Saturday, March 31, 2018

Step One

I see a strong correlation between what we're doing now at the end of grade school to make gains on the TTWBN and what we did years before simply to gain entry into a special program.

In the this series of articles I'm going to rehash the groundwork and put a bookend on it.  I think reading is the foundation, so I'm starting with reading.

In the last article, I stated that success in education is highly correlated to the level of discussion that takes place in the home.  There are only 3 areas of research that have identified a cause of intelligence (roughly defined as permanent academic skills that manifest themselves in a strong, accelerated academic performance).

The first is summarized in Welcome to Your Child's Brain and concludes that if you maintain an ongoing one way discussion with your infant, your infant will reach age 4 reading at a 6th grade level.  I've see parents do this and it's breathtaking. 

The second area of research is more important because most of us are too busy being a parent to talk.  This line of research concludes the level of vocabulary used in the house will determine you're child'd education potential.  I like this line of research better because it allows for a late start.

The third area of research is presented in The Read Aloud Handbook and states that reading to your child will put them permanently ahead of the crowd.   I like this approach even better because I was never good at having an ongoing discussion with my child because he was always knocking something over, and 'Please refrain from disassembling you're brother's block tower until he has indicates disinterest' didn't seem as appropriate as shouting 'Stop it right NOW!'.  During nightly reading, however, we could have some fairly productive Q & A.  Nightly Read To is good parent training.

What I like best about reading, however, and the reason I put it number one is that many kids get into special programs simply because they do nothing but read.  They struggle mightily with figure matrices, and it takes them extra years to finally get past the test.   But once they do, they generally end up permanently at the top of the academic heap.   Whereas my approach is simply to cheat with lots of logic and problem solving.   Why spend 6 years reading when you can just spend 3 months in thinking and working memory boot camp?  Being the underdog and trouncing readers is quite satisfying.  Then I stepped back and wondered 'What if a child did both?'  Light bulb.

In the introduction to Pre-K Phonics and Conceptual Vocabulary I lay out a reading program that goes way beyond over the top.  It was the most fund* I had with my kids.   I probably only need a few changes to my advice:

  • 'Pre-K' is somewhat misleading because it goes straight through 2nd grade material.
  • No child will ever grasp the difference between 'dew' and 'due', but presenting a fairly advanced and confusing concept at such a young age pays dividends for test prep.  (I should write a whole article on this bullet, but in short a child who knows there is a concept lurking out there that is extraordinarily complicated and thought consuming is on the verge of some serious thinking when faced with cognitive skills workbooks.)
  • You will definitely want science and nonfiction represented in your reading list, but do not show any enthusiasm or push this in any way.  As soon as you hand your child the Magic School Bus and indicated that it is really important to know science, science will become uncool automatically and you may discourage a future scientist.  Same with history.  Try to look at science books nonchalantly.  
*Fund is a typo.  It was supposed to be 'fun'.  But I'm going to leave it as is because I think fund is just as appropriate.  However, reading was a lot of fun.

When we read, I'm more than happy to short circuit the learning process and define words, share background and history, point out logic.   The child will get enough time testing their skills in silent reading and picture books.  As a bonus, eventually you will lack all credibility and merely stating the obvious becomes an exercise in your child pointing out why you are wrong.  But that comes later.  In the meantime, this is the best of all times to make up for the fact that you didn't carry on a lively discussion at ages 2 and 3.

The classical approach to education reserves this time in your child's life, maybe up to 4th grade, for packing their brain with as much information as possible.  Pack it in.  Then jam some more in there.  Reading together will help you do it.  This is a low pressure exercise.  Throw spaghetti at the wall and see what sticks.  You can do this a little at a time or use a spaghetti cannon like I did.  It's not really about gaining anything but just having fun.

Wednesday, March 28, 2018

The Covert Blog

I'm trying to minimize the SEO on my blog.  SEO stands for search engine optimization, and it means that you put key words in your articles so that it shows up on search engines.  If my editor finds out, then I'm in trouble.

In this article, I'll answer a common question that I get.  Where is this heading?

