Wednesday, November 11, 2015

Winning the Math Battle

When I first discovered cognitive skills, one of the first things I learned was that these skills could be lost by age 10.   There are a number of reasons.

First, a super bright child at age 5 or 6 is going to spend the next 4 years not using their brain.  When the curriculum finally shifts in 5th grade, they are skill-less.  The first few years of school should build the skill set for 5th grade, but unless the child is way behind in 1st grade, few skills are required.

The second cause of the 4th or 5th grade disaster is the emphasis in the US math curriculum of telling a child something followed by practicing it.  This is not learning.  A child who devours learning before entering first grade is starved to a waif 4 years later.  The child begins to expect to immediately know each concept.   5th grade is a wake up call.

The final reason for the 5th grade train wreck is the concept of "correct or incorrect" that is enforced in math.   It's either right or wrong, and generally speed is involved.  This approach provides a child with attitudes and skills that I would define as the opposite of smart, something like anit-academic skills.  "Did you get it right" is the opposite of "Did you learn something?"

If you dig through my blog you'll see over a year ago I predicted this for my 4th grader, and then later in the year confirmed it.

As part of my research, I've been tracking down parents of children that were enthusiastic learners in Kindergarten, did lots of extra work at home, and generally started school at the "A" level.  So far every single one of them is running into the 4th or 5th grade train-wreck.  Symptoms are frustration, inability to understand a new problem, tears at incorrect answers, sloppiness, impatience, and in many cases bad grades.

I've really enjoyed these discussions.  First, it confirms that I'm not wasting years trying to solve a problem that nobody else encounters.  Secondly, I have the antidote and I've been passing it on.

Here is the antidote.

#1.  Make sure your child has material that would take a person at grade level an hour to do 40 problems, but your child has to spend 45 minutes on a single problem because they are way below grade level for that material.  Think reading comprehension books.

#2.  Assign them a problem or two and let them flounder for 25 minutes.  Then go super slowly through the material to see what they can learn.   Focus on learning how to navigate difficult material, find clues, do things over and over and over.

#3.  Do not look up the answer.  When a 10 year old is doing a math problem for a 14 year old, it doesn't matter if they get it right.  You the parent have to break this bad habit - in yourself.  What matters is learning how to work with difficult problems.  If your child learns to work with difficult problems then the will eventually teach themselves how to get things correct all of the time.  If you announce whether or not they got the answer correct, you are providing a reward for the wrong thing.  (Of course, they will ask and you will have to tell them they got it wrong so that they can do it again.   My experience is that doing this on 100 consecutive problems makes both of you immune to any negative emotions associated with getting things incorrect the first few times.)

If your child spends 45 minutes doing a problem and gets it wrong 5 times, will you announce "Good Job!" with genuine enthusiasm?  If I had a child who spent 45 minutes working on a problem and got it wrong 5 times, I would be 100% confident that this child is prepared to get perfect scores in school at some point, maybe within 12 months, provided they practice this skill on a periodic basis. Conversely, if I had a child who zips through their work at lightning speed and gets 100% correct, I would expect a pending disaster without intervention.

We had our train wreck last year in 4th grade.  I spent all summer practicing this antidote   Picture the best your child could conceivably do in school and all of the best attitudes and practices.  The outcome was actually way better than that.  In math, we focus on these higher level executive skills because other than being good problem solvers, I don't expect my kids to become math professors.  I expect them to learn how to think with the official goal that they think better and do better in their other subjects.

Saturday, November 7, 2015

Coaching the NNAT

I've been slowly working may up to an article roughly entitled "How to Crush the COGAT Without Really Trying".  Unfortunately, "Not Really Trying" is going to be a lot of work for a lot of parents. It's all in this blog somewhere but it's really going to be fun synthesizing it in a ground breaking article. .

As a warm up exercise, it's time to crush the NNAT, specifically the puzzle question where there is a puzzle piece missing.  This is the easiest of all question types and I never gave it much thought.  I don't spend much time thinking about the Weschler, IQ tests, or tests for older kids.  Nonetheless, readers ask anyway because if you want a website written by researcher dedicated to getting every child into a GAT program, I'm the only game in town.

