Don't worry about wrong answers on the first try, or teaching him how to master figure matrices. The most important thing is reading carefully, taking time, looking at all of the answers, and not being in a hurry.

  5. Thank you so much !
    Now it is just keeping calm and focus.

  6. Just found your blog and it's riveting! Wish I had found it sooner. I am in Texas and planning to apply for some Magnet schools for my dyslexic son going into 6th grade this year. It's going to be a tough situation made tougher and I am looking for a specific game plan. Do you do private consultations?

  7. One more question.. Do you suggest we give up on reading and comprehension (which I have continued to do even after school has reopened) or put it on a hold till the GAT test. ITBS will happen 2 moths after GAT and we can get him to pick up the writing part after GAT. As ith most boys, writing is an effort at this stage. There are some good days and some not so good ones.

    1. The article that will be posted on this Thursday will answer your question.

  8. Thanks so much! Once we are past this round of testing, I will e-mail for private consultation. Had it not been for your blog, we would still have been reading Greek Mythology & American History(figuratively speaking) to prepare for GAT.

  9. I frantically need your help on this since testing starts 2 weeks from now.

    Under Figure Matrices: I have a clarification to seek on one of the problems.
    If arrow pointing right is to arrow pointing up
    Then arrow pointing down would be to what
    Options are :
    a. Arrow pointing down
    b. Arrow pointing right
    c. Arrow pointing up
    d. Arrow pointing left

    Smart Cookie (grade 2) has answer to this as option b. – method of rotation

    Mercer (grade 3 test 1) has answer to this as option d. – pattern completion ( North South East & West).

    I could have given Rotation as the best option. But then we are looking at Pattern completions as one moves along higher grades, with second grade testing straddled between the two.

    Which one would you suggest to go with. I checked the teacher’s practice paper that they go over with the students before the test. For second grade they call this Figure Matrices (not figure analogies) but still show arrows as in case of analogies.

    Thanks so much !!

    1. These are both correct. The first row has the arrow rotating 90 degrees counter clockwise, but the problem set as a whole could just be showing the different major orientations of an arrow. Only one of these answers should appear in the answer set, or it should be clear from the question type. I've seen both cases in figure analogies. The point I make is that you don't know until you look at the examples prior and the answer set. That makes for a really great question because it requires some thinking. It's all about thinking or learning on the spot, not learning ahead of time.

  10. You make a super point!! Thanks so much. Yes one crucial thinking to be done on the spot.