Saturday, February 17, 2018

Totally Doable If Done Right

In the last few weeks, I've stumbled across a whole new group of people who are suddenly concerned about their child's education either because they decided it would be nice to have an actual child in the next few years, or they have an actual child and just found out about the COGAT, or they are getting COGAT scores back and deciding that it's time to get serious.

My Power Mom's Group, or PMG, from last year is officially demoted to Last Year's Power Mom's Group because your kids all met their ridiculously high cutoff goals (and are solidly on their way to additional goals).   There's one more item on the todo list for the next few months and then I'll declare a 100% success rate based on selection criteria that includes a) great parents and b) capable kids.  The new members of LYPMG are going to get heavy doses of my super secret program to crush the MAP test in the coming years.  How similar are the COGAT and the MAP?  COGAT skills are a prerequisite of the MAP, but the COGAT type math isn't what people generally consider to be math and the MAP has way more math than anyone realizes.  If you are not in LYPMG, then you'll read about my super secret MAP program but you won't realize that you're reading about it until I can get everyone in the house past the 7th grade MAP.

For newbies, I've been working on a less insane sounding description of my math approach, with a nice sounding title like Easy Fun Math*.  (*Also known as Ridiculously Hard Insane Math until you get it, and then it's just Ridiculously Hard Math.)

Here goes.

First, read read read read.  If your child only has 60 minutes per day of at home schooling, devote 40 minutes to reading.  If your child has 6 hours a day because it's Saturday, devote 5 hours and 40 minutes a day to reading.

Secondly, do not, under any conditions, every teach math.  The skills your child needs to excel in math are organizing, seeing patterns, trying again, iterating, comparing, trying out different options, defining, extending, explaining, rethinking, simplifying (ie organizing), decomposing (ie organizing), and not being put off by mistakes, lack of information and clarity, and total confusion because if your child isn't working in on a math problem that starts with mistakes, lack of information and clarity, and total confusion then they are not working on a math problem that will develop the skillset.   The super advanced skill set for math includes good executive skills and a lot of Grit.  If your child develops these skills under your guidance, your child will excel in math.  If you teach math, your child won't need any of these skills, won't develop them, and then someday will fail at math.

Look at 'First' and 'Second' again.  Higher order math skills are developed by reading.  This really matters when your child is 2 and 3.  By 4th grade, it will be assumed but not a major factor in the program.

Third, at the 99.8% level, which is totally doable if done right (Totally Doable If Done Right, my new motto, and this just replaced the original title for this article which was Advice for Newby Math Parents), there are a lot of parent skills involved.  While the child is learning each new skill, you will be learning a new skill.  Your child will see math in a different way, and you will see coaching math in a different way.

Forth, your child's math score is going to be constrained by working memory.  I can't stress this enough.  School math needs one or zero working memory buckets in the brain.  Think 'Ann has 2 apples and Bob has 5 apples.  How many apples do they have together.'  Test Prep Math starts with 2 and ends up with 3 working memory buckets - or more - on every problem.  I've settled on 3 since it appears after 3 a pencil is needed.  

Test Prep Math emphasizes messy, sometimes unanswerable problems (in clumps of 3, all mixed up and interspersed with vague words and ridiculous plots).  Now you know why.

There is an ongoing debate on whether or not children should memorize their math facts.   Teachers who need to get all 30 kids in the class past arithmetic errors in 2nd or 3rd grade are generally stuck with memorization exercises  - even in GAT classes.  Researchers who are figuring out how to get kids to the upper levels of math excellence can explain why memorization is counter productive. 
If you search 'Boaler Memorize Math Facts' you should find a few really good articles explanating why memorization is a bad idea by the leading researcher in this field.  You may also come across an counter argument from Greg Ashman that totally misses the point, but get's so close with this diagram that he's one sentence away from solving his own problem.  Look at this diagram:

Note to Ashman, the goal here is not to use long term memory to help with the math facts but to triple working memory.  Also note that this diagram makes me want to sneeze.

Boaler attributes number sense to strong math skills.  Number sense and math fact memorization are two exclusive roads to math, and memorization falls short.   In my ground breaking research I found that use of working memory isn't just a tool for math, it's a math skills generation factory.   The child learns the next level of math skills while working arithmetic in working memory.  When people see the term 'Working Memory', they see 'working MEMORY'.  It's more accurate to view this as 'WORKING memory AND MATH SKILLS GENERATION FACTORY'.  Please note that Boaler's research concerns making math accessible to everyone, but my research concerns a child who just blew away the COGAT and is looking for the next big leap in skills.  

Maybe groundbreaking doesn't cover it.  Here's what we got out of the workings of working memory in action:  an 8 year old who is solving problems off of middle school competitive math tests.

When I wrote, and rewrote, and refactored and added to Test Prep Math, I met my goals to tackle working memory, base skills, and no math if it can be helped.  I failed on the no math part because I couldn't help sneaking in math.  A little geometry, a little algebra, and if you look closely, you'll see the makings of other maths, but I generally avoided division, and avoided decimals and anything else that is on a Common Core list.  This approach doesn't work for everyone.  Some people are short sighted and think of math as topics from a math book.  Others already taught their kids math and the horse already left the barn.

