Sunday, June 7, 2015

COGAT Question #7

The Figure Matrix
So far, I've reviewed one of the 3 verbal question types and the first math of the 3 math question types.  I've got more to say about math, especially for older kids, but now I'm going to switch to the first of the convoluted shape question types.

Question #7 is the figure matrix.  I've always thought that this one was the most important.  I have no basis for this preference other than if you do a lot of math from a young age because your parent is insane, math should be easy, I gave up on the verbal section at one point, and I thought the figure matrices would be a good candidate for cheating.   If you haven't seen the punchline yet, instead of finding a way to cheat we found a way to be smarter.

Lesson 1
There are quite a few studies that try to teach normal or disadvantaged kids advanced cognitive skills.  In each of these studies, the kids cognitive performance goes way way up and then 2 years after the study, it's back to normal.  Your child's cognitive ability is a direct result of what your child is doing.

Today, I brought my 2 sons, 2 math books, and 2 vocab workshop books to Panera along with my computer.  On the way, we passed a dad with 2 little boys in soccer uniforms on the street.  These kids are going to be in the top 5% of great guys.  But you can't be in the top 5% academically if you spend all of your time acting like the bottom 50%.  I'm hoping my kids crack the top 65% of great guys, but that's a problem to be solved later.  Also, sports will be an issue to fix later as well.  Maybe Stanford's graduate school has a bowling team for the Neurophysics Chemical Engineering Applied Abstract Math Theory Law and Public Policy joint degree program.

In the mean time, think about how the top 5% or 1% spends their evening and weekend time.

Lesson 2
Here is an example figure matrix.

The only rule to this problem is whatever happens in the first row has to happen in the second row.  This has always been a big challenge with boys and a different type of challenge with girls.   Boys go through all 4 stages of loss:  Anger, Denial, Crying, and then more Denial.   The rule will prove to be counter intuitive and define normal convention for shape changes.  You don't see it in the example above, but what if nothing happens?  What if the shading changes but there is no answer with a shading change?

I've noticed smart little girls struggle in different ways, but I've only worked with a few of them so I can't make a sweeping stereotypical generalization based on gender.  It appears to me that girls are too polite.  In short, boys are way to bold and get things wrong and girls too timid and get things wrong.

Practice material helps a lot because your child can totally screw up the practice test and you can withhold food and water until they follow the rule above.

Related to this challenge is the general theme I've talked about repeatedly which is to give each problem plenty of time.  Read the question, each of the answers, think about it like a brain teaser.  The average kid coming from the US education system will try to rush it and expect to either know the answer or not.  A really bright kid who approaches the test like this will get a really bad score.

Lesson 3
The second problem is that this problem type is vocabulary intensive.  It looks like a nonverbal problem and is billed as a nonverbal problem but it is highly verbal.  This is primarily an advantage for little kids.  By 4th grade, I think the vocabulary advantage will wear off.

Look at this problem again.

What is the transformation?  With a weak vocabulary, the answer is "it got bigger", which is the 2nd choice. This is incorrect.   It got wider, which is the 3rd choice.  I can get 5th graders on this trick.

The Sylvan Kindergarten math book is very verbal and that's why I recommend it.  Ideally, you can do this book before Kindergarten and before you start 100% test prep.

Here is a list of words I put together to make sure my kid was Vocabulary Ready.  Later I found out that you can pack a kid's brain with a ton of vocabulary and knowing these concepts will make the kid smarter (using my usual definition of smart).  I took this list from 1st through 3rd grade vocab words focusing on words that I thought we could use.

Counting how many one two three four five six count seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen twenty number zero amount tally tens ones odd numeral quantity count backwards hundred count forward even
Arithmetic half halves quarter add addition afternoon calendar clock date day difference estimate hour hour hand measure minus minute minute hand month morning second second hand subtract subtraction sum tens time today value week year yesterday
Size long longer longest tall taller tallest short shorter shortest small smaller smallest medium big bigger biggest height high higher highest low lower lowest narrow narrower narrowest wide wider widest thin thinner thinnest deep deeper deepest least coin dime dollar money nickel penny quarter cent
Orientation between bottom first last middle top above below after before right left row column bottom left bottom middle bottom right middle left middle right top middle top right top left inside outside close closer closest far farther farthest beginning ahead of back behind beside end front/ in front of next to under number line order place sequence start within
Logic and Sets group same more most few fewer fewest different do not have group into equal parts less color more compare similar table contains collection contain cut in half equal except have hold input intersection join match neither object opposite or/and output pair put together set sort split apart venn diagrams add alike and arrange both
Geometry circle triangle square shapes rectangle oval side trapezoid parallelogram pentagon hexagon octagon quadrilateral pattern line semi-circle box cone cube cylinder halves pyramid sphere corner curves graph heptagon isosceles triangle point slide angle symmetry symmetric right triangle face number of points number of sides
Colors red green yellow blue black white orange purple pink grey brown light lighter lightest dark darker darkest silver? gold? shade Time/Space Before After Together Concurrently
Sequence and Class alternating color alternating size/Dimension alternating shape size number of sides combinations rotation. letters numbers two at a time two and one common unique many few cut in half Pictures - flowers rearrange fourth fifth second third

Lesson 4
It is very helpful to explain to a young child the concepts of doubling and tripling and quadrupling, and then once your child gets that, halving, cutting in thirds, etc.  Use lots of different language for this, use your hands, use paper.   This concept plays a minor role in the figure matrices but a helpful role elsewhere.  Using shapes to introduce doubling helps when I introduce it quantitatively in a forthcoming article.

Lesson 5
There are really great ways to trick a child with these matrices.  I'm not going to give anything away because a) I've never seen the actual test and b) that would be cheating.  If your child sees a problem+solution that is not expected, has a missing element, is usual or not customary, he can react by ignoring the inconsistency and getting it wrong, picking the answer that is usually correct but getting it wrong, or figuring out the trick and picking the logically correct answer.

For older kids, rotation versus flipping is a big issue.  I'm not sure younger kids will see rotation because little girls haven't developed that skill yet.  It probably doesn't appear on the test because the test questions are chosen to put girls and boys on par.  So we practiced questions that had the flip/rotation for the 1st grade test because it was hard.  My theory is that if you can do something harder than the test, you can do the test.

Some of these questions are easy but to get into the 95% to 99%, the child has to master the unexpected, unusual, missing, vague, and inconsistent.  It's not about the shapes.  It's not about the matrix.  It never was. That's the dark secret of the COGAT.

So what is it that is unexpected, unusual, or inconsistent?  How will your child react?  If you've read my last few articles and wonder why I am so big on brain teasers, now you know.

Lesson 6
All of the gifted sites that I have seen like Hoagies or Davis assume or state that giftedness is inherited and their recommendation for test preparation is a good night sleep.  The members of gifted parent forums generally ridicule parents who ask how to prepare for a test, especially forums in the Washington D.C. area. Some of the sites of test prep consulting services flatly state that they can't take a kid at the 50% and make him 95%.  That leaves online test prep sites which provide unknown and dubious value, but will charge you for it anyway.

We are only 1/3 the way through a review of the test, and now you know that there is a lot you can do besides a good night sleep.


  1. Thank you so much !

  2. I am always wondering which one is my priority and focus for my 5 and 6 year old (they have about a year or two until NNAT/COGAT) - being advanced in school math or building cognitive and thinking skills. Maybe the answer is both? Thoughts?

    1. Good question. The answer is both at this age. I'll be addressing this in more detail when I talk about the 2 new COGAT question types. However, leading up to the test in Feb of Kindergarten, we did barely any math, for at least 6 months before the test.