Saturday, December 12, 2015

Stop Spoon Feeding Your Children

A good parent is eager for their children to know all of the things children need to know so they can grow up and fix the world, which totally needs fixing all of the time.

A tiny little child asks a lot of questions and has an unlimited memory for the answers which he will use against his parent when he's a little older.  The official classical curriculum emphasizes knowing, aka memorizing stuff at this stage.  Since US curriculum is two years behind the rest of the world, there's a lot of stuff to memorize at home.

So the child asks questions and the parent answers them.  Before long, the child is baffled by 32 / 8 and asks what the answer is, or, as in the case of many of my readers, the child is baffled by a figure matrix.  In a worst case scenario, the child is in the 99th percentile on standardized tests, because below the average on GAT tests.  The reason for this train wreck is that the child has grown up asking questions and getting answers and the curriculum is suddenly requiring thinking.  The only skill the child has is asking questions and getting answers.

If your child does a question of any type and asks you for help before spending ten minutes staring at the problem and guessing, you blew it somewhere along the lines and you stink as a parent.

When I talk to the really bright children in the best GAT programs, asking and answering conversational questions, the children smirk as they calculate how much humor and sarcasm I am using, not because I am humorous or sarcastic, but because they never get a straight answer from their parents.  My kids are eye rollers and arguers because of all of the dumb answers they get at home and the arguments that ensue when they ask questions.  The point is simple.  Don't every answer a question your child asks.

The problems is that great parents have been not answering questions since the birth of their child, and their child now has between 4 and 10 years of thinking experience.   A parent who just discovers that their child has no thinking skills needs A Emergency Fix-It plan.

There are a variety of things going on when a child is figuring things out:  patience, working memory, figuring out skills, and cheating.   If your child is missing any of these, telling your child "read the question again" is going to be frustrating for both the child and the parent.  I took this approach and I don't recommend it anymore until you are sure patience and working memory are both there.

Rule #1:  All reading of any type is good so none of this applies to reading.  Of course you want your child to gravitate to thoughtful challenging reading material, but this is a completely separate problem.

Rule #2:  If your child is doing problems that could take a top student 10 seconds to do, throw them away.  Throw the whole workbook away.  These problems are ruining your child.  I'd rather have my 5 year old spend a day figuring out what 5 x 7 is than doing 4 + 3.   The ideal curriculum is one problem and 15 minutes for age 4 going up to 30 minutes for age 7 or 8.  After that, the time age equation doesn't mean anything.

Rule #3:  Don't ever, ever, ever answer any questions.   Ask your own questions, figure them out together, read the question together, draw pictures, have your child make up their own question instead, but don't ever ever read questions.

Rule #4:  Your child is at a certain skill level so work step-by-step to go from complete spoon feeding to independence.  If you have a really hard problem, like one of my problems, the child may not have what it takes to get the whole thing done on their own.  Look for a 5 minute figuring out task for your child and do the rest.  Here are all of the things that go into fully answering question.  Write this list down and post it for you and for your child.  Start with the child doing one of these steps properly. Just like when your child was starting to read and picked a single word out of the sentence to read and you read the rest.  Just remember, when you are doing the rest, you need to display dumbness, ineptitude, confusion, bafflement and other such behaviors.   These behaviors are the key as I mentioned in a previous article, not because I just made them up, but because of really powerful research.  If you are not totally baffled, and your child is, the child will come to the conclusion that being baffled is a bad thing, when in fact being baffled is most of math.

  1. Read the question
  2. Read it again
  3. Identify unknown vocabulary words, look them up
  4. Draw a picture to organize thoughts and understand the question
  5. Organize the question in the sub-problems or devise another solution strategy
  6. Calculate
  7. Check calculations (aka do again) to make sure they are correct
  8. Check to see if the answer is correct
  9. Read it again to see what was missed
  10. Do it again
If you can make your child comfortable doing #1 and then one other step except for step 6 which doesn't count, then you're on your way to a capable child.

If you don't have material that requires these 10 steps plus more, you are at a significant disadvantage and you need to get some better material.  If your child is in second grade, we're hurrying as fast as we can.  My fifth grader just did 12 of the ridiculously hard "F" questions which make the cognitive skills test look ridiculously easy and my 2nd grader did 10 more questions today (he already has mastered the list above).

One parent I know makes their child clear the table after dinner and do the dishes.  My children are so overwhelmed by this onerous task that they spend 25 minutes complaining and we got no actual work out of them.  So we started with "take your empty glass to the kitchen" and 6 months later we can get 75% of the table cleared by one child if one parent helps.   Getting to 100% on math should take a lot less time.

Wednesday, November 11, 2015

Winning the Math Battle

When I first discovered cognitive skills, one of the first things I learned was that these skills could be lost by age 10.   There are a number of reasons.

First, a super bright child at age 5 or 6 is going to spend the next 4 years not using their brain.  When the curriculum finally shifts in 5th grade, they are skill-less.  The first few years of school should build the skill set for 5th grade, but unless the child is way behind in 1st grade, few skills are required.

The second cause of the 4th or 5th grade disaster is the emphasis in the US math curriculum of telling a child something followed by practicing it.  This is not learning.  A child who devours learning before entering first grade is starved to a waif 4 years later.  The child begins to expect to immediately know each concept.   5th grade is a wake up call.

The final reason for the 5th grade train wreck is the concept of "correct or incorrect" that is enforced in math.   It's either right or wrong, and generally speed is involved.  This approach provides a child with attitudes and skills that I would define as the opposite of smart, something like anit-academic skills.  "Did you get it right" is the opposite of "Did you learn something?"

If you dig through my blog you'll see over a year ago I predicted this for my 4th grader, and then later in the year confirmed it.

As part of my research, I've been tracking down parents of children that were enthusiastic learners in Kindergarten, did lots of extra work at home, and generally started school at the "A" level.  So far every single one of them is running into the 4th or 5th grade train-wreck.  Symptoms are frustration, inability to understand a new problem, tears at incorrect answers, sloppiness, impatience, and in many cases bad grades.

I've really enjoyed these discussions.  First, it confirms that I'm not wasting years trying to solve a problem that nobody else encounters.  Secondly, I have the antidote and I've been passing it on.

Here is the antidote.

#1.  Make sure your child has material that would take a person at grade level an hour to do 40 problems, but your child has to spend 45 minutes on a single problem because they are way below grade level for that material.  Think reading comprehension books.

#2.  Assign them a problem or two and let them flounder for 25 minutes.  Then go super slowly through the material to see what they can learn.   Focus on learning how to navigate difficult material, find clues, do things over and over and over.

#3.  Do not look up the answer.  When a 10 year old is doing a math problem for a 14 year old, it doesn't matter if they get it right.  You the parent have to break this bad habit - in yourself.  What matters is learning how to work with difficult problems.  If your child learns to work with difficult problems then the will eventually teach themselves how to get things correct all of the time.  If you announce whether or not they got the answer correct, you are providing a reward for the wrong thing.  (Of course, they will ask and you will have to tell them they got it wrong so that they can do it again.   My experience is that doing this on 100 consecutive problems makes both of you immune to any negative emotions associated with getting things incorrect the first few times.)

If your child spends 45 minutes doing a problem and gets it wrong 5 times, will you announce "Good Job!" with genuine enthusiasm?  If I had a child who spent 45 minutes working on a problem and got it wrong 5 times, I would be 100% confident that this child is prepared to get perfect scores in school at some point, maybe within 12 months, provided they practice this skill on a periodic basis. Conversely, if I had a child who zips through their work at lightning speed and gets 100% correct, I would expect a pending disaster without intervention.

We had our train wreck last year in 4th grade.  I spent all summer practicing this antidote   Picture the best your child could conceivably do in school and all of the best attitudes and practices.  The outcome was actually way better than that.  In math, we focus on these higher level executive skills because other than being good problem solvers, I don't expect my kids to become math professors.  I expect them to learn how to think with the official goal that they think better and do better in their other subjects.

Saturday, November 7, 2015

Coaching the NNAT

I've been slowly working may up to an article roughly entitled "How to Crush the COGAT Without Really Trying".  Unfortunately, "Not Really Trying" is going to be a lot of work for a lot of parents. It's all in this blog somewhere but it's really going to be fun synthesizing it in a ground breaking article. .