One of my favorite exercises is to do Every Day Math Grade 2 in K.  For those that missed the opportunity in K, it's simply known as Current+2.   I think of this as an exercise in Grit and not math, kind of a warm up to the challenge that will follow.   Last week, a reader shared her child's current math situation which sounds so dire, what with mistakes, frustration, and not getting it.  Once again, my children are even worse in comparison, but we manage to score consistently in the high 90's (like 99, which is what I expect) and do almost no work at all.  One year ahead in math for us and maybe 40 to 60 minutes during the week.  That leaves plenty of time for reading, crafts, and projects.  My secret isn't smarter kids but kids who don't quit.  And we do things totally different, like work smarter and not harder.

After successfully avoiding the memorization of math facts, I've extended the counter cultural approach with not really ever learning math or being remotely competent in any one math topic.  Focusing on underlying skills for years at the expense of math has really paid off in a big way.

You'd think the next step after Test Prep Math would be learning actual math, maybe tackling Pre Algebra.   Instead, we took a detour into competitive math, not really like school math at all, and then I've opened up 7th through 12th grade math topics for any given weekend.  I think we have about 3 20 to 30 minute sessions each week, and the topic could be a first look at derivatives, exponents, polynomial zeros, 'What is sine and why am I making you go through this pain?' or anything else.  One week it was exponents, and the next week my older kid saw logs for the first time and had to invent and derive formulas for logs that corresponded to the exponential formulas that we worked in the prior week.  When this child sees logs again in a month, he will have remember exactly zero of it, but he's got the tools to make short work of it.

After 4th grade, the little one will spend the next year or two working through SAT books.  Other parents will try this and find that it's a disaster.  Our experience will be even worse, but we'll plod on come out with 2 completed books, about 18 practice tests in all, and then move on to the reading comp sections.  I've recently summarize the parent coaching skills needed to get through this approach successfully.  When the 9 year old gets through the first page, 3 problems attempted, 3 wrong answers, and a lot of complaining and tears, I'll wonder why the heck I'm doing this.  Then I'll remember that I've done this type of thing many times before, and it will magically work out in the end.

Saturday, February 10, 2018

Visual Math Et Cetera

For years, I have been asked for a recommendation for 4th grade math.  I now have one, and one for 5th grade as well.  It's called Visual Math.  These are not expensive books.  The authors are from a ground breaking group of researchers that I've been following since the beginning of  Back in January, I wrote an article where I said that our current math curriculum needs to be flushed as an artifact of the Industrial Revolution.  There is equally challenging, more engaging, more pertinent math to the information age.  Visual Math.

Except that I'm stuck on fractions, polynomials, mononomials, exponents, algebra, trig and calculous because darn it, they show up everywhere in math and all fields whether you're doing machine learning, number theory, or Hollywood CGI.  I guess I'm always one rebellion ahead of the next trend.

I don't face the same broad classroom education challenges that the authors of Visual Math face.  I face the challenge of a single kid.  My idea of visual math starts with COGAT test prep, Building Thinking Skills, and the rest starting ASAP, like age 4.  See my curriculum page.   In a house enriched with crafts followed by Minecraft, visual skills are overdeveloped.

But the genius of Visual Math isn't just a much better more appropriate visual (and thus more timely) curriculum, it's the approach outlined by Jo Boaler years ago that is question heavy and solution light.  In other words, spending time understanding and defining the problem, whatever that may be, in the process really learning math, and as an after thought deriving a solution.  You've heard it before from me, and this is where I got it.  There is much more to the approach beyond this.

I'm a big fan of a single problem that is hard, multi-step (working memory intense) and requires a lot of time to solve, preferably something goofy or non-sensical, if that's what it takes to turn a predictable answer into an argument.  I don't want a child to come out of this having mastered 3 x 5, which is useless, but having mastered getting there from the unknown, or better yet, an unknown mess.

And that brings us to 1/2 and 2/3.  A few months ago, a reader asked what to do about struggling with fractions.   I offered to get on Skype, but since I'm insane, and can turn any 30 second problem into a 30 minute challenge, the reader declined.  Too bad.

There are 2 parts to a good fraction problem. 

The first part is 1/2 takes about 3 brain clicks to understand.  I think 98% of the problem with fractions is that kids expect 1 click, they don't get it on one click, and they are frustrated or worse.   I watch this with the brightest children trying to tackle fractions at a totally inappropriate age.  The second part is the fraction in a more complicated setting of a pre-algebra problem.  Too hard for younger kids, but doable at a pace 10 times slower than a 5th or 6th grader.  Solving a fraction problem is multi-step.  When I work with fractions and children, or algebra, or exponents, I expect a few weeks to get them to admit that they have to work the problem step by step.  They are determined to do one single step, because it's one problem after all, and if they have to do 3 steps, then it becomes three times the work.

Kids who are trained in math hit a wall with fractions.  Kids where are 99.9% wizzes hit a wall for the opposite reason.  Both groups underestimate the problem.

Lately I've been working on the next challenge.  How quickly can I get kids to be adept with pre-algebra, exponents/logs, functions, geometry proofs, algebra, trig and calculus?  By quickly, I mean a small number of problems and weeks per topic.  My group is 4th to 7th.