From the beginning, I've found summarizing my research for the public allows me to scrutinize my evidence and edit out failed experiments so that what's left is reliable advice that you can bank on.  In the first year, when I was competing for a spot in a "special school program" (you know what I mean) I nailed that test for that program.   As I was writing, and reviewing past articles a month or so later, I would see things I missed, obvious things, and the door was opened.

I feel like this special test (you know what I mean) is 100% crushable way beyond the required cutoff score.  The pedagogy to get there is counter cultural and counter intuitive.  I don't see evidence that it can be replicated in a school setting except in a few standout programs led by visionaries.  Most parents will never meet success because they can't let go of 'learning something'.  'Something' always interferes with 'learning'.

I'm turning my attention to that other test that 40,000,000 kids take every year in school.  My research is sneaking into my blog whether I like it or not.  Our target is this year and then again in 3 years.  It is much more competitive than the first test mentioned above, and the approach is almost identical with the exception of shapes being replaced by advanced math and the pictures replaced by unknown vocabulary words.  I refer to this test as the TTWBN (the Test That Won't Be Named test).

Most parents face both the special test and the TTWBN test for entry into a special program. Before 2nd grade, the best way to prepare for the TTWBN is just to be 2 years ahead in school.  Somewhere around 2nd grade, other bright kids catch up, and it's not enough to be ahead.  A child has to master academic skills at a very high level.   I'm going to write more about this test without giving away the most critical competitive element - its name.

The common view of special programs is that that the children of wealthy parents will always have a competitive advantage.   The skill set behind this test is almost always attributed to inherited or genetic intelligence, a myth which has been dispelled.   The genetic link only makes sense to researchers oblivious to the scientific method and who have never met an actual child.  'Intelligence' is not definable let alone measurable, and you can't correlate an unmesaruable variable to anything else no matter how much wishful thinking is passed off as results.  If you sit in a wealthy household, you'll observe educated parents maintain an environment rich in vocabulary, discussion, and reading.  Education is highly correlated to wealth.  Vocabulary is the foundation of the whole enterprise.  Thus wealthier households are much more likely to produce gifted children.  The research on vocabulary as the predictor is strong, compelling, and generally ignored.  If you sit in the house of a poor science teacher, you'll see the same dynamic in action and the results are the same.  If you don't have a stack of data on household discussion and test scores you'll miss the dependent variables.

So my first long term goal is to put vocabulary and reading into the poorest households at the level that my children experienced.   It's unlikely I'll do this, but one of the children who went through my program (thanks to a parent who found out it's possible) will decide on a career in education.

The other long term goals, in order of priority, are for bright thinkers of the next generation to tackle poverty, violence, and the propensity of governments to spend the money of the next generation and bankrupt their educational and social systems.  This makes me a liberal and a hard core conservative at the same time, so I'm throwing in a forth goal that one of our future leaders will get democrats and republicans to work together, something along the lines of 'let's spend money on poverty by doing something effective' subject to 'we can't steal money from the next generation to do it'.  Sounds like a republicrat program to me.

I've been watching young people step up in two areas recently; both areas have been in the news.  They are beginning to touch on the core arguments but are not tackling the lies and fallacy and mislogic and ingrained misthinking that need to be overcome .  They're close and they're hearts are in the right place, but we really need a few young John Locke's to step up and transform the world in these areas. 

I'm too busy to do it myself.   I have too much education research to do.

Saturday, March 24, 2018

Really Bad Advice

My google news feed has delivered articles from the SAT experts.  I've been reading how to solve the hardest math problems on the SAT to see if I can improve my super secret strategy for the TTWBN test.  I'm learning that the experts don't know anything useful.

The goal of an expert is to dissect the problem down to steps that lead to the solution.   This teaches nothing, of course, except for a memorized list of steps for a problem that will never be seen again.  The solution advice has an element of time management, as in narrow down the problem to the work that has to be done in the shortest time possible.  This approach will backfire, because once you short circuit the analysis with time pressure, it's much harder to find the right path.  Dead ends will be stress inducing.  Unless you are an expert and already at the 1600 level, in which case it's easy. 

