COGAT Question #4

The Quantitative Matrix
Question type #4 on the COGAT is the quantitative matrix.  We started practicing this question type early because I thought it would be easy.   It was a lot harder than anticipated.   At the time I my primary goal was to beat the test.   Much later I found out that I was developing advanced cognitive skills in my child.

Here is the beginning version of the quantitative matrix for grade 1.  Everything I'm going to talk about applies to the other grades that uses numbers instead of pictures.  I will describe in more detail the numerical versions of these questions at the bottom.

This is a well formed problem.  To begin with, it is 2 step.  First, solve the top row.   Second, do the same transformation on the bottom row.  The arithmetic is very simple, so it's just a matter of careful thinking.   Even though this question is simple, the test makers can pile on complications and surprises.   I can even stump adults with this question and not use a number greater than 2.

My 3 year old couldn't do the easiest of the problems.  We waited almost until the age of 4, and he still couldn't do it.   This was a major setback to my test prep schedule.

My solution was to cover the bottom row with my hand and concentrate just on the first row.  I ended up with problems that looked like this:

This was still too hard.  In desperation I came up with this formula:

My story was this:  "In this square, these cats are having a party.  Then what happens next?  Either more cats come or go.  What happened?"  Now he could see that a new gray cat showed up.   Much progress.  We did about a hundred of these and then moved on to this version before going back to the boring shapes on the COGAT.:

When I made these, I simply used all permutations for numbers 1 through about 6 which is all I could fit on the page.  There was special emphasis on anything that was also division and multiplication, since 2 - 4 is plus 2 and doubling as well.  I could usually stump him on one of these.   These questions can get harder, but you don't need me to tell you this.

How To Do This
If I had to do this all over again, I would just use blocks and a bag of skittles.   The main reason I ended up with all of these pictures was because I was researching intelligence theory and early childhood development and thinking that there was some mystery code I needed to crack.  The  only mystery is why any intelligent person would think intelligence is hereditary.

The Results
The first result was a really strong number sense.   I could see as he was figuring out the top row that he was assigning identity to each shape in the top row to see who just came or just left.   I found this odd.  Later, when he did his first few triple digit addition problems in his head at 6 1/2, I knew that he had developed a strong number sense, because this is one of the predictions.  The other thing I noticed was that he would solve problems with his own algorithms instead of memorized calculations.  Finally, he can figure out most math concepts for grades 1 through 6 with a little effort.  If you read this blog from 2 years ago, you'll see that we did a lot in math, but most of his quantitative skills came from our practice on this question.

The second achievement was a permanent boost in working memory capacity.   I think he permanently burned in 4 buckets into his brain for numbers, and 2 buckets for operations.   That's six additional working memory buckets, and probably 2 additional processors.  This makes for a huge advantage in early academic work.

Other Grades
Page 18 of the COGAT review presents a few of the more advanced versions of this question.

Question:  1-2, 3-4, 5-?  Answer Choices: 6  5  4  or 3
This one is primarily interesting because it can distinguish addition from multiplication.   1-> 2 could be plus one or doubling, and 3- > 4  is a third more and plus one, so the answer is definitely plus 1.  These problems are in a the form [x->y] = ax + b = y where either a or b is zero.

Question:  [2->5], [4->9], [3->?]  Answer Choices:  4  5  6  7  or 8
This one is kind of cool because it uses 2 equations and 2 unknowns.  [x->y] = ax + b = y, and just plug a bunch of a's and b's into a spreadsheet, and you've got your own test prep book for this question.  I have no idea how a 1st or 2nd grader could do problems like this, but if you start with easy ones where a or b is zero and work your way up, allowing for a 50% error rate, it's painful but doable, and lots of cognitive skills will bloom in the process.

