Wednesday, March 29, 2017

The Thinning

I stumbled across this trailer last Saturday.  I was searching for something from MadTV. At first I thought it was a comedy.  After laughing my way half way through, it dawned on me that this was a serious distopian drama about a world with high stakes testing.

There's a scene where a mom is drilling her small child on random facts.   Earlier in the day, my son and I took a walk to get donuts because he finally made some progress on algebraic proofs.  During our walk, I was shouting out things like "Prove the sum of an odd and an even number is odd" and he was articulating the proof in between gasps of air while he tried to keep up with me.  Ever since he expressed an interest in wrestling, the pace of our walks has increased to a moderate jog.

I'm not sure what is scarier, the TV series where children are 'eliminated' if they don't pass an academic test, a country where cognitive skills are tested instead of taught, or a dad jogging with his 8 year old while quizzing the child on algebraic proofs.

It was algebraic proof at older ages where I identified the missing skill.

Some kids look at a complicated math problem and expect to answer it in one shot. That's the absence of the skill.  Skills usually manifest themselves to me in their absence.

Problem decomposition is a series of skills that is used to break a big difficult problem into smaller easier to solve steps.   The core skill is simply to acknowledge that the every problem is made of multiple problems, and that is the missing skill.

I prefer to teach core skills instead of non-core skills.  The non-core skills, including all cognitive skills, math skills, reading skills, and all other kinds of testable skills take too much time to diagnose and teach. By focusing on the core skills, a parent or academic coach can create an environment where the child can teach themselves.  This is preferable, because the term for children who teach themselves is "gifted".

For example, the first 2 core skills are to be comfortable being totally confused by a problem and to be OK getting it wrong multiple times.   In this type of an environment, the child can take on new and challenging learning tasks.  With these skills, the child will acquire a very long list of cognitive skills. In the absence of these two core skills, the child is condemned to being spoon fed grade school level work.

Up to 5th grade, problems that are "confusion worthy" have lots of moving parts and problem decomposition has never been an issue because it falls out naturally while the child rereads the problem (core skill #3).  After 5th grade, multiple steps can hide behind a short problem and I'm observing children looking at the problem expecting to know the answer immediately.

Lately I've been decomposing figure matrices and folding questions.   I've always assumed that problem decomposition was obvious, but as I refine the solution strategy steps and work through previously challenging adult level problems, I'm coming to 2 conclusions.  Problem decomposition is not obvious for these 2 classes of problems and once you see the multiple steps the problems are fairly easy.

I'll keep you posted.

Saturday, March 25, 2017

What To Do With A Five Year Old

This article is going to answer the question "what do I do with my five year old?"  A reader asked the question, and it was a great question that required days of thought, and any time I don't answer a question immediately the reader deletes it.  Curse you, great question asking parent of a 5 year old for your impatience.

There are wonderful At Home Schooling activities for each age.   The At Home Schooling programs I generally recommend are geared toward a really solid year of test prep, both standardized tests and cognitive skills tests.  I wouldn't recommend an intensive course every year, but a couple of times before high school is wonderful because it puts the child way ahead, usually permanently, and contributes to work ethic and grit, test or no test.

You could settle for the "average" that is taught at school, but if you did, you wouldn't be reading my blog.

Age five is by far the most magical time for At Home Schooling because a) the child can't really read yet and b) the child isn't ruined by the awful boring approach to math and reading that is used in school between 2nd and 4th grade. Learning to read is really important because learning to read exercises 100% of all cognitive skills, including those used in math.

Here's what you can do in a year.  First, you can read every leveled reader by every major publisher. It might start slow but by the end your child could do 2 in a day.  After that, you might get through about 10 Magic Treehouse books and who knows what else from the library.  Secondly, you could start with the first Vocabulary Workbook, the pre reading level, and get through it and the next level by the end of the year.  Finally, you could introduce your child to the first Every Day Math Student Journal and do this one and about half of the second one in about 9 months.

If you need a break, you could give your child Building Thinking Skills Primary, and if you want to spend more time with your child, have him start with BTS Level 1 and do it together more slowly. There's also Mind Benders if your child likes this type of thing and maybe a 2nd grade reading un-comprehension test to see if the child can think on her feet.

I've assume that parents in the US would hand their child Every Day Math Student Journal 1 and expect the child to actually be able to do it.   My experience is that the child will take about a week on the first page and get all the answers wrong and complain that they don't know how to do it.   Doing this 4 times a week, week after week, will result in a 5 year old who can actually do second grade math at a reasonable pace for a 5 year old.  But that's not the big payoff.  The big payoff is a child who takes on really tough problems and figures them out, because they will have no choice. Giving a 5 year old child 20 minutes to do a problem that a 2nd grader will do in 1 minute paves the way for big things in the future.  I think this is the secret to gifted in a nutshell.  