The TTWBN test has no time limit, and we're going to take full advantage of that fact, like 4 hours per topic.  The difference between preparing for the TTWBN test now and the SAT in high school is that we'll spend one or two sessions under time pressure before the SAT .  The prep process is going to be identical, including spending 10 minutes per question.

I've rarely mentioned one of George Poyla's strategies for solving geometry problems.  Rarely mentioned it, but we do it all of the time and it's behind 'Read The Question' for little people preparing for the COGAT.  He warns readers that geometry proofs will need to use prior results, maybe from the last proof or from last week, to solve the current problem.

The version that I use for grade school is that if you see a geometry, solve everything before you read the question.   I want every line labelled with a length and every angle with degrees.  If it's an algebra problem, be prepared to rearrange and transform.  I've written before about this in the context of verbal analogies.  Here's what inevitably follows:

  • We get stuck because someone forgot that a + b + c = 180 or adjacent angles sum to 180 or something else that we didn't cover yet.  So we cover it.
  • During this process, the characteristics of the problem at hand become clear.
  • The solution strategy presents itself and the answer usually becomes known before the pick list is surveyed.
This is a much better approach than "What I am supposed to do?" followed by me explaining solution steps.  I might as well talk to the wall.

Before 4th grade, this skill is called 'Read The Question' and involves me asking lots of what if questions about a figure matrix or verbal analogy for 20 minutes before we actually pick an answer.  I originally did this because really challenging COGAT test prep questions take me a long time to create and aren't found on practice tests so I wanted to get the most out of each question.

I'm currently experimenting with similar approaches to Reading Comp.  When I get to the end of a boring passage, I remember very little about the passage, maybe 2 nouns like bridge and engineer.  Then I get a list of questions that ask who the author is, what type of writing is this, how are they feeling, how many arguments are in the passage.  Then I go back and reread the passage to find out.  3 years into this, it dawned on me that I'm going to be asked this stuff anyway, so I might as well look for it.

A parent might be fooled by the engaging quality of most reading comp passages.  Don't be fooled.  You're an adult now.  Everything is interesting to you.  Your child is totally bored beyond comprehension.  So I announced that after the passage is read, and before we begin work on the questions, I want be told a lot about the passage, like who's writing it, what type of writing is it, what's the point of each paragraph, when did it happen?  I'm inching our way toward not having to read the passage a second time thoroughly (thinking ahead to a timed test).   I'm the same way about the questions.  Was line 32 about eclectic dissension?  Exuberant facilitation?  Ascetic abnormalism?  If we're luck, the answers will have about 20 words that need definitions analysis in the context of the narrative.  Unless it isn't a narrative.

Will the child take the hint and adopt this approach to reading or math?  Certainly not in my presence, out of spite, but probably in the classroom and when it counts on the test.  I've caught them both doing things properly when they thought I wasn't looking.

So here's my bad advice.  If you follow my approach properly, your child will get through very little material, probably do it wrong 5 times, forget the next day what was learned, and not have any academic knowledge to show for it.   All the while, the important skills will be forming.  Then one day they will magically know everything and things will be really easy.  The first few months are a struggle.

Saturday, March 17, 2018

The Test That Won't Be Named

In this article, I'm going to jam 7 articles into one because I'm really pressed for time on the weekends.

Review of Home Schooling Literature
I've been reviewing home schooling guides lately to see if there's anything that I can add to my At Home School curriculum.  "At Home Schooling" means doing a little extra work weeknights and weekends to make up for the slow pace of learning at school.

Home school curriculum guides are pretty disappointing.   If I were full time home schooling my child, I would be planning to send the child to Stanford at age 14 because home schooling is so easy.  The curriculum guides shoot for something more average.

As most curriculum guides point out, trying to teach anything to your child is really hard.  What they don't point out is that your child will learn at an accelerated pace once you stop teaching.  The impossible becomes the easy.  The secret is in the approach, which I will describe in the next article (below).