I've also seen problems in COGAT test prep books of the form [12 - 3  =  4 + ?  ].   This form was used in a study of 4th graders that found only 5% of them even recognized that there was a 4 in the equation.  I've used worksheets of this type to teach number facts, since it involves a 2 step process and does more for working memory and number sense than simply memorizing 12 - 3 = 7.   Simply memorizing 12 - 3 = 7 is a math train wreck, by the way, and you should never allow it.  If you are forced to use math fact flash cards, ask your child to make 12 - 3 into an easier problem (6 + 6 -3 or 10 - 1) and ask for the answer secondly. Also, don't provide any cheats or formulas or mnemonics.   If your child doesn't figure these out for himself, he'll lose out on developing cognitive skills and will end up at a disadvantage to his Princeton bound peers.

Teaching Math with COGAT
Because of the 2 step nature of the COGAT questions, this is my preferred method of teaching arithmetic.   For a solid year somewhere in grades 1 to 4, we would drill COGAT questions until a deep numbers sense exists and we have expanded working memory.  I would normally teach math with a lot of thinking, problem solving, and conceptual vocabulary, but for a brief training period we mainly do calculation.  This training period coincides with the period in school when kids have to memorize their math facts.

There are 2 other quantitative formats on the COGAT.  Ideally, with the skills picked up doing these problems, your child will excel at the others, but as with most things, it's not that simple.

The strategy I just outline requires some time, patience, and diligence.   The cutoff for most GAT programs is about 95%.   My guess is that the kids scoring in the 95% are have this score solely because they have parents in the top 95% of time, patience, and diligence.

COGAT - Sentence Completion

In my prior article, I stated that I didn't have much to say on the verbal section.  I lied.  I've also said that there are no papers on test questions.   We'll, apparently I lied about that too.  When reviewing some of the literature, I found these papers.   I'll be borrowing heavily from Lohmans excellent paper from 1990.

This article discusses the sentence completion section.

The problem with sentence completion is that it can cover so many different skills and abilities as well as knowledge:
Yesterday, we ______ to the store (went/go/goes).  This is grammar.
The scientist filled the _______ with 3 chemicals for the experiment.
The boy scounts ________ the fire with kindling wood.
I am older than Bob, but Bob is ____ than I am.  (Shorter/taller/older.  I stole this one from Lohman 1990).

These questions could cover syntax, grammar, vocabulary words, any field from science to history, and logic and critical thinking.   The goal of the COGAT is to find kids with critical thinking skills and cognitive skills who could do really well in school, not kids who are already doing really well in school.  I think grammar and syntax on their own would not be tested, nor would and general knowledge questions that can't be inferred from the context of the question or the prior questions.

What makes the 4th example above so interesting is that it not only presents opposites, but it presents a 2 step problem that includes a type of analogy.   Old is to Tall, but this is the opposite so it is short.  This has all the hallmarks of a good test question.  The words won't be hard, the grammar shouldn't be hard, but the thinking in the question should be hard.

Even if we narrow down sentence completion from "could be anything" to "thinking questions", here are the cognitive skills I'm trying to sort through that are fair game for the sentence completion questions.  I need to put this into a hierarchy of teachable skills.  I wonder if that's going to be the same hierarchy found by researchers.
1.  Inductive reasoning
2.  use of working memory (has it's own list from the stuff below)
3.  encoding
4.  inference
5.  Executive skills - filter stimulus, create action plan or strategy, implement it, adjust it
6.  Remember, Transformation
7.  Abstraction/Abstract reasoning
8.  Concept formation
9.  Perception
10.  Learning (in this case, across the test questions staring with the example.)
11. Eduction of relations
12.  Reading Comprehension and Vocabulary
13.  Visualation of 3d shapes and spacial visualization
14.  Synonyms and opposites
15.  Auto critisim and learning
16.  Handing Vagueness (Questions that have no good answer or a corner solution.)

I can find or create a super hard exercise for my son, but the test probably includes a harder one.

