Monday, July 22, 2013

Kumon Versus AntiKumon

As I mentioned a year or more ago, I have a carefully crafted approach to math that is dramatically different than Kumon.   A few friends at work a few years ago described Kumon to me, and my general reaction was shock and horror.   As my my children reached the age of math, they were enrolled in AntiKumon.

What Is Kumon?
Kumon is a successful, proven method to improve your child's math grades.   From what I can tell, it also gives them confidence not only in math, but other subjects as well.    This is a Japanese program and it is obsessed with perfection and mastery.  The kid does a lot of worksheets, starting about 2 years behind grade level, and must meet time and accuracy requirements to pass to the next level.  [Note - the school math program in Japan is better than the U.S. and from what I'm told doesn't look at all like Kumon.]  The main benefit of Kumon is that once the child has thoroughly memorized math facts, they make less mistakes, and it's easier to get through more complicated math problems.  Recently, programs like Eye Level and Mathasium extend the Kumon approach a bit into the realm of algorithmic problem solving, but AntiKumon is anti managed math programs of any kind until the US stops training math robots and starts creating thinkers.

What is AnitKumon?
AntiKumon, is a successful but relatively unknown way to improve your child's math grades to the point where you need to start thinking seriously about Cal Tech or MIT.  The child does about 1 to 6 problems a day, starting about 2 years ahead of grade level, has no clue what they are doing, takes 20 to 30 minutes to get it right, after about 4 or 5 tries.  The end result is a child who is accustomed to thinking their way through really challenging material, having patience until they get it, and checking whether they got the right answer because they're never sure the first time.  The main benefit of AntiKumon is that the child becomes a solid thinker with the grit to overcome obstacles in any advanced subject. The side benefit is that they have a tendency to not make mistakes on key tests.

After a year or more of either approach (managed math program or AntiKumon), you're going to end up with success. The question is success in what.

Level One and Mathnasium
Since I originally wrote this article, I've been worked with kids who have attended these programs.   I'm going to include a well done Singapore Math program because the outcome is very similar.   I have a really mixed view of these programs.  They work and they don't work.  On the positive side, these kids thoroughly know math to the point where I have to throw much more complicated problems at them to make any progress on cognitive skills.  I also see a much higher starting level of working memory.  If you need a 99% this year on a standardized test, and you work, and you don't mind seeing your child even less than you do, this program is not a bad idea.  In some circumstances, I would highly recommend it to the general reader, but it has a long term cost that has to be dealt with later.

But I don't normally work with the general reader looking to get from a B to an A in math.  I work with parents who want their child in a Gifted Program.

Here's the totally weird counter intuitive thing.  If you teach and train your child to do math, and give them lots and lots of practice applying what they learned, they can zip through math at high levels with 100% accuracy.  During this process, they are picking up some skills.  If, on the other hand, you make the kid earn math on their own (AntiKumon), you get a different skill set, a much higher skill set, and a skill set that happens to be the one that the COGAT is looking for.

Choosing A Starting Point
If a learning center can take a struggling child who is 1 or 2 years behind, and get them up to grade level in a reasonable amount of time, then I can take a child who is at grade level or above, who is not struggling, and give them math that they will see in 2 years, and there you go.  I don't know why no one thought of this before. Probably because they have a classroom full of kids of varying skill sets and 7 other subjects to teach.

In AntiKumon, the starting point where ever the kid is now plus 2 years.  This means backtracking as needed to a workbook for grade level + 1 when the child comes across a math concept that they skipped and just can't do.

The problem with the starting point is that a child who is past first grade but not yet in 5th grade is going to see some pretty boring, useless math.   What 6 year old needs to do long division?  None.  A bright child will conclude that math is useless, because it is.  So instead we focus on the part of math that is not useless, the part that includes logic, seeing, thinking, making mistakes and trying again.  The part that is going to pay off in a big way in all subjects.

Work Differently
The goal of a drop off math program is to get the school doing a lot of really hard problems at grade level or above quickly and with 100% accuracy.  I've seen the results of this.  The websites for these programs state different goals, but the end result is a little worksheet machine, and not just on routine problems.  I can extend the problem with reasonable twists and complexity, and the little math machines still plow through them.

I don't want a child plowing through anything.  I want the child to accumulate, problem solving skills, grit, logic, and analysis skills, usually in that order.  Take something simple, like 9 + 6.   No part of AntiKumon is going to help the child memorize this math fact.  When the child is in 7th grade, they are going to look at it for a moment, and think '10 + 5' or '6 + 3 + 3'.   I'm not exaggerating.  This is literally what happens.

