Putting Skills To The Test

I've been working with a few hypotheses since about 2011 based on my research into the COGAT. Six years later, it's time to see how these hypotheses faired over time.

Since I am the only person in the universe who a) believes skills exist, b) believes that skills are learnable and c) isn't making you buy a product or service to learn about skills, this website is pretty much your only resource. It would be nice if it were accurate as well.

Here are my hypotheses.

1. The COGAT measures the skills that predict academic success.

This hypothesis is based on the simple observation that school districts pay a lot of money for the COGAT in order to populate their gifted and talented programs.  I read the research of the current test author and determined that he stands apart form cognitive skills researchers - all skills and no genetic intelligence.

Any parent who forgoes COGAT test prep (or a similar cognitive abilities test) has no interest in a child with cognitive abilities.  

Unfortunately, future academic success is dependent on a child who has continued interest in academic pursuits.  If the child lives in a house that devalues academics or goes to a school that devalues learning (aka most schools governed by No Child Left Behind) then hypothesis #1 may be undone. What started as an assumption is now ongoing research.  So far, so good.

2. The skills are age independent.

Another way of stating this hypothesis is that once the skills are learned, the child has them forever.  A child could pick these skills up at age 3, or age 15.   Everything I've seen in the last 6 years supports this hypothesis.  A corollary to this hypothesis is that the probability that the child will pick up these skills decreases every year after 1st grade, probably because of NCWLB, with the exception of age 15 (which I haven't personally researched yet.)

I first came up with this hypothesis while reading a description of the classical education in the Well Trained Mind. The classical education has a breakpoint every 4 years and is based on the development of the child, brain or otherwise.

I've noticed leap in skills around 5th/6th grade academic material, certainly by middle school, which I've had some fun with recently and describe below.

3. The list of skills is boring and unremarkable.

I'm not going to restate my skill inventory here, but if you read the list in prior articles, it's not really earth shattering.   I think I would have more readership if I could come up with clever sounding names for the skills or write articles like '10 Things You Didn't Know About Skills', but there are only 4 or 5 things you didn't know, and those are the skills. 

What I find more interesting is watching a child go through the transition from not using the skills to overcoming very difficult material by applying the skills.  Take Mistakes, for example.  A child doesn't need this skill, and is not incented to use it because it requires some effort and controlling emotions.  The reason the child doesn't need this skill is because parents and teachers are willing to explain the mistake, show the solution, explain the solution.  There is a high price on making mistakes in the first place.  Once the support structure and penalties are removed, the child has to go through the process of proving to himself the value of mistakes, as in make one, learn something, try again and again, and achieve the solution with no help.  It's like military boot camp.  Not fun when you're there, but it pays off.

In practice, I observe the emergence or application of about a dozen sub-skills during this process.  The sub-skills are germane to the subject and child specific.  I've never seen a reason to discuss most of these (except the big 5) because we'd end up just replacing spoon-feeding-training subject matter with spoon-feeding-training sub-skills and be back to a helpless child who's not getting it.  Right now I'm tackling middle school reading comprehension with a vengeance and we are heads down on the sub-skills, but that article will wait until we get past the high school entrance requirements.

Recently, a 4th grade buddy came over to play Minecraft.   In Math House, the rule is no math, no computer.  In this case, 'math' meant learning algebra from scratch in 25 minutes or less.  This child is solidly at the top of the gifted spectrum.  I don't know why his parents didn't bother to teach their 9 year old algebra yet - probably because they are not insane - but it qualified him for my research.

During this experiment, I noted that there is a leap in skills required of algebra.  I'm not talking about- abstract thinking or a new language in the form of different syntax or seeing pre-algebra for the first time.  Because of this leap, the child went from 99% in skills to 0% in skills before working his way back.  Also, note that parentheses alone work a magic spell on children that makes them forget everything they've ever learned. 

Here's a transcript of the experiment.

Me:  Solve this equation:  3 + 5 = ? (He responded 8, then looked at me like I was a moron.)

Me:  Solve this equation:  3 + 5 = ___  Does it matter that I changed the question mark with a blank?  (He responded no.)

Me:  Now solve this equation:  3 + ___ = 8.   Is it totally confusing that the blank has moved?  (He answered no.)

Me:  Not solve this equation:  3 + x  = 8.  I am replacing the blank with an x.  Instead of telling me what goes in the blank, tell me what x is.  Is this to confusing for you?  (He answered no.)