The Secret to Learning
Almost every week, I have to remind my kids that they have to slow down.  I had to tell the younger one this story again.

There were two equally bright, equally capable children.  One was dumb and one was a genius.  The dumb one looked at a hard problem, became frustrated because he didn't know it, and started guessing.  He got the wrong answer.   The genius looked at the same problem, became frustrated because he didn't know it, and started to work on it slowly one step at a time.  He tried 3 times to do it, and finally chose the answer, which was also wrong.

A third child who was equally bright and capable also struggled with this problem.  He was smart.  He also took a long time to work through this frustrating problem, and after his fifth try, he bothered to check his answer, found a mistake, and fixed it.  The smart child got the correct answer. 

The smart child is getting 99% on the Test That Won't Be Named, but the genius is stuck between 85% and 95%.  Both are learning about the same amount.  Maybe the smart child is getting a bit more out of the learning process because he's checking his work.  What's the problem here?  The problem is that the smart child is fixated on the goal of a solution, especially the correct solution, and the genius is more interested in the learning process.  Eventually, the smart child is going to be in an advanced accelerated course (or maybe pre Algebra) and the work is going to be really hard.  Both the genius and the smart kid will make lots of mistakes, and this will bother the smart kid so much that he drops out.  But the genius, who doesn't care about the answer in the first place, will just plod on as usual until he has a PhD in a joint Law Medicine Chemical Engineering Medieval Slovakian Literature.

I've warned the genius that he better start checking answers because if he doesn't get a perfect score on the TTWBN test he can forget about AP courses because he won't get into a good school.

The Secret For Parents
Among equally capable parents, we find dumb, smart, and genius parents.  The problem that parents need to solve is that you have a child doing a problem - whether it's a cognitive skills exam, or one of the 2 main sections on the TTWBN test - and your child is totally not getting it.  Dumb parents expect their child to get it, smart parents expect their child to get it after a long struggle, and genius parents really don't care.

Once you see a child go through this process, you get it as a parent, and work and frustration is replaced by work and learning.  For this reason, the 2nd child should always end up twice as smart as the oldest sibling, given a fraction of the learning time.

When I was a dumb parent, I came up with the parent skill set in order to survive the first few rounds of my ridiculous At Home School curriculum goals.  The very first goal was to skip first grade math and do 2nd grade math starting on winter break in Kindergarten.   This was the worst and best idea I ever came up with.  (Tip - if you do hard core COGAT test prep at age 4, 2nd grade math at age 5 isn't all that challenging).

As a reminder, my survival steps include start every problem by acknowledging that you are totally baffled, take a long, long time reading the question, going so far as to do a workbook on the topic before you get to the answer, make a lot of mistakes and go out for ice cream any time the child gets 100% wrong, and if a test is coming up, check the #%$!!!! answer.  The parent will encourage these steps.  For the parent, I'd like to add 1) set your expectations at zero, 2) I really mean zero, not .0001 but zero, and 3) stop looking at the solutions.

You can't practice learning skills (see prior paragraph) if your child is doing a 30 question timed worksheet or knows the material or doesn't make mistakes.  That's why we have a pace of 1 to 5 super hard problems in Math House.

I always considered reading to be a filler activity.  I'm beginning to think differently.  Competition for GAT seats is between kids who read 6 hours a day, and those of us who will just become really good problem solvers (aka shapes, math and logic) and cheat our way into the program.  Cheating is much more satisfying and is the basis for higher order math.

To be on the safe side, we did lots of vocab ( and 2nd grade phonics starting on day 1 (Pre-K Phonics Conceptual Vocabulary and Thinking).  But it was always primarily silly and fun.  Why discourage a life of reading by putting pressure on the first year?

I think my casual approach to reading is the reason language arts thrived in Math House.

Yes, I grilled the kids at the Word Board (How would a commander on the battle field use the word 'dispersion' in a sentence?), but they didn't actually have give me a proper response and I didn't want to take the words down because I was going to quiz them on the synonyms in a few days anyway.

But mainly we went slowly and had fun.  When I say slowly, I mean when you try to slow down to nothing the child learns at a highly accelerated rate.  That doesn't make sense until you see it happen, but it always does.