There are downsides to a successful At Home Schooling program.  The first one is that the child will be bored in school.  Think of school as an 8 hour break in preparation of the 30 minutes of hard thinking that will take place at home.  A place to learn social skills, cutting, and pasting.   My kids never complained about school after getting through EDM.  The second downside is the need to find a GAT program as quickly as possible.  The third downside is that your child will start to see through some of the things you say and start arguing with you.   The 4th downside is that you won't be able to do this in 1st grade.   This would be a great year to do nothing if you can get away with it, or just focus on test prep if it's a testing year.

Everything I listed above can be done in about 30 minutes a day of workbooks + 60 minutes a day in reading/read-to.   We generally stuck to a pace of 4 days a week for workbooks + 30 minutes extra on Saturday for vocabulary workshop.

Tuesday, March 21, 2017

Figure Matrices and Folding and Lie Groups

Lately I've been dissecting folding and figure matrices and evaluating the core skills that go into these processes.

The goals of all questions on a cognitive skills test are to:

  1. Present the student a brand new problem
  2. With unspoken rules that can be derived by doing the problem itself
  3. Using rudimentary skills that all students should have
  4. To test the student's figuring out skills
  5. Because these figuring out skills determine how well a student will do in school.

GAT programs across the country have been raising the cutoff score.  In Chicago, it's approaching 99%.  It's been 99% in New York for a while.   I used to get emails about lower cutoff scores from around the country, but lately the emails from parents mention scores above 95%.  I'm surprised how many times 98% is mentioned.   In this context, the list above can be refined to include 'really hard problems' with 'complicated rules' using 'advanced skills' to determine who will get straight A's in school on their way to Stanford.

In theory, a student should be able to manipulate a square by flipping it or making it wider.   Older kids will also have to rotate a shape.   Flipping a square is tricky business, because as you know, once it's flipped, it doesn't look like it changed.

My core approach to coaching students works really well, so well in fact, that after studying for a few months for the COGAT, there is a huge leap in academic ability, as in a 4 year old goes from counting and coloring to tackling 2nd grade math on their own with little effort by age 5, or a 10 year old C student fills the report card with A's and reverses declining standardized tests cores.  Of course, context is everything, and the term 'little effort' in the context of Test Prep math takes a long introduction to explain.

But in some cases, there's one fatal flaw in the whole process.  Some kids don't have rudimentary visual spacial skills.

To review, the test prep process looks like this:

  • Work on a few hard problems over a long period of time.
  • These problems should be complicated and require a range of skills.
  • Mistakes should be common.
  • The student should work things out without the help of a parent

When I work a COGAT problem, for example, we spend a lot of time analyzing the picture and the potential answers before jumping into the solution.  If the child doesn't 'see' yet, I make them describe the diagram to me, and point out that a) I'm blind and b) I'm going to draw what they say.  Of course, when they try to describe a pentagon, for example, my drawing looks nothing like the picture they are describing.  For my own kids, I added c) I'm also 3 years old so don't use big words.  I added this last condition because they tend to miss the obvious in their complicated explanation, and the solution rests on the obvious.  When I get to this point, the blind 3 year old academic coach with poor drawing skills, it's because they just don't see the problem in enough detail to solve it.  When we do Test Prep Math, I'm a 4 year old who doesn't understand the problem so please explain the word problems to me, because I'm 4 years old, in terms I can understand.

The fatal flaw in this whole process is a student who doesn't have the rudimentary visual/spacial skills that a test like the COGAT assumes the child has.   Teaching the figuring out skills is a straightforward recipe which I've expounded on here at length, but teaching the "seeing" skills is something else.  My goal was that anything would be easy after the skills developed by the Test Prep Math word problems and quantitative sections, then I met a child who couldn't flip a shape. Apparently this book needs a visual spacial section before I can guarantee 100% on all tests of all type.  That and you child has to be familiar with 5th grade math to get a 99% on the 3rd grade MAP test.

The material behind Shape Size Color Count imparts the rudimentary seeing skills to 4 year olds in a very methodical way at a very high level.   After this, practice tests take on new meaning, or the student can graduate to Building Thinking Skills Level 1, at least for the nonverbal material.