In each case, a few problems can be used to explore the basics.  During this time, there is wonder involved with the new syntax and the concepts that it articulates.  Like the first time a child stumbles on negative numbers or square roots.   A few problems get the job done.  To take the next step requires a special problem solving approach for each field.  We avoid the complicated applications that fill 90% of a decent text book and just stick with the basics. 

I've come up with a one session introduction to trig that addresses many of the questions (about 25%) on a good trig final.  One session for a 9 year old.  I remember struggling with this exact same material for about a month in high school, trying to remember formulas.   I'm really disappointed about how bad the course was and how unprepared I was (not having studied math between 1st grade and trig). But I'm mainly disappointed with the approach to math from the 1920's which I used in high school. 

The last thing I'm going to do is explore the other 75% or so of each of these topics.   I think this will be an 8th grade exercise.  Is it possible to send a child to high school prepared to be bored with A/B calculus or chemistry?  Can this be done with almost no work whatsoever?  I'm starting to think so. 

I enjoy getting articles from readers that include an age and a topic and a description of how much they are struggling.   I think, wow, we struggled much worse.  I can tell them that and actually solve a problem.  I can also state, if needed, 2 or 3 ways to get past it and how long it will take (longer than you think.)  In some ways, this is just like potty training.  Some parents wring their hands over every trip to the potty, and others let their kids poop all over the place until the problem takes care of itself.  The only thing I did differently was discuss plumbing while cleaning the poop off so that I'd have someone I could count on someday to clear clogs.

Someday is almost here in math.  In plumbing, my 13 year old routed the pipes right before his birthday.

Saturday, February 3, 2018

Innovations in Math Education

I promise as soon as I complete this article I'm going to start populating the reading list in the prior article on reading.  But first...

My 8 year math program is about to come to fruition.  In April, math Experimentee #1 (a newly minted teenager who started K with a bunch of my newby missteps) is going to take the MAP test, and after a long interval of not caring, this score counts and it has to be a 99%.  In this article, I'm going to summarize where we are, demonstrate the leap in math skills that happens in 4th grade, demonstrate how my math program is dramatically different than regular programs, and present it in such a way that I lose most readers before I get to the end because that 99% is competing against about 10,000 other kids in Chicago who's parents are all googling 'How To Get 99% on the MAP So My Child Gets Into A Decent High School'.  Also, I'm going to discuss my approach in purely in 4th grade terms to help parents of younger children plan ahead, and explain why Test Prep Math is the way it is. 

Let's start at the beginning.   My first goal back in K was to conquer Every Day Math.   We didn't have to pick everything up at once, just a lot of hard work to show 'You Can Do This'.  My goal was simple.  For Experimentee #1, the goals focused on entering a GAT program in 1st grade, given that we were totally behind because we did nothing to prepare for it, not even phonics or learning to read, but at least the math would be familiar (it would be EDM Grade 2 - a complete repeat) and he would have some confidence.

After crying, forgetting, getting them all wrong, spending a week or two on a single 6 question worksheet page, having to find 1st grade books to practice concepts and skills we never saw before, I transformed the following survival skills into Academic Coaching Skills that we would use for the rest of our lives and pass down many generations (hopefully) of bright descendants until one actually wants to study math in graduate school.  Here they are:

  1. Set Your Expectations To Zero.  Don't expect your child to get anything correct, understand it, remember it, work on their own, or anything.  Even if you do the same problem every day for a week and it's 7 + 6 = ?  This is the parent skill.  The child-parent team skill is to enjoy 'Being Baffled' on totally hard work that has never been encountered before that will take a lot of time to sort out.
  2. Make Mistakes.  Mistakes are the key.  After a while I stopped looking at solutions because I expected mistakes.  
  3. Take A Long Time.  When we slowed down to 30 minutes per problem, we started making progress.  This is also known as 'Read The Question' where we spent more time thinking about 7 + 6 and what it could mean and how to work it before solving it.  
  4. Other tips I put in the blog over the years, but the top 3 were the key.
So here's what we got.  At one point, we sat down and looked at Student Journal #1, with every single problem answered.  Every single problem.  No child anywhere does every single problem in a math book, or every page or even every chapter.   This is a rare and invaluable life lesson.   Experimentee #1 has an extremely high tolerance for work, chores, painful work, hard chores, ridiculously hard chores.  Even better, Experimentee #1 is not put off in the slightest by being totally confused on material that is way beyond his abilities.

Somewhere during this process, the speed of learning and work accelerated to match the challenge, and by about 1/2 through Student Math Journal #2, we quit because the challenge was gone.

Experimentee #2 experienced hard core phonics (Pre K Phonics Conceptual Vocabulary and Thinking age 4.0) and hard core math (Shape Size Color Count age 3.9) because I wanted to address any gaps I found in GAT preparation and more importantly COGAT prep, and did it with a sledge hammer the size of an SUV.  Experimentee #2 has math skills that Experimentee #1 will never have, like a child who learns to play the violin from birth will always outplay a child who picks it up at age 6, but Experimentee #2 has a completely different work ethic.  Experimentee #2 will sit down with something quietly for hours and master it, but not without a lot of complaining about the fact that he can't pick it up immediately.  Experimentee #1 never complains.

There is a completely different path for K and 1st grade that will produce almost identical short term results.   Many parents enroll their children in an after school math program.   In a good program, the child learns problem solving skills and solution strategies as well as practices math daily.  This is not a bad approach, but it is not consistent with the goals I mentioned above and a few I am going to add shortly.