As a warm up exercise, it's time to crush the NNAT, specifically the puzzle question where there is a puzzle piece missing.  This is the easiest of all question types and I never gave it much thought.  I don't spend much time thinking about the Weschler, IQ tests, or tests for older kids.  Nonetheless, readers ask anyway because if you want a website written by researcher dedicated to getting every child into a GAT program, I'm the only game in town.

NNAT puzzles, IQ tests, and tests for older kids.  What do these 3 things have in common? The answer is algorithms.

The difference between thinking through a never-before-seen tough problem and zipping through way harder versions of the same problem is the algorithm.  This can be a mental construct or predefined approach to a class of problems, and it can be multi-demensional like a decision tree.

The difference between cognitive abilities tests and IQ tests is the need for algorithms on the IQ tests. That's why my IQ is never going to be great across the board.  I simply don't care that much about creating an algorithm to unscramble words and I'm not drawn to activities that really "smart" people are drawn to that would require this algorithm.  I'm not even that great at number patterns.  When I have to do things like number patterns, I quickly build an algorithm and its usually just trying out every type of operation sequentially to see which one works.

When I was pairing cognitive skills to problem solving skills, an exercise really designed to pair how I think to approach the test versus what the tests own definition of itself, I came across "algorithms" on the cognitive skills list.  Of course, kids develop algorithms when they are first learning how to read but I doubt any children can verbally describe the ones they use.   Algorithms come into play at much later ages.  In the problem solving literature, "trying each operation to see which one works" is a solution strategy that corresponds to the cognitive skill of using algorithms.  The higher order skill is patience derived from having nothing better to do because your loser parents make you do test prep instead of soccer.  But it's given a fancy sounding name, and terms like "number fluency" kept me off the right track for 4 years.

I tried to teach solution algorithms for the COGAT (eg shape, size, color, count) but these were never adopted.  Instead, my children developed their own approaches and I think this is a much better policy for young children when preparing for the COGAT.

Algorithms come from repetitive problem solving.  That's how an IQ test can accurately identify truly bright individuals, by defining true intelligence as "sitting around doing jumbles and cross word puzzles all day".  That's why people think the contrived definition of "high intelligence" is suspect and one of the primary problems motivating Gartner et ilk to pull things like the theory of multiple intelligences out of his back pocket.

Synonyms for the word "algorithm" are "short cut" and "trick".  I don't like these terms because they imply that thinking is not involved.

Back to the NNAT puzzle question.  The algorithms jump right off the page when you see the problems.  Take this example.  What is the missing piece going to look like?

Keep in mind Step #1 in my article on coaching when you do this problem because it points the way.
Here is my algorithm.
1.  Notice that there is a line touching the corner, two corners have a single line in this case.  Eliminate all solution options that don't have 2 corners with a line nearby.  I call this the "corner check".  This could be a line or other type of shape, and it may or may not involve a color adjective.  It could be top/bottom/middle, it could be wide, thin, and many other adjectives.  Coaching sessions would be heavy on the vocabulary.  Hopefully, the pieces in the answer set aren't rotated.  Since girls are deficient in rotating at young ages (because Lego Friends hasn't caught on yet) I think rotation is not used on tests before 2nd grade.

I'm sure the test makers are smarter than this so this would probably not be enough.  The child might look to the interior next.

2a. Look for crossing lines in the middle.  In this case there is one.
Eliminate all answer choices that don't have 2 lines crossing in the middle.  There would be a longer list of terms beside "crossing".

Did you notice the "a" next to the "2"?  Test makers want to find thinkers, so 2a is not complete.
2b.  Imagine that the lines (or shapes of some kind) move in an unexpected direction, like looping.  Uncross out the answers that could have unexpected twists and turns.

Obviously, 2b undoes 2a, unless the picture has a strong pattern, in which case it holds.  A strong pattern is something like a checkerboard.  So 2a/2b is part of the algorithm with strong patterns, but then if you are looking at a strong pattern, you are probably just back to the corner algorithm as well.

Questions that can't be solved by corner or edge checks can result from proportion aspects of splitting shapes.  This is just a starter suggestion.

If you are coaching your child on the NNAT, look for algorithms while you are spending lots of time investigating the picture.  While I'm confident of the corner check, I haven't looked much deeper.

Saturday, October 31, 2015

A Good Coaching Session

This article is necessary because my guidelines for coaching are very clear and I never follow them. They only work with the ideal child who is alert, well rested, just had a snack, and is ready to learn, as well as a parent who is cheery and patient.  Since these two conditions never hold in this house, I have a second set of rules under the heading of Parent Survival Guide.

The goal of a coaching session is to get 15 good minutes of concentration and learning out of a 5 year old.  With academic material, this might be 30 to 45 minutes.  With older children, maybe 20 or 30 minutes on cognitive skills work.  The reason for the 15 minute rule is that thinking is hard and I generally pick material so that after 15 minutes the child is mentally exhausted.

Rule #1  You will have bad days 40% of the time or more.

On a bad day, your child is sick, tired, or hungry.  An inexperienced parent will not realize this until much later.   An experience academic coach expects it.   If you start yelling at your child (guilty) it will result in crying and frustration and the whole session is wasted.  If you let them chose the material to do that day, they will pick something easy and at least they will exercise work habits if nothing else.

Rule #2   You don't know how it will go

I'm willing to bet that I have no readers who have experience teaching figure matrices to children where the trick in the question is that a square flipped but looks like nothing happened.  The problem is that your kid is making no progress.  Maybe it's way too hard for the kid at this juncture ("juncture" is an inappropriate word that coaches use in "pep" talks).

Plan B comes in many forms.

We take an unexpected detour to the shape box to start flipping shapes. We have this fantastic game from age 3 where you build patterns from shapes.  We'll flip them and I'll let my child describe what happened.  Flip the square.  "I already did."  No you didn't.  "Yes I did..."  This is the best way to learn anyway, but time constraints make it rare.

If I see that the child has exercised some of the skills and gotten the problem past the first step, I'll do the rest.   For younger kids, this works fine sometimes because they don't care if they learn by doing or watching.  With books, I used to read every other page.  For older kids, I do this more often because many of the problems I give require a team and since there are only 2 of us, I'm the rest of the team.

Note that I never do any figuring out or solving on test prep questions.   There isn't enough material out there.  For test prep questions, I'll just circle it on the chart and we'll try again a few weeks later. In fact, with an early enough start, you might circle a whole section or book if the child isn't ready. But on really hard math problems and reading comprehension, I'll jump right in there and work away side-by-side with my child, although I've been known to randomly get things wrong sometimes until they don't trust my help.

I may set aside my goal of 6 problems and we will spend the rest of the time dissecting the hard problem.

Or we can just read.   I don't know why, but strong reading families pick up these skills anyway, just not in time for the test.  (Curse you, strong reading families.)

Speaking of Dissecting
There is so little good material (aka hard) out there that you want to squeeze every last drop of learning and behavior planning out of each and every problem.   This is good, because it enforces the right skills.  I think we once spent 3 months on a practice test doing this, probably a year earlier than it should have been covered.  I never planned or expected to do a full length practice test just for the sake of doing a full length practice test.*

Step 1:  Describe what is happening in the problem in excruciating detail.  The kid, not you.

Step 2;  Ask questions about what they are describing.   What if?  Show no interest in hurrying into the solution.

Step 3:  Describe the solution set.  Again, this is not you.

Step 4:  Ask them to explain the rules of this problem because you are confused and until the child is about 10 they won't realize that you are the dumbest parent on the planet.  (By age 10 they are convinced you don't know anything because you always just ask dumb questions and never help them do their homework in any meaningful way.  The downside of this is that when they are struggling to finish their math homework at 9 pm they won't take your suggested answer.)

If they are really floundering, ask them to explain the example to you and then come back to this problem.

If they are totally clueless and you're getting desperate, ask them to memorize the mantra "Shape, Size, Color, Count'.   I did this because one of these things was always changing, although now that I think about it, the test may have been in black and white and "Shape" doesn't really mean anything.   I actually sent my child into the test asking him to use the mantra anyway.  Maybe he was baffled by the test (100% certainty because it's designed for that and way harder than anything you will practice) and the mantra brought him back to the practice rounds when he was figuring things out.  Maybe not.

Step 5:  Let them try to solve it as many times as necessary to get the correct answer.