For 1st grade, there's quite a bit of material on the market, and for 2nd grade and older Test Prep Math covers a whole new level of skills with the high bar in mind.

The issue I've been thinking about is the older kids who don't have any of the fundamentals of shape transformation.   Apparently there are 9 year olds who have never seen a Lego set or taken an art class.

One of the math books at the 8th grade level that we're almost finished with in preparation for 7th grade is devoted to geometric transformations.  The whole book would be great COGAT test prep if a 10 year old could understand any of it..   Arthur Tresse created a graduate level treatment of transformations that ended up being a brand new math before he tragically died in a dual over a girl. These are called Lie groups.  There is a Lie Group for all possible rotations of a circle, for example. The concept is simple, but the presentation is so complicated and full of terms and notation that I'm the only person who can see how this field is of direct importance to passing the COGAT if you are lacking visual spacial skills.

Some readers may doubt my summary of history or the fact that Lie Groups represent a field of mathematics.  Nonetheless, there is a big gap in systematic evaluation of transformations between Shape Size Color Count and 8th grade Algebra 1.  My goal between now and the 2017 test prep season is to fill this gap.  I'm just starting.  Give me about 3 months.

Of course it will be thorough like Shape Size Color Count, and much more complicated, but I've got one more goal in mind by tackling #1 from the list above by making brand new problems.   I've created COGAT Transformations 101 in the past, but it seems to be counterproductive by "training" the child to solve COGAT  problems instead of training the child to see and think.  The last thing you want going into a thinking exam is a child who has memorized formulas.  What you really want is a child ready to tackle new and impossible problems, preferably with a graduate level understanding of transformations.

The nice thing about training in transformations at the system level is that it's a really powerful way to approach math.   Entire topics can be disposed of in weeks instead of months.  I realize that most readers have a much shorter time frame in mind, like passing a GAT test, but I have to deal with the longer term consequences of test prep, like 192 grades on report cards and 52 standardized test scores before college applications are complete.  A few months of test prep has a much bigger payoff than you realize if you do it right.

Monday, March 13, 2017

The Roseta Skill

I had a  busy weekend of coaching.

This weekend I uncovered a coaching skill that I don't have yet.

When I coach, I bring a few hard problems for the child.  Learning happens with really challenging problems, and I don't have any challenging problems that only take 60 seconds to do.  I will begrudgingly admit that routine school math homework done daily has it's place, but our 45 minutes of At Home weekend work needs to be a) not boring, b) not routine, c) not easy and d) full of learning.  In this way, it should make you feel like you just went to a Tony Robbins seminar on motivation.

With a child who is on the verge of tears with the first problem, I can spend 45 minutes diagnosing where the parent and child are in terms of my skill list.   In this case, the Tony Robbin's moment isn't going to come for about 6 weeks.  When the child has all of the core skills, I can just sit there and respond to questions with "You tell me" and it's mostly the child working and me sitting there thinking about coaching.

This weekend I more silence than expected and spent my time thinking about how some parents sit there anxiously waiting for their child to announce the correct answer to a problem that they should know the correct answer to.  We've all been there.  What's 9 x 3?  When you're child says "28", you're frustrated.  The kid already knows it's 27.  That's what it was yesterday.

I realized that I sit there impatiently waiting for a child to see a key word or a missing term, using their skill of rereading the questions carefully.  I know this child can reread a question.  They could reread the question yesterday.  Did they forget that all of my questions require rereading?

Is it possible that I just shifted my impatience to a higher skill set?  If my kid says 9 x 3 = 28, I don't care and they usually correct themselves after seeing my facial expression, the classic raised eyebrow look which I've mastered.  But when they are working with a problem, surely they can see the anxiousness that I have while they navigate some ridiculously hard logic using the skills that count.

I was pleasantly surprised to find that diagnosing reading comprehension problems is identical to doing Test Prep Math.   By the way, the solutions are now correct on Amazon and the errata page is complete.   I was somewhat surprised to find as many mistakes in Level 3 as I did, but I was somewhat not surprised because we never use the solutions.  I'll have to explain this in the next few months but I won't do so now because it seems like a lame excuse on my part.   My one Amazon reviewer was 100% correct that this book should not have mistakes, at least by the 3rd edition, which is what is on Amazon now..

Anyway, while I'm working with Test Prep Math, which I did this weekend, I'm also working with the COGAT and I'm also working with the SAT and I'm also working with Algebra proofs and competitive math.  I'm was thrilled to find that diagnosing SAT reading comprehension questions is identical to doing a Test Prep Math problem word problem.  I totally nailed this even though it was accidental because Test Prep Math is supposed to be about math.

