Sunday, May 21, 2017

How To Teach Cognitive Skills 4 of N

This article covers Making Mistakes.  Being Baffled and Making Mistakes are the two big stones that form the base of the skill pyramid.  The skill 'Reading The Question' sits on the next row up next to 'Seeing'.  The rest of the pyramid above these 2 levels includes almost all of the technical skills that you would find if you spent the last 6 years researching cognitive skills.

The front page of today's Chicago Tribune decry's the poor state of college readiness and blames high school.  Not a bad article for journalists.  The real problem is that grade school does not teach any cognitive skills.  Grade school just teaches 'stuff'.  'Stuff' doesn't prepare anyone for high school or college.  Only thinking does.

What does thinking have to do with success in high school?  Everything.  Learning 'stuff' is a byproduct of thinking.  A kid who knows how to think can't help but come to know large amounts of stuff.  A thinking kid is a 'stuff' vacuum cleaner with an infinite dust bag.

When a child is trying to memorize 'stuff', mistakes mean they don't know a particular item of stuff. The problem is when a child is learning how to think, and parents are using mistakes as a gauge to progress and effort.  When it comes to learning, mistakes work in the exact opposite way that they do with 'stuff'.

Here's a quote from today's paper by an administrator at Hinsdale Central High School.  "I think the idea is that you want to have an appropriate amount of rigor in a class which stretches a child out of a comfort zone but not so much that they get overwhelmed and they shut down..."

I used to think like that.  My starting point was educational literature.  That's the conventional approach which results in conventional results.  Conventional results stink.

When the child is anywhere near their comfort zone, they have one quick step to the answer.  This step defines the distance from their comfort zone.  All the child needs to do is ask the parent to help or explain, this closes the gap with no effort, and the answer can be quickly calculated without any significant thinking on the part of the child and little or no learning.  The parent thinks 'you just learned multiplication' or 'you just learned decimals' and is happy.  But multiplication and decimals are nothing more than stuff and the opportunity for learning is lost.  No learning.   A kid trained to do multiplication or decimals is a Forth Grade Train Wreck in the making.  The problem becomes much more severe when we're talking about pre-algebra and beyond.

To get to thinking therefore requires two steps.  The first one is to get as far as possible from the child's comfort zone.  That gap defines how much thinking is required by the student.   For students who want to obtain the 75% on a cognitive skills test, this will be a pretty big gap.  For parents who want their child to get to the 98% so that the child can go to a gifted school, this gap is going to become a chasm.  The chasm is enabled by Bafflement.  The second step is to shut the heck up (as a parent) so that your kid can start thinking, and that's were mistakes come into play.

If you have suitably challenging material, and your child is thinking his way through the problem, the inevitable result is going to be mistakes.  Lots of mistakes.  Mistakes on top of mistakes.

To get your child from 50% to 75% to 99% means learning, and learning means mistakes.  The only way you are going to survive as a parent is that you expect mistakes, are totally OK with mistakes, embrace mistakes.

I go even farther for parents who are starting with conventional and trying to go down the road of learning for the first time.  Stop looking at the solutions.   All of the learning takes place in the 'trying to get a solution' work and as soon as you announce the solution, learning comes to an abrupt end. It's even worse than that.  Consider about this conversation.
Child: Is the answer 13?
Parent:  No.  The answer is 12.
Child:  Then I must be a total dummy because I'm wrong.
When I start working with some kids for the first time, I have to battle this ingrained attitude.  The first thing I do is throw out the solutions entirely.  'You got 13?  Show me how you got it.'  Whatever they say, I know learning took place, and we move on.  Later I'll come up with '7' as my own answer and we'll rework the problem together to find out that we're both wrong.  It's only after a few weeks of this when I start asking them to prove it or simply ask them to try again as many times as it takes. At no point will I ever measure progress by comparing their answer to the one in the solutions.