The Building Thinking skills book for grades 2/3, which we did in K leading up to the 1st grade COGAT has plenty of elements that are fair game for the sentence completion testing, including analogies, synonyms/antonyms, classification etc, but in each case this book only presents 1/2 of the logic of a good sentence completion question like the example presented above.  This book is pretty light on the thinking for verbal skills, not even up to the 75%, even though the vocabulary becomes fairly advanced.  This is the opposite of what I would want for sentence completion practice.

Vocabulary Workshop all the way to the first book has mainly two step logic, which is good, but it is primarily inference and deduction and doesn't cover the full range of logic that can show up in the sentence completion question.  There are synonyms and opposites.  It is hard and requires guessing.  So I'm happy with this as test prep.

The old Steck-Vaughn test prep book for 1 and 2 has plenty of verbal thinking practice, but the new Spectrum workbook removes most of the thinking.

The only test prep that I see that has the range of thinking skills required and is really hard is Reading Comprehension, preferably 2 grades up to make it really hard.  In preparing for the test with my first son, when I knew zero about the test, half our time was spent on reading comprehension questions because they were really hard.  I had to do the reading because he couldn't read.  With my second son, we skipped ahead until I had to help with the reading and vocabulary, and again it was super hard.   We used Steck-Vaugn and SAT/Iowa Basic test prep books, as well as 5th and 6th grade released tests (which are about a 2nd grade level).

I could probably put together 100 two step logic sentence completion questions that incorporate all of the fun tricks of a test like corner solutions, vagueness and learning.  Nothing exists like this.  I thinking publishing vocab words on the fridge and making each into a brain teaser would get the job done, but the Vocab Workshop and Reading Comprehension exercises are better.

I think there are probably 100 words that make good test questions.   I did this for math and will show that list later.   I think it would be fun to do this for the verbal section.

Taking on the COGAT - Part 1

This is the first in my series of exploring the COGAT, my favorite of all tests.  I tried to start with an introduction, but I just ramble on, so instead we're going to jump into question 1 and I'll comeback to the introduction later.

There is a sample on the web from the publisher, but it will never come up with a google search because of all of the money to be made from the COGAT.  Here is a power point presentation from the test maker, David Lohman.  He also has 50 other academic papers on this site and they're all worth reading if you are insane.  On page 15 he introduces a same question for each section.

There are 3 sections on the COGAT: the verbal section, the math section, and the figure section.   I decided that we would read a lot to cover the first section, master math at the PhD level before the test, and then spend most of our prep time on the last section to give us a competitive advantage, hopefully making up for any weakness we have in the first section.

Most of the parents I've talked to have told me that their child magically got into the program (aka became braniacs and passed the test) by simply reading a lot at all times most of the day.  I agree with this approach, but test prep doesn't diminish your chances.

It's not a bad idea to do some test prep for the 1st section to give your child an opportunity to familiarize himself with the way the test works and get some wrong so that he learns to pay attention better and not think that he knows everything.  But the problem with vocabulary is that there is a lot of it and making your child memorize 1000 vocabulary words will leave permanent psychological scars that I'm still paying a therapist to fix.

In PreK, we struggled a bit on the verbal section of the first test (it was the OLSAT).  I won't tell you the word, but he could have figured it out if he crossed out some of the obviously incorrect answers.   After this, we started the first book of the Vocabulary Workshop series.  There's nothing more motivating for a child to learn to cross things out  than having to do vocabulary on a Saturday morning.  There was no better test prep for a verbal section than this book if you child has learned to read.  Because of this book, we did much better on the COGAT the following year which was the test he needed to pass.

I think my approach to reading was pretty good, but some of the kids go a year or 2 beyond this before 1st grade. I'll cover a special example after I describe what I did.

Below is what you do from Age 1.  For those of you reading this a few months before the test, the only thing I would do is either the verbal section from the Building Thinking skills book or the first Vocabulary Workshop book.  My first son passed the test with almost no reading skills (my bad) and only 2 months to prepare after I found out about this test.  Our strategy was to concentrate on the other parts of the test and we did very little for the verbal section.