After 1st grade, we stopped learning math and went more hard core into Test Prep Math.   This series is not about becoming adept at advanced math topics, but becoming adept at navigating convoluted questions, staying in the 'math game' because the questions are somewhat on the goofy side and don't include boring, manufactured math book type questions, and building working memory.  This book is not designed for children already at the 99% level for math, it's designed to get them there shortly thereafter.  I've had a few parents who's kids finish 2 years of after school math (and are at 99% already) complain that the beginning of the book is too easy.  Kind of a 'duh' moment for me, but one I need to mention for those kids, Test Prep Math Level 3 in 2nd grade is preferred.  The purpose of this book is to lay the groundwork for 99% thereafter, not to put a 99% kid at 99.9%, except by accident (which is what we experienced, by the way). 

Instead of more math, we went directly from Test Prep Math into reading comp questions.   This should be obvious from the problems in Section 1.   Section 2 takes us directly into competitive math questions (because I need something to fill the gaps before ramping up real math in 4th grade).  But the MAP score is only half math; the rest is reading comp.

From 1st through 4th grade, we only stayed a year ahead in math while I put together the basic skill set that we need.  This basic skill set is very similar to the skill set that kids would use to survive an advanced engineering or abstract math course in college but it's missing formal solution strategies.  College is the other goal, and I'm thinking ahead as usual.

At inappropriately young ages, while we were biding our time putzing around with current + 1, I started introducing advanced topics, just for fun, just to exercise thinking and start to explore the wonder of math. It was enormously enjoyable to surprise a kid with these types of questions:
  1. What is 5 minus 3?
  2. What is the square root of 4?  9?
  3. What is 1 divided by 2?
  4. If 1/3 of my donuts are chocolate, what percent of these are not chocolate?
If your child sees any of these questions for the first time in school, I guarantee the wonder, fun, learning and enjoyment of math will be totally crushed out of the experience because your child will be presented with definitions, comprehensive examples, and a long list of routine problems that have nothing to do with anything.   It then just becomes a pattern matching and lookup referencing exercise.  The child will 'learn' math, but not know how to learn.

Sometimes we would resort to backtracking, which is finding a workbook or online resource to practice the material during the learning process.  If we got '1/4' kind of but not really, a worksheet might fill in the gaps.  If a concept (fractions in this case) requires an understanding of division that is not there, we would certainly backtrack to a division worksheet and then come back to fractions.

Over time, however, I discovered the power of bucketing, which I subsequently labeled 'Power Bucketing'.  This is very similar to what I witnessed with Experimentee #1 going into 1st grade and being handed the same EDM Grade 2 workbooks that were completed the previous year.   Math is much easier to understand the 2nd or 3rd time than the first time, and quick mastery is the likely result.

With '3 - 5', I would just leave the question out there and not answer it.  Or maybe I would answer it, but then a month later I would ask it again and watch the same process starting over again from the start, but going a bit faster and progressing a bit farther.  When this come up again out of nowhere the third month, we might end up with mastery with almost no work and exactly zero practice.  Even better if the child sees negative numbers on his own in a book, he dives right in and the result is not only self-mastery, but he owns it.

SQRT(4) and also 5x - 13 = 2 will demonstrate the leap in skills that takes place around 4th grade.  Kids coming off work like Section 2 of TPM can calculate both of these without understanding how they do it.  Good little mathematicians iterate through possible solution values until they arrive at the answer, and great little mathematicians add weighing with high-low bands that narrow to the solution strategy to arrive at the answer more efficiently.

After 4th grade, when the brain is capable of higher order thinking, these two exercises gain new meaning.   The definition of SQRT(4) is the number when squared that equals 4.  In other words x^(1/2) is solved backwards.  Square roots present the opposite syntax of squares, and the solution is to back into the answer.  This is critical for topics that are going to come later. 5x - 13 = 3 is a simple introduction of y = mx + b, which is an important framework for characterizing more complicated problems, and the elements of y = mx + b have additional meaning besides finding a number.

There are also new skills that come with these math concepts.   A 3rd grader will jump in and solve either problem to get a number.  It's all one step.  A 4th or 5th grader will decompose the problem, spend more time analyzing the question, and learn more during the problem.  I've introduced younger children to the next level of math skills, like problem decomposition and making a hard problem easier; this exercise can take 20 minutes and is really good for thinking.   It requires a lot of working memory which is why in 2nd and 3rd grade working memory is most of the focus.  But older children do this intentionally, quickly, and know why they are doing it.

Let's look at some pre-algebra concepts that have been a real struggle for me to teach.   

First, x^2x^3 versus (x^2)^3.  Per formula, the first is x^(2+3) and the second is x^(2*3).  But we're not interested in formula's, because formula's produce math dummies.  

The way to do these problems is to work the question and not solve the problem.  x^2x^3 is simply (xx)(xxx) = x^5, and (x^2)^3 is (xx)^3 is (xx)(xx)(xx) = x^6.   Eventually, the child will memorize the formulas in the same way they used to count on their fingers for 5 + 3 and eventually knew that 5 + 3 is just 8.  Before 4th grade, the best I can do is lay the ground work for decomposition, restating the problem, multi-step solution operations, but they still jump into more advanced problems trying to get to a number in one (hard) thinking step.   I've noticed that after school program kids are drilled in multi-step solution strategies, but I don't want a child trained in math solving.  I want a thinker.

