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.