Age 1-2
Talk all the time to your child.  Narrate everything that you are doing, e.g., "Mommy is taking her keys out of her pocket and opening the door.  I am unlocking the door with my key.  I turn my key to the right, and the door unlocks.  Now I am removing my key and putting it back in my pocket..."

Any parent who pulls this off for a year creates a super genius.   I couldn't do it.  My conversations were more along the lines of "Get your finger out of your brothers ear.  Stop touching his head.   Get away from your brother..."

Do not use baby talk ever.  Ever.

Age 3 
Read a lot to your child all day long.  Get really good books.  Find a list of book awards and illustrator awards.   Find a list of every book that won the award and check all of them out of the library.  Read them to your child, and with the good ones, read them over and over and  over.

Age 3 1/2
Start with the letter blocks and teach the letter sounds but not the name of the letter.  Three months later, start with C-A-T and see if he can read it.  This will take 6-8 more weeks, and when he can, move on to D-O-G.

Age 4
The most important part of reading is Read-To, so we kept up the Award Books program.   Then I made a list of each book in every Beginning Reader Series and checked 12 of these out of the library per week.  Of these, maybe 1 or 2 would actually be at the appropriate level, and I'd make a note to get the others again when we got there.   The leveling is horrible.   I created my own leveling system by marking ordering the list on the books I returned without reading, and then I checked them out again later.

I read most of the book, and he read a word, then a sentence, and increased from there.

At this time I got an older version of Hooked on Phonics, and we started on page 1, again a little at a time. This series was worth it.  If the price is too high, you can just google phonemes and make your own list for each sound, starting with 3 letter words for the simplest of all sounds, and then going to 4 and 5 letter words, then bigger ones.  It takes about 5 minutes per phoneme.   There are only about 30 of these.

Here is the "at" list.  Cat, bat, GAT, hat, mat, Nat, pat sat, scat, etc.   That's it what the series used to be. HOP included about a dozen little books specially made for each section, but with all the beginning readers from the library, we didn't make a big deal out of the books.  Just a list of words with similar sounds that we read each week. We also made letter cards (c,a,t,m,p,s from the list above, one letter per card) and he arranged the letters into words as I read off the list.

Age 5
Once he got through all of the Beginning reader series and started to move to easy chapter books, I got the first Vocabulary Workshop book.  He loved it.

By this time, I had been studying the tests for about 2 years.   While I wasn't great in the verbosity department, I do appreciate the nuances of words, so I was happy to explore opposites, synonyms, and similar yet different words.  We covered a lot of new vocabulary, and with each word I would be happy to explore it and its neighbors just for the fun of it.  Take the words Hold, Grasp, Clasp, and Clutch.   Grasp introduced to my son by Hooked on Phonics, and we ended up talking about all of them.   Kids love to learn and can pick up a lot quickly, but I wanted him to pick up on the concept of shades of meaning and appropriate context for each word choice.  If he asked what a word meant, it was a long discussion.  That was my way of making up for not talking nonstop during his first 2 years of life.

The Building Thinking skills books have very easy sections on figures (more on what we did later) so we moved quickly.  By the time we got into the 4-6 Grade book, the figure questions were hard, but the verbal sections were downright impossible.  He didn't even know much of the vocabulary in the question let alone the official vocabulary words he was supposed to consider.   We did a little bid, and spent a lot of time exploring word meaning and guessing.  I think this helped.

We also tried 3rd and 4th grade reading comprehension questions.  I don't know if this helped, or even if this required the same cognitive skills used by the COGAT.  But it was really great for the executive skills needed for the test, like high degree of concentration.