Me:  Now I want you to use algebra.   Instead of just solving for x, you have to transform the equation one step at a time.  You can either add a number to both sides, subtract a number from both sides, multiply both sides by a number, or divide each side by a number.  (There are a few more transformations, and I didn't mention expressions, but we're keeping it simple because we only have 25 minutes for this experiment.)

Me:  Here is everything you need to know about algebra.  Look at these 2 equations and tell me what is wrong with the second one:

• x = 2
• 3 + x = 8 - 5x

Me (after a brief discussion): The first one is perfect.  I know the answer immediately.  The second one is broken because it doesn't have a letter on the left side and a number on the right side.  Fix it.  You can only use 1 of the four transformations, and you can only do one transformation at a time.

Rules:  a) apply one of the 4 transformations to both sides, b) only apply one transformation at a time.

We took a break at this point to remember the scale problems from 2nd or 3rd grade math (which he forgot) and assure ourselves that the 2 sides stay equal when these transformations take place.  Then he had to tackle these 2 problems:

• 3 + x = 8 - 5x
• 7x - 15x = x(x + 5)

It's really fun to watch what happens next.  First of all, rules a) and b) from above are both violated repeatedly.  "Both sides" is forgotten.   Gifted kids are gifted in part because they can solve complicated expressions in one shot.  In practice, they combine steps.  Doing only one step and writing it out is like eating broccoli.  When I teach algebra to young kids, I'm always battling them trying to figure out the answer in their head, which they can do.  I'm asking them to stop doing things in the way that they are good at, and start doing things in a way that they are not good at and will likely lead to an incorrect answer.  It's more than Baffling for this reason.  

Next, they forget how to add and subtract single digit numbers.

Any pre-algebra kids learned up to this point is also forgotten.  This includes parenthesis and not adding x to 5, because you can't and x to 5 and get 5x or 6.

I made some really cool observations during this experiment.  The subject wondered what 5x means, and then realized why dot means multiplication - because writing 7 x x to mean 7 times x doesn't make sense.  His skills of analyzing the question were strong.  Analyzing the question in algebra, at least initially, means learning quite a bit on the spot that was not previously known (which I minimized in the problem above).  It's a leap in this skill.  Once we get beyond simple one variable equations, the question analysis takes a leap.

It's hard to make the leap to 5x + x.  What does this mean?  It means that you have 5 x's, and I give you another x, how many x's do you have now?  It's like working with a 3 year old on addition.  Did you forget to add?  Do you want to do it on your fingers, butter bean?  Do I need to invite the 3 year old down the street here to teach you how to count on your fingers?  I really need a control group where I don't antagonize the subject.

The most remarkable observation for this experiment is that the child typically (100% of the cases) get's stuck on what to do even though according the rules, the only thing to do is apply one of the four transformations to the equation.  Maybe they can clean up the expression by making 7x - 15x equal -8x, but that's not what they are stuck on.  Without doing enough of these problems, it is not clear which arithmetic operation to apply to each side.  Addition?  Multiplication?  Subtraction?  Division?  These kids break the transformation down to a simple question & answer, and they don't know the answer.  The correct approach is to try all 4 and see if the resulting equation is getting fixed (aka easier) or more broken.  Algebra has the skill of Mistakes build right into the process.

That is the biggest leap in skills.

At age 5, a gifted child will make a mistake, not be bothered, and try again until the solution is correct.  Really gifted children (on standardized tests, anyway), check their answers to verify that they didn't make a mistake.

With algebra, initially, on each step there is a 75% chance that you will make a mistake, and you may have to try all 4 to see where the equation is going.  That is a 25% error rate built in to each and every step.  Sometimes you might even have to do 2 or 3 steps, trying a series of transformations, before you know you are on track, and you've ended up with a score in the single digits before you get past the first problem.

I've occasionally mentioned that I think drawing is a valid way to teach a child to be gifted in math.  Hand your child a 2 inch stack of paper and a dozen pencils, and ask them to draw a realistic looking horse.  All of the cognitive skills are used to their extreme in this exercise.  Children who draw for a living should become math powerhouses*.  

*It depends on what they draw.  Horses aren't good enough.  Needs something with lines and circles in it.

I prefer crafts for math training to prepare for algebra.

Anyway, the subject passed the 25 minute algebra lesson and his parents didn't complain yet about any signs of psychological damage.