Step 6:  When they finally get the correct answer because there are only 4 possible answers and their guesses on the last 3 were not correct, ask them to prove it to you, or at least explain why it's correct and the other 3 aren't.  I always make my kids prove it to me because their work with Vocabulary Workshop have made them expert guessers, and guessing is not one of the skills I'm looking for on the figure matrix problem.  When they guess correctly because they eliminated 2 impossible answers, I'm proud but we start over with Step 1.

Successfully problem solving a novel test problems rests heavily on your child's ability to do Step 1 and Step 4 as a matter of practice.  This is not at all like school and I'm not sure where kids will learn this approach if it is not coached.  Step 6 is a high level of Executive Functioning and reinforces  the bookend skill of checking the problem.  Making them live the problem elements during the discussion burns in working memory if it's not strong enough yet.  (I'm 10% sure of that last statement.  I'd like to think it is true because a project centered curriculum is a strong test prep method.  This may just reinforce executive skills).  Again, let me reiterate that they will be confused by the test and the practice material is not going to give them an edge because they recognize one of the easy questions.  You are teaching thinking, and not 7 + 8 = 14, which it doesn't anyway.

Remember these steps, because you will go through something very similar from ages 6 through geometric proofs in AP Geometry and can help even though you don't remember who Pythagoras was.

Getting It Wrong
Take the reward for getting the right answer out of the culture.  This is about learning, not getting right answers.  The general rule is that if your child is getting more than 50% correct, then you have the wrong material.  This rule of thumb is derived as follows:  they get a problem incorrect, thereby proving that they just came across something (skill or otherwise) that they needed to learn, and they get a problem correct (at some point, maybe not the next one) to show that they actually learned something.

How are you going to coach the thinking skills above if your child doesn't need to learn them?  I've had days where the error rate was closer to 100%.  If my child ever hands me a page with a score of 0%, we cancel the rest of the night and go out for ice cream.  I've had to adjust the policy a bit with bad report cards, because I'm not the one who feels bad, but not my general rule that failure is not against the law.  Does a report card with bad marks across the board guarantee straight A's will show up some time next year?  I think so.  That's an article for down the road.

*The Full Length Practice Test
I not only did a full length practice test, I made a deal to have a teacher give my son the test one-on-one in her classroom, all the while assuming a stern and intimidating persona.   Did this do any good? If it was worth a quarter of a percentage point, it was a quarter of a percentage point that we needed to get over the bar.  Unfortunately, we needed another 1/4% but I was out of ideas.

The other one managed to get in with nothing but ridiculously super hard problems I randomly found or created like roman numerals and zenn diagrams and reading comprehension problems when he couldn't read. Did this do any good?  Yes, I think it was more important than a practice test.

Readers often ask "What do I do?"   This is easy to answer when you have to get a 99.9% on the test and there's plenty of time. The answer is all of it.  I'm happy to give this answer because if they don't have enough time, they can start right in where they left off the day after the test.  Like I did.  Three times.  Although it turns out it wan't always necessary but it was always helpful.

The prescription gets harder when there's less time or the bar is something like 95%.  Then it's a matter of "what are my priorities with my limited time?"

Here is my answer, in reverse time order starting a week before the test:
1.  A practice test to prepare for the format of the test.  (3%-4%, $30)
2.  Really hard reading comprehension questions 2 grades in advance, even if you have to read these to a non-reader (5%-10%, 10$)
3.  Really hard problems of any type.  (5%-10%, not much on the market except for me)
4.  A practice test to coach like I describe above (5% - 15%, $30)
5.  Vocabulary Workshop and Building Thinking Skills, Mind Benders, etc, but this would be over a period of months
6.  Lots and lots of reading, which you should be doing anyway, test prep or not
7.  A good math workbook a year ahead of your child's level.  (Level, not grade.  You can only pull this off once in grades 1-4 so use it wisely.  After that, you need to stick to level or they will hate math.)

I may move #5 up above #4.   It's odd that practicing the test is so low on my list.   We did the practice test coaching a year in advance, which made it a learning exercise.  By the time of the test, the material is much too easy if your child has the approach down.  If not, it makes more sense.  Rest assured that it doesn't matter if they are struggling with an easy practice test and the test is rapidly approaching.   The cognitive skills are not that hard to learn if you have the proper approach to coaching.

I use my coaching steps above on everything, not just practice tests with an emphasis on #1 and #6.

Reading only comes in at #6 because test prep is for kids who didn't teach themselves to read at age two, which is most of us.

Good luck!

Tuesday, October 20, 2015

The GAT Skill List

The purpose of a cognitive skills tests appear to be measuring cognitive skills.  Or does it?  This is the first of a 2 part series evaluating just what the heck a cognitive skills test is measuring and how to beat it.

For the last few years I've been happily working with a framework that seemed so obvious to me.  I am double checking and it before I get to obvious we have to wade through a dark and murky swamp.

The Big Picture

#1 Cognitive Skills + Interest + Will To Do It = academic and life success.

The aspect of teaching cognitive skills without destroying interest or crushing will is called coaching. If you google my blog and the terms "crying" or "whining" I'm referring to coaching.  The last post is half on an article on this concept, and a discussion of coaching will complete the picture that this article begins.  (I'm going to be adding to the coaching article over time and will warn everyone when it is complete.)

#2 Cognitive Skills + Interpersonal Skills (e.g., empathy) + Intrapersonal Skills (e.g. self control) = The Full Skill Set

If you child is missing one of these skill sets there is work to be done.  I think band and Cub Scouts/Girl Scouts are really good activities for little kids to address the last 2 skill sets.  Executive Functioning programs are good for preK training if you have $30,000 to spend on pre school; if not, projects, crafts and art help.  Music in general is great for the first and last skill set.

I don't think team sports at young ages are good at all for any of these skill sets.

#3  The Classical Education
For a really inspiring discussion of the classical education, read the first 30 pages of Susan Wise Bauer's The Well-Trained Mind.

Here is my butchered summary:  Grades 1-4:  Cram as much information into their brains as possible. Grades 4-8: Think analytically.  Grades 8-12: Think logically, and grades 12-16 (yes, there is overlap in grades) I haven't gotten this far yet.

If you pair this with Piaget's Theory of Cognitive Development, then you can see that there are things expected of older children that would be impossible for younger children.  This is obvious.  What is not obvious is whether or not later skills like logic need new cognitive skills or just refinement of an underlying skills.

Since my focus is grades K-4 and I only dabbled in 5+ (because I found out the SAT is using problem solving skills and cognitive skills to improve their test), this theory will have to be explored later.

I'm interested more in training the brain at ages 5-9 to handle info and teaching higher order skills, but I can assure you that I've done as much information cramming as anyone into my kids' brains.

#4  Is 99% attainable for long periods of time with a normal kid?

Every 4 years the bar moves and the list deepens.  Cognitive skills training at age 5 only buys so much for a 9 year old, especially if he hasn't practiced his skills for 5 years.   So far, my plan is simple.  Find out what the skills are and what the level is, and provide suitable learning material.   Test prep is a great opportunity for this effort.

But at some point the only people who really need 99% in anything are those who really want it. When I get to the point where I'm helping with sign ups for AP Calculus, AP History, AP Literature, AP Civics, Orchestra, Play Practice, Cross Country and I don't know what else, we're going to have a goals planning session and make some choices.  But that is many years away and I've changed my mind before.  If I'm dropping $250,000 for college, we're back to 99% and this is not negotiable.

#5  Tests
There is a really great article here summarizing the NCBI's grouping of skills.  What I find most interesting is the discussion of problem solving on the PISA, that international test on which US students deliver a spectacularly inept performance.   The paper also evaluates graduate placement exams.  Cognitive skills and tests go hand-in-hand.  A cynical parent might be motivated by the need for their child to pass tests.  A benevolent parent wants their child to have the same skills that test makers use to predict success.

Types of Research
Research comes in 2 flavors.  The first half is totally made up intelligence crap that provides a lot of useful sounding words, and the second approach is watching kids work, succeed and fail and applying these words to what is really happening.  I think you know what side I'm on.

There is a third branch of research and that is super secret GAT tests which are good at predicting academic outcomes, and to some extent, life outcomes.   I spent quite a bit of time gleaning cognitive skills from this area and apply it to problem solving skills.   Angela Duckworth's Grit research almost fits into this category but she made it publicly available from the get-go and is the fourth inductee in the Competitive Parent Hall of Fame behind Jo Boaler, Susan Wise Bauer, and George Poyla.  (David Lohman is on the fence.)  The difference between cognitive skills and GAT tests is that GAT tests use a much longer list called "cognitive abilities".  I note these on the chart below.