Was all of this test prep worth it?  I'm not sure how it impacted his score, but the skills he picked up along the way make him a great reader, not just processing verbal coding and syntax, but thinking deeper about the content and retaining most of what he reads.  There's very little he doesn't understand when he reads, and vocabulary is one of his strong points.   I know many dads who spend hours each week teaching their six year olds how to master a sport.  It is much more likely that my son will benefit from the time we spent reading and mastering vocabulary then he would benefit from the soccer travelling team.

Special Cases
We have a friend who has kids are at least 3 times as smart as us.  They have a family room full of bookshelves.  The dad went to the Brown Elephant and other resale shops and bought boxes of books for just a few bucks.   He won the Competitive Parent Magazine's Competitive Parent of the Year award in 2012.

Last year's Competitive Parent of the Year award winner is this couple from Poland who speak with broken English but produced a 6 year old who reads at the 3rd grade level in 2 languages.   "She taught herself to read" they claimed at the award ceremony.  Liars.   They won't tell me what they did other than they make her take a Polish immersion course every Saturday for much of the day.   I told my son that this classmate of his is his Nemesis.  "What's a Nemesis?" he asked.   Rival, arch enemy, competitor, opponent, adversary, challenger, foe...

What's Next
I didn't bother to dissect and reverse engineer the 3 verbal sections of the COGAT.   In my next article in this series, I'm going to take on at least one of the math sections and things are going to get a lot more interesting.

Another Review of Testing Mom

I'm trying to address 2 important issues about testing mom.   #1 Why do I get so many negative comments about this website and #2 should you spend the time and money.

I'll take the issue about complaints because it is easier.  Testing Mom uses a subscription model with automatic recharge (according to the complainees).  There is also a price differential between testing season and the off season.  

When I used it, I ;prepaid a whole year in the offseason.   That solved both of the problems above.   Testingmom advertises 20,000 questions.  A child isn't going to get through 20,000 questions in a month.

The second issue is whether or not to buy it.  Let's walk through a decision tree.

Step 1 - Will You Use It
First, will you use it?  Can you and your 4 or 5 year old sit through 20 to 30 minutes of a complicated work sheet?  Does he do most of it on his own?  Will he do this 4 or 5 times a week?   Or are you a wreck during this process?

One complaint I hear frequently is "I bought testingmom, but we barely used it."  Why don't you try something like ixl.com - do harder material and do it 20 minutes a day.  You can use the ixl.com site for free up to 10 or so questions per day.  If this works, then you've passed Step 1. By the way, doing super hard material on ixl.com is not incompatible with test prep.  (ixl.com provides a few questions each day for free.) If you like ixl.com, you can come back to it after the test and buy a subscription.

Step 2 - Will it Work
It didn't occur to me that testingmom might be incompatible with my test prep goals until I spent six months practicing with a 2 foot high stack of testingmom test questions.  By that point, we were probably in the 90-95 percentile range.  This might be good enough for some people, but we needed to get into the 99.8% range or higher.

My neighbor recently got their child into the same school as my son without begging me for advice weekly. I'm personally offended.  I talked to them 2 years ago, when we were right in the middle of test prep hell and that's probably all I talked about, so I gave them the 60 minute version when I noted that there son was precocious.   They home schooled him for Kindergarten, advanced on reading by about 2 or 3 years, advanced in math at least a year.  That was it.

I hear from a lot of parents who just read a lot to their child - and encouraged their child to learn to read at a young age.  They did nothing else.  That's exactly what we did (with lots of test prep as an insurance policy).

What I've discovered the hard way is that 1 good question that takes 20 minutes of really thought and exploration is good test prep, and 100 questions that your child can zip through and get mostly correct is really bad test prep.

I think of testingmom as the first semester of test prep.   A few months before the test, we switched to ridiculously hard oddball brain teasers that I found in a variety of places.   I expected about 50% correct.  If you are subscribing to testingmom a month before the test, cover the intro material and skip right to the really hard questions related to the test you are going to take.  You will find these on the site, just not 20,000 of them.

Again, this has turned out to be a weasley recommendation that is not a definitive yes or no.