Thursday, September 14, 2017

Experiments in Thinking Skills

This is the 2nd part to my previous article on what is hard and what is not hard in the context of cognitive skills and GAT tests.

A couple of weeks ago I had the privilege of sitting down with a wee one to do the first problem in Test Prep Math 2.  This book is for for 2nd to mid 3rd grade children.  It should be called SAT and MAP Test Reading Comprehension Prep Disguised As Math because the cognitive skill set is so similar.

I'm also getting the play-by-play from a tester who helps too much (stop it!) and want to clarify something that I put in my video on verbal matrices that is really important to keep in mind.   According to the purpose and nature of a GAT test, academic potential is measured by:

  • Surprising and confusing questions
  • That are new and different
  • The parent is not in the room to answer questions
  • That have multiple parts and multiple steps
  • Where the probability of wrong on the first try is built in to the test
  • Other things mentioned in the presentation.
  • And the parent is not allowed in the room to answer questions
The math and logic of the test are not advanced.  There are no decimals or long division.  It's all about finding kids who could do well in an accelerated learning environment with little help, not kids who are already one or two years ahead due to training.

Let me walk you through an example.

Here is the first word problem from Test Prep Math Level 2.  I'm going to describe what I'm looking for when a child works through this and why it is critical not to worry about whether or not the child actually gets to 11 on the first, second, fifth or any try until later in the book.  (For those of you who think this problem is easy, the questions get harder. This is problem #1.)


Hannah just turned 3.  Hannah’s mom made a birthday cake for Hannah, and Hannah’s older brother Oliver put enough candles on the birthday cake for his age plus 4 extra candles that he found in the box.  How many candles did Hannah’s mom have to take off of the cake if Oliver is 10 years old?

I invite the child to read the problem a few times.  I'll read it outloud if necessary later if that helps the child put the pieces together.  After a few attempts, or if the child is frustrated because he is asked to think, I'll invite the child to draw a picture, explain the problem to me one sentence at a time, providing an executive presentation to the world's dumbest parent.

Getting to 10 + 4 = 14 and 14 - 3 = 11 is not easy because the problem is not in the spoon-feeding order of 2nd and 3rd grade math books, and this problem has two equations, not one.  The goal isn't "There were 4 candles and 10 more.  How many were there altogether?".  I don't care if the child can add and subtract because this takes care of itself, and when we get there, we'll have a formidable skill set way beyond arithmetic.  Plus, the book is preparing to sneak in a 3rd equation or maybe some multiplication.

Two important goals are working memory and logic skills.  These go hand in hand.  

The 'memory' part is exercised and built up while the kid tries to keep all of the partial equations in memory while blanks are filled in on the way to solving.  For this reason, I'm hoping the problem takes 25 minutes and multiple attempts, and I don't explain it because the longer the better as far as memory is concerned.  I'll be rewarded later in the book when the questions get a lot harder.

The working part is finding the 3 and the 10, which are out of place, and trying to solve the equations one step at a time.  (I find that numbers keep dropping out of memory during this process early in the book).  Multiple subskills will emerge from this process if you don't help.  All kids won't make it on the first try for at least some (if not many or most) of the problems that follow.  That's the whole point.

When I have to go the picture route, the working memory demands decrease, so I increase demands on verbal presentation skills by making the child compare the picture to the problem step-by-step because I'm still confused.  This is also great for working memory.  That's why we hold off on the picture until at least a few readings and maybe a few attempts.

I wanted to hammer away at core cognitive skills.  Confusing?  The child has to fix this question, at least the order of presentation.  Get it wrong, shrug it off, and try again?  Solving 2 or 3 easy math problems at once works wonders for this. The likelihood of error is high.

Later in the book I'll start asking the child to prove their answer instead of reading the solutions.  Checking the answer is also vital for tests and homework.

When child gets to problems that are more challenging, it's really hard to do 6 + 7 = 13 and 16 - 5 = 11 and 13 - 11 = 2 in just one try, especially if arithmetic skills are still developing and the wording is vague or tricky.  If I'm really lucky it will take 5 tries (which might take 30 solved equations, not just 15) so on top of all of the really great skills the child is picking up, I just out Kumoned Kumon on repetition.  I expect flawless school work to follow Test Prep Math without having to do a boring worksheet or even correct 6 + 7 = 14 because eventually the child corrects it herself later.

In the meantime, a child learns to deal with confusion, figure out and explain without the help of a parent, get the answer wrong, try again, build working memory, and eventually learns to add and subtract slowly and carefully because eventually the child tires of having to do things over because of speed and sloppiness.

When it takes 25 minutes, I've got a child who is on the steep part of the learning curve and the 25 minutes are worth it.  When it takes only 10 minutes because the impatient and perfectionist coach can't stand it that the child is struggling and making mistakes, the child is short changed on 15 minutes of learning and working memory growth. When it takes 10 minutes because the child happens to be ahead already, we'll just move forward until things get harder.  

To repeat what I said above, you're not allowed in the room for the ITBS, MAP, COGAT, NNAT, Raven, PARC, SAT, or any other test.  So stop helping.  Your child is not going to think unless they are allowed to think.  Getting the correct answer or even gaining a full understanding of the question is not our goal until all of the pieces are in place.  The goal is for the child to do it.  At the 15 minute mark, I jump in and start helping, preferably with lots of questions.  

Then I'll ask what Oliver's mom said to Oliver.

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