Blooms Taxonomy
I was hoping to start here, but this is a depricated construct.

Poyla's Problem Solving Method (1945)
This is pretty close to my approach to cognitive skills.  I have lined up cognitive skills to the problem solving steps and this is my focus for teaching.  If a problem solving step requires a cognitive skill that isn't there, we work on it.

Some math workbooks start with a very detailed section on problem solving strategies.  I was very excited about this section until my son applied a strategy to successfully solve a problem without knowing what he was doing, then I ripped the section out of his book.  I've noticed these books work step-by-step with scaffolding.  I've talked to parents who's kids used these books and struggle to get a high score on the COGAT.  I'm not using them anymore or recommending them.

Critical Thinking
I think there is a big overlap between Critical Thinking skills, Cognitive Skills, and Problem Solving Skills.  Any 2 should almost define the complete system with the addition of Working Memory. Working Memory is a necessary prerequisite to using these skills.

The critical thinking list strikes me as overly detailedThese appear to be things derived from lower order cognitive skills.  For example, a critical thinking skill is "observing similarities and differences" which should follow from the higher order Problem Solving skill would be "stare at the problem until you understand it".  I think the COGAT test agrees with me but I'm not sure what they would call that skill.   Maybe "ability to compare things", maybe "see details in things".

The List

I'm going to take Poyla, a critical thinking list, and an Executive Functioning list and organize it into my biased construct with cognitive skills.  Finding a list of cognitive skills is impossible so I created an unathoritative list from the lists available that I think appear on GAT tests. There is a great list on that looks like it is reading-comprehension-centric but I don't use it.

My interpretation of Poyla is over simplified so that it applies to 5-9 year old children.  I would have a different presentation for different age groups.

I'm surprised that no one has done this before (curse you cognitive researchers) but if researchers had been on the ball for the last few decades I wouldn't have started this blog, my writing skills would stink even worse than they do, and my slightly above average children would never have had a shot at cheating their way into a GAT program nor succeeding in it.

There is a much looser connection with Grit than I would like.   Duckworth's research is on a longer term connection between work and fortitude and outcome.   I need a really short term connection, like the time it takes to sit for a test.  The Grit column has weak associations so I didn't include Grit in the chart except as notes under Executive Functioning.

It wasn't until I sat down to do this comparison that I realized just how bad the list of cognitive and critical thinking skills are.  They are either too narrow, incomplete, or more commonly too broad to base a curriculum on.  I have found that problem solving skills are well defined and concrete, easy to diagnose and best of all, make a great approach to beating a GAT test or getting an A in a course. For this exercise, in the back of my mind I'm thinking about GAT tests and how different problems would use what skill, and this approach is tailoring my framework.

Note that the "Understand the Problem", "Solution Strategy", and "Execute Strategy" sections have such a high degree of overlap that many of the activities within either section could easily happen in the other.    In fact, for most children the first 3 steps are a blur of activity.  For example, on a pattern problem does pattern recognition happen when understanding the problem or solving it?  Part of the problem is that cognitive skills tests have well defined rules and the solution strategy is almost a foregone conclusion.  The example tells the child exactly what to do.  The other problem is that children are not properly trained to spend most of their time analyzing the problem and usually just jump in to solve it - prematurely I might add.

Poyla Problem SolvingCritical ThinkingCognitive SkillsExecutive Functions
Understand the Problem
  • Read the problem
  • Understand the problem
  • Use all elements in the problem
  • Fill in missing or implied elements
  • Eliminate distractions
  • Highlight key elements
  • Make assumptions
Information Seeking

Visual Spacial Processing
Working memory
Attention to Detail
Identify Patters
Identify Similarities/ Differences
Inductive and Deductive Reasoning
Resolve ambiguity (GAT)
Ignore Distractions
Flexibility (thinking modes)
Pattern Recognition
Solution Strategy
  • Look for short cuts
  • Eliminate incorrect answers
  • Apply examples
  • Draw a [mental] picture
  • Break problem into steps
  • Find subset that solves the problem
  • Try an easier problem, work up to harder one
  • Look for patterns
  • Solve it backwards
  • Guess/check or try all options
Problem Solving
Working Memory
Problem Decomposition
Apply examples (GAT)
Eliminate answers (GAT)

Problem Solving
Decision Making
Apply rules
Sequencing (Project Management)
Set Goals (Grit and EF)
Execute the Strategy
  • check progress
  • Try different approach
  • Abandon assumption, try again
Analogous reasoning
Similarities/ Differences
Applying rules

Working Memory
Meta Cognition
Spacial Reasoning
Analogous reasoning
Mentally fold (GAT)
Self Control
Overcome setbacks (Grit)
Maintain Interest (Grit)
Diligence (Grit)
Check the Answer
  • Check solution
  • Try again
  • Start over
Evaluation Rethink assumptions when answer
isn't ther (GAT)
Finish the Job (Grit)

The solution strategy section is the biggest gap for Critical Thinking and Cognitive Skills literature.   The Poyla list has an important set of learned skills.   Experiments with EF programs proved that kids with EF training do much better on GAT tests (by a ridiculous margin).   Conversely, Problem Solving skills don't really define "Understand the Problem", yet cognitive skills break this section down. This difference is most pronounced on non-verbal tests.  After 1st grade, all tests have a greater portion of verbal and quantitative questions.

I think the main difference is that Poyla's list as I represent it doesn't care what the problem is and is silent on the assumed skill set.  In practice, it is usually geometry theorems.   GAT tests have a well defined set of skills for problem solving, but don't care about problem strategies because the problem strategy is pre-defined.  For GAT tests, the most important competitive advantage comes from the first and last sections - understanding the problem and checking the answer.  I know that from coaching.  Anyone can learn to rotate triangles.  It's much harder to teach patience,carefulness, and diligence.

There is a list of critical thinking skills that can be found here that looks like it applies almost 100% to reading comprehension questions.   My list primarily applies to all other question types but not reading comprehension.  Ironically, I feel strongly that reading comprehension is a great practice for non-verbal and cognitive skills tests.   The two reasons are working memory and understanding the problem, which combine to form about 65% of the magic.   Reading comprehension is great practice for both skills.

This brings me back to my goal of Test Prep Math and why I'm spending my week off working on it. My working theory is that a child who is patient (understand the question) and careful (check the answer) and diligent (tries again) will have an advantage both in school and on any test over a child who does 1,000's of figure matrices or arithmetic problems.  In fact, hurrying through a worksheet with lots of problems may teach speed over patience, carelessness, and boredom.  Working memory is essential and working memory is not exercised with fast, easy problems.   I'm closing the gap.

For first grade, this is what I have in mind.  Take a figure matrix.   Throw out the format, because it's copyrighted.  Come up with something that has the same cognitive objectives but is so convoluted that when the child asks "Did I get the right answer?" the parent has to spend 15 minutes staring at it to see if the child was correct.  I'll work on it this summer.

Saturday, October 17, 2015

Impact Coaching

My kids woke me up this morning at 6 am which would have been great if I didn't stay up late last night reading a book I couldn't put down.  One of the TWO children's librarians at the library at the end of our block recommended it.

As you know from previous articles, reading for a boy between the ages of 8 and 10 is a big challenge.  We managed to survive on reading junk food.  As a competitive parent, however, I'm feeling nervous about middle school, especially the big testing year.  One Saturday morning, recently, my 2nd grader and I were loudly searching the children's shelves when across the room came the response from the children's librarian. I thought she was a student.  Instead, she has read every book published for kids and teens and we left with a stack of good books.

A week later, we went a bit earlier to the library and found a different children's librarian, again appearing to be just out of grade school, albeit with ear rings and tattoos.  I described my older son in detail and he recommended some of his favorite books.   He warned me that some of them were for teens.   Therefore I am reading these ahead of time to ensure the content is appropriate (my values don't match most authors or screen writers).  So far each book is better than the last.

My reading coaches are at the end of the block.

On to the GAT test.  I like to leave my best advice at the end of my article to weed out impatient readers. Impatience is taught by parents and impatient kids are at a distinct disadvantage on the test. Perhaps these parents are too busy because of all the things they have to do, things which they really need to eliminate, starting with their cell phones and social media pages.  Since this whole articles is important, I thought I'd start it after a boring preamble.