But here's the new challenge.  Can you get a 4th grader to answer this question:  "Is it possible to find a 3 digit number where the product of the digits equals the number?"  How about having a 6th grader prove that the sum of every odd number is even or the product of 2 odd numbers is odd?

Or to translate this challenge into what I'm thinking, is it enough to give a child all of the skills that they need to pass the COGAT, and in doing so you can guarantee a passing score on the COGAT?   What if you could just give the child a super advanced skill set, the kind that empowers the child to see y = mx + b as a system and not a single equation.  Would this be even better?  I think so.   Why send a child into any test prepared to get a 97% with a little effort when you can send them in prepared to get 99.9999%?  Conversely, if the COGAT is such a great predictor of academic performance, what skill is the COGAT looking for that endows the ability to do math proofs, and how is this skill taught to a child?  Is it really just the core skills we've used before, or is the last question on the COGAT, the one needed to get to a 160, secretly measuring the 'proof' skill?  I think there's something much more important here.  Maybe 2 kids do the same thing, and parents behave the same way, and one kid accidentally gets a skill and one kid accidentally doesn't get the same skill.

Right now I feel like I'm looking for the Roseta Stone of skills.   The 3 paragraphs above are a bit foreboding and cryptic.  I'm on the verge of discovering this skill.  Over the next few months I'm going to be working with Test Prep Math graduates on brand new curriculum that I can only describe as diabolical (because I only describe my new curriculum's as diabolical).   During March and April, there will be a large group of kids who should have passed the GAT test but didn't, because they had a bad day, didn't pay attention on one single question, or whatever.   If you have an experience like this, check in with my blog before the summer.  There's this post-pre-algebra-but-before-algebra curriculum for 8th graders that looks to me like the Super-Mega-Test-Crushing Roseta Stone for much younger kids.   There's already a version for 4 year olds called Shape Size Color Count, but it wasn't until the last 3 months that I started to realize that there's a version for 8 to 10 year olds waiting to happen.  I'm not yet sure that it will magically lead to doing proofs at another age, but I think this is in the mix somewhere.

Wednesday, March 8, 2017

The Music Recipe

Music has a well known connection to the intellect.  At least one brain part will grow 60% in the first year of music practice.  Music and math go hand-in-hand.  There are numerous soft skills to be gained through daily practice.  Many bright parents who have reached the pinnacle of academic success such as teaching at Harvard require music for their children.  Many of these children will perform at a venue like Carnegie Hall, perhaps play professionally for a while, before they have to give it up to start graduate school in a field like genetic brain manipulation.

Last weekend one or two scenes in our grade school play were accompanied by ragtime on the piano. I'm always impressed when professionals play ragtime because it's hard and exhausts player's hands. My 3rd grader pulled my arm and whispered 'The piano guy is in 4th grade'.  I had to stand up to verify this assertion.  And so he was.

I'm going to guess the ragtime player practices 3 hours a day.  Suzuki recommends 3 hours a day starting at age 3 to master an instrument.  Weekly lessons from the best available teacher are also required.

I recommend 20 minutes a day and no lessons.  Here's why.

I studied decision theory ad nauseum in grad school.  I didn't have a purpose for taking these classes, but there is a lot of cool math involved.  Years later in an MBA program I took a few decision theory classes to see a more practical side of decision theory with no math (and get an easy A) and now I can explain what we're doing with music and how we got here.

The foundation of a good decision is the frame of reference or information set.   It is possible, but highly unlikely, that your frame of reference should be a child who practices 3 hours a day on his way to teaching at Harvard.  This is one hundred millionth of the equation.   The other 99.9999 % of kids learn to hate music, hate lessons, and hate practice and then quit at the first possible opportunity.

The second part of a good decision is alignment with your goals.  My goals are that my children will like music, gain as many cognitive benefits that they can in 20 minutes a day, and maintain music practice as a constant in their daily routine so that the doors of music never close.  If they want to march in a band to get free trips to football games, or form a jazz band, or write an amateur musical, or major in math and music in college, it won't be out of the question  They'll probably have a lot of catching up to do, but it will be possible.  I told my kids that 'not quitting' is the gift I am going to give them.