This is the biggest difference in my goals and methods.  I don't want a child who is trained in math, a a child good in math, a child who knows (advanced) math topics or a child who is 99% because of this training.  I want a child who does really well in math he has never seen before or mastered because he is a thinker and a learner and can apply thinking and learning to math.  I've always said if you need a 99% because it is required for GAT entry, do what ever it takes this year and forget your principals.  In 7th grade, I can't say this; it is not possible to short cut your way into a 99% without a solid learner-thinker.  Also, we've never actually deviated from principals or practiced rote math and we have always either been at 99% or been within striking range (in a bad year).  I will say that it's never too late to start.  There are advantages to starting early, but starting late does not preclude achieving the ceiling on a test.

The most challenging topic using my approach on pre-10 and post-10 children is parenthesis.   I will illustrate with this problem:  (6^2 + 18 + 2 + 4^2)) - 2^2.  This is not a complicated problem, but it is not possible to do a page of these problems with a child still learning exponents and parenthesis without writing down at least 3 or 4 steps in order to check steps for errors.  In other words, it's faster and easier to let the pencil do the work than the brain.  Before 4th grade, I'm happy to endure 4 or 5 wrong answers from mental calculations because the impact to working memory (not to mention arithmetic practice) is useful.  But with the problem above, working memory gets a work out and the child still has to write down each step to survive the problem.

In our 1 year ahead math program, it is common for kids to fall to 85% by about 6th grade.  The program administrators - geniuses way ahead of their time - are focused on the final result and this interim dip is a researched based way to achieve the final product.   The extra 14 points are achievable with a bit of extra work.  If you review this article from the beginning, you'll see 3 or 4 math education concepts that all work together to produce 99% without a lot of extra effort.  I don't think this approach would work very well in a classroom situation without modification, but it certainly can at home.  Once any topic above is presented above, the next step depends on the child's response in the context of the child's individual skill set.  A parent who gets to know their child and experiments a little with backtracking, repetition, exploring the question will stumble toward success.

Now back to the 7th grade challenge that introduced the article.  We have a very ambitious goal but not a lot of time to achieve it given homework and nonschool activities.  The topics, approach, learning environment, and general mess of our preparation is in my opinion an exact mirror of the test.

Sunday, January 21, 2018

A Decent Reading List

I’ve been asked to recommend good books to read for 2nd to 3rd or 4th grade.   I’ve search for a decent source so that I wouldn’t have to do this, but there is no decent source.  There are many recommended reading lists, including grade schools, libraries, and sites that bill themselves as good sources, and none of them provide even a tiny fraction of the good books that are out there.

In the book Pre-K Phonics Conceputal Vocabulary and Thinking I provided a comprehensive recipe for strong reading.  It was inspired by the very inspiring introduction to Susan Wise’s seminal work The Well Trained Mind.   She said that she would take a laundry basket to the library.  I did this for 3 years.  It’s enough to put your child squarely into ‘Chapter Books’.  In Pre-K Phonics, I took this to the next level, and maybe the level after that.

By 4th or 5th grade, your child will be reading books of their own choosing, books that take a week or two to read and have 10 more in the series or genre, and your recommendations will likely be ignored for the next 15 years.

That leaves a very important 2 year gap where the child needs help finding good books.  This is also the last time that Read To (super important) will be easy to do.

In this article, I’m going to lay out the approach, and then over the next few months, I’m going to fill in the blanks.  The math work that I provided for the early years is now coming to fruition in 4-7th grade weekend math (because of homework it’s no longer daily).  We simply need a 99% on both sections of the MAP test in order to get into high school.  That’s not asking much.  Some day I’ll tell this story, and it will sound a lot like age 4, only with much more advanced topics.  In the mean time, it’s time for reading.

Here are the buckets.

Mandatory Books
I’m convinced that the Hobbit and Roald Dahl’s complete works (including autobiography) should be mandatory reading during this age.  The list is much longer and needs work.  If your child reads the Magic Tree House somewhere between late K and early 2nd, you are where you should be.  The mandatory books will get you to the next level.  (When I say ‘reading’, I mean Read To as needed, especially with the Hobbit.)

Top Notch Books
Gifted programs have a formidable reading list that includes classics like Kira Kira.  These books are easy to spot because if you query the book in Amazon, you will see teachers guides in the search results.  I suppose that’s not easy if you don’t start with the list.  This is probably the most important list for my readers and the one I’ll work on first.

To put this list together, I’ll simply steal it from a dozen programs I’ve watched over the years.  Feel free to add to this list in the comments.  At some point, I’ll just move this to the permanent pages.

[Feb 3 - I've been trolling through material and it's so bad I'm going to have to go through all of the publisher's websites.]

2nd Grade

  • Dear Mr. Henshaw
  • The Miraculous Journey of Edward Tulane
  • Bunnicula
  • Sarah, Plain and Tall 
  • Charlotte's Web
  • A Long Way from Chicago
  • Harry Potter (not in school; I recommend the whole series spread out over the next 5 years)
  • Boxcar Children
  • The Story of Pilgrims Progress (not sure about the age yet)

3rd Grade

  • Fair Weather
  • Mr. Tucket
  • The One and Only Ivan
  • A Wrinkle in Time
  • Bud Not Buddy (pair with historical context and there is a play on this as well that's pretty good.)