When I started my quest, all of the material I found specifically on the GAT test was prepared by people who believe that giftedness is some how hereditary or a gift.  Like it magically happens.   I can't take advice from people so stupid.   I felt like a lone survivor on a raft in a sea of morons.  I had only one person on this blog challenge the law that intelligence is 0% genetic, but just in case  I developed overwhelming crushing logic to silence those who need a little help thinking more clearly.

A few years later, I know exactly which books do what and can lay out a program for 12, 6 and 3 months for anyone.  Suppose this stack arrives in the mail.  What do you do next?  The problem for most parents is that they have no experience "teaching" or "coaching" a child through this type of material.  Worse, you only get one shot per child and you can't blow it in some cases.  In other cases, you can try every year.

I've been putting bits and pieces of coaching advice in my articles over the years.  I want to highlight the starting elements in this article.

The Books
Unless it's crunch time, the books I use cover the full range of skills and skill levels.  I always keep easy and hard, academic and skills based material for both language and math.  For lack of time, vocabulary comes in one flavor - slightly hard.  On 4 nights a week and during a double or triple session on Saturday morning, the material and my child's attention span and energy level determine what will get done.

In most cases, I encounter a problem with the material that there are only 2 types.   The first type is too easy, and the second type is way too hard.  The test prep material is too easy unless you start at age 4, but it has a different role.  Since we have a definite time limit, and this test is all about thinking skills, we're going to use the material that is too hard.  When I start this type of program with a kid for the first time, I usually just jump in with way toi hard material and 6 months of hell later use a balance.  I call this Catch Up.

The Chart
The biggest problem with the test prep program is that it has a definitive time limit.  The goal is to cram as much skill into your child's brain as possible before the test.  You might only get about 20 good minutes a day.  Your child might start out taking 20 minutes just to answer the first question. This can be unnerving for a parent.

My solution is to create a poster.  Across the top, I draw a time line ending with the test date.  Down the left side, I list all of the workbooks that I am going to use and other activities like reading/read-to and forced fun. In the row for each workbook, I'll just write all of the page numbers sequentially in the space allowed.  For something like Building Thinking skills or a COGAT test prep book, where we jump around a lot, each section gets its own row, or I draw boxes around the page numbers and mark the section.

As we go, I cross out page numbers.  I write check marks for things like forced fun (HAVE 20 MINUTES OF FUN, DARN IT!)

As the weeks go by, I can see how quickly my child is going and this calms my nerves.  Sometimes we have to adjust the  material, which I can do because I'm carefully gauging progress.  Sometimes I notice that we are going to fast and will run out.  Usually I just notice what started out as painfully slow becomes much faster over time.

The Process
This topic is going to be a series of articles on its own or you have to dig through the whole mess of my blog to find tips.

For starters, the process I assume is a parent sitting with the child coaching the whole time, checking the work.  In my experience, it takes a long time, maybe 6 to 12 months, until the child can work independently.  This is probably the biggest single benefit of my mission - redirecting parents from a myriad of distractions back to one-on-one work with their children (i.e., throw away your cell phone.).

The main benefit, over and above an increase in academic skills, is a social secure and socially effective child.  I can watch a group of children and spot a child who spends a lot of time with his parents in a matter of seconds.  Try it some time.

Next, a child working on one really hard question for 45 minutes is very powerful, doing 30 worksheet questions in 20 minutes is practically useless.

Finally, a coach is a coach.  Watch a baseball manager (go Cubs!) or a football coach standing on the side lines.  What do they actually do in terms of throwing balls or catching them?  Nothing.  In your case, this means not explaining things and not figuring things out for your child.  Just keep score and ask lots of questions.  Be like Yoda.  Let the child fail.  Don't make it painful.  Don't pressure your child.

I reserve the right to add to this article, but the cryptic coaching proverbs will end up being future articles.  For now, this summarizes my mission:
  • You have a duty to build the cognitive skills of your child.  It's not going to happen in school.
  • There is material out there that you need.
  • You have to pace yourself.
  • You have to invest lots of one-on-one time with your child.
Once you subscribe to this approach, and many, many readers have already, you are on the way to a successful child through 4th grade.  After that, you have to do it all over again at a different level with different goals.

Monday, October 12, 2015

Oragami Jazz Festival

Last Friday night, I had to baby sit at my arch rival's house.  Conveniently, his name is Arch Rival.  His wife Nem was busy and he had to speak to a preschool program about his children's gifted program.   In Chicago, we call GAT "options". 

I sat there for an hour in the family room while the kids slept.  This room looks like a library only with more books than could fit in a library.  Archie goes to 2nd hand stores and buys boxes of children's books.  But that's not the worst part.  There was a book on tape coming from the room of the 2 girls.  It was audible when I arrived a few minutes before their official bed at 8 pm, and it didn't end until about 8:40 pm..  Are you kidding me?  Books on tape during bed time?  Curse you Arch.

Saturday morning, I went to the library with my youngest and we checked out stacks of books on tape.   After a few hours of listening, my kids and I decided that this was not going to be our thing.

It's hard to compete with the Rivals.   They don't follow my academic regimen.  Instead they become super readers and eventually their kids get into gifted programs.  Nem teaches high school math so I am going to have a hard time competing on that front.  The kids are super nice and socially well adjusted.   And we both do music.

Music is one of those activities like reading wherein if you do it well, everything else will follow, everything else being success academically and otherwise.  My oldest and I practice together every day, so he gets a daily lesson if needed.   The youngest is going to join this routine when he starts band, but for now he is expected to teach himself piano.

For my wife's birthday, we took the kids to the Jazz Showcase to hear a Tammy McCann with the Chicago Jazz Orchestra.   On Sunday's at 4 pm, the Jazz Showcase has a 60 minute performance and kids get in for free.  The performance was amazing and I'm glad I live in Chicago.  We went so that our kids could see a big band.  I didn't expect Tammy McCann to be so darn good.  (Normally, I would have invited the 5th grade Rival because he's a friend of my son's, but this was a birthday outing with dinner to follow.   There was a 3 piece jazz band playing at dinner, by the way.)

Here is a picture of the Test Prep Pioneer and his brother Test Prep Ninja with Tammy.  We almost always talk to the performers after each show.  In this case, it was hard not to.  Tammy was extremely bright and her extremely bright children were there.  I wanted to interview them at length, but since that would be totally inappropriate, I had to settle for confirming the fact that her kids are very friendly and articulate. Her husband was in attendance, and from the stage she announced that he is running for a judge position.  If we lived in Beverley, they would make great rivals, but we don't, so I'll just admire the family from afar.  

During the show, my kids replicated the stage with origami.  The oldest is on the left, and always liked origami.  The youngest is on the right, and looks a lot bigger than he really is because he is closer to the camera.  He went to COGAT folding question school so can fold almost as well as his brother.  If you look closely, you can see Origami Tammy next to the piano.

This doesn't fully address my problem with the Rivals, but it's a start.

Thursday, October 1, 2015

Test Prep Math Level 3

August 2017 Update - This article is now a bit dated, but I am reluctant to delete it. Test Prep Math Level 2 and Test Prep Math Level 3 are big hits. Both are now in their 3rd edition, and both have the addition of a quantitative section and a visual spatial section that followed the same successful formula as the word problems.  I had all of this material but thought then and now that the word problems would pay off the most down the road, so this is where I started.

Test Prep Math Level 3  is making it's debut.

I created this book because after buying and trying dozens of workbooks from 1st through 5th grade, I've been really disappointed.  There are 3 primary groups of math workbooks: one group is too easy, one group overdoes computation and calculations with no learning or thinking involved, and the third group goes into advanced math.  My kids don't care about number theory at a young age.  The GAT practice test books are great for their role - to review the format and find out before the test if your child is going to get confused and blow it - but these books aren't good at teaching skills and are really easy in my opinion.   By age five, my second child completed all of the GAT test prep books through 6th grade and I don't think we learned anything.  I didn't even use them with my first child and just stuck with more difficult material that I created.

I spent 5 years researching GAT tests, 2 of it trying to reverse engineer them.  You'll see in my articles that I slowly built a list of skills and abilities that these tests were trying to measure, and then focused on teach them.   The problems in Test Prep Math are designed to teach these skills.

