Saturday, July 15, 2017

Crushing Math at Grade Level + 2

I have been the proponent of teaching math at a level 2 years ahead your child's grade.  There's a way to do this correctly and produce amazing benefits and there's a way to totally screw up the learning process.

Here's a nice article explaining the difference.  The article is kind of long and doesn't explain how you actually pull it off, and it's written by a PhD from Ukraine who assumes that our kids are as smart as her kids, which is not even remotely true.  Nonetheless, I'm going to have to buy her book and report back here what I've found.

I came up with the idea of Grade + 2 in an act of desperation.  We just finished taking the COGAT, and I had another child who needed to study for the COGAT and the OLSAT, and at the time I had no test prep of any type, not even practice books, so I bought Every Day Math Grade 2 and gave it to my child. I speculate that it helped a little with the COGAT, but it helped a lot everywhere else.

The first requirement to go ahead in math is a big working memory.  Every single math problem worth doing (as well as all problems of any other type like reading or science) has multiple parts and either new concepts or new techniques.  All this newness while trying to solve anything requires a place to store it during the solving, and that's what working memory is.   Reading and Read To are good working memory builders.   Test Prep Math is a working memory Special Forces Seal Team Six Boot Camp of working memory for older kids.   If your child doesn't have working memory yet, each problem goes really slowly and takes multiple re-starts and multiple attempts.

Crying is usually a sign that working memory is still a work in progress.  Yelling is a sign that working memory is there but your child is thinking 'why can't I just be average like everyone else'.

The next thing you need to know is that every math problem is really multiple math problems rolled into one.  You don't realize this when your child does grade level math because they've learned to do all the steps in one and solve it like a single math problem.     With Grade + 2, it's your job to help the child break it down.

The last thing you need to know is that this problem is too hard because your child is not yet adept at 23 + 19 or 12 x 12 or 4.24/15 or whatever but this is part of the problem so you have to figure it out on the spot.  The way to do this is to start with the simplest possible problem, like 2 + 2 or 2 x 2, and work your way up from there.  In the example of 12 x 12, 2 x 2 takes a few hops to 10 x 10 on the way to 12 x 12, which is really 10 x 10 + 2 x 10 + 10 x 2 + 2 x 2 and requires 4 intermediate steps and a final step.

As I write this, my 8 year old is yelling at me as he tries to solve 15 - [15 - (-5)2]/(-2), which he has no skills to solve, then he looked at my blog and stormed out of the room.

With 12 x 12 and a 6 year old, and it takes us 25 minutes, but the kid barely understood addition to begin with.  With problems of this type, the 25 minutes eventually shrinks down to about 5 minutes with a bit of repetition.   I chose EDM because there isn't a lot of repetition.  Who needs a kid who is good at 12 x 12?  That's what calculators are for.

In the end, will your child be good in math at Grade Level + 2?  Who cares?  The child just went through 6 or 9 months of a) break it down into smaller chunks, b) solve one chunk at a time, c) find a simpler problem and work back from there, d) read it again, e) solve it again, f) check the answer because you've gotten the last 53 out of 53 wrong on the first try.  This is not the makings of a calculator. This is the makings of a future 12 year old who's ready for graduate school. This is also 50% or more of the battle on a cognitive skills test.

The last thing to know is that you are not a Ukrainian PhD in math, so your 5 year old isn't going to learn calculus.   Even more importantly, your experience on a daily basis is going to look like the following conversation.   I asked my kid to do a Grade + 5 problem that had 3 years of unknown material to conquer.   The only difference between now and age 5 is that he yells instead of cries and didn't roll up in a ball under the table when he had enough.

Me:  9.9 is about 11% of what number?
Kid:  I don't know what decimals or percents are and barely know algebra.
Me:  Do it anyway.
Kid:  Waaaaa!
Me:  Ok, 11% of a number means 11/100 of that number.
Kid:  ?
Me:  Give me an easier problem than this to do first.
Kid:  ?
Me:  Ok, 10 is about 10% of what number.   50 is 50% of what number?   20 is 10% of what number? 50% of 100 is ?  25% of 150 is ? ...and on and on and on. We spend about 15 minutes on this.
Me:  State this problem as an algebraic equation.
Kid:  ?
Me:  OK, 'what number' means x.  Write it down.
Kid:  9.9x = ?
Me:  Why are we doing this?
Kid:  You tell me.
Me:  No, you tell me.
Kid:  No, you tell me.
Me:  No, you tell me.
Kid: (eventually on the 9th try with my help) 11/100 x = 9.9. Now what?

I could see after about a week of this that we started to pick up the concept of percent and some insight into decimals.   I expect him to flunk the chapter test. Starting with EDM Grade 2, we have flunked our way up to 8th grade math, in the process to flunking our way into lots of other great academic skills and a consistently strong academic performance.

What I get with Grade + 2 is a lot of thinking practice every day.  With grade level math, a child is practicing how not to think.  Think about that.

No comments:

Post a Comment