Monday, August 11, 2014

Two step logic

Test preparation season is only 19 days away, and I'm waking in the middle of the night sweating and yelling out "It's the red square!".   Fortunately, my parent support group Veterans of Freakin' Tests, or the VFT, has resources available to help me with my transition to the civilian life.  Alas, my next tour of duty starts in a year.

Sitting there writing thousands of questions has taught me one thing.  Most test questions apply 2 step logic.  The very first question my first child remembered coming out of the test was a simple picture math problem, but the correct answer was split into 2 awkward looking groups.  Most test questions set up with 2 formal steps, and you'll see this in the test prep literature.  (Except the OLSAT literature errs on the easy side, and I think it's OLSAT in format only but not complexity.)

Most math word problems have 2 steps.

Most problems at work and in life have at least 2 steps.

I think this skill is a big predictor of success in school.

There are a variety of ways that a child can learn two steps.   First of all, it's the nature of our language and most speaking and writing.  There is at least a subject and a verb. Reading a lot will teach this. Reading a lot is great because most of us are tired by the time we see our kids, and reading together will do the work for you.

Puzzles will teach two step logic.   Puzzles are puzzles because there is more than 1 step.

Talking in big sentences from birth gets the job done like a sledge hammer.  Ever wonder whether or not baby talking to your child is good?  It's good to teach talking and proper pronunciation so you don't have to go to speech therapy when you should be doing test prep.  After the child can pronounce words properly, switch to talking to your child like they're in grad school.

Two step logic has some intermediate skills, like identifying the steps and formulating mental models of the problem.  Short term memory and concentration may play a role, but I think something different is going on.

There are a variety of things that can interfere with a child managing both steps to solve a problem. Sleep, hunger, belligerence, and not understanding the language hurt.   It doesn't matter whether the test is verbal, or disguised as non-verbal.

When I do test prep, I take a simple problem, and then pile on the complications.  Or I take 2 simple problems and put them in the same problem, either by stringing them together or by asking that they be solved at once.  My original objective was to make a problem that was twice as hard as the test, just to be on the safe side, and cave man logic determined that 2 problems at once would achieve this objective.   The approach inadvertently got the job done.  If there is not a word yet for that, you may refer to this approach as "Norwooding" the problem.

My most recent graduate of the program that I like to call "Two Steps Away From Hell" is going into first grade.   He likes to shout out the answer to problems that I'm explaining to his older brothers.  (In fairness to them, he answers first because they are not listening to me.)

Sunday, August 3, 2014

The Key to Hard Core Test Prep

On June 28, I presented my review of test prep books for one of the common tests.

After that, I have a few rambling posts that spell out exactly how I turned 2 marginally intelligent kids into test performers.  But I think I need to spell out my secret formula very carefully.  I'm going to work this into the next update of the test taking chapter, and it should probably be my new top 10 list.

Step 1:  Have a stack of material, both books and workbooks on hand at all times.
Step 2:  Reading should be at all levels and all topics, but the workbooks should be 2 grades up.
Step 3:  No fun whatsoever until the workbook page is done.
Step 4:  The parent has to be prepared for the inevitable - the child can't actually do work 2 grades up.

I think step 4 is the real problem.  It's one thing to hand your Kindergartner a 2nd grade test prep book, but it's another thing to get him to understand any of it.  More likely, he'll just cry and you will get frustrated.

Unless, of course, you had a toolset to deal with this situation.  And if you read my chapter on math (past all of the boring parts down to problem solving), you'd see that one exists.  Once a kid knows these techniques, then he's officially gifted.   I think preK (or pre 1 or pre 2) is a perfect time to teach these tricks to future geniuses.

Right now I'm teaching this skill set to a 10 year old and the results are stunning.

Here we go, in order of importance:
1.   When stuck on a hard problem, start with an easier problem of the same type and work your way up a little bit at a time to the harder problem.
2.  Look at all options, try them all, and eliminate ones that don't work.
3.  Draw a picture.  (Not very useful with nonverbal tests).
4.  Look at similar problems for help.
5.  Start over and look for a different answer.
6.  Skip the hard one and try the next one.  Come back to the ones skipped.

The difference between a GAT kid and one who just sits blinking is that the GAT kid has a toolset that he can bring to bear on super hard, new material.  The way the child learns this tool set is that the parent and the material teach it.

The Tipping Point

Why is this toolset the difference between GAT kids and regular kids?

I'm trying to teach a native French speaker who is way behind academically, both math and English at the same time so that he's prepared to start 5th grade.  I have a stack of math word problem books (which are awesome).  We're on page 43 of the 3rd grade book.

"CJ has 2 bags of birdseed, and each holds 90 ounces.  The birdfeeder takes 10 ounces of seed, and the birds eat it all each day.  How many days will the birdseed last?"

We went back and forth on this and he finally came up with 9.   Arrgggghhhh.  He's not dumb, but he doesn't understand any of the English.  He's happy if he can just pronounce the words, let alone know what they mean, let alone translate it into math, let alone solve the problem.

My youngest son who just turned 6 was reading nearby.  I asked him to pick up some paper and try the problem.  "There are 2 bags, not 1", he said, and went back to reading.

The Break Through

Up to this point, my 10 year old and I were fighting.  He has 10 word problems to do, and he thinks the fastest easiest way is just to do the word problem.  This method will guarantee at least 20 to 60 minutes of pain per word problem.

I told him he has to follow these steps:
  1. Search the problem carefully until you are sure you know every word and what is being asked.  Leave no stone unturned.
  2. Write out an equation to solve, and change the big numbers (eg 90 and 10) into small ones (such as 9 and 1). 
  3. If you are still unsure, draw a picture.
  4. If you are still unsure (is it multiplication? division? adding? subtracting?) try each possible approach until you find the one that makes sense.  (This is also the way to pass the Mensa test.)
  5. Once the lightbulb goes off on the easy problem, write out the equation properly (in this case 90 x 2 / 10).
  6. Solve it.
  7. Prove to me that you got it right.  If it's a division problem, reverse multiply.  If you added, subtract.   (There are only 4 of these for arithmetic).
He looked at this list like it was hell.  It's bad enough solving the problem, but now I'm asking him for 7 times the work!

After being humiliated by his 6 year old brother, he was so crushed and demoralized that he gave up arguing and just did what I asked.

The first couple of problems were hard because he was a bit unmotivated, to say the least.  But he started to see the results of these new toolset, and he started to move quickly, even though he doesn't know what the words "display case", "marbles", or "knitting" mean.  Even with the English tutorial, he's solving each "Problem of the Day" in less than 2 minutes each.

This is almost exactly the same process that I went through with the other kids with GAT test prep.

The 5th grade book has much more difficult English vocabulary, but the math concepts will not be any harder for the toolset.

As a bonus, I'll get another confident, determined kid who knows how to work hard and how to work smart.  It's a bit early, but I'm now thinking Selective Enrollment High School.