Chapter 2 - How To Teach Skills

Copyright 2013, 2016 - me

How To Teach The Skills

A cognitive skills test will determine how well your child is going to preform academically, and assign a rank between 0 if they are sick and miss the test to 160 if they should just skip 2 grades. Standardized tests used to be really long and were fairly poor predictors of student capability until they worked cognitive skills into their questions.  Now standardized tests are basically cognitive skills tests with a test format that looks like a school work.

School is either all cognitive skills, which is called learning, or no cognitive skills, which is called a waste of time, depending on the teacher, the child, and the curriculum.

If you're doing At Home schooling, maybe some math, reading or science, and you teach cognitive skills instead of the material - a totally doable proposition - then you will put the child on autopilot and domain learning will take care of itself.  Think of cognitive skills as learning how to learn.

There is this great book written by a 7th grade author named Karen Ge called "Dissecting the New CogAT" which describes all of the different tricks of the COGAT.  I started my research with a stack of books like this.  If you're wondering which of us spells COGAT correctly, read the about the author page and it should be obvious.  You probably want your daughter to turn out like Ge.  85% of Ge will get you to Stanford.

Ge is all Level 4 skills, completely useless for my purposes. I've tried her approach and it's a total failure.  You'll see why shortly.  Ge is like the captain of the Death Star.   Marching around in white armor is totally unsuitable for my rebel crew.  "Dissecting the New CogAT" is not plans to the Death Star, which by the way we're going to blow up.

A Summary of the Teaching the Skills
From the last chapter, you learned that there are 2 core skills: Reading the Question and Checking The Answer.   Ge's book features these skills.   There are also facilitators, however, and reading the question and checking the answer are really painful without facilitators.

What I'm about to present applies to children of all ages.  We could be talking about a 3 year old, a 6th grader, or a young adult contemplating the GRE.   I have a list of people in mind in this age range who I've sat with day after day month after month watching this recipe go from batter to the glory of a wedding cake.

Step 1 - Vocabulary
In many but not all cases, the best place to start is vocabulary.   The process of learning new vocabulary warms up working memory to about 1.5 or 1.8 on a scale of 1 memory bucket to 3 memory buckets depending on the cognitive load of the word.   We need 3 on the end of 99% scale, but the brain needs time to work out to get in shape.  I think the COGAT is at about 2, maybe 2.5, so getting to 3 is basically going to amount to cheating.

Vocabulary is also a facilitator.  If you come across the word 'dim' and a young child doesn't know it, the question at hand is going to take a lot more time while you backtrack to grapple with dim.  If your child already knows 'dim', then more of the time is spent with learning advanced skills.

One third of Test Prep Phonics is vocabulary.  The actual title is Pre-K Phonics Conceptual Vocabulary and Thinking.  One third of Shape Size Color Count (this is the plans to the Death Star) is vocabulary.  Early cognitive skills training, phonics, beginning math, and beginning reading are perfect times for vocabulary.   Also, science is accelerated by starting with a boot camp of vocabulary training.

In these cases, I'm not thinking about an institutional step-by-step approach with a bunch of 90% plus storm troopers marching along, I'm thinking about a bunch of less than 90% - maybe way less - rebels stealing a space ship and blowing something up on their way out.  I'm thinking of a motley crew going to marine boot camp.  The recommendations below are how to teach skills to kids below 90%. I suppose if there was something special about any of the kids I work with this advice would be much different.

When I was in the pilot stage of this approach, I would take an expanded list of vocabulary words in math, for example, grades K through 2 (minus arithmetic) and work through memorization of the words.  This works really well, and the accelerated math training that follows is successful.  But this is level 1 working memory.  Then I found out that you can do conceptual vocabulary at the same time.  Conceptual vocabulary is the words themselves in a bit of context and use, and you're at 1.5 buckets of working memory, understanding is more complete, and some rudimentary cognitive skills are being used.  The vocabulary phase is a bit slower but eliminates the inevitable back tracking when working questions in the next step of training.

Step 2 - Everything Else In One Big Gulp
There is nothing between the first level and the second.  A step-by-step approach is called Telling and not Learning. First, I'll explain why, and then I'm going to explain how to get from the 50% to 99%.

Picture a child of 11 or 12 who needs a math tutor.  This child is facing pre-algebra and is just not getting it.  The parent hires a tutor and grades improve.  Once a week the tutor comes by and explains the math concepts in terms that the child understands.  The math concepts appear on the math test, the child knows them, problem solved. The problem here is that the child doesn't get it because he doesn't have the learning skills to get it, and in helping the child, the tutor is ensuring that the child never learns to learn.

This child doesn't need a tutor, the child needs a coach.  Picture a coach chomping a cigar on the sideline of a football game.  Does the coach play?  Of course not.  He's totally out of shape.  He just yells and devises plays and makes commentary on how bad that last play was executed.  Plus he's constantly telling the players to stay focused and try harder.   The players become skilled players because they are playing.  Have you ever seen a top coach at top levels pick up the ball and shoot a basket?  Of course not.

Well, actually there are coaches that demonstrate shooting.  They're called shot coaches, I think.   And I've been known to do COGAT problems for a 4 year old who's totally stuck.  I only do this if I have plenty of problems left for the child to do because it wastes a problem.  I do it to show that I'm willing to share the work and not mind if I get totally stuck and need help and get it wrong a few times, which by the way, is what happens when I do a problem.

I didn't convince myself that there is no step-by-step approach, let alone the reader, so I'll just present my step-by-step approach. Don't be fooled the steps.  Your child is going to get a problem that is going to take a dozen mental operations at once.  The big gulp I'm talking about is the numerous academic and cognitive skills which are none of your business because they make up all of the little pieces of learning to learn.   Just stay focused on the question and the solution or you'll undermine learning.

Read The Question
At least half of all cognitive skills reside in the phase of understanding the question.   In some math problems on the SAT, once the question is fully understood, the answer is obvious.  In other cases on the SAT, and the COGAT, the answer set is really part of the question.  For example, something happens to a square.  Did it flip?  Rotate?  Nothing?  What do you do with the pentagon?  You don't know until you examine the answer set.

Something might happen when they see that their expected answer is not among the choices. Sometimes it doesn't happen and they just remain baffled and parent and child are not comfortable enough with baffled to plod on.  Sometimes on different problems, like classification problems, there is a lot going on and they don't see it.   In two part math problems, their brain might not have the 2 buckets needed to hold the problem while they solve it.  Maybe they don't understand the question and lack the skill to investigate the question more thoroughly before they start guessing.

Ideally, a bright child will not have any of these challenges but simply have to work through a learning experience that requires induction or intuition.   Their learning skills (a host of sub skills) are going to be at some level which will make this process easy or hard.

If you reduce the problem to a core operation like adding and subtracting or evaluating a shape transformation, you are focusing on facilitators. This is a great idea under certain circumstances, like a 3rd grader who stinks at arithmetic, and with very young children as a precursor practice tests, but a facilitator is not a cognitive skill and it doesn't address all of the elements they need.  Young children are the exception because everything is new and hard to young children so everything requires cognitive skills and learning skills, even learning to add and subtract or sounding out words.

Many parents complain that their child who is way ahead in school math just bombed the COGAT. The reason is simple.  The child mastered the facilitators, which is about all school math curriculum is good for, but hasn't learned learning skills.

There is well know statistical effect in testing wherein it is much more likely that a child scoring at the margins is going to move inward.  A child at 95% is statistically more likely to go to 80%, and a child at 25% is statistically more likely to go to 40%.  Cognitive researchers provide a mathematical explanation that is totally incorrect because they have not met any actual children in an actual learning environment.   A child is likely to go from 95% to 80% because at 95% he doesn't need to use any real skills during the next year because the work is so easy.  A child at 25% is using all of the skills just to figure out what the heck 3 + 4 is, and these new found skill will get him to 40%.