NNAT puzzles, IQ tests, and tests for older kids.  What do these 3 things have in common? The answer is algorithms.

The difference between thinking through a never-before-seen tough problem and zipping through way harder versions of the same problem is the algorithm.  This can be a mental construct or predefined approach to a class of problems, and it can be multi-demensional like a decision tree.

The difference between cognitive abilities tests and IQ tests is the need for algorithms on the IQ tests. That's why my IQ is never going to be great across the board.  I simply don't care that much about creating an algorithm to unscramble words and I'm not drawn to activities that really "smart" people are drawn to that would require this algorithm.  I'm not even that great at number patterns.  When I have to do things like number patterns, I quickly build an algorithm and its usually just trying out every type of operation sequentially to see which one works.

When I was pairing cognitive skills to problem solving skills, an exercise really designed to pair how I think to approach the test versus what the tests own definition of itself, I came across "algorithms" on the cognitive skills list.  Of course, kids develop algorithms when they are first learning how to read but I doubt any children can verbally describe the ones they use.   Algorithms come into play at much later ages.  In the problem solving literature, "trying each operation to see which one works" is a solution strategy that corresponds to the cognitive skill of using algorithms.  The higher order skill is patience derived from having nothing better to do because your loser parents make you do test prep instead of soccer.  But it's given a fancy sounding name, and terms like "number fluency" kept me off the right track for 4 years.

I tried to teach solution algorithms for the COGAT (eg shape, size, color, count) but these were never adopted.  Instead, my children developed their own approaches and I think this is a much better policy for young children when preparing for the COGAT.

Algorithms come from repetitive problem solving.  That's how an IQ test can accurately identify truly bright individuals, by defining true intelligence as "sitting around doing jumbles and cross word puzzles all day".  That's why people think the contrived definition of "high intelligence" is suspect and one of the primary problems motivating Gartner et ilk to pull things like the theory of multiple intelligences out of his back pocket.

Synonyms for the word "algorithm" are "short cut" and "trick".  I don't like these terms because they imply that thinking is not involved.

Back to the NNAT puzzle question.  The algorithms jump right off the page when you see the problems.  Take this example.  What is the missing piece going to look like?

Keep in mind Step #1 in my article on coaching when you do this problem because it points the way.
Here is my algorithm.
1.  Notice that there is a line touching the corner, two corners have a single line in this case.  Eliminate all solution options that don't have 2 corners with a line nearby.  I call this the "corner check".  This could be a line or other type of shape, and it may or may not involve a color adjective.  It could be top/bottom/middle, it could be wide, thin, and many other adjectives.  Coaching sessions would be heavy on the vocabulary.  Hopefully, the pieces in the answer set aren't rotated.  Since girls are deficient in rotating at young ages (because Lego Friends hasn't caught on yet) I think rotation is not used on tests before 2nd grade.

I'm sure the test makers are smarter than this so this would probably not be enough.  The child might look to the interior next.

2a. Look for crossing lines in the middle.  In this case there is one.
Eliminate all answer choices that don't have 2 lines crossing in the middle.  There would be a longer list of terms beside "crossing".

Did you notice the "a" next to the "2"?  Test makers want to find thinkers, so 2a is not complete.
2b.  Imagine that the lines (or shapes of some kind) move in an unexpected direction, like looping.  Uncross out the answers that could have unexpected twists and turns.

Obviously, 2b undoes 2a, unless the picture has a strong pattern, in which case it holds.  A strong pattern is something like a checkerboard.  So 2a/2b is part of the algorithm with strong patterns, but then if you are looking at a strong pattern, you are probably just back to the corner algorithm as well.

Questions that can't be solved by corner or edge checks can result from proportion aspects of splitting shapes.  This is just a starter suggestion.

If you are coaching your child on the NNAT, look for algorithms while you are spending lots of time investigating the picture.  While I'm confident of the corner check, I haven't looked much deeper.