I'm getting questions about whether or not younger kids could use Level 3.  Since the "View Inside" isn't available yet for the book, I'm going to show you sample problems and describe how they unfold, and then comment about Level 2.

I expect the child to do the arithmetic in their brain, even though that might take a few tries to get it correct. There is a 5 page coaching guide about how to get through this book, and in the solutions I include commentary on harder or unusual questions.

Here is the first problem.  I tried to make it as easy as possible simply to introduce the thinking that is going to be required and encourage the child to do the problem mentally.  This seems easy enough, but I'm surprised how many bright kids get to the end of the question and forget what was asked.

Dragonflies and damselflies were sitting on a boat.  There were 5 dragonflies and 4 damselflies.  4 more dragonflies landed on the boat.   8 more damselflies landed on the boat.   How many more damselflies are on this boat than dragonflies?

Bonus Question:  A flock of birds comes by and ate half of the damselflies.  How does this change your answer?

Notice that the child has to solve 3 equations.  The pattern of matrices problems is 1 and 1/2 equations (solve one equation and apply the delta to another number), so I doubled it to be on the safe side. There is a new word in the problem that you'll have to google.  Then for this question, there is a bonus question that requires tapping the working memory once again.

Question 2 has the wrong answer!  Arrgh.  I'll have another edition out to fix it in 2 weeks.  I undermined myself with a last minute edit to the question.  Fortunately, all of the solutions show the equations so mistakes are easy to spot.    Ironically, since I've been making my own material, my kids and I have had lots of questions and/or solutions that didn't work   They have a whole different approach to math, but I wouldn't intentionally put this in a book.

During the next 40 or so questions, the characters are introduced and the plot slowly unfolds (as much of a plot as I could muster given that I'm working with as much space as a haiku).  At about the middle of the book, the questions look like this:

In the center of Metroville, there is a super villain named Destructovil breaking into the Metroville bank.   Rubberband girl got a distress call on her cell phone, but she is on the south end of the city in a train station. There is a train leaving at 3:00 pm that will take her to the Metroville bank.  The train takes 12 minutes to go from the train station to the bank.  She has to wait 4 minutes for the train.  Speedy Man is in the next town over, but he can get to the bank in 8 minutes because he is Speedy Man.  First, he needs to finish his cup of lemonade because he's too thirsty to be speedy.  That will take 7 minutes.  It is a very large cup of lemonade.  Destructovil's getaway car is coming to pick him up at exactly 3:14 pm.  Who will save the bank?

Bonus Question:  Who is Rubberband girl?

My 10 year old told me "your problems aren't lame."  I think that was a compliment.

If you had been doing all of the problems, you would be able to figure out who Rubberband girl is.  If not, you have to refer back to a previous problem (officially an academic skill which I call for repeatedly) to figure out.  Note that this is not a question a child can read once or twice and then solve.  I also use time a lot because it requires an extra degree of thinking to do the arithmetic.

By the end of the book the questions fill the page and become even more convoluted and goofy (all with proper grammar except when the pirate character talks.)  At this point, we're basically in math-reading-comprehension space, which I invented.  I'll write a whole article on reading comprehension because I'm becoming more and more convinced that it is a pillar of success on a GAT test, and by way of the GAT objectives, to a strong academic career.  As the book progresses, I start to move on to more advanced skills and because of that, some of the questions look like brain teasers, but they aren't, because everything can be derived logically after a few days of debate.

I'm working on Level 2 for younger kids which removes the need to read questions over and over again to understand what the problem is.  I'm using a math abstraction that I invented to make things really taxing on the brain.  I think some kids will find Level 2 harder than Level 3 and vica versa, but in both cases I'm seeing results and am pleased.  Level 2 will take a few months to finish.  By next year, I'm going to introduce Level 1 which I can only describe as diabolical.  Level 1 was in the works since the beginning, but 3rd grade is the biggest gap for people right now so I started there.  Then if I'm not completely exhausted, I'm going to work on Level 4 which teaches the Most Powerful Math Skill ever, which I can't find anywhere in any elementary aged book, but which we routinely use to solve anything.

So if this sounds like something that fills a need in your At Home Schooling or test prep, give it a try and let me know how it goes.  Provided I don't sell more than 12 copies (which is going to be the case unless I find the time to do any marketing), I'll respond quickly.

Friday, September 25, 2015

Advanced Math - Or Not

I'm haunted by recent reader comments about which is the best 3rd grade math book to use with 1st grade kids.   The small issue is which book to get.  The bigger issue is whether your 1st grader should be doing any math at all.  I say this as a parent who put kids through advanced math - because they are perfectly capable of doing it - and watched them completely lose interest in math altogether.

First, which book?  At least one reader recommended Challenging Word Problems published by Marshall Cavendish.   This book includes 2 types of material: standard math, on par with the Every Day math program that our school used to teach, and word problems which have 2 parts.   The word problems are good, and I think it's doable by advanced second graders and super advanced first graders.  It's better than the other workbooks I've seen.  If I home schooled math, I might use this book.  I'm a fan of Every Day math with supplemental material.  It's a toss up.

The problem with advanced math is that a kid will gradually get to the point where the concepts like fractions and decimals are understandable, as well as the extra calculation required by 3 digit problems, become time consuming, tedious, and irrelevant to a 7 year old.  From that point forward, the child is learning to dislike math.  Then the 4th grade train wreck happens.

Now the big problem.

Our school just switched to the Connected Math Project (CMP) from Michigan State for 5th grade on.  (It's an accelerated program so the kids in 5th grade use the 6th grade text.)  The approach is to assign homework every night, which the kids hopefully get most of it done, but wrong, which they discuss the next day.   It is problem centered, and no help, examples, or text book is provided.  Just problems introducing new math concepts.  This program is the cutting edge of math education research (aka Jo Boaler) and I was stunned to hear it presented.  This is how I think math should be taught.

For 1st to 4th grade, there is still the need to introduce math concepts and computational skills.  There is nothing out there like CMP below the 6th grade level.  The best research, including Boaler's, appears to be at the middle school level.

Before I spent 2 years reverse engineering the GAT test, I did a lot of research on early math.  I put together a summer math camp for 5 and 6 year olds (which was a blast for all of us).  We did stacks of workbooks and flashcards at home.  But post GAT test, I have a completely different attitude.  If this test is a good predictor of academic success, and it is based on measuring academic and thinking skills, why not just teach these skills to kids and let them teach themselves math?  If they have the skill set, they can just walk in to math at any age and master it on the spot as their interest dictates.  This is the same skills set that kids can use to walk into a test completely unprepared and do really well because they can think through the questions.

We're now working through Test Prep Math Level 3 which I'm going to release on Amazon.  I've been crafting problems using fairly simple math (by my standards) that are designed to exercise the skill set I see in the tests.   The first problem is doable if you can keep 3 equations in your brain at the same time, but by the middle of the book I expect an advanced child to spend 10 minutes just trying to figure out the question and will most likely take more than one try to get it right.  All with basic math.

If GAT tests required a certain level of concentration and skills, I think a good way to prepare is to spend a few months struggling through material that requires 2 or 3 times the thinking.  That is what we did.  The biggest disappointment in the test prep industry is the lack of challenging material.  I speculate that if a test prep book requires the 97th percentile of thinking the book would not have much sales.  That is why my first printing run is going to be about 20 copies, and it will therefore probably have a high price.  Nonetheless, you can check it out soon to see where all of this has led me.


Wednesday, September 9, 2015

Skill #2 For Test Prep

A while back, I outlined skill #1 for test prep, which is "Read the Question".  I've had a hard time articulating Skill #2, but I've been practicing with my Parent Forum and I think I'm ready.  Brace yourself.

Skill #2 : Get Problems Wrong

The general consensus on learning is to keep kids in the learning zone where they have some competency and can apply it to a stretch problem.  The teacher provides scaffolding, the child learns, and everyone is always happy.

When we do test prep, academic work, or other important life activities, I'm generally looking for my kids to screw up and get things wrong.  I choose material with this in mind.  This is a really counter intuitive parenting and academic coaching but it is, in the end, the way to go.  Everyone is not always happy.

When I do test prep, I'm much more interested in material that is way, way, way over their heads and mistakes and wrong answers are the norm.   There were two things that motivated me.  First, it seems way more efficient to cut out all of the stuff they already know and just concentrate on the stuff they don't know.  Secondly, when I studied for the GRE about 100 years ago, I consistently got 50% or more wrong on practice tests leading up to the big event and managed to get way over 99% on the test.  This was back in the day when there were 193,234 vocabulary words on the test.