I formally call the drop above 'The 4th Grade Train Wreck'.  I was was so frustrated with getting beaten up by test scores between 2nd and 4th grade resulting from a school curriculum that is calculation heavy and light on real skills that I created Test Prep Math.  Notice that I didn't say 'math' test scores.  If it's not obvious in Level 2, by the middle of Level 3 parents should have a clue that I'm taking no prisoners on the reading comprehension questions either.  As I watch sales on Amazon increase for these books, I can't help but think that these parents have no idea what their in for.  When I published these books, I knew I had no time to go into all of the detail on education theories and why these books are solidly designed to get the kid to 99%, so I just put pictures from Special Forces Seal Team 6 Black Ops Boot Camp on the cover.  Once I finish the part on older children in the second part of this chapter,  I will change the cover to something more pleasant and I'll just refer parents to this page.

Getting Past The Question
If your child actually understands the question and is doing well with the material, get harder material.  Grade + 2 appears to work well for this purpose.   Next year's COGAT practice tests don't work well.  I have grade level, grade +1, grade +2, grade +3 on my shelf and they're all about the same.   If your child is in the 2nd grade, you're using about the same material we used in K with a slightly less picture friendly format.

If you are lucky enough to be stuck on a cognitive skills practice test, a Building Thinking Skills problem, or a reading comprehension problem, or you're using one of my books, the advice below will explain how to get beyond stuck.  I really like the NNAT 3rd and 4th grade book for the purposes of this exercise for older kids because there is more going on in the diagram.  For younger children, the book might be too much and you can just google Raven matrices because you're not going to need as many examples to find a hard one.

Let's start with a four year old.  You've got a diagram; they're staring at it.  They totally don't get it and don't have a clue what to do.  Nothing is happening.  Here are the steps:
  • Start by asking the child to describe the picture using words.  Just the question. 
  • This usually doesn't work so go through the next 2 or 3 exercises and do the same thing.
What's really great about this exercise is that it makes the entire problem just the question.  That's how capable students should think.  Unfortunately, what with math facts or problems like 'Which one is the circle', the problem and the answer are one in the same and it trains the kids to go right for the answer quickly or they feel like dummies, which they now are because smart kids have been trained to work the question first.

Suppose this doesn't work because the child needs to improve their skills or the problem is too hard. Next step:
  • Get out a piece of paper and a pencil.  Tell you're child you are blind.   You are going to draw the question, but they have to tell you what to draw using words.  Of course, you've already seen the diagram, so when they tell you to draw a rectangle, yours looks nothing like the picture so the child has to start over and provide a more careful explanation.
There are quite a few cognitive sub-skills being exercised during this exercise, and it captures the core of my skill list at a lower level of the skill pyramid, the level you should focus on, the level that supports learning.  You're taking your time to do focus on the question.  You're being silly in the face of bafflement and frustration.  In short, you're creating an environment for your kid to start learning. In this case, the child is not only learning how to verbally describe a diagram, but their learning how to see it.  Common Core now requires verbal explanations of math concepts, so, as a bonus, you are preparing for Common Core.

How long should you spend on this exercise?  As long as it takes.   There's no time limit on how long your child gets to learn.  In fact, it's a required time minimum as determined by your child's own brain.  Keep going:
  • Once you graduate from the question diagram, you have to do the same thing, but now with both the question diagram followed by a description of the answer set.
  • Then do the question, the answer set  and what could possibly be happening to get from question to answer.
When you get beyond description to what is happening, you might have to backtrack with younger children.  Since they have shorter attention spans, like 15 minutes of thinking, and it might take 25 minutes to realize that a square is flipping even though it looks like nothing is happening, you have to backtrack.

When I use the term backtrack, I mean set the problem aside and work on facilitators.  In this case get some shapes, list the 6 ways a shape can change, and let them figure it out for themselves.  Beyond K, this includes rotate.  I don't think rotate is included on cognitive skills test for younger kids, but it doesn't hurt.  Obviously, getting wider requires a big stack of shapes or drawing.  I'd like to point out that in the previous chapter I mentioned that cognitive skills tests are 75% vocabulary even though they are 66% non-verbal.  When you talk through this exercise, you'll find out why.

When you are working though the question, the answer set, and what transformations are possible, you're using working memory.  The only way to build it is exercise.  When it's not there, you have to start over and over again and it's really painful.  Reading every day helps a lot.

Check Your Answer
At this age, I rarely catch even the brightest students checking their answer.  Usually, they triumphantly announce whatever answer they settled on and look to me for confirmation.

I hate this.

What am we doing here, training dummies?  Yes, that's exactly what we're doing. That's how I started out as a parent, that's what you're doing as a parent because that's what you're programmed to do.  In order to get to academic coach of a top performer, you need to go back to the coach I mentioned above.  The thing that I like about the best coaches is that they had their faces surgically altered to prevent facial expressions.

The two worst mistakes that a parent can ever make is to be happy with a correct answer and be not happy with an incorrect answer, which is anything you do if you showed happiness with a correct answer.  If you do this, all of your work to get your kid to patiently focus on the question and think through it carefully just went out the window.  Maybe not all of it, but it's still bad enough that you're setting your kid up failure.  On the test, there are problems designed for incorrect answers.  You will recognize these because your selected answer does not even appear on the list.  As soon as the child goes through the answer set he will know that he just got it wrong and has to do it over.

[Unfortunately, I'm still picturing the coach while explaining this so bear with me until I have time to rewrite it so it doesn't sound like I'm yelling at you.]

Even more importantly, tests and advanced academic work are tricky.  Incorrect answers are inevitable. We need a child who checks every answer.  Or a genius.  But a genius didn't get there by not checking answers or she wouldn't have learned anything.

Here's how it works:
  • Rip the solutions out of the back of the book in front of your stunned child and throw them away.  (Later, fish them out of the trash and hide them because you'll need them.)
  • Have your child do a question.
  • Pick another answer and declare that you think it is this one.  Make sure it is the wrong answer. Have your child explain their reasoning.
  • Announce that you are wrong, on further review, and ask the child to start over.
  • When the child gets the answer correctly, look at them quizzically because you're the dumbest parent in the world and ask them to prove it.
The problem with this approach for an active academic coach is that I don't always do this with little kids.  I remember to do this once the kid is looking at me for thumbs up or thumbs down or guessing.  I ask them to prove right answers a lot, but then after a while they're on to me, then I go back to "explain what you did" and that buys me a few questions, but I'm racing the clock.  A 4 year old has 15 minutes of solid thinking per session, so if they get the right answer and we move quickly to the next problem we might get through 5 problems a day.

Even worse, when the child actually concentrates on a really hard problem and gets it right by guessing, I'm almost cheering, and it makes everyone feel totally psyched.

Let me put this in context for you to resolve the apparent contradiction.  When a child starts out, we can't even get through the first question on the first day.  This is followed by 6 weeks where we battle working memory to get through every question.  By this point, we're getting things mostly wrong. By the time I'm ready to wrap things up as a job well done, the child is consistently missing half of the problems all the way up to and including the last section of the last practice test.  At this point, I'm usually confident that we succeed.  Even more importantly, I know the heck that the child just went through because as a coach (not to mention parent) I broke my arm ever time he stubbed his finger.  If you're doing a good job of not really caring about the answer, the kid knows why you're so happy.