As soon as they could sit still (somewhere between 4 and 6), I bought an electric piano and Piano Adventure books.  I spent too much money on the electric piano.  It had weighted keys and looked like a piano.   At the time I thought there was a possibility that either of my children could end up playing the piano for a living, but this is like buying a Power Ball ticket because there is the possibility you might win.  I could have saved a lot of money keeping my emotions out of the decision.  Emotions are bad for decisions.  The good news is that a more expensive piano has a better sound, the kids learned to have music ears and sing on key, and this has opened the door to theater.  Piano Adventure is an awesome course.  It's fun, easy, rigorous, yes easy and rigorous at the same time, and fun.

In lieu of a qualified piano teacher, I would spend time on the internet finding out how to play the piano a step ahead of my child's lesson.   For the first year, I was able to keep up with Piano Adventures with a bit of practice on my own.  After lesson 5 in the first book, I would mandate that my child work out each lesson on their own.  On day 1 of each lesson, I got 'I will never be able to play this' which was true, and 14 days later they would just zip along through the lesson with or without the music in front of them.

Working out the music syntax, eventually with 2 hands, plus the timing, and the inflection notation has an extraordinary payoff.  Each lesson is like a mini COGAT.  The first 3 days I just left them alone and they plunked away at one key at a time.  Then the next 3 or 4 days we would take each staff or phrase at a time.  The 2nd week we would work on timing and before I drew a big X through the lesson, the song needed to be perfect. We'd start the whole process all over again with the next lesson.

By the end of third grade, my kids have no interest in the piano.  This is expected.  There are things we could do to just keep plodding along, and one of these would be to find a good piano teacher.  But instead, I announce with aplomb that they have the exciting opportunity to choose their very own instrument of their very own choice and join the band.  My older child chose the trumpet because it's the one instrument I don't have and have never played.  The younger one is going to play the clarinet. This was really hard for me to pull off.  I told him he can play the flute, saxophone, alto saxophone, e flat clarinet, and stink at all of them if he would just please, please, please play the clarinet.  Instead, he found an old wrestling dictionary and our deal is that if he plays the clarinet we practice wrestling together for an hour afterward.  Walking down the street with him has become painful.

My number two goal of music, behind not quitting is that they figure things out for themselves and have a continuous bi-weekly challenge of not being able to do something and now they can do it 2 weeks later through their own hard work.  Goal #2 has been achieved spectacularly, especially when I was banned from practice time because I stink, and I'm tentatively ready to announce that I succeeded on Goal #1.

To make band work, I had to find movie music books.  We practice these in lieu of whatever the band director assigns.  If a child maintains 20 minutes of practice a day, this child will end up way ahead of the rest of the band.  Movie music makes practice much more enjoyable.  Trying to work out the songs from Frozen, for example, even for a boy, is more fun than songs from 1910 in the band book, despite the fact that Frozen is 10 times as hard.

A few weeks ago, the older one competed at competition for the 3rd time.  The judge pointed out that he is actually pretty good, despite the fact that he obviously doesn't know anything about proper trumpet technique, because his teacher (me) doesn't know anything about trumpet technique.  We discussed this at length, and I pointed out that he needs to start taking trumpet lessons and practicing for more than 20 minutes a day now.   Age 12 is one of the most likely ages for quitting music.  I quit playing at age 12 because I hated lessons so much.  But my son agreed to lessons.  Success!

One final note.  It is well known that the easiest way to crush the budding interest a your child is for the parent to get involved.  How many future biologists end up as disgruntled journalists because their parents made them go to biology camp?  Lots.  Music is slightly different because the kids have no choice in the matter.  There's no way a parent is going to forgo lessons for a kid who shows an interest in music in the absence of budget constraints.  Future musicians will just have to suffer from an enthusiastic parent.

If my child showed an interest in biology, I would do my best to discourage it the same way I'm attempting to discourage wrestling.  I discovered that old wrestling dictionary when I was in 4th grade.   Later, I discovered a few more books, including Dan Gable's biography, which will mysteriously show up in our bookshelf at the appropriate time.  I'm like the spider in Coraline.  For mysterious reasons, the ribbon I'm the most proud of was stored in the clarinet case with no explanation from me.  It just sits there.  After I won this ribbon, the wrestling coach from one of the military academies called me to find out why I didn't go farther in the state wrestling tournament (strep throat) and the next day I surprised everyone by winning a ribbon in the regional calculus competition.  I wrestled in college, but I wasn't on scholarship, but I didn't go to that that military academy and didn't major in nuclear physics.

For now, I just complain that I don't want to practice wrestling.  My neck hurts.  I'm too old.  We don't have a mat.  I'm sick of defending against the double leg takedown on the walk back from scouts. But I know where to buy a wrestling mat for the basement and to heck with decision theory.