The Magic of Slow
I've decided that I'm no longer teaching math in Math House.  Once again, I want to teach How To Figure Out A Problem.  We lost that last summer trying to tackle high school math.  Figuring out a concept is a much more useful skill than getting a correct answer on known material.  That was the whole point of TPM.  If your child masters Figuring Out A Concept, then At Home Schooling is more productive.

In order to prepare for TTWBN, we've been working with an SAT test prep book.   This doesn't mean that we're tackling high school material at a high school level.   The SAT is more like grade school material for an advanced child in really convoluted problems.  This characterization of the SAT motivated Test Prep Math and it's been paying dividends ever since, until we started doing high school math last summer and started to focus on knowing match concepts.

Here's a problem that demonstrates the full range of skills, those listed above, and the skill of Seeing (aka take time to look at every element of the problem and see the things that other kids miss for lack of vocabulary or patience).  No matter how old your child is or how long he's received this training, he still forgets to practice the basic skills because he's in a hurry to finish math and get on to something more enjoyable, like going to the dentist.

The triangle above is isosceles and AB > AC.  Which of the following is false?

I'm going to omit the answers because of an important technique Poyla's How To Solve it  (1945).  When I translated Poyla for 5 year old's preparing for a gifted exam, it becomes 'Read the Question'.  The translation applicable to preparing for the TTWBN is 'if you see a geometry problem, solve everything before you look at the actual question.'  (If this were age appropriate SAT test prep, then I'd take Poyla at face value because the topic of the book is geometry proofs for high school students and we'd be working under time limits.)  The version for algebra is 'you're going to transform the equation so stop trying to solve it in your brain' and for trig, 'get out the basic formulas and be prepared to do geometry or algebra on top of that'.

Anyway, we reviewed the definition of an isosceles triangle (totally forgotten since age 5 training), the sum of the angles in a triangle, and a hint where the base of the triangle is.  There are the 3 steps that require Working Memory.  Love this problem.  Don't care about the solution.

Initially, this problem resulted in guessing so I had to jump in and 'help' by asking questions.   When I work with other people's children, they are more than happy to work thoroughly and patiently, but when I work with my own children they get frustrated and guess.  Am I exaggerating?  No.  This is why it's so much work for a parent.  Other kids just assume that I'm a teacher and therefore this will be a doable problem or else I wouldn't teach it, and things go well, but my own kids assume I'm an Insane Tyrannical Cruel Math Despot and am torturing them.  You will face the same problem with your own children, which is why the survival skills above are so important.

We've been working consistently at a pace of about 5 problems per day, and over time the child might do 3 problems on his own (incorrectly) and only need help on 2, and before you know it, he's back to needing help on all 5 problems because I had to switched to much harder material.

Anyway, it was this problem where we ran into guessing and I decided I would much rather have him just work the question than try to solve it until he substitutes his subpar approach with '15 minutes of reading the question and 1 minute of getting it right'.

I've been happy to ignore reading until now, just doing the minimum lots of vocab and a couple hours of reading a day, an approach that paid dividends, but this year the older one has to take TTWBN for real and the younger one would rather do the verbal sections than the math sections to spite me.  So it's time to get serious.

When I bought the SAT books a few years ago (2nd dumbest and smartest idea ever), we had a lot of success but my 5th grader and I failed at the reading comp.   We never made it past baffled.

I knew a high school English teacher named Yoda who taught SAT test prep classes and begged the little green guy for advice.  He said, 'Ask why you got the question wrong, you must'.   I'm not kidding, aside from the Yodese accent; this is the only thing he said because we were sitting in a Boy Scout meeting whispering and then got shushed, and I haven't seen him since.  For a year, we kept coming up with the answer 'Because neither of us know what the heck we're doing trying to do with SAT reading comp questions in 5th grade' and then gave up.