For the longest time, I couldn't understand why so many kids who end up in GAT programs tend to get no more than 50% correct on practice tests.   Our personal experience exactly 3 times was that 49% magically showed up in between practice tests and the real thing.  A few years later, I found that the difference between practice math work and standardized tests is a whopping 99%.  I'll give you a minute to digest what I just said before I reveal the answer.

Here's the answer.  If cognitive skills training is done right, the optimal setting to train cognitive skills is in the face of material where the student will get about half right.  Otherwise, the kid isn't learning any skills.  The optimal setting to use these skills is when the parent is not present.

There's another reason.  On the first grade test, the poster child of test prep came back and starting writing out test questions.  This tests really is about measuring learning skills.   It's interesting to me to compare practice tests and what I saw from these questions.   A practice test is useful to understand the test format and the rules for the tests, especially with an overly creative child that makes up his own incorrect rules.  A practice test is hit and miss on presenting challenging questions, depending on the publisher, and you can use it for the basic learning skills and coaching skills that I outline above.

It appears to me that the test is so challenging that the only 2 good ways of getting a score past the cutoff is either to be really lucky or to make sure your child has really solid cognitive skills.  The only way to cheat the test is to make your child legitimately smart as quickly as possible.  This chapter is devoted to cheating the test the right way, which has the added benefit of annoying snooty parents on gifted forums by becoming gifted even though you don't deserve it.  Go rebels!

A Note On Facilitators
Before I move on to older kids I've got one more trick up my sleeve.  I call it the plans to the Death Star.

When I was working through my phonics course the very first time with my 3.85 year old, I made the mistake of handing him a practice COGAT test.  The test we were preparing for was the OLSAT, but the OLSAT practice tests are totally lame and useless.  Plus, the older brother's program starts in first grade, and the test is the COGAT, to be taken the following year.  We spent 3 days on a single matrix problem and he had absolutely no idea how any of it worked.  The steps above didn't work.

I was already a master of backtracking.  I learned the hard way by introducing the older brother to math starting in February of Kindergarten, the day after he came out of his test, because I was convinced that it was a disaster.  When you see the article entitled "The 8 Week COGAT", you'll find out what I did right.  I handed him a second grade math book, and since his previous math work consisted of nothing, we did a lot of backtracking.  Both of these experiences were the best thing I did.  If you want to know how to do 2nd grade math in Kindergarten, reread the material above.

So here I was turning the phonics process into a course on test facilitators and cognitive skills and I needed to backtrack on test prep for the non-verbal.  Why not create a course full of facilitators for the non-verbal part of the test?   Is it possible to create a phonics course for math and what would this look like?   Actually, I wasn't thinking this.  It just happened out of desperation and fear of putting two little kids on different buses.  I worked for a large bank that just went through both a merger and the loan crisis at the same time, and I found myself in an empty building with 7 industrial strength color copiers, all the software I could want or develop, and 8 hours a day to kill.

Now you're thinking, "Give me these facilitators so my child won't get below 99% again on anything." The facilitators are the silver bullet, that's true, but this whole chapter is on the gun that the bullet has to go in before you can kill the werewolf.  (For those of you wondering about this analogy, old monster movies involving werewolves were mainly about the fact that the only way to kill one was with a silver bullet and a climax involving dropping the gun. My primary job as an academic coach is keeping the parent from dropping the gun.  Ge's book has cute little cat and and dog characters to explain test prep, and I'm telling kids not to get eaten by a werewolf.)

I'm about a few weeks away from releasing Shape Size Color Count.   It's way beyond a silver bullet. It's more of a combination of training with Yoda it is, or the plans to the Death Star.  No, this doesn't cover it.  The plans to the Death Start are covered in the next section for older kids.  This is more like the keys to the Death Star, like moving in and blowing up planets.  But parents of 3 and 4 year olds are so overly nervous about getting into gifted and talented programs, especially when their child is not showing any signs of giftedness, that I'm giving them the plans to the Death Star.  But it's really the keys. Just be forewarned that the material is not easy.  It's for a 3 year old, but it's of the one to 5 problem a day variety.

After 1st Grade
While the basic skills are the same as above, and the basic methods to teach these skills are the same, the rules change after 1st grade.  You might want to read this chapter from the beginning to understand the basics. While you're reading it, you might be depressed to learn of all of the things you could have done between ages 3 and 7 but didn't. Rest assured, this chapter is about catching up in a big way.  Thanks to the 4th Grade Train Wreck, you'll be on equal footing with most children anyway.

What's great about 2nd to 4th grade is that in addition to work with test prep material you can find cognitive skills within academic material if you look hard enough.  You will have to look hard, because you can't get to 99% by doing what the other 98% of people are doing.  The 1% is the profoundly gifted, and they don't read how to guides like this.   This section is going to focus on the other avenues.

The two biggest problems with curriculum in the United States are reading and math.  If it weren't for these two subject areas, the US would only be behind in Science, Art, Music, and Gym.  Since the US is the only country in the world that doesn't lie to itself about its own History, we will likely maintain our lead in this subject.  2nd to 4th grade is all about kids spending 8 hours a day learning how not to think in school, and precious time at home undoing the damage.  The good news if you need to get to 99% on a standardized test or a selective enrollment test is that there is much less competition.

Some of you may have a child that is currently getting a C in math and you're wondering what the heck I'm talking about when I mention 99%.  This is exactly what I'm talking about.  What's different is that we were already in a gifted program, but the big fat C and the low test scores kept me up at night.   If you read chapter one, you might already have guessed that we went on a crash course in cognitive skills instead of worrying about grades or homework.

During the learn-to-read process, many cognitive skills are learned and exercised.  After that, reading is about building vocabulary.  You can extend the benefits of reading simply by finding better, more challenging books.  I have prior articles with my frustrations and efforts to get past Diary of a Whimpy kid if you need help with boys.

In order to use reading to build cognitive skills, simply ask two questions: "Why?" and "What will happen next?"  Do not expect answers.  These questions are not meant to be answered.  The purpose is to start thinking, to use those cognitive skills, and as soon as you answer the question, the thinking stops.  If you want to take this exercise to the next step, ask about setting and other characteristics of the material that might point to answers.  Want a free test prep?  Write a note for yourself to pick up your child's book every day and ask these 2 questions about whatever is on the page with the book mark.  This isn't a fast way to get there, but it helps over time.

I didn't realize that reading was one big question until I read The Mixed Up Files of Mrs. Basil E. Frankweiler and started looking at homework assignments on this book.  It looked like it was a mystery of some sorts.  It appeared to me that every book is a mystery, and in being a mystery, it is one big cognitive skills practice question.  I thought I'd do some research so I searched "every book is a mystery".  I was furious to find that many books have been written on this topic, it is well known in education circles, and here we were at the top GAT program in the country, with a veteran teacher no less, and I'm having to figure this out on behalf of my child.   I'm generally not one of those uptight unreasonable demanding pushy parents, so I just threw the homework assignment away and we started working on next year's curriculum.  When you're the worlds top academic coach, you can do things like this.

The 4th Grade Train Wreck
The biggest challenge you face is that the goal of 2nd to 4th grade school work is to teach concepts to children.  In the Classical education, this was the time to exercise memory, but at least the Classical education overload memory and then packed more stuff in. Because of No Child Left Behind, a teacher can't risk her bonus or her job on low test scores that require knowing stuff, so instead of risking letting the kids learn it, she just tells them.  Very little learning is going on.

Math is the worst.  Math should be the primo subject for imparting cognitive skills.  Instead, it's memorizing math facts and doing one-step routine calculation problems.  Decimals?  We spent a day on it.  Long division?  The opposite of learning.   Just skipping to 6th grade math is a big leap in skills, and more of the same at grade level isn't going to help.  I tried "x" and it didn't go over well.