It turns out that there is very solid logic behind this approach as it applies to cognitive ability tests like the COGAT.  These tests aren't looking for children trained at getting lots of problems correct.  These tests are designed to find thinkers who can come up with an action plan when things aren't going well, who can navigate the unknown.  The tests are designed to lead the child into an answer set that doesn't have the answer the kid is looking for, or doesn't have one clear answer.  As far as I can tell, there is very little content in a test prep book that is anything close to the actual test.

When your child is used to getting things wrong, good things happen:
  1. The child is not bothered by failure.
  2. The child learns to go back to the question and read it again.
  3. The child learns to just plod through options one at a time to find the right answer.
  4. The child learns to mistrust questions, to be suspicious and skeptical of answer sets.
  5. The child learns a bunch of survival skills that aren't learned on an arithmetic worksheet.
These are the qualities of a good inventory, scientist, or researcher.  These are the qualities of a good student.  This is the stuff of which grit is made of.  These are the qualities that make for a high test score.

There are downsides to this approach.  First, it takes a few months for both the child and the parent to be deconditioned of the normal approach of spoon feeding the kid concepts and then expect perfection on lots of routine, easy, boring problems.  This can be a time for whining, complaining, arguing, and sometimes shouting on the part of the parent, not to mention the child.

The second downside is that when you have a kid who is unafraid to work ahead 5 or 6 grades, normal academic work is really a downer and bad grades on easy tests might result.  I'm personally hoping that by middle school or high school the material rises to meet the skill set.  Fortunately, 4th grade math scores don't show up on a college application.  If anyone has an answer to this problem, please share.

If your child consistently scores below 50% on material or workbooks that I recommend for test prep, now you know why.   This is exactly why I recommend the material.

Monday, September 7, 2015

Smart Cookie NNAT Review

I bought Smart Cookie's 3rd/4th grade NNAT test prep book.  Chicago doesn't use the NNAT, but I am wondering if this would be good practice for cognitive skills in general.  I would say "Yes" if you are studying for a 1st grade test or doing a final format check for the NNAT with older children.

The evaluation was performed by a 7.09 year old  who will start 2nd grade tomorrow.

He did the 1st 10 questions in just a few minutes, which is bad.  Even worse, he did 8 more without being asked.  His error rate was 40%, which was good, but he corrected the incorrect answers immediately with only one more mistake.  I got no complaining at all, which is also bad.

For cognitive skills to get a workout, I would expect each question to be more of a struggle.  This summer we've been working with more advanced material that I created.  Each question takes 20 to 45 minutes and 5 tries to get correct.   It's really easy subject matter.  The only thing it teaches is thinking.  

Overall, I'm pleased with the Smart Cookie content for younger kids and those who are just starting out their test prep for the first time.  For most of the country, 95% is a good score on a GAT test and this book is good enough for a 5 or 6 year old.

We'll finish the book and report back later.

Wednesday, September 2, 2015

How To Test Prep for the NNAT.

Here is the scenario.  Your child is in Kindergarten and you have to study for the NNAT.   You don't want to spend $500 on practice books, especially ones that don't help, and your time is limited.  Your child can concentrate on super hard material for up to 15 minutes maybe 4 times a week.  If your child can concentrate for more than 15 minutes, then you and I are probably not using the same material.

My idea strategy is to get a sixth grade practice test and spend a day or more on each question.  Maybe a week.  Of course, your child will be baffled.   So you ask him to tell you verbally what is happening in the question in terms of the big 4 - Shape, Size, Color, Count, and then describe any movement or rotation.   Movement is horizontal, vertical, diagonal, and the pattern where there are 3 items in each row or column and they switch positions.  He will describe what is happening in each and every answer choice.

If he lacks the vocabulary to describe anything or he doesn't see something you ask questions and provide the vocabulary. Give him synonyms and antonyms for everything you see.  Use big words and big sentences. His brain won't really understand a concept until it has the words to describe it.  Maybe on the first few problems, you help after 20 minutes, like a brainstorming team member.  For the first 20 minutes, I usually just say "Keep looking" while my children are subject to this exercise.

Early on, every problem will be new and baffling.  Go slow.  The 15 minutes might be 45 minutes on a bad day.  Wrong answers will be the norm, and there will be bad habits to correct.  As the test approaches, you'll wonder if the pace will pick up.  The pace will pick up as concentration skills grow and he begins to see things.  The error rate might always be high.

Next, you spend the other 10 hours of weekly At Home Enrichment on learning tasks like reading, projects, puzzles, reading, maybe some phonics, a few pages of Vocabulary Workshop once a week, and you reading to him.  There are a few families that I know in Chicago who get multiple siblings into the same GAT program (never 2 boys, however, which is an honor that belongs solely to me until proven otherwise.)  These people, as far as I can tell, without watching in through the window, simply read a lot.   Curse them.

You keep backup material handy, like an easy math book or activity book of some kind.  On bad days (40% of the time), he's sick, exhausted, sleep deprived, or generally crabby.  In order to maintain and improve the daily routine, and not waste your precious test prep material, you compromise and give him his choice.  He chooses the easy workbook.

Also, for $10, you can get a 2nd grade standardized test and just do random sections.  This prepares him for walking into a test and being surprised with new and hard material.

This may not seem like an obvious approach to test prep, and it isn't.  It's an approach to building the cognitive skills and academic skills that the test is looking for.  It's a much more sound approach.  This approach is much more similar to test conditions than doing 20 easy problems in one sitting.

My ideal workbook has 100 questions and is for the 6th grade.  $30 or $40 is a good price.  I have a problem recommending these books because we didn't buy any and no one is paying me for a recommendation, but I can offer some ideas.

Mercer did a good job with the COGAT books, and has level E.  But Mercer offers a single practice test for $30.  (Note to COGAT parents - going up levels means switching from pictures to math and words, which is a problem.   Get a NNAT book instead at higher levels.  I wish I knew this before.)

Smart Cookie does a great job, and for $36, they offer 4 practice tests. I liked their COGAT material because it was less standard fare.  The routine stuff was already taken before they entered the market.  But they only offer up to Level D for the NNAT unless you can find a used Level E.

Bright Kids is a New York company and prices for New York.  I never bought any of their material.  For $45, you can purchase a single test.  But they have level E.

My main question is whether or not the difficulty level of the Smart Cookie Level D (3rd/4th grade) is hard enough for a 5 or 6 year old and whether or not level E is overkill. Probably.  There are 4 tests, so there has to be a mix of material, including easy questions, which would be a good thing for optimal learning conditions.  I think I would go this route.  If I had a year to practice, I think I would do this a little at a time over a 6 month period, and then break down and buy the Mercer Level E a few months before the test.

And that's it.

Friday, August 21, 2015

COGAT Question #9

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

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

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

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

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

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

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

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

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

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

The correct answer is the last one.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Saturday, July 25, 2015

The Perfect Day

I'm haunted by the tripart equation for giftedness:  cognitive skills, interest, will.   As a mathematician, I'm very comfortable with exploring, measuring and improving cognitive skills.   At some point (it's 4th grade), the child has to fly free along the dimensions of interest and will, and all the cognitive skills in the world won't save him from drowning if he doesn't care.

I have one rule to deal with this issue.  Rule #1:  If the child devises an interest or project, drop all preassigned At Home Academic Material from the schedule to make room.  We've ended up with goofy stuff over the years because of this rule, including lots of crafts.   I feel like I need a rule #2 or #3, but I am still a parent of young children, so I haven't invented these missing rules.  For now, it is clear to me that the projects or interests that are self-devised are the ones that produce interest and will, or from the standpoint of a different theory, grit and success.

Today was the perfect example of what I'm talking about.   With the older one away at camp, the younger one has been thinking about what he could do for camp.  Why don't you have your own camp?  I suggested.  Great idea.  There was lots of signage and planning and other preparation.  Fortunately, the "campers" were his peers at school, and we ended up with a slightly unorganized reluctant counselor and 8 Type A Leadership-type campers.  This pilot only included kids from his school who lived nearby to avert disaster for me.   Worked really well today, and when we do it again I'm going to expand the program.

Here he is checking the schedule.  We made T shirts as well.