Now I've got a 4th grader and a 7th grader with identical books (each have a copy) and I'm starting to get it.  If you've got a 99.6% GRE level in vocabulary (because on the pre-test you got a 50% so you did some serious test prep back in the day) or a good dictionary, the reading comp section boils down to...but first I should point out that given the age difference, it's a totally different experience with each and the 4th grader finds those small passages that ask about sentence structure - saving the long passages for 6th or 7th grade.

By the way, to overcome the vocab deficit, I've found that about half the time if you just add a 'y' to a word it's good enough.  Decisive becomes Decisiony and we can move on.  The rest of the time its a longer discussion.

Anyway, it once again boils down to Math.  It boils down to math.  It's all just logic, one word at a time, counting sentences, iterating.  If Math is 100% language based (I've said that before) it's only fair that reading becomes 100% math based.   The left-brain-right-brain theory turned out to be totally wrong.

Or, if you don't like that answer, it boils down to math in the sense of be baffled, spend a lot of time on the question (including the pick list), go slow, make mistakes and try again, and check your work.

It's also patterns.  By the time we're done, I'll know every technique, aspect, variation, and trick of the SAT.  For example, when an answer choice is 'the author reluctantly agrees partially', you need to find concrete evidence in lines 30-33 of reluctant, agreement, and partial not whole.  Applying Poyla to this material, you better be able to tell me the author's life story after you read the passage and before you start answering questions.  It took me a year to figure that out, but now it seems obvious.

The Danger of Test Prep Classes
The problem of a classroom of any type is that to serve all 20 or 30 students, you have to TELL them the material.  All kids are paying the same amount, and they'll all come out KNOWING the material and performing well on a test if you just tell them.   This will work on a standardized test or even some gifted tests for some kids with specific learning styles.  I worry about the longer term impact (jury is deliberating).

The problem of TTWBN is that there isn't enough time to teach all of the material that the test covers at the level we need to be each year, and this is the big year.  So I'm back to focusing on figuring things out.

How important is At Home Schooling?  Is it important enough for me to set aside a few hours a week, maybe a few more for research and preparation?  Is it important enough for me to go through the frustration and headaches?

What will the child think if I say 'This is not important at all to me to spend any time on it, but I'm going to make you go to this totally unimportant class'.  The child cannot visualize money and he doesn't visualize you sitting in traffic.   If you are not physically there going through the same pain, a bright child will conclude you do not value this activity at all that you are making him do.   You won't see an impact with little kids, but you will see it later.

Sunday, March 11, 2018

The Kindergarten Challenge

Here's a challenge I received from a reader. 

The 1st grade child scores 99% on the NNAT one year than falls to 80% the next.  Reading and math scores also fall.  All scores have to be near the 100% mark in three months for GAT entry.

The child is going to be home schooled.  I'm very excited about this.  It only takes a few hours a day to give the child 8 hours of education, and the child can sleep in every day which is critical for intense instruction.  This leaves about 50 minutes for test prep and 2 hours for art, crafts and projects every day and 3 hours of reading.  I consider science to fall under crafts and projects at this age.  Think sorting rocks, vinegar and baking soda.  First grade will take about 4 months under these conditions, and second grade another 4 months.

The parent needs to find out the times of day when math works.  Is math first thing in the morning, or is it morning painting and Read To?  Test prep needs 2 times, one in early, late or mid morning, and one sometime in the afternoon.

There are a few reasons why the scores fell year-over-year.  I could write a whole article just on that topic. For now, the things I care about are a) anything score 50% is not a bad starting point, b) three months of prep is better than eight weeks, and c) we need to slow down the pace of learning, probably by about 90% and ramp up the complexity of the material.  If the child did not do well on the test because the parent teaching methods and attitude are a total disaster (been there) then we need to fix this, which will be a separate article.

Yes, I said slow down the pace of learning.  This is probably the biggest factor in GAT preparation.  My pace when I coach is 1 problem in 20 to 30 minutes (depending on the child's age) and 5 or 6 problems when the child works alone.  We're just as slow in math, and I've managed to get two kids into high school math at age 9 or 10 on 5 problems a day.  Not that they're especially talented in math.