The Solution To The Question
The great thing about working with older kids is that you can just tell them what is going on, set up the challenge, and then let them struggle.  You get more than 15 minutes of attention, and they usually don't roll out of the chair onto the floor.  Plus, they don't drop their pencils 3 times per problem.  Middle school is even more fun because I get to be that football coach that I mentioned above, minus the cigar and yelling.

"So here's a question (or diagram).  It's hard.  It's tricky.  It's meant to fool you. If you get this problem right on the first try, I just wasted your time and mine with an easy problem that taught you absolutely nothing."

Above, I described working with a figure matrix.  Now I'm going to describe a conversation I've had 100 times in the context of a word problem or a question at the end of a reading comprehension question.

The child might start by asking a question.  If it's a concept like 'square root', we'll look it up together or I'll walk them through square roots starting with 2 x 2. (Yes, we start with 2 x 2.  That's not a typo.) Once I got a question about '39 + 42' from a kid who had never seen double digit addition before, and we started with '10 + 10'.  20 examples later and he got it.   With cognitive skills questions, there is nothing in the problem that can't be derived by the student, and doing this for the student undermines the learning experience of the question.  In these cases, I'll say "You tell me. You're the one doing the work" and it will take a long time.

When a child asks "I don't understand this", I reply "Then explain it to me."

I should win a Golden Apple award for this method, but I'm not a teacher.   The genius here is that I don't need them to know something.  If I did, I would just tell them.  But I don't.  I need them to start thinking on their own, carefully, with patience, and not worry about not understanding the question immediately.  Sometime it takes a month to get there.  In this month there was zero spoon feeding going on.  It's cold turkey.

Back to the question.   I can see a word placed in the question that they skipped over, and this word is central to the meaning of the problem.   Here's how the conversation goes.  It's me talking, a bit of reading, and them bafflement or a complaint that they don't understand.
  1. Read the question again.
  2. Read the question again.
  3. Read the question again.
  4. Read the question one phrase at a time and explain what it means.
  5. Read the question one word at a time and explain what it means.
In response to the last question, I usually get a frustrated kid with the "duh" look on their face explaining the meaning of 'the' or 'of' to me like I'm a dummy as they go through the question one word at a time.  I would love to challenge them to actually provide a useable definition of 'of', but this is about cognitive skills.  I sit there and wait.  In the battle of waiting, I always win.

When we get to that special word, the lightbulb is going to go off.  It may not be today, but once they've won the battle on their own once, many pieces fall into place.

Here is question #48 from Test Prep Math Level 2 for a concrete example:

Jeffrey Sincomhoff delivers pizza.  One night, he had to deliver a pizza, but he forgot which house on the street ordered the pizza.  He knew that the house that was exactly in the middle of the block.  On one side of the street, there were 8 white houses and 4 yellow houses.   On the other side of the street, there were 6 brick houses, 7 wooden houses, and 2 houses made out of loaves of whole wheat bread.   All of the houses and the yards were exactly the same size.  How did he know which house ordered the pizza?

Bonus Question:  Is it possible that the house is made out of whole wheat bread?

The questions before this maintain a pattern of 3 equations, two equations in the problem plus a calculation with the two results.  The child has learned to extract these equations and solve them mentally, which is about the limit of working memory.  The clue is the word 'exactly'.  I'm not sure this problem will work as well stand alone but if you have a 2nd grader or 3rd grader, you can try it.

For fear that the child might actually get the right answer, the bonus question is 'No' or 'Yes' depending on whether the child answers 'Yes' or 'No'.  Obviously people who live in a whole wheat house don't eat junk food.  Unless they're sick of healthy food.  Or building materials have nothing to do with eating preferences so it has no answer in case they answer 'Yes an No'.

In the heat of battle, kids are concentrating on figuring out complicated problems and are happy with a solution.  So I'll ask 'Are you OK with that problem?'  I tend to be a bit more subtle than a house made out of whole wheat bread.

Suppose you're using a conventional math workbook  Everything I just said applies, but it is going to involve more math than cognitive skills.  I have some recommendations on the math page.  If you simply need to improve grades, this approach with any material is the way to go.

While Level 3 is much more challenging, you might be wondering why I took this approach when faced with falling test scores and a big fat C in 4th grade if we didn't have to sit for the COGAT. First, I should point out that there is a whole section 2 in each book that has 120 problems of this nature. This is #95 from Test Prep Math Level 2, with the 94 before it leading up to this one:

2 F + 2 = 21 – 9
2 G + 1 = 16 – 6

8 F = 3 G + ?

Even if the first problem only has 2 equations, you're probably thinking that this is way too hard for 2nd to 4th grade.   If you think in terms of conventional math, more than one problem a day, with a correct answer expected on the first try, no struggle, no growth, you would be correct.  But this is a facilitator for cognitive skills, and I'm thinking that it's going to take 2 months until a problem like this can be done in 15 minutes or less, hopefully with no pencil, in 2 tries or less.

Even though I expected it, I was still surprised to find skills rising to the occasion by about month two.  I warn everyone, the word problems are there to break bad habits and change the mindset of the child.  Until that happens, the child might cry when you expect them to do a hard problem that takes more than a minute and the probability of error is high.

The Midway Point
A parent may have to step in and help a 4 year old who is no where near a solution and their 15 minutes of concentration is nearly up.  A parent of a 10 year old might have to step in to help when the 10 year old is reaching the limits of patience and is about to cry.

Your goal is that the child is learning to think, learning to learn, and picking up the cognitive skills on the way.   It would be a shame if they make progress for 20 minutes and actually demonstrate some new skills only to end with nothing to show for it 25 minutes later.  If you think of this as a 2 or 3 month process, and you're happy to see progress, just try again the next time.   After a few months and some mastery, the child will feel like they climbed Mount Everest, instead of just Mount McKinley.

On the other hand, if you're not ready for such a drastic shift in approach, finish the problem.  They did a great job, showed some thought, figured out much of the question, made some progress. Explain the question throughly, show how you answer it.  Please get the answer wrong at least once.

If this is a question from a cognitive skills practice test, you can't afford to do this for numerous reasons.  Feel good about progress, tell them it was better than expected so you're stopping early. Move to the next problem the next time, and come back to this one later.

If it's a really bad day, and nothing happened, go out for ice cream to celebrate.  We celebrate 0% on any worksheet with more than 5 problems.  It's a house rule.

The Solution
The solution to a problem is the opportunity to check the work and nothing more.  In school, on tests, wherever, the best a student can do is spend time understanding the question and check the answer. In middle school the third step of devising the solution strategy is added.  If the answer is incorrect, what went wrong?

Starting in 2nd grade, students are expected to memorize "9 + 5" and regurgitate the answer immediately.  This is not math, not thinking, and frankly not very useful.   The best students meet expectations, but they also take away these expectations and that's why you might face crying later on when they are forced to do a problem that takes more than 10 seconds of thought by a mean parent.

When you're focusing on cognitive skills, the emphasis is on learning how to learn, not obtaining a new fact to memorize.

Put these things together.  You have some options when responding to an answer:
1.  It's wrong.  Try again.
2.  Prove it.
3.  Explain how you did it.
4.  Look at the problem from a common sense perspective (eg estimate).  Does it make sense?  By this, I mean is the result is supposed to be 1/4 of something, is the result less than that something?
5.  I don't care about the answer.
6.  Good job.

Only #1 involves actually checking the answer, although you might do that with #2 and #3.