This is the crux of AntiKumon.  When a child spends 3 years analyzing regrouping and reformulating problems because they've memorized nothing, they will walk into Algebra II and discover a long lost friend.  A child who has done zero thinking for 3 or 4 years because they have been applying memorized math facts and mastered solution algorithms is going to walk into PreAlgebra having spent the last 3 or 4 years not having to use their brains.

This is not to say that an AntiKumon student ever misses anything ever.  They don't.  They just get 100% for completely different reasons.  They are really slow, they usually have to do problems a few times to make sure they got it right.  In other words, they have to think through everything.  They don't get answers incorrect because they are convinced of their own ineptitude and check every time because AntiKumon prefers the student work at a curriculum level where a 50% error rate is common.  Once the child is getting 75% correct on the first try, it's time to move on to something else.

There are three important reasons why I can get away with this.  First of all, the MAP and the COGAT aren't timed usually, especially the MAP.   Secondly, the COGAT isn't measuring whether or not a kid knows their math facts, or even knows math.  They are measuring whether or not the child has the learning skills  necessary to thrive in an accelerated DIY project based learning environment.  Finally, accelerated and gifted programs and standardized tests rarely go beyond grade level +1, and the advanced material on the MAP test isn't that hard.  When you present a child with grade level material and they've been struggling all along with grade level plus 2, it's a nice easy break.

Daily Work
Managed after school math programs provide worksheets to do every night, with comprehensive coverage and repetition on each topic.  The child goes to the center weekly for evaluation and pointers, tips, and direction.  The quality of instruction varies, but it certainly doesn't hurt.

I've tried this approach once.  It works for a while than inevitably produces a child who can't think through progressively more challenging math on his own. The down side is that it makes math seem boring and irrelevant, which it is.  Name a math topic that a grade school child needs.  The really smart ones figure this out.  It's not just that calculators make math facts irrelevant, it's that the switch from an industrial society to the information age make the entirety of math curriculum irrelevant and the smart kids know this.  Problem solving and learning on the spot, however, are critical and pervasive, even in school work, especially in science and literature.

Daily work with AntiKumon is a page in a math book that might have 6 problems or a single challenging word problem.  I am looking for 10 to 15 minutes of figuring out what the question or problem is asking for, or 10 to 15 minutes figuring out a solution strategy.   I expect 3 or 5 tries on either of these learning subsets or maybe 2 to 4 wrong answers on the way to the solution.  The student learns dozens of skills in this type of environment.  AntiKumon has a very specific definition of 'age appropriate'.  It's the exact work that results in a child who is mentally exhausted after about 20 or 25 minutes.   This could be 2 or 3 problems (for younger children) or 1 more complicated topic for an older child.

When the problem is not exactly matched to the skill set, the child hits the wall before the problem is answered.  This is hard to watch with a parent present, because I'm seeing a bunch of sub-skills blooming and the parent is seeing the child falling short of the answer.  For example, the first subskill that emerges is the realization on the part of the child that he has to actually think through the problem and figure it out on his own.  Reaching this point is a major victory with some kids and it's a prerequisite to the next stage of developing solution strategies, instead of just giving up. 

Word Problems
The odd thing about Kumon is that their word problem workbooks for grades 4 and above are pretty good.   By 5th grade, Kumon Pre-Algebra books almost qualify as AntiKumon  if you rip out the section in the beginning of the book that provides a step-by-step method of solving every class of problems and thus removes the thinking from the workload.

AnitKumon targets word problems by 1st grade.  Word problems are the opposite of memorizing math facts and tie math to the rest of academic subjects. The word problems have math, but not advanced math, and are buried under a mound of logic and thinking.  The premise is that if the child thinks at the level of a great but tiny mathematician, the math will take care of itself.

Math Concepts
AnitKumon works on fundamentals and leave math concepts for later, whereas managed after school programs focus on math concepts.  I don't ever want anyone to teach my child a math concept.  There is an enormous amount of valuable learning in between that child and the concept, and to take it way is short changing the child.  In order to get there, you may have to back track and use problem solving strategies just to get to a basic understanding.  Of course, you can't do this in a classroom setting.  It only works one-on-one.

Parent Training
I probably need 5 or 6 articles on how to create the proper learning environment to get your child beyond 99.2%.  To summarize - expect nothing, welcome mistakes and do-overs, take a super long time on just a few problems, don't let a problem go by without asking if there's a better way to solve it, and forget checking solutions and keeping score.  In short, be the opposite parent than you would normally be.  It is counter intuitive and not at all average behavior for a parent.  It's not average, it's not above average, and it's not well above average.  It's above that. 