4th Grade:

  • Chasing Vermeer
  • Because of Winn Dixie
  • Love That Dog (poetry)
  • Kira Kira
  • The Mixed Up Files of Mrs. Frankweiler
  • Call of the Wild (boring)
  • Amulet (graphic novel series - not taught but all kids read it)
  • The Hitchhikers Guide Guide to the Galaxy (I don't know why this is here)
  • The Watsons go to Birmingham (pair with historical context)
This link from Mensa for 4-6 grade is not bad, but dated.

New Books That Are Classics In The Making
We have two libraries near us that are the 2nd and 3rd largest in Chicago.  Because of this, we get to see all the books worth reading somewhere in the shelves.  We tried them all.

Most of these are for girls and have a girl theme.  We really enjoyed these, but being boys, ignored the girl themes and simply enjoyed the creativity and good story.  I’m sure there are good boy themed books, and I’ll list these, but mostboy themes seem formulaic.  These books are 3-5th grade.

    • Keepers Trilogy (2nd or 3rd grade advanced) 
    • Savvy (my favorite, definitely a girl book)
    • Tale of Desperoux 
    • Percy Jackson and The Olympians (my 4th grader also recommends the Magnus Chase series)
    • I have to wait for a few kids to get back from Boy Scouts to complete this list, including one boy (not mine) who read the Lord of the Rings trilogy in 1st grade and got a 100% when I grilled him on it.

    Books You Didn’t Think About
    I am a big fan of picture books and winners of foreign book awards.  The ones we choose tend to be small in words and big in mind blowing concepts.  I had to do inter library loans to get many of these.

    Shel Silverstien is on this list.  We bought his books and read them daily.  Jack Prelutsky is on this list.  David Weisner (Flotsam) and Brian Selznick (all his picture books).

    One day my child was writing a few poems for school.  They were really, really good.  It wasn’t a fluke.

    Books To Enjoy Reading
    If you search for lists for a 2nd grader (or a 4th grader because your child is an advanced reader) you’ll see a list that includes mainly junk.  It might as well be comic books or romance novels.  But we read all of these because it guarantees that your child will have one or more books in hand at all times.  The child is not gaining anything out of these books (think Diary of a Wimpy Kid and Middle School) other than the habit of reading all of the time.  So we read all of these.  But not at night, when it was reading time, and a quality book should be in hand.

    James Patterson (top selling author) started writing books for reluctant middle school readers because his son was one.  This list includes some really great works for advance 2nd and 3rd graders, especially boys, such as Treasure Hunters. You can’t put one of these books down.  There isn’t much cognitive value to his books.  That’s not the point.  It’s about becoming addicted to reading.

    Sunday, January 14, 2018

    Struggling in Math

    I have gotten a lot of questions in the last 2 months that I will summarize and then answer:

    • My child is struggling with their At Home Schooling math, which consists (usually) of me making them do a math work book that is 2 years beyond their grade level.
    • My child started school at 99% and is now at 85%.

    I tend to stay focused on preparing for a strong high school math experience; neither of these two issues ever bothered me and your children are smarter and better than mine.  We did have a dip in test scores and I went into RED ALERT mode until it was corrected. Both of these topics have been covered over the years, but it's pretty hard to dig through my blog to find answers.  In addition, I already deleted the 300 articles that had a play-by-play of my struggles.

    Both of these are linked, because in order to get to 99%, your child either has to go to expensive after school math programs that will gradually make them hate math, or your child will work ahead at home.

    Struggling In Math
    The answer to all of your struggling questions is called 'Backtracking'.  We do it all the time.  I can't imagine doing any math above grade level without a lot of it.  Here are some examples that I've written about while we were doing it:

    1. If we were doing EDM Grade 2 in Kindergarten 3 days a week, at least one day a week we did a first grade math workbook that was just adding and subtraction.  Some times this is a nice break, sometimes it's catch up, some times it's practice.
    2. Sometimes I take 2 or 3 weeks off to cover a concept that we never had or a concept that we just plane stink at.
    3. Sometimes an entire section in the workbook is almost all wrong.  Sometimes it's just a page or an important problem.  The kid just doesn't get it.  I circle the pages and we move on.  A month or 2 later, we'll come back to the circled pages and do them again.
    4. When the child is younger, there are some bad days because of hunger/sleep/sickness issues and we just do flash cards or arithmetic worksheets.  Bad days happen rarely at older ages (always the day after a sleep-over), but when they do, we do nothing at all that day.
    5. Sometimes we take time off from math and do projects like a puzzle or sewing something or a craft or a writing project or art, a comic book, whatever.  In each case, the child just starts doing it and I will not interfere.  I am convinced that these activities will produce a stronger mathematician than actual math.
    6. We like to do things backwards.  So if the book does it one way, we redo the whole thing backwards.
    7. We like to do things step-by-step.  Identifying the mini-steps helps you find backtracking material.  Here's a really simple example.  23 x 15.  This has 4 separate multiplication operations and 3 addition operations.   Maybe your child should just practice multiplying 3 x 4 and 30 x 40, 9 x 2 and 90 x 20 etc for a while before coming back, or 20 x 15 and 3 x 15.