#1 and #2 are critical in the early stages of test prep and math catchup while you are reinforcing reading the question and checking the answer.  #3 and #4 is a transition to higher order analysis of the problem.  #5 demonstrates that the concept of correct and incorrect is not going to be part of this house.  This house is about learning and thinking.   #6 is when cognitive skills get to the point where you actually don't care because you've now got other problems to solve, like the gutters.

If you succeed in getting a child to spend enough time with a question to thoroughly understand it, and that question is suitably challenging, and they check their work, and you give them a practice cognitive skills test, then they are ready for the test.  Of course, if you want them to get a 99% on the test, they have to be prepared for the hardest question.

This is a chapter on how to teach cognitive skills.  Look closely at the approach:  Don't help.  Expect to take a long time.   Do things over without becoming irritated.   Make the kids do the work.  Put them in charge of learning.  Give them things to do that are hard.  Ask big questions.  Expect a few months before progress.  No where do I actually mention a list of cognitive skills, like verbal acuity or visual spacial tom tumbery.  The test is measuring the ability to learn.  Question types like figure matrices are just the mechanism.  If the child is doing the work, the child will learn the skills necessary to succeed n the problem at hand.  If the parent is doing the work, a list of cognitive skills is not going to help.

The only gap on the curriculum page is material for visual spacial skills for grades 2-4.  My best recommendation is an NNAT book for grades 3 & 4.  I think of a cognitive skills test as more of a thinking test than a shape test, but there are children deficient in this area.  I think the best practice in visual spacial skill is a lego set with complicated instructions, but these cost $200 or more.

In 4th grade, we decided to focus on cognitive skills work and wait out math until the curriculum is more useful.  I announced to my 4th grader that "4th grade math is a writeoff".  That was the first time he heard the word "writeoff" but he didn't need to ask for a definition.  The big fat C in 4th grade math is currently an A in 6th grade.  5th grade involved a year long debate on doing homework and turning it in, but test scores hit a high.  By the end of 5th grade, we were starting 8th grade math. That turned out to be easier than I thought and we're now biding our time with a 9th grade Chemistry initiative, doing SAT problems, and thinking about what to do next.

At this point, it seems unlikely that the younger brother, the original graduate of the world's first phonics course for math and the 3rd guinea pig for Test Prep Math, is going to experience the 4th grade train wreck because we have been doing 5th grade competitive math work for lack of anything else to do.

[What follows is a summary of my early research when I was in the process of trying to identify these skills.  It's interesting to see how I solved the problem from where I started.  When I first started, my thinking was just find out what the questions were and practice them.  Alas, it's not that easy.]

Content From 2013

As I mentioned in the previous chapter, I was disappointed that I could find no research on how to design a question for a cognitive ability exam.  I did find, however, numerous studies on what is correlated with scores on these exams.  This chapter exams these correlations in the hopes of discovering the "magic bullet", some skill or interest that gifted kids have that helps them pass the test.  The question of what material to cover is critical.  The typical parent will be lucky to get 10 minutes of concentration per day out of a typical 4 year old, and depending on when this parent gets serious about the entrance exam, study time will be between 6 months and 1 month.  So time must be used wisely.

Some of the key correlates to test scores are vocabulary, reading ability, and academic performance.    From what I hear from other parents, standard math ability is not as highly correlated with exam scores as the parent would prefer.

The challenge with these correlations is what causes what.  I want to know what types of academic skills will cause test scores to rise, and then I will focus on teaching those to my child.  Alas, it would be really hard to create a study that demonstrates practicing a specific skill (reading for example) improves test scores.   Of course it does:  studies have shown that doing anything besides TV and T-ball improves test scores.

A a deeper level, my problem is that the entrance exam for the CPS is a secret, so I'm wondering what to study.  If the test is primarily classification questions, will studying classification questions by the hundreds give us a higher score, or should we focus on reading lots of science books instead?  What cognitive skills go into a classification question, and what's the best way to learn these skills?  In this chapter, I'm looking for broad categories of activities, and later, I'll look at specific cognitive skills and question types.

One of the best predictors of exams scores is academic performance.   Richardson pointed out that these tests were designed to predict academic performance, and are officially used for this purpose, and academic performance is pretty stable over time.   Even if academic performance - and the effort behind it - raises a test score, what about the academic performance really matters?  So is it academic abilities that the test uncovers which can be gained by focusing on studying traditional academic subjects like math and reading?

That's what I'm going to try to untangle in this chapter as best I can.   My conclusions will motivate the test prep curriculum in the chapters that follow.   Unfortunately, correlation does not imply causality, and many of my conclusions will be based either on intuition, or fear of blowing the test.

Raven's Matrices

These analogy type matrices are highly correlated with the scores on cognitive ability tests.  In fact,these have the highest correlation.   I consider Raven's matrices to be nearly equivalent to vocabulary, but vocabulary that is conceptual and instrumental in nature, not just simple nouns or descriptors.   "Potato" is a vocabulary word, but  "opposite" or "wider" is what I call conceptual.   Is a word that can be used to solve a puzzle or challenge like a Raven matrix.

Raven's matrices can include all of the quantitative and figural matrices of the COGAT.  I'm guessing that the scores are highly correlated because the questions are highly correlated.  I think that almost anything can be put in the form of a Raven's matrix.

The COGAT has a short form which is a pretty good substitute for the longer form, and the COGAT is highly correlated with future academic performance, which is what it is designed to predict.   The short form of the COGAT is the picture, figure, and quantitative matrices.   I have never seen a COGAT test or a Raven test, but I've seen lots of examples and practice questions put together by others.  And I tried to put together every permutation myself categorized by cognitive skill.  But at the end of the day, I'm guessing.

Any type of question, including classification questions (see my example with the potato below), can be put in a matrix form.  I also know that arming your child with a big vocabulary, including a comprehensive vocabulary of math and language theory terms is vital to tackling these matrices.   In my opinion, vocabulary and Ravens/COGAT matrices are equivalent.  Sentence completion tests are also very highly correlated, but I consider these the verbal form of the Raven's matrix.


The number two predictor of exam scores is Vocabulary.  I've read in a paper of one of the test authors (which I can not find at this time - it might have been a Lohman presentation) that a good vocabulary test can be substituted for a cognitive ability test for a large number of kids and the results will be nearly equivalent.

There are two ways to approach this.  First, I think the tests primarily test word and concept vocabulary.  Secondly, vocabulary increases a child's cognitive skills by giving him tools to work with.    Look at this question.

This picture was included on a presentation to demonstrate how culturally loaded nonverbal tests can be.  (Problems Using Nonverbal Tests by David Lohman on his website.)

Think of all of the vocabulary needed to solve this matrix.   First of all, the names of each of the fruits and vegetables.  Then, in addition to their names and shapes, the child should know which ones grow in trees, on bushes, on the ground, and under the ground.   A child who has "fruit" and "vegetable" in his vocabulary, and classifies each of the items in this way is 50% of the way to solving the puzzle.  The trick is the term "root vegetable", which includes potatos and carrots.  That is a lot of vocabulary encompassed in a single picture.

If you don't know the definition of root vegetable, you have to sort through other possible relationships, like shape, the leaves, color, when you eat these, orientation, and on and on.  My children prefer the lumpy vegetable because it looks like the potato, but of course this is not consistent with the relationship in the top row.  But they think it is and can logically argue this point.   It would be so much easier if they just knew "root vegetable".

The root vegetable question can also be presented as a classification question as either "what doesn't belong" OLSAT questions or "which item belongs in the group" COGAT questions.

Next, look at a figure matrix.

This question was on a very expensive COGAT practice test.  It stumped me and my son.   Can you guess which one of the triangles goes in the empty box?