My favorite math book is the 8th grade level of CPM math.  This inspired by the work of my math idol (Jo Boaler), work that was successfully used by her graduate students inner city middle school students from get D and F students to A and B.  This book has no solutions.  Some of the problems are designed to have multiple solutions, each one as good as the next.  The reason why its my favorite because, in addition to making advanced math accessible to remedial students, it also makes advanced math accessible to my kids.

While mastering Bafflement and Mistakes your ideal starting point is an environment where it's OK to be baffled and mistakes are irrelevant.   There is a long list of missing skills to tackle so bafflement and mistakes is probably going to characterize every session.  You'll see in later articles why learning is happening the whole time.

Between the last article and the next few, we're going to take this to the extreme.   To give you an idea of where this is heading, let me describe the results.

In the next few weeks I'm going to meet with a 5th grader who is struggling with pre-algebra.   I feel like Yoda waiting on the planet of Debogah to train Luke.   She's about to get a big dose of the Force. To prepare for a mega session of thinking, I chose 3 problems from a middle school competitive math test, the 3 problems on the last page that are suitable only for 8th graders.  Baffling?  Check.  Are mistakes inevitable?  Check.  Do I know how to solve these problems?  No.

Yesterday, my 8 year old demanded to use the computer so that he could create his own website.  This is a big 'computer time' request and demanded 'big math'.  So I handed him the middle school competitive math test that I was reviewing and told him since he's probably going to need the computer all day, I am only going to accept his math ONLY IF ALL OF THE ANSWERS ARE CORRECT. He did the first 24 question.  I had to take a break from my work to give him a tutorial on algebra, permutations, and probability theory, but I didn't help in hopes that he would just quit and do something more productive all day like reading.   I failed.  He got them all correct and now has a web site on wix with the world's worst coloring scheme.  I looked at wix and their website builder is too complicated to use.  How did he figure it out so fast?

This morning, he came back with an equally inane request for computer time, and all I had left to defend myself was the 8th grade page from the math test.  I gave the 3 problems I don't know how to solve.  That's why I chose it for the aforementioned 5th grader.  After defining 'consecutive' and an 8th grade level lecture on graphing theory, he not only got the questions correct, he ignored my suggested approach and prove that his ad hoc solution method was mathematically sound.

Some people think he's smart.  If you were in this house for the last 4 years while he was baffled, and I was learning how to be baffled, and you saw nothing but stupid mistakes, not even good mistakes but the stupid kind, you would know better.

Here's the best part of all.   When he failed on one question, he yelled and stormed away to his room. A deal's a deal, though, and he sat in their for 5 minutes thinking about his options - have a normal day reading and playing, or get that dang problem correct and add content to his new web site.  He emerged with a sour look on his face and tacked the problem.   Best of all, he showed me a correct answer that was not my answer.   So I asked him what he learned.  He replied that he didn't learn anything, so I drew this picture:

This is the last of the lessons that mistakes teach.  It's the one built from countless failed attempts on the way to a correct answer.   You can teach your child this lesson once they have an arsenal of cognitive skills to work with.  Before you get to this point, here are the lessons that mistakes will teach on the way:
  1. Answers aren't important.  Answers are involved with learning 'stuff' and we're trying to learn learning skills.
  2. If you get an answer incorrect, it means that learning is taking place in this work.  If you got the answer correct, that means you already knew the answer so this is a waste of time and no learning took place.
Once we get beyond the next skill (Reading the Question), the dynamic is going to change and we'll focus on getting the right answer (in one or two tries) in 5 minutes versus spending 25 minutes getting the right answer (in one or two tries).   The importance of mistakes never goes away, but like Bafflement, these are starter skills at the bottom of the pyramid, and we need to go way past that some day which should be obvious from the little story I shared above.

Let me conclude by saying that getting past Bafflement and Mistakes is 90% of the battle.   Learning to work a question and 'See' is challenging, but I've never once had to teach a child an actual official technical cognitive skill.  They just learn like magic once they're in the right environment.   I can guarantee that this environment is not going to be school.  It has to be home.  Therefore, half of the battle is getting the parent in the game.  The other half is changing the child's expectations (based on everything they've learned since about age 4) about expectations and bafflement.

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