The premise of "slow" is slightly counter intuitive under a deadline.  Here's the explanation.  When you build an academic culture where a little work goes a long way, you're using the skills measured by the GAT tests, skills that are also critical to standardized tests like the MAP.  Unless it's a timed test, but we can account for that after the learning takes place.  When you have a culture where problems are easy, correct answers are expected, and worksheets are long and fast, the child is going to totally bomb on a test like the COGAT and NNAT.

I would make time for Vocabulary Workshop because it's so much fun and children learn how to eliminate answer choices as they quickly progress toward harder material.  I would have a Word Board for something because it's where adult discussions take place and where the child has to stand up and deliver.  Or fail.  There's always the next day.

For math and test prep, let's teach this child so that he or she gets to 99%.  I've been going back through my articles thinking about my teaching methods.  I don't think articles are clear on my preferred approach:
1.  Give the child super advanced material and let them flounder.  Eventually they will pick up the skills to work with super hard advanced material.
2.  Give them advanced material and let them do all the work before you don't grade it.  (No typo, read that again.)
3.  Walk through the super hard material together, one question at a time after they do it.
4.  Do it with them, one question at a time, mostly just asking questions.
5.  Give them simple material on a super advanced topic so that they can learn one step at a time on their own.
6.  Give them last year's workbook (last year may actually be next year depending on the circumstances) so that they can catch up on material they need to know in order to keep up with 1 to 3 above.  They can do this on their own, or with some starter help.
7.  Lay 5 skittles on the table, one of each color, and provide a skittle each time your child gets a correct answer.
8.  Give them a skittle just for making an attempt.
9.  Do the problems yourself while they watch.

Lately I've been doing 4b, which is to break down a problem entirely and a class or rules, but I didn't do this in first grade.  I did say Shape Size Color Count over and over when they were stuck to remind them not to look at a problem for 15 seconds and announce that they were stuck, because that's called 'The Beginning of the Work'. 

Which approach do you use?  I used them all.

I used a variety of material, not because of the Spaghetti approach, but because sampling is the best way to find out what works, a child needs to learn from all materials, and a child needs to learn all learning styles and accommodate all teaching styles.  It's not a matter of what the child likes best (aka the easiest), but what works best on which day to meet our goals.

Finally, both cognitive kills tests and the upper levels of standardized tests in math and reading require deep, careful thinking over an extended period of time, mistrust of answers, tackling something unknown, surprising, new, with subtle, hidden complexity.  How to you train a child to have these skills?  #1 through #5 on the list above.  It works the best with 1 super hard long 25 minute mind numbing problem, but in practice, this is a total disaster with crying and yelling, so I've settled on 5 medium really hard problems in 25 minutes.   After that, brain exhausted.

I almost forgot.  We also did music starting in Kindergarten.  I gave my child an electric piano and the Piano Adventure series, and no help what so ever except for tempo. 

Remind yourself that the child will be sitting in some advanced class someday without your help.  The child will be taking a test without your help.  This is what you are preparing them for.   So many people get hung up on them having to know math because they have to get above 95% on the math section.  It's so much easier to train them to think and then math comes really easily after that.

What would this take?  I think a few reading comp books, about 10 to 15 each, maybe 3 math workbooks, judicious use of the web, 2 vocab workshop books (current followed by current  + 1 for starters), maybe one reading comp book, but lots of reading of all kinds.  I would go to Michaels and buy lots of cheap crafts and things like that bead thing, concentrating and creativity activities, painting, and then whatever test prep books you want. 

Origami.  Almost forgot.  Origami is really good for visual spacial and fun, and the test we're challenged with in this case is the NNAT after all.  You can create all sorts of animals.  Do not let you're child do an activity that requires you to do it.  It's kind of the opposite of test prep and how I do math. 

Totally excited about this.  The thing I got out of this time period is a) I learned how not to be impatient or expect anything or care about correct answers and b) I ended up with a much closer relationship with my children and some credibility with them.  a) led to b).  a) also leads to a boatload of learning in a short period of time.

Saturday, March 3, 2018

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.
  1. 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.
  1. 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.