At first, I tried to help my son understand the visual-spacial comparison of the two objects.   This was fruitless.   He understood bigger and smaller, but something else was going on here, besides him being 3 years old and having an insane parent.   We started to talk about words like "wide" and "narrow", "grow" and "shrink".   I added think, thin, and the "er" and "est" form of each word.  As well as "more", "most", "less", and "least".   Also "height", "width", "length", and finally "base".  The list goes on.

The answer is that the wider rectangle looking object with the round top in the top left corner of the matrix shrinks at its base and becomes narrower.  When this operation is applied to the triangle, it doesn't become shorter, but narrower.

This is how we tackled most of the OLSAT and COGAT practice.  I introduced hundreds of vocabulary words that I thought would be pertinent to the exam.  If there was a discussion of apples, it had to be more than just "they are a red fruit".   For math, we didn't stop at "bigger" and "smaller" as you will see in Chapter 5.

I remember studying for the GRE and memorizing a list of 3,600 vocabulary words.  That is the cynical test prep version of tests, and I'm not sure it helped me succeed in subsequent pursuits, and I would never use most of these words because less people would understand my writing than now.   The picture for a 4 year old is much brighter.   Inserting all of those vocabulary words into that little brain makes it grow.  Each new word is a new concept to try out and a tool to use.  It is quite amazing to watch.  It makes the child smarter in the most conventional sense of the term.

One day we were reading through an old Hooked On Phonics book and we came across the word "grasp".   My son, probably 3.9 years old, stopped and asked what that word means.   I explained the difference between hold, grasp, and clutch, and physically demonstrated these three words.   He just stared into space for about 2 minutes, and then was much more interested in what was before a pretty boring exercise, because he got to look for new words.   That was the one moment where everything changed.  Personality, interests, school, everything.   About 2,000 new words would follow very quickly.

There are certain studies I've heard mentioned but could never find that indicate vocabulary increases cognitive ability not because it is required for getting high marks on a cognitive ability test, but because it makes the child smarter.   What I witness are increases in general mental ability, conversation, creativity and art, but unfortunately, with my sample size of 1, I'm also seeing a the effects of a child become older and acquiring a variety of new skills for that reason as well.  So my hypothesis of a strong causal relationship - vocabulary makes a child smarter - lacks the proof I need.  If anyone finds any studies on this topic, please add a comment to this chapter.

Next, a Raven matrix.

Here is a matrix that has lots of things going on in addition to my sloppy drawing, but the primary thing, and the only valid differentiator that is going to show up in the answer set is the little lines above the middle.   This is simply "two is to three as three is to..." and the answer will be a shape with some random design, but four little lines.   There is a whole bucket of Raven's matrices that is achievement in nature, and some are quantitative   I am presenting this example to warn you that there is more going on than vocabulary, although at this age, I wouldn't expect most kids to get the problem correct.

With the exception of quantitative practice, I am going to oversimplify these tests and flat out state that the COGAT is 78% vocabulary and the OLSAT is 80% vocabulary.  The rest is going to show up in my math chapter.


How is a city boy supposed to learn about root vegetables?  How about a poor kid on the South Side of Chicago who doesn't eat vegetables?  The answer is reading.  And therefore, it should surprise no one that reading is the next highest correlated factor to cognitive ability test scores.

The reading correlation has a second dimension as well.  For older kids, reading comprehension test scores are correlated with cognitive ability test scores, and for little kids, the ability to read (decode) is highly correlated.   Why are these correlated?   Here are some options.
1.  The more a child reads, the bigger the vocabulary, and these tests are all about vocabulary.
2.  The more a child reads, the bigger the vocabulary, and bigger vocabulary makes the child smarter.
3.  Reading teaches concentration and sitting still, and these skills are important for completing the test.
4.  Reading involves the brain exercising the cognitive skills that are exactly the ones used in solving test questions.
5.  Reading comprehension skills are the same skills used to decipher test questions.
6.  The tests are designed to evaluate success in school, and both reading and the cognitive skills used in reading are the most fundamental requirement of success in school.

I think these six items are as true for a 3 year old as for a 16 year old.   With a 3 year old, however, decoding words on a page is only a small part of what I call reading.  The primary part, especially the comprehension part, is being read to by the parent, or "Read To" for shorthand.

According to Jensen (p 270, p280), reading comprehension is the most highly correlated of all types of tests to general cognitive ability tests for 2 reasons.  First, the cognitive skills needed in reading are required for academic success.   (Jensen quoting from Thorndike 1917) "The mind is assailed as it were by every word in the paragraph.  it must select, repress, soften, emphasize, correlate and organize, all under the influence of the right mental set or purpose or demand."   Each of these word describes a skill needed for getting an A in algebra, or solving a classification problem.  Modern researchers would add add to this list working memory and other cognitive processes.  For this reason, classification problems are such good predictors of school success because they measure the cognitive skills required to read adeptly.

As I mentioned before, "reading" for a 3 or 4 year old is primarily the parent reading to the child.   Also, reading comprehension is more correlated with test success than decoding.  The child is not going to learn a strong vocabulary by reading Bob books.  There are studies, however, that show the more a parent reads to a child when he is young, the better a reader he will be when he is older.

Now the question.   Given that reading comprehension skills are the highest correlate with cognitive test scores, is it reading that causes higher comprehension skills and thus higher test scores?  Or do "smart" kids read better and take tests better because of their smartness?  An old professor sitting alone in his office with a stack of 15,000 test scores will likely draw a different conclusion than a dad teaching his child and observing other children and their parents.

When I began interviewing the parents of children in gifted programming about their philosophy, values, and parenting styles, the common denominator was reading.  I had this item on my GAT top 10 list before we even started studying for the test.

When my son matriculated, most kids were 2 to 3 years ahead in reading.   It never occurred to me that a first grader would be reading 3rd, 4th, 6th grade books, but most of them were.  I drew 2 conclusions from this.  First, we were way behind and had to catch up.  Secondly, instead of all of the Raven's matrices I drew for test prep, we could have just read Flat Stanley.

For younger children, there is a very simple test that I call "The Room Full of Children" test.   I stumbled across this test one day when watching my son's play group.  There amidst the group of 1 and 2 year olds, including my son, drooling and sticking things in their mouths, working on one word sentences or grunting and pointing, was a little late 1 or early 2 year old girl who said, "Look mom, it's a picture of the Eiffle Tower."  All of the parents jaws dropped.   I thought to myself, Holy S___.    This is also known as the HS test.

A child matriculating to a GAT program in Kindergarten or first grade, at least in Chicago, will be reading two years ahead of grade level or will be struggling to catch up.   Therefore, a parent who doesn't believe my unproven claim that reading is the key to the cognitive abilities test will need to invest in reading regardless.

Problem Solving Skills

Here is a very interesting study in that it is right on the money in terms of my objective.  Nisbett quotes a study by Herrstein that investigates the impact of teaching problem solving skills on cognitive ability scores (page 74, Intelligence and How to Get It).  45 hours of training on the scientific method and problem solving skills were taught to 7th graders in Venezuala.  Problem solving skills, as measured by Herrstein, increased significantly, but more significantly, in my opinion, was that OLSAT scores increased by about 7 points over the control group.

This is a very simple experiment with one controlled factor and a positive correlation is established.
Here are the skills that were taught:  classification, hypothesis testing, ordering according to different dimensions, analyzing analogies, the structure of propositions, the principles of logic, complex arguments, probability and expected value, and the relevance of data.  This list is very amusing to me because it is the set of skills needed to answer questions on standardized tests of cognitive ability for little kids.  While the correlation isn't spectacular, the list of skills is, and for that reason, I'll be coming back to this line of research in the chapter on test preparation.