Recommended AntiKumon Curriculum
The only thing that varies with this curriculum is the supplemental material and the amount of backtracking we need to do.  Backtracking happens when your child comes across double digit addition and is barely able to do single digit addition, so you find last last year's book and take time off to catch up.  Because you skipped last year's book.

Just jump in at your child's current age.  There's no better time than that age to catch up.

  • Age 3 is a great time to read to your child.  100% of all of the cognitive skills that your child needs will be present and active between now and the end of phonics during reading.  This will never happen again, not even in math.  By the end of 3, make sure your child can count to 20.  Try some addition but don't over do it.  You don't want to train - ever - or practice so much that your child doesn't have to think.   
  • Age 4 and 0 months the perfect time to try Shape Size Color Count.  I've been told both that this is 3 months too early by some and 3 months too late by others.  My experience is that 4 years 1 month worked for us.  It's an expensive color book, but I've watched 5 year olds who did SSCC shout out answers to questions that their older siblings are doing in the other room.  It's creepy.  Plus, it gets to about the level of the nonverbal side of BTS 2nd and 3rd grade, so you are saving on a stack of books.
  • The second half of Pre K is a good time to do Sylvan's Kindergarten book.  I love this book.  It's the last time math is relevant and fun until about 8th grade.  It's good direction reading and pencil holding practice but more importantly, it's good practice for your child sitting alone doing work without me having constantly badger him.  There's no hurry so take some time to enjoy being young.
  • We usually take half the year off from math at this age to work on cognitive skills, crafts, oragami, puzzles, or anything else that has more math in it that school curriculum will for a long time.  Everyone else who got off to a late start can catch up at this time.  I broke down and bought a first grade math book from Spectrum just to have something to do.
  • Then during Christmas break of K, we start Every Day Math Grade 2.  I've had numerous crisis calls with parents over this one and anyone can email me at getyourchildintogat@gmail.com for help.  The first page might take 3 weeks.  A few months later, maybe 4 months, the child is actually doing an adequate job of getting 50% on each page, and by 8 or 9 months, we stop because it's not challenging anymore.  The crisis calls with parents generally go like this:  "Help, my child spent 3 weeks on the first page!"  Then I respond, "Of course she did, she's only in K and this is a second grade math book."  "Then why am I doing it?"  And the answer is quite long but I'll summarize.  First of all, because 9 months later your child will be doing a fair job of 2nd grade math and things will never be the same. Second, because at some point the first journal will be complete, every page, every problem, and this lesson is a game changer when your child is holding the finished book.  On the way there, your child is going to pick up rare problem solving skills and grit that kids who are taught math one spoon at a time will never have.  The pace will magically accelerate on it's own.  Be patient.
  • I'm currently trying to close a huge gap in AntiKumon called first grade.  Doing a 3rd grade math book doesn't work and I suspect it might actually hurt.  I've been working on this for about 2 years and I'm almost finished.  Up to now, we've been doing some cognitive skills training or just taking the year off or dabbling in multiplication, factorization and negative numbers.  To be clear, the solution I'm working on does not include multiplication, factorization, and negative numbers because AntiKumon does not teach math, just learning skills.  The child is responsible for learning math on their own.  I don't ever want to see a homework assignment or math test again for the rest of my life.  (I secretly peek in the book bag but I don't want to see a low score.)
  • Ages 8 to 10 is a magic time of brain development and Test Prep Math Level 2 and 3 take advantage of this.  It all started with this math problem from a text book "Johny has 3 apples and Sue has 4.  How many do they have altogether?"  Are you kidding me?  Who's idea was it to design lame boring math that actually makes our children dumber?  The first edition of TPM included 100 word problems and the target was to blow away the COGAT and the MAP test.  The next edition included a quantitative section simply to extra-blow away quantitative sections on tests.  Why not?  Then I started getting a steady stream of requests for help from shape impaired refugees in homes that don't have 100,000 Legos scattered all over their basement and the 3rd edition addresses this with a visual spatial section but this section presents visual spatial problems with a vengence.
Forth grade is a battle between AntiKumon and math facts.  I hate 4th grade.  I told one child that 4th grade is a write off year.  He took me up on it and brought home a D.  His teacher was really mad because his test scores were always very high.  I no longer recommend this.  Anyway, Test Prep Level 4 is an SAT practice book.  AntiKumon is currently accumulating exercises to get from TPM Level 3 to the 7th grade MAP.  The 7th grade MAP test is the big test in our school district, the one that counts for high school enrollment.  It's one thing to get to 99% with a first grader.  It's an entirely different challenge to get there with a teenager.  Or is it?  We'll see.

No comments:

Post a Comment