Saturday, December 23, 2017

The Makings of a Thinker

Here's a rough non-copyright violating approximation of a figure matrix question from my favorite COGAT practice test, grade 2. 

This is the last question in the book and the hardest.

In this article, I'm going to show you how much mileage you can get from a single question.

When I coach, usually at the behest of a parent who provides a compelling reason or academic puzzle that I want to add to my research, I'll start with whatever material they have available and do a single question.  There are many other things I do with a practice test besides a single problem, but my favorite Academic Coaching Session Agenda is the Single Problem because the student picks up the most skills.

This may be the only time I'm working with the child, and my primary goal is to train the parent who is lurking nearby, and I want an impact, so I do it exactly like I would with my own children.  Like this:

Step 1:  I instruct the child to do the problem.  Take as long as you like, and before you answer the question, I want you to tell me that you're ready to answer the question but not what the answer actually is.  I will probably announce that this is a really hard answer and I'm totally confused so I hope that the student can do it because I sure can't.

Step 2:  The child either announces the answer or announces that they are ready to answer. a) If they announce the answer and it's correct, I'll tell them I think it is the 2nd one and be prepared to prove your answer* b) if they announce the answer and it is not correct, my favorite case, I announce that they are wrong - try again and c) if they just announce that they have completed the question and are ready to answer, I announce that they probably got it wrong so go back and double, triple, and quadruple check the answer, followed by a) or b) when they announce the answer.

*At some point during this training, the child will learn to check their answer.  I am going to encourage this behavior in multiple ways including saying 'Check your answer'.

This approach is the birth of skills.  If the child answered incorrectly, then we're going to get double the skills from this exercise.  It's not clear to most parents what these skills are.  These skills are the skills of kids who will go into an accelerated history or reading course, teach themselves, and do well.  

When I announce to the child that they are wrong, they are probably wrong, or their answer does not agree with mine, the child can sense that I'm happy about this situation, and I genuinely am happy because we can learn something.  I love mistakes, even the ones I make.  Mistakes drive learning and it's one of the 5 core skills.

Step 3:  Explain the question to me.  First of all, I want to know what the transformation is.  The first shape undergoes 3 transformations.  Zooming through problems is the way to miss subtleties like the height of the shape diminishing by about 10% before it is rotated 1/4 turn counter clock wise.  Some kids say rotated 'to the left' which is OK with me provided 'to the right' always means clockwise.

In this phase, we're learning how to see, the names of things (like rotate 1/4 turn counter clockwise or decrease in height slightly).  I will correct the child's grammar or terminology, expecting that they eventually use the adult level words that I do in adult level sentences with multi-clauses.  It's the opposite of Baby talk and the reason why my books have that awful looking graduate text book themed covers.

When the child thinks they are done, I'll point out that explaining the question includes explaining what is happening in each and every answer.  I would like to know what transformation took place to make each of the answer choices, or what transformation failed to take place.  That's 4 additional problems as far as I'm concerned.  

I've never found a problem in a COGAT book that can't be solved with a thorough out loud explanation.  Sometimes when I'm working with my own material, I get the problem wrong, repeatedly, and I look at my answer and wonder what the heck I was thinking.  Then I go through it the way using the steps I expect a student to use, and oh year, it makes sense again.  When you say the transformations out loud (problem and answer choices) hard problems are turned into easy problems.  I can't over stress the importance of this technique.  This is why Shape Size Color Count is so verbal

I call this skill 'Reading The Question' because most kids can't do it without a lot of training, and most parents lack the patience to wait.  I know as a parent I used to lack the patience, and sometimes I still do.  To accommodate my coaching inadequacies, I'll just turn over the material and go clean for 20 minutes before the teamwork begins, shouting out things like 'Read the question again' while I do my work.  

There is a prerequisite skill I call 'Seeing' that children have to develop.  In this case, 'seeing' is visual and includes proportions and the ability to mentally rotate images.  It takes some practice.  In an academic household, those places of non-stop learning that produce GAT standouts, this practice started at age about 2.  For the rest of us, COGAT practice is as good a time as any.

I should point out that this is not a hard problem because it's missing the magic of the COGAT.  The quadrilateral lacks symmetry.  A problem like this would be practice for K.  This is why practice tests are practice for the format of the test and not the thinking of the test.  Also, there are 3 transformations, which you'd think would be good for working memory, but the shading transformation removes answer choices right away, making the problem easier, not harder.

Step 4:  If the child can't get to the correct solution on their own, I'll mark the page and come back later.  This question is still holding learning.  If I have to announce that the shape is shrinking in height before turning, I just destroyed the learning opportunity.  If there are 10 more questions with this transformation, I'm stuck having to announce it.  It's a judgement call and depends on how much time is remaining before the big event.  If you have a lot of time, you can back track by drawing 10 or 12 shapes, and ask your child to shrink one dimension and turn it 1/4 turn in one direction.  Backtracking in this way is a version of finding an easier problem to solve before tackling the harder problem to solve.  No branch of mathematics can withstand this approach, and every single super hard complicated advanced problem can be solved in this way if needed.

For one child, we spent a solid 4 months doing cognitive skills training (including BTS and much much harder material of my own making).   When we finally came back to math, we followed this approach from that point forward through SAT and calculus.  I learned that these core skills are universally applicable.  This is probably why the COGAT is such a great predictor of academic success.  Take any topic, like fractions or exponents or roots of a 2nd degree polynomial, or multiplication or anything, and at one point we slowly went through a few problems using this approach and learned months worth of material with a small amount of effort.

At some point during the actual test, the child will come to the questions that differentiate the 97th percentile from the 99th percentile.  These are the questions that differentiate those kids who probably would do well at Stanford with a little effort from those kids who will be sitting in a GAT program next year because of the ridiculously high cutoffs in almost all states.  The kid who gets these question correct will either be the child who is already 99% because his parents both have PhD's from those who have learned the skill set and go super slow on these problems:
  • They are not the slightest bit discouraged by not knowing the answer right away or being confused.
  • They take a long time to thoroughly investigate the problem
  • They have a few techniques to fall back on when it gets really, really hard.  
  • They are not discouraged when they don't see their expected answer in the pick list.  They try again as a matter of course.
  • They check their answer, and all the answers, at least twice if not more.
I think the best way to teach these skills is to approach the training in the way I described above.  You should see how the approach is consistent with these skills.  It should also be clear that the other approach, I call this the school approach - explanations and lots of routine practice in the hopes of memorizing or mastering a set of question techniques - is not consistent with the skills needed at the top.

For parents a week or two from the COGAT who reach out to me the first time for help, and have done zero of anything before that, this approach is the way to go.  Of course, if you plan ahead, you'll be able to go much, much farther, but the approach is roughly the same.

1 comment:

  1. We are a few weeks away from second grade Cogat testing (they are pretty secretive here about when they will administer the test). We found out the test will be on the computer, and it's the screening version of the test. Do you have any tips or info about the test being taken on a computer? We know it was taken on paper only a few years ago.... But this method is new to us. Thanks.
    We have been using many different methods, including Test Prep Math, and it has been amazing to see our child's progress. We went from crying and whining at reading the first few words to solving the TPM questions in 5 minutes or less (which has also led to us skipping ahead for harder material, of course). I can finally understand how building this type of skill in a child is so advantageous for future academic studies and I am very encouraged to continue this type of learning whether the Cogat goes well or not.
    Thanks again.

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