I've seen a few other studies that measure improvements in academic performance based on coaching techniques.  I think this is a small dimension to test prep.

Academic Performance

From the early part of the 20th century, the primary usage for cognitive ability tests is to predict academic performance.  I think that is where the test publishers get most of their revenue.  It's to screen kids for gifted programs, especially the COGAT and the OLSAT.  The best predictor of future academic performance is current academic performance.  I've read this from David Lohman a few times.  The SAT has a very high correlation with these tests.

Let's apply some logic here.  The test makers know that current academic performance predicts future academic performance.   And these programs run at least 1 year ahead academically, so if the child is not already there, the risk is high that he will not succeed in this program.  In theory, that is what the test tests - academic aptitude for next year's material.  And you can logically conclude that you just have to help your child get a few years ahead academically at a young age and he's in.

But it's not that simple.  This exam is not trying to find those A students who will get A's next year.  There trying to find the A, B, and C students who can work at a level 2 years ahead.  Or, in the case of the preschool kids taking the exam, they are trying to find the kids who may or may not have any schooling of any type and can jump into an accelerated program.  And we know that reading, writing, and arithmetic are not on the test.   The test makers are not testing academic skills under the stable relationship of current academic skills with future academic skills, they are testing the same cognitive skills used in academic work.  In terms of test prep, not all academic skills have the same value.  For example, reading comprehension is a better predictor of test success than spelling.  For math, general math is a better predictor than arithmetic.

I know parents who got into trouble focusing on traditional academic content only to have their kids bomb the test because it is not traditional academic content.   I'm not 100% sure whether their children are really at the level they think the parents think they are.   But I do know that the tests are an odd animal, and cover a much broader set of quantitative concepts than adding and subtracting.  So if little Billy is a wiz at counting and addition at age 5, he may end up in the 40th percentile on the quantitative battery.

We'll look at this in later chapters.  For now, see how differently these three math problems will tax the brain of a 4 or 5 year old:
  1. 3 + 4 = ?
  2. 3 + ? = 7
  3. 3 + 4 = 2 + ?
  4. If Sue has 7 nails, and 3 of them are too long to use on the bird house she and her ailing father are building in the garage, and she really needs 12 finishing nails and not the kind you use in house framing, who's door should she knock on - the carpenter, the doctor, or the guy who is writing test questions?

Quantitative skills used to be highly correlated with general cognitive ability test scores.   There are also inherently strong correlations between verbal and quantitative skills at young ages when kids have to take both subjects.  The kids who are forced to read are the kids who are forced to do Kumon.

These days, quantitative skills are less correlated with verbal and reasoning skills, and the test makers (at least the COGAT) refined the quantitative questions they use to distinguish between cognitive skills used in math and cognitive skills used for other academic tasks.  Or so I am speculating without seeing an actual test.  This differentiation would make the different sections of the test more useful, and then a psychologist could make money by interpreting the results in some medical sounding way.  "Your child shows a gap between the verbal battery and the quantitative battery for subset 3G blah blah blah."  I have read numerous case studies on this.  For free, I would just say send your child to Kumon.

A well balanced cognitive skills test is 1/3 verbal, 1/3 spacial/figural, and 1/3 quantitative    The COGAT fits this definition.   The OLSAT waters down the nonverbal parts a little, substituting questions to gauge school readiness, like following directions, and thus this test is more verbal in nature.   Regardless, if the quantitative tests are becoming less correlated with the other scores, we have a bit of math to do, in addition to reading, and I cover this in Chapter 5.

But before I dissect the test, I'm asking a broader question from this different perspective.   Can teaching math to your 3 and 4 year old raise his test score?  That is a really tough question and has a variety of answers.
  1. Answer 1 - Yes.   General math achievement skills are more highly correlated with general cognitive skills than general verbals achievement skills (or at least they used to be).  That means any time a parent spends with his 3 year old covering the basics of counting and adding is time well spent.
  2. Answer 2 - No.   The math on the test is dramatically different from counting and arithmetic, especially as the children get older, so you wasted your time.
  3. Answer 3- Yes.   But you have to study "test math", which is very comprehensive, and not "arithmetic".
  4. Answer 4 - No.   Instead of wasting your time on math, focus on general problem solving skills using the same cognitive processes needed to solve quantitative test problems.
  5. Answer 5 - Yes.  It's easier to teach and practice problem solving skills with a child who is ahead in math.

What To Study

This chapter asks the question "What type of academic material will increase a test score"?  Saying vocabulary is correlated with cognitive ability only qualifies vocabulary for consideration.   The more important question is this: "Will increasing your child's vocabulary increase his test score?"  Or do children with big vocabularies do well on these tests simply because smart kids have bigger vocabularies?
When I do test prep, it includes reading, math, and test math, and a host of other activities.   It's hard to untangle the impact, especially with a small sample size of one, but here is what I have concluded for now.   COGAT math is a phenomenal way to teach math, and paves the way for advanced academic math.   Also,  knowing academic math helps speed the progress of studying test math, because the student has a larger vocabulary of terms and concepts that the student understands, like counting, and test strategies can be conveyed and understood quicker.

Here's a diagram from 1983 that represents the close correlations of various types of tests.   It appears in many books and is reprinted here without permission.   The clusters represent types of test questions.  Gc represents learned skills, verbal and numerical, and Gf represents the types of questions on a cognitive ability test for gifted students.  Gv is visual spacial reasoning - important for the NNAT, but not likely necessarily on the Chicago test.     Note that this is a study of high school students and not preK.

You can see the usual suspects in the circle around Gc, which is our target.  The Raven, Verbal achievement, Quantitative achievement  Vocabulary and the Raven.   The Terman test is an old test that looks like the verbal section of the SAT.  I am surprised to see Letter Series here.   Also there is something called Nec. Arith. Oper. which is defined nowhere, but probably doesn't apply to preK.  I'm guessing it's "fill in the missing operator" which shows up in first grade, maybe combined with fill in the missing number or algebra using shapes instead of X's and Y's.

Here's a different version of correlations to cognitive skills by Snow, Kyllonen, and Marshalek (1984) that displays question types from cognitive ability tests.  Again, closer to the center is the sweet spot, because these tend to be the complicated, multi-skill, multi-step questions.

According to this diagram, practice classification and verbal analogies, maybe number series and arithmetic reasoning, and build the vocabulary needed to answer these questions.  Is it that easy?
Let's take these correlates one by one again and draw some practical conclusions.


Reading is a foregone conclusion.   My first son's GAT program is 85% strong readers - up to 3 grade levels ahead, and the program skipped ahead 2 years with no problem.   There are a few kids who got into the program the hard way, but even these caught up quickly in reading.

I am speculating that the only thing these kids did was read.   I've talked to parents about helping get child #2 into the program, and not one of them knows anything about the test prep material.  But they can read.


Vocabulary is also mandatory.   How can a child gain from practicing verbal analogies and classification, if he doesn't have the vocabulary to match what the test asks?  In other words, you can practice (in picture form) "fish : whale :: cat :", which reads fish is to whale as cat is to "?", and the answer is lion, if your not hung up on the whale being a mammal.   But what if the test had, for sake of illustrating my point, "clam : oyster::girl:?"    The child needs thousands of vocabulary words to do well on classification and analogy questions.  I'm not even sure thousands of practice questions will help, because it is unlikely that a 4 year old is going to learn anything about an oyster from test prep.   By the way, the answer is "princess".

Alternatively, the test makers might choose vocabulary words that all children are familiar with, but have some attribute or characteristic that requires cognitive ability to discern - like root vegetable.   In my experience, if the child has the vocabulary word a priori, he can just skip the thinking part and fill in the bubble, saving precious cognitive energy for the next question.  (How did you like "a pirori"?  It means ahead of time, but it's not supposed to be used in this context.  Just thought I'd work it in anyway.)