    There are two difference between you and me.  First, as previously mentioned, your children are smarter than mine.  Secondly, we back track a lot.  Why continue to struggle with the same material?  Do something else, practice something, come back to it later.  It will all get done in the end because we are both picky and uptight parents about math.

    Test Scores

    Lately I've been getting a lot of feedback from many parents that test scores are falling.  I get this from almost all parents (like 85% of the ones I talk to) at some point during grade school, usually right around the midpoint.  Here are the reasons:

    1. Your school program teaches and practices math at about the 85% level.  Over time 99% children will end up working at the 85% level.
    2. Your child is sick of doing math and needs a year off.
    3. You are not doing daily math at home at a suitable level and 15% of the country is.
    None of this is a bad thing.  I think our program starts pushing math at the appropriate time and produces graduates who are really strong in math.   This will not make a parent happy in the following 2 circumstances:  #1  Your child needs a 99% right now on an annual standardized math test this year.  #2 You have some other objectives in mind that requires a 99%.

    Here is my 3 part recipe:

    1. Get math at a suitable level.
    2. Do it.  Backtrack a lot.
    3. Focus on problem solving techniques and not math.  Math will take care of itself.
    I can now see that I need another article because the leap between 3rd and 5th grade and it's called problem solving skills.   My particular approach can be summarized as focusing on nothing but problem solving skills during 2nd and 3rd grade and it works.  Not just any set of problem solving skills, but the core skills that are the foundation of all others.  That, in a nutshell, is 95% of the motivation behind Test Prep Math.  The other 5% is making math less boring than it normally is.  

    But I'm hearing from parents of 3rd and 4th grade children that didn't go this route.  I've got some thinking to do.  It's solvable.  Anyone can catch up to any level you want to get to.

    Friday, January 12, 2018

    The Language of Math

    There is a strong and important connection between math and language.

    Think about a child learning language before the age of 2.  You point to a blue ball and say 'blue'.  The child sees round, blue, rubbery, your finger, you making some weird noise, you're looking at him or the ball or both, and you're probably smiling.   What is blue?  Then you point to a blue wall and say 'blue' and the kid is more confused than ever. 

    In order to figure out blue, ball, yellow, green, box, toy, your child has a lot of confusion to sort through, is going to make 5,462,298 mistakes, and you're going to be smiling the whole time, and on top of that the child is going to have to identify patterns, sort through permutations and eliminate candidates until he comes down to blue is an attribute of color.   The child may not see round or plastic or squishy yet, maybe he can sense it, but when there is a word tossed out there for 'round', his ability to think logically will be substantially improved.

    By 1915 or 1911, I'm still debating, cognitive psychologists determined that the process of reading uses 100% of all cognitive skills.  100%.  This will never happen again.

    If you want to know why I'm so over the top obsessed with reading and vocabulary during age 4, so much so that I created Pre-K Phonics Conceptual Vocabulary and Thinking to jam as much 2nd grade material into the brain of a child who can't pronounce C-A-T, you now know why.

    Don't Lose The Magic
    Learning to talk and learning to read, not to mention learning to walk, are much harder by a factor of a gazillion than anything a child will learn thereafter, including Pre-Algebra.   But somewhere after learning to read, maybe around addition, the parent loses the Magic Learning Environment that allowed your child to overcome insurmountable learning objectives.  You used to sit there smiling dumbly mistake after mistake totally happy every time your child rose an inch off the ground and then fell.  Now you're yelling at your child for forgetting what 8 + 4 is or struggling with x-1.  At least I am.  We ALREADY discussed the exponent graph 3 times.  Would you just pay attention once?

    The magic was that you were willing to try to teach your child what words mean, despite not having the slightest clue how this works, through mistakes and trying over and over and over again, usually smiling the whole time, and learning just exploded.

    This is the first connection between language and math and it's pretty lame compared to what follows.

    Reconnect the Two Dots
    If math uses a certain sub set of cognitive skills, but learning to read (definitely) or learning word definitions (probably) used 100% of cognitive skills, wouldn't it be great if you could bring the missing cognitive skills back to the math learning process?

    I think this is theoretically possible and in practice I just ask them to explain verbally to me how to what the question is asking, what do they know, is there anything they have learned before that can help, can you articulate your solution strategy?  I also throw in anything I can think of related to a problem, like 'Polyhedron' or some other word to get that verbal section of the brain working.

    But mostly I like to talk through problems and concepts.

    Recently, we came across this question:  What is 42% of 66?  This is an advanced post TPM problem.  I got it off a high school Algebra I final that has 190 questions and would be very hard for high school   We're doing about 5 problems per session and learning a lot.  This is an opportunity for a long discussion involving fractions, decimals, and %, as well as problem decomposition and lining up multiple steps, followed by cheating with algebra.  In other words, in addition to math, it's going to be about 25 minutes of talking.

    Here's some fun verbal math discussions for a younger age.  In these cases, I did very little talking and just left key questions out there for 3 or 4 weeks while the math sank in.  Then we discussed, and I asked why? or prove it to me.

