Friday, August 18, 2017

Little Skills Part 2

In the last article, I presented this diagram of 2 squares and asked for a description of what is happening.  (It's supposed to be a square but the diagram is poorly drawn.)  Here is the diagram again:

Here are the possible transformations:  The square can turn in 1/4 increments, flip horizontally, vertically, or diagonally up or diagonally down.  If a shape before and after looks identical, then the possible transformations define the symmetry of the shape.  The square can turn the opposite color, or it can become white regardless of whether it is white or dark to begin with.

The shape presented to be transformed into the answer can take on any of these transformations.  If the question says which one is not possible, then a 1/8 turn is not possible, and changing from dark to dark is not possible.  Obviously dimension changes are not possible because this is supposed to be a square*.

I've never met a child or parent who saw this for the first time on a practice test and had the slightest clue what is going on.  This is a good problem to kick off test prep to alert your child that the days of getting things correct on the first try are over.

The solution to this problem and others relies on the big skills, otherwise know as core skills or higher order skills.  This problem is not possible unless the child prepared to spend plenty of time investigating the question and answer set, make multiple attempts in the face of wrong answers, check the answer on their own before asking.  In addition to all of this, there's a lot going on, and that 'a lot' needs to be kept in the brain in some organized fashion while the problem is being solved.  Working memory is active the whole time.  If your child gets frustrated or upset because they are baffled and don't immediately know the answer, none of this is going to happen.  If your child is crushed by wrong answers, there will be no progress.  These are the Big Five of skills.

Nothing on this list is magic, except working memory which takes 6 to 12 weeks to build.  School teaches the exact opposite of these skills in early grades, emphasizing being told things up front, memorization, routine practice, speed and accuracy on 1 step problems.  These are the Big Five Anti-Skills.  If you don't undo this damage as a parent, no one will.  (Technically there are 6 of these, but routine practice is an Anti-Little Skill that I have to explain later.)

As work progresses on the right material, little skills emerge that make actual progress possible.  It's one thing to analyze a problem.  It's another thing to solve it.  And when it's solved immediately on sight, you can say things like "My child is such a genius.  I hope he can lead a normal life."  But even more importantly, the little skills allow the little genius to crush advanced academic work.  Oh yes, somethings going to get crushed, but it's not going to be my academic powerhouse.  I've always said that COGAT or NNAT test prep, when done properly, is nothing more than building academic skills.

Solving things on sight is just working really quickly from practice.   There's nothing magic, and when researchers give fancy names to cognitive skills like 'visual acuity', it's because they don't work with actual children enough to identify what is taking place when a child solves a problem.

Here's a demonstration of the single most important test taking, school crushing, advanced math course decimating Little Skill.  It's called the 2 Step Skill.

Turn this shape 1/4 turn counter clockwise.
This hexagon has become my favorite shape of the 160 I chose for their properties because it exemplifies the Two Step skill.  If you are a child who is not adept in visual acuity, this is a hard problem.  By the way, the solution set also includes a horizontal flip, a vertical flip, and a measurement of whether the child is going to read all of the answers before starting their work by choosing an almost good answer in C followed by the correct answer in D.  B is a clockwise turn, testing 'check the answer' for a kid who just saw 2 clockwise questions and is going too fast.

The solution strategy is to break down this shape into a rotating problem that is much more doable. Step 1 - find a shape that is easier to turn counter clockwise, maybe like a clock hand or something else, and turn it.  Step 2 - reconstitute the original shape from the part.  Here are some possible shapes that you could turn instead:

Turning just a line is obvious and works well because it can be compared to a clock.  The second version works better with regular polygons that have an odd number of lines (like pentagons or heptagons).  The 3rd version is not intuitive, but it turns out that a square is easy to rotate and the hexagon can just follow.

There are similar two step processes for judging changing of dimensions of the shape and dealing with the vertical and horizontal flips.

By the time we're talking about competitive math, algebra or the SAT, the Two Step skill will be split into problem decomposition, translating the problem into an easier one to solve, or solving the whole just by solving a part.  I don't bother explaining this during coaching because everyone gets Two Step.

All questions on all cognitive tests are at least two step, but at younger ages there are questions that play the role of introducing the next question and other skill measuring techniques involving the answer set like the one presented at the top of this article.

There is a prerequisite little skill that is much more powerful.  It's called 'Seeing'. To break down this problem into steps, you have to be able to see this shape differently, to see it's details.  It would be nice to see that there is a symmetry in this shape, but that's not germane to the problem.  Seeing that there is a piece that is easier to turn is the key.  I call this more powerful, because if you're only armed with Seeing, half the battle is won.

The Two Step skill and the Seeing skill emerge from application of the Big Five Skills.  Watching this happen is the most satisfying experience for an academic coach.  I try as hard as I can to avoid teaching little skills. With younger children, we have to review clocks and work our way up to this.  Somewhere between ages 6 and 8, I usually have to help and suggest or demonstrate.  But after age 8 I'm more than happy to wait for 25 minutes on a single problem for the child to devise and choose their own method and then explain it to me.  That's why there are 3 examples above.  I don't care which route they choose, I'll be rewarded that they took ownership of the whole process, and ownership is a Mega Skill somewhere in the Grit realm.

Rotation plays a minor role in cognitive skills tests before age 5 or 6 because girls lag boys significantly and the tests strive to be gender neutral.  Lately girls have gained this skill and the tests haven't responded yet.  Be forewarned that the tests are going to have to change to keep up with scores.  More on this later.

You're probably thinking that Legos play a big role because Lego builders spend a lot of time rotating diagrams in their brain.  I thought that Lego's play a role because Lego builders spend a lot of time figuring out what the steps are to get to their goal.   Maybe the edge goes to boys because they are developing 'Seeing' and are used to looking at shapes by their component parts and dimensions.

But in fact I have a lot more problems with boys on the Two Step skill.  Girls spend much more time thinking 'I don't know how to do this, but my academic coach keeps saying find the steps so I'll try that', whereas many boys are thinking 'screw you academic coach, I'm going to solve this just by looking at it and knowing the answer', which they don't.

The way I generally teach this skill is to never give a one step problem.   Shape Size Color Count for 4 year olds is mostly about the skill of seeing and visual number sense, but all of the problems have at least 2 parts, albeit doable parts. The questions emphasize vocabulary, because the easiest way to see something is to name it.  One step problems don't teach the Big Five skills. The difference at this age is that the steps can't really be linked yet.

Between 5 and 6, there's so much material on the market that I've never bothered to compile a thorough, methodological course.  I just rip the pages out and reorder them or use Building Thinking Skills Grade 2 and 3 (the non-verbal half, not the more advanced verbal half).  Shape Size Color Count put us about half way through the non-verbal part of BTS Grade 2 and 3 by age 5, because when you teach skills at an early age, they gain their own power.

Test Prep Math formalizes the Two Step skill in a multi-step format that covers the Big Five thoroughly but hammers away specifically at Two Step and closes any gaps in Seeing.  By 5th grade math is all multi-step, then multi-multi step, so there is a lot at stake.  That's the problem with 5th grade. There's a big leap in academic skills and no training, whereas with a little training, a 5th grader could be blowing through 7th and 8th grade work, which is what kids are facing in many gifted and talented program.

*The asterisk near the top of this article is a hint that my poorly drawn diagram required some organization first, although just a little.  You had to translate my rectangle to a square before proceeding.  Sometimes this little skill stands on it's own, sometimes its a prerequisite for finding the two steps.  It's a skill for older kids.  I'll cover it later.

No comments:

Post a Comment