This concept is based on something quite extraordinary that happened down the street from us a few years a go.  A group of 7th grade girls started a 1 week day camp for little kids.  I think they ended up with 30 kids each week for a few weeks.   It was an extraordinary camp and became competitive to get a slot.  It was known as "Camp Norwood".   Our kids attended.   The girls went on to college, graduated, did something service oriented in Kenya, and generally exemplified what I consider a Job Well Done for their parents.  I'm still in awe of all of the effort and results.

Therefore, as the inventor of UnOriginality in Parenting, I stole the idea, downgraded it to age 6, and went for it.   I'm not sure what my child got out of the whole program, but I could see the beginnings of something really good for a few of the other kids,  I think this endeavor was win-win-win-win...   My kid got to make posters and lists, and a few real leaders emerged from among his friends.  

One final note from my experience today as the helper and cook.   Girls and Boys are so different in every way that they might as well be from other planets. I've got a friend who teaches high school math, and this type of thinking causes her endless headaches.  She says "They are 'People'", and I know what she means; girls tend to get the short end of the stick in stereotyping as far as math is concerned, which is totally unfair because they are perfectly cut out for real math in the eventuality that the US school system will ever get around to teaching real math.   But these people are really from different planets.

Thursday, July 23, 2015

Struggling Through Test Prep

A reader commented recently that her child was struggling with a some math/vocabulary question:  "Struggling with summer math.  My little one is not getting this 'more than' and 'fewer than' question, A has 7 coins, B has 4 fewer than A, how many coins A and B had altogether?  Concluded today's homework by screaming for an hour".

This situation seems very normal to me, and I lived through it, and my reply is to give the kid a snack and expect to spend 1 to 3 weeks on this question.

A few days later I started having flashbacks to all of the crying, and the high error rate, especially with the word "fewer".   My child took months to get the word "fewer".  It used to drive me nuts.

The process of learning vocabulary for little kids is a mirror of the cognitive skills test.  Parents are tossing out big new words left and right in long, multi-clausal sentences from birth (the good parents are) and the child has to use context, inference, similarities and differences, classification, analogy, and a host of very sophisticated mental skills to figure out what the words mean just to survive in his own house.

"Fewer" works at even a higher level, because it challenges the child's world view.  "More" is much simpler. More means "give me more".   It means better, and it means me.   "Fewer", on the other hand, introduces injustice, fairness, trade offs, and the fact that if I get more than someone else will get less.   Once you start using the word "fewer" with a little kid, you've introduced philosophy, and it takes a while for the child to digest it.

Learning vocabulary is Extreme Test Prep for a 2 or 3 year old.

I've been reading the works of this guy named "Robert Thorndike" who said essentially the same thing about reading some 80 years ago.  Reading early is Extreme Test Prep for 3 and 4 year olds, and it is the test in a nutshell on a daily basis in the same way I outlined above for vocabulary.   Way back then, the psychology industrial megaplex was on the verge of figuring out how to make kids smarter until then they discovered all of the money to be made from assessment tests. The only country that escaped this trap was Finland.  When a child is born in Finland, an agency worker delivers 2 books to the bedside, one for the child, and one for the mother.

I read an interview from 2006 from the author of the COGAT, David Lohman.  In the article, Lohman laments that practicing for a cognitive skills test can increase scores 5 to 10%, and even more if coaching is involved.  I have found in my own work that consistent parent coaching can raise scores by more than 50%.  Lohman complains that this effect has undesirable consequences.   Personally, I have found desirable consequences, including a brighter child who is more apt to do well in and enjoy school, a child who demonstrates insight and sympathy, a child who has good judgement and who I can trust.

Here are your options on how to pass the test:
1.  Talk a lot at age 2
2.  Read a lot at age 3 and 4
3.  Test prep a lot thereafter

Now that I'm past the early test, awaiting the next one, I've become a lot more interested in developing really good thinking skills and a love of learning than I am with grades or the annual academic challenge called the achievement test.

The undesirable consequences that Lohman was referring to are related to the reasonable observation that academic achievement is comprised of cognitive skills, interest in the subject matter, and the will to do it.  He noted that giving a child the edge in cognitive skills who doesn't have the other two qualities can result in a more desirable candidate being left out of the program.

My problem with test prep is that building cognitive skills might jeopardize or diminish interest and/or will and in the end undermine the eventual goal.  This is weighed against the assumption that if a child doesn't have the cognitive skills and you don't teach him these skills, the likely result will be frustration and not interest in academic subject matter and the will to avoid it.

Second grade is the year I stop all at home academic work of any kind other than lots of reading.  Last time I did this, it resulted in 2 years of A's.   The problem this year is that I'm working on A Very Special Math Book and my editor is the second grader in question, so he's stuck doing these math problems.

Sunday, July 12, 2015

Summer Update

I've been reading academic papers and building test questions.  Thanks for asking.   I saw a quote in one of the two papers I read tonight.   I'll have to paraphrase because I didn't write down the page number. Vocabulary and Math Problem Solving Ability are the best predictors of success on these tests!

So for anyone following my advice, you're on track.

Also, I've been mentioning reading as the #1 thing to focus on.   The psychology researchers who motivated these tests state that learning vocabulary words and reading teach a person how to think.  I'm paraphrasing, but talking and reading can basically put your kid 2 years ahead before preschool.

Also, there's this great paper by Lohman describing how researchers and practitioners start with this idea that intelligence is fixed and well defined, and little by little in their papers over their lifetime they change their opinions.

Anyway, my steady diet of math and vocabulary workbooks has been derailed by Big Activities.  Big Activities exercise grit (perseverance and resilience), which trumps Cognitive Skills as the biggest predictor of life success.  So if any child comes up with a project they want to do, I put my own agenda on hold.

One of my children likes all things people.  Older kids, younger kids, any kids.  Any class that involves teamwork and brainstorming will be a hit.  We signed him up for theater classes, which he liked because it involves working together, but not because he is committed to acting.  5 years ago, I created a summer math camp on Saturdays for 5 year olds.  It was a huge hit, and I assumed he would be great at math.  It was a huge hit because other kids were involved.  It is safe to say that this one is safe from me ruining his interests because as an introvert, I don't really understand him.

The other one is the opposite.  He doesn't hate people; he just doesn't really need them right now.   At the end of the school year, he wrote, directed, and acted in a play with his buddies in class.   It wasn't better than the plays his friends wrote, but they worked as a team and politics destroyed the effort.   The last week of school he showed up with a complete play and it won by default.

We saw Jurassic World and everyone liked it except for me (worst movie I have ever).  I explained to the kids the role of all the different players involved, from early production, script writing (worst script ever), copyrights and trademarks, marketing ("painting the pig"), and keeping actors from saying nasty things about each other on Twitter between sequels.  I'm trying to make up for all of the talking I was supposed to do but did not when he was 2 years old.

So he said that he would write a book called Dinosaur World.   In between sentence #1 and sentence #5, which is where he is now, he spent a week asking about how to get trademarks since this will be a 10 volume series with movie rights.  He spent hours trying to get past sentence #5 with little luck, since he can't type and at age 6, doesn't have much to say.

Last night his older brother had a friend over.   The little one created a sign called "Book Helpers Registration - Ages 6 to 10" and taped it to a little table we built.  He sat down with pencil and paper behind the table.   I was desperate to find out what would happen.  This was like a sitcom unfolding before my eyes. I yelled for the older boys to come up from the basement.  "What is it?" they asked.  I have no idea but please register so I can find out.  So they registered.

"Book Helpers will help me with ideas about what to put in my book Dinosaur World."  Oh my gosh.   "Really?  Are you kidding?" the older boys protested.   The friend had a better idea.  "I think what we need first is to give you ideas about your book titles.   Maybe it can be Book Title Helpers."

How I envy stereotypical Asian mom's who simply demand that their kids study for medical school.  I don't have a clue what to do with my situation.  Who are these people?  What are they evolving into?

Here are the 10 titles they came up with.

1.  Attack of the Volcano of Frogs
2.  Pink Fluffy Pickles Dancing on your Nose
3.  Attack of the Pink yellow Glasses
4.  The Zombie Nostrils That Came from Above
5.  Monkey-Colored Tissue That Lives in a Pitcher
6.  The Evil Tacos
7.  Attack of the Elephants from Outer Space
8.  The Swirly Toothpaste from Under the Couch
9.  The Bunny from Mordor
10. The Maltesian Birdy