    • The definition of 'square root' is this.  2 is the 'square root' of 4 because 2 x 2 = 4.  What is the square root of 9?  Does 10 have a square root?  (Not yet, but it will later).
    • What is the square root of negative one?  It's call 'i'.  What is i * i?  Why is this important (because the Fundamental Theorem of Algebra does not hold true without i in case you're wondering).  What is the square root of - 4?  
    • What is 2 - 5?  I love this discussion.  It goes like this: "Three".  If 2 - 5 is 3, what is 5 - 2 and why are they both 3?  This can't be right.  If you have 2 and you give away 5, what do you have left?  "You can't do it".  Oh yes you can my friend, yes you can.  
    If I can't find something to discuss in math work, I'll start looking for more math.  y = mx  + b and f(x) = mx + b are great topics for discussion and not writing.   That's why we end up covering advanced math at a young age, simply to have something to talk about.  How's this going?  About as well as learning how to talk in the first place.

    Is Any of This Going To Help?
    I'm not 100% sure yet, but it might help with math learning.  It's definitely helping with writing.  Trying to compose an explanation for a complicated mathy topic just learned is really hard.  It is a foundation leadership skill.  It's similar to a reading comp skill, but only vaguely.  It's easier than any classroom speaking task.  I'm certainly not going to end up with a wall flower, what with me demanding a thorough explanation to a complicated explanation.

    Product Recommendation
    I highly recommend IQ Twist or IQ Puzzler Pro.  We've had these sitting around for the last few years and my kid and his class are now obsessed with them.   His 4th grade teacher is buying them for the classroom.

    It wasn't until I solved a problem myself that required turning and flipping multiple shapes when I realized that it's NNAT and somewhat COGAT training.  We started talking through the solution to one tough problem and how one shape could only go in one certain place before I realized that this is all logic, visualization and math.  If you run out and buy these for a 1st grader like I did, feel free to reach out for help because it took me a few years to figure out how to use these with a younger child.

    Monday, January 8, 2018

    Real Math

    My son complained about his daily math.  It was some problems from two Pre-Algebra topics.

    If we do pre-algebra every day it's going to get boring.  I refuse to do either decimals or long division or math facts or anything between kindergarten math (totally engrossing) and pre-algebra (marginally useful) because it's all boring and useless. 

    I need a fall back plan. He's been playing IQ Twist lately (highly recommend this game even though I don't get paid for any of my recommendations) and that got me thinking.  There is this great math book called Mathematics 1001 that has 1000 math topics in addition to 2 pages on trig that allowed us to cheat our way through it.  One of the topics in this book called 'Net's looked like the shapes in twist, and a little reading later uncovered this idea.

    Here are two Nets for a triangular pyramid.  If you cut out either Net, you can fold it into the triangular pyramid. 

    There are 11 nets for a cube.  Draw them.

    I watched two sets of skills in action.  First, there was geometric visualization, including rotating, flipping, and 3 dimensional manipulation of shapes which trumps the two dimensional manipulation on a cognitive skills test.  If we were facing a test this year, I would have only shown the diagram on the left above and asked for 2 more nets for the triangular prism (even through there is only one because cognitive skills tests test your ability to come to terms with incorrect questions).

    Secondly, there were budding permutation skills at work, which is an extremely important math skill.  Since no kid is going to get to 11, this gives me the opportunity to suggest permutations.  "What's a permutation?"  Well, take the letters a, b and c.  I can write them as abc, acb, bac, bab, cab, and cac.  There are 6 permutations of the letters a, b and c.  Please give me the permutations of 1,2 and 3.  This should be pretty simple.  Then look at the basic T shaped Net for a cube, and start permuting the squares, one square at a time.

    We got to 7, which is pretty good for my 25 minute time limit.  I need to stop at 25 minutes to save room for follow up questions, like telling me the rules for building a Net while staring at the 11.

    Real Math
    I expect this child to go far in math.  He's not going to go anywhere without some intervention.  Here is my intervention.

    I showed him a web diagram of the 11 nets for a cube.  I stated that some guy (Albrecht Durer) asked how many ways you can create a folding diagram for a cube, and he came up with 11.

    Then I showed my kid the pre-algebra worksheet of about 20 equations. 

    I asked this question.  If there is a mathematics professor and researcher at some university asking questions and writing papers and going to conferences and helping his colleges in the Physics and Information departments apply abstract math to their work, which math is this professor doing right now?  (And by way of association, which math are the physicists and computer sciences clamoring for?)  Does it look like this (pointing to pre-algebra) or does it look like this (point to the 11 nets for a cube.) 

    The Answer
    The answer is the net stuff.  And why is it that your school curriculum looks like pre-algebra, the type of math that mathematicians don't do?

    Here is my (mostly inaccurate but totally) true history of math curriculum in the United States.  In 1930, a vice president at Ford Motor company created a list of skills needed by factory workers and accountants and dealers to create and sell cars.  This skill set was widely applicable to industrial work of all types.  A curriculum was created to teach it and used throughout the United States.  Lots of cars were produced and everyone was happy.  This curriculum is still used in 2017 in the midst of the Information Age.

    Of the 96 maths out there, school is going to consist of the 5 that would help you build cars by hand or build a bridge, which you are never going to do.  The maths that you actually need to get through your life - starting now - are not taught at all.

    What I find most interesting is that the 5 maths taught in US curriculum are almost devoid of skills compared to the maths that could be taught.