Tuesday, April 18, 2017

How To Teach N+2 to N

I was recently asked by a high school teacher (the anonymous one from the prior article) what my kids will do in math in high school.  They are way ahead.   Will they take algebra as freshmen, and sit there bored each day, or will they take AP Trig as freshmen, and struggle each day to keep up?

I never considered either possibility.  I don't even care if they study math in high school.  We started 2nd grade math in K not because math has any value on it's own, but because working with material 2 years ahead is a great way to learn how to learn.  We since done this in other subjects and at different ages, but by far the easiest way to prepare your children for a life of learning is to go ahead in math. It's easier on the parent who's just getting started with coaching skills.

The key to the whole endeavor is to do it the correct way.  Keep in mind that math achievement is a pointless exercise unless your child is 1 in a million and actually likes math. Math is absolutely essential for thinking and problems solving and general academic skills.  I've done the exact same thing with writing and reading with great results.  I've dabbled with science and it works there too.  It doesn't have to be math.  I really like this exercise with Chemistry.  But before 4th grade, I can't see doing this with Chemistry because math skills (the thinking kind, not the calculating kind) are prerequisites.  I'm going to talk about a 5 year old, but I like this exercise at any age.  In fact, I like this exercise at exactly every other age until high school, with rotating subjects.

I could already see the core skills emerging during the first time we tackled 2nd grade math starting Christmas of Kindergarten.  It took me a few years to name the skills and refine my approach.  When these skills are learned, nothing is impossible.

Here is an explanation of why working ahead 2 years with a child who is barely adept at grade level works magic.

The obvious starting point is material that is incomprehensible.  The child might read a question and know 2 of 10 words.  Work slows to a crawl while new terms are dealt with.   The poor child is trying to fill in the gaps one new concept or vocabulary word at a time.  On top of this, there are skills and concepts that were supposed to be learned in the prior year, but you skipped the prior year and maybe the 2nd half of the current year.

Suppose your child can add 5 + 7 using fingers and is starting to get 7 - 5.  Suddenly this child sees 12 + 43 and doesn't even know what 43 is supposed to mean, let alone how to add it to 12.  We've been in this exact situation.  On top of this, 2nd grade math carries a bunch of additional concepts beyond arithmetic.

It's not only the backtracking to 1st grade math that's needed.  In this case, backtracking might include finding a 1st grade workbook or teaching something like 3 x 5 on the spot to get through the next page.  What is needed is an aptitude for dealing with the 15 minutes and 12 mistakes needed for a 5 year old to get through a problem that a 2nd grade child would be able to do in about 20 seconds.

There's quite a bit that comes out of this exercise:

  • The child is stuck with 6 new concepts that he barely understands for days or weeks will each one falls into place one at a time.
  • The child (and parent) know that it will take a lot of time and a lot of thinking if the parent maintains the proper role of encouragement and avoids the disaster of doing the child's work because the parent doesn't have enough patience to let the child do it.
  • The child (and parent) learns to accept multiple attempts and lots of wrong answers.
  • The child (and parent) has to come to terms with the true meaning of 'I can't do this', which of course they can't.
Something happens during this process week after week, month after month, to the child's learning abilities.  They explode.  Regular spoon feeding step-by-baby-step curriculum at age level never get into the realm of learning abilities.  It's all about concept A is next, do you know concept A because you just had 30 concept A questions on a worksheet so we can move onto concept B?  If concept A is so important, thinks the parent, the best thing to do is to explain concept A to the child and be done with it.

With N+2, the child is thrown in to M, J, I, H, L, and T in that order.  My approach is that I don't care if you know concept M or the rest, since you are only 5, and this is 7 year old curriculum.  What is essential is that you go through all of the mental work to figure out and master concept M on your own.  Or not master it.  I don't care about M - I can about you going through the process on your own to get there.  If you don't get M without help, there's plenty more opportunities to try again.

Even more importantly, both parent and child learn the pace of true learning which is a big mountain of dirt that needs to be moved one spoonful at a time.

But most importantly of all, maybe 65% of the way through the exercise, the child learns that he just got from 'I can't do this' to 'I can do this'  They may not know how they did it, but there are emerging skills at work.

I turns out during the first 6 weeks that M is impossible, so I find something with F and G in it before we take another shot at M.   In the next 6 weeks, I help less because I've got a child who isn't crying anymore.  Maybe I see 10 minutes of real trying before I jump in.  If I can just maintain patience, after 12 weeks I'll help not at all and be rewarded with 2 correct answers out of 6 before we redo it together one question at a time.

I'm not a big fan of a 2nd or 3rd grader leaping to 4th or 5th grade math because there is also a leap in cognitive skills that involves brain development and maturity, so I created Test Prep Math as the 1st official curriculum designed to stump the child with cognitive demands just out of reach.  It doesn't involve pre-algebra, but I can't imagine a child be challenged with pre-algebra after doing Test Prep Math.  It is supposed to be N in math and N+2 or higher in core thinking skills.  It's more like N in arithmetic and N+2 preparation for higher order math.

I like 6th grade pre-algebra during the summer after 4th grade for a child who's never been through this exercise before.  TPM Section 2 sets up algebra, so we're skipping right to 8th grade math after TPM.   I like the SAT practice books after 5th grade; these books aren't that hard once you get into them so it's really N+2 or N+3 on the parts of the book that are doable..  A solid high school chemistry book has turned out to be a really interesting exercise in N+3.   For 4 months, I turned every writing exercise into N+2 grammar and sentence formation, which involves an extra few hours analyzing a writing assignment and rewriting it. I always start out vocabulary at N, but any reasonable carefree pace simply moves to N+2 on it's own before we set it aside, usually in about a year or two.

My official goal is to go N+2 in math, then do nothing.  If my child just picked up a bunch of great skills, he can go off an use them and I can rest.  However, my kids insist on screen time on the weekends, and there is no screen time without some work first.  This is why we're doing high school algebra already.  Those spoonfuls of dirt add up.

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