We'll talk about the sources of vocabulary in the test prep sections.   For now, I think the main source of vocabulary for a small child is reading.

Raven's Matrices

I am the only person I know who used Raven's matrices as my main source of test prep.   This was my first attempt at reverse engineering the super secret Chicago selective enrollment test.   We were at a private school, and I had only short period of time because I learned about this test late in the game - my son was in Kindergarten and it was October or November.  So I researched how to make IQ tests and started producing my own.

As I know now, and as you can see from the 1st Radix diagram above, this was probably a good thing to do.   I paired it with a quick vocabulary course, and the results were acceptable.  We barely made it in, two weeks after school started, and only because so many more qualified people declined.

Nonetheless, I learned something about Raven's matrices.  First of all, you can put any question into a Ravin matrix.  Analogy, classification, etc.   I think the high correlation of Ravin to other cognitive ability test scores is simply because it's an alternate way to test the exact same mental processes you see in all other question types.  Secondly, you can teach vocabulary using these, including the types of vocabulary that is not generally found in children's books, like math vocabulary.  I wouldn't use it as my primary way to teach vocabulary, obviously, but only certain math concepts.

So are Raven's matrices a good way to improve a child's cognitive skill by 30 point, or does Raven practice simply boost a test score by 3 points because it familiarizes the child with the types of skills a test will test?
I'm going to present Raven's matrices in the chapter on Hard Core Test prep and you'll see exactly why I think these should be a mandatory part of test prep training.   I do not think test prep books and online test prep services are in the ballpark of what I did.   When I review their questions - which they charge dearly for - I see a sampling of skills, even in very large question banks, and the level is fairly easy compared to what the test will test.

Every matrix question is a set of vocabulary and a relationship and an operation.  The same concepts can be rephrased in classification format, although one might need a different number of questions in each format.   In the same way that a child can learn what is on a farm from reading books, and can learn to add from doing workbooks, a child can learn specific math related concepts and terms (larger, rotate, double) from doing matrix questions, and sometimes even enjoy the challenge.

I also see learned problem solving skills and task organization skills that are applied to a wide variety of other situations.  Unfortunately, I have a sample size of only 2 so I can't definitively say that Raven's matrices gave us 30 additional points of cognitive skill.

Letter Series and Nec. Arith. Oper.

When I prepare test prep material, I generally look for advanced material.  My reasoning is very simple.  Your child will be tested starting at grade level.  Then the test will slowly ramp up to grade + 1, grade + 2 and so on, albeit in a format that can be understood by a preK kid.   So I throw in lots of 6 and 7 year old material at my 4 year old child, again in an understandable format.

But what should I do with letter series?  There is a correlation between letter series questions and cognitive skills among older kids, but I don't see this helping small kids because the types of logic that go into these series are beyond the beginning reader.  For exampe, try this on your four year old:  "abcd::lmn?".  The kid may get "o".  Then try "dcb::zy?", or "ace::mo?".  These are the simplest number series questions I can think of in the simplest format.   The other 200 questions are beyond a young child, simply because has not yet mastered the order of the alphabet.

On the other hand, take the complete set of operations that can be performed in series form on shapes  colors, numbers and letters.  Skip one, skip 2, backwards/forwards, 1-2-1-2, alternating, etc.  With this alternate approach, have I broadened his general intellectual capacity, or have I just helped him get the last point he needs on the test to get a seat in the program?

I think I just answered the question.   But I am asking this question a full year before the next test, which give me plenty of time to draw up the material and teach the skills.  Try teaching "A C E ?" to a 4 1/2 year old.   I'm guessing 95% of parents would give up in about 5 minutes because it's pointless.   The other 5% will slowly wait it out and a month later the child will understand why the answer is G and will generalize this to other problems.  But that is a different chapter.

Nec. Arith. Oper. NAO is intriquing to me because a) I have no idea what it stands for, b) it can't be googled, and c) there are lots of number puzzle type questions that I never tried on a small child.
Take a very simple example.  X + 1 = 3.   X + 2 = 4.   From algebra, you know that X is 2.  But a 4 year old does not.   How about X + Y = 5.   X + 1 = 3.   The X and Y's are typically replaced with shapes.   And the operators can be replaced as well, as in "5 ? 2 = 3".   If this shows up in a first grade math book, it's fair game for the Kindergarten version of the test.  Or to be more accurate, if this type of question shows up in a first grade math book, there will be questions on the test that require the same cognitive processes that are required to solve NAO questions.

In order to determine whether or not this exercise will increase cognitive skills, and then the test score, this skill category is evaluated by this logic:   What type of cognitive skills does this question address?  Are these cognitive skills covered on the test?   Is studying this type of question a good way to learn these general cognitive skills, and will the child be able to generalize this skillset to the test questions?

The skills needed to solve NAO and letter series are highly correlated with general cognitive skills, so they can't be dismissed outright, and I can't find a more general skill that can subsume them in the way that reading subsumes vocabulary.  Here are my conclusions:
  1. The same cognitive processes used in solving these questions are probably used in reading, classification and analogy type questions.
  2. The basic skills can be rewritten in other formats.  For example:
     - If John ate 2 candy bars and now has only 5, how many did he start with?
     - 1, 2, 3, 1, 2 ?  Instead of A, B, C, A, B, ?
  3. Since I can guess the cognitive processes used in these questions, but am not sure whether or not these specific question types will teach these cognitive processes better than other approaches, I'm going to introduce NAO test prep questions next time, in small quantities, just to be safe.
It's January, a full year before the test.  I've started trying out the 1st grade complete the number sentence questions for addition and subtraction on a 4.5 year old PreK kid.   7 - ? = 5, ? - 2 = 5, and ? + 2 = 7, for example.  Like most test questions, there are multiple steps to solving these.   It is so much easier than 5 + 2 = ? and 7 - 2 = ?, which simply require learning to count and computing the answer without spending much time on thinking.  I'll provide updates down the road in a blog post.

Other Tests

There are many other test types in the first Radix diagram, covering a multitude of question types shown in the 2nd Radix diagram.   In this chapter, I'm simply interested in the ones that help us spend our time wisely in the year leading up to the test, a test I expect to be in the neighborhood of Gc in the diagram.   It looks like reading and certain types of math are the winners.  I will work the Raven's matrices, the series, and the NAO questions into "certain types of math", and this will include heavy doses of math vocabulary.

A Note On Cheating

Let's suppose you came across this free online book on how to get into a gifted program by doing well on the entrance exam by typing in "How to Cheat on the COGAT and OLSAT".   I've done that before and all I ever get are those horrible GAT parent forums where they brag about how gifted their child is and accuse others of cheating on the exam.  Anyway, suppose your intent is just to cheat.   If you follow the advice in this book, and you have more than a few weeks to do test prep, you will end up with a child that is much, much smarter than before you started.   In short, you will end up with a gifted child.

Based on my findings presented in  Chapter 1, I've come to the conclusion that all kids are academically gifted.  It's just a matter of whether or not they practice and develop their academic gifts, or whether their parents leave the TV on all day and give their kids video games.

If you spend 6 to 12 months with your 4 year old doing "test prep" at about 10 minutes a day (if you're lucky), and you pair this with a strong reading program, maybe throw in some math at the appropriate time, you will end up with a much stronger child who is prepared to succeed academically.  If you throw in heavy doses of fun, project oriented directed play, you will end up with the prototypical gifted child.

Did you cheat?

Or do you get an "A" for parenting?

No comments:

Post a Comment