Thursday, July 3, 2014

Coasting Through Math

For the last 4 years, I've been overseeing math homeschooling a few times a week to supplement the school curriculum.   The results are stunning, and some of the goofier things that I did turn out to have a big impact on all academic work.

I'm going to describe how I implement it and where the payoff is.  I'm not really concerned that my kids are ahead in math, or even learn math.  Instead, I'm using this program to teach really powerful academic skills and cognitive skills.  That's were the big payoff is.

This program does not have to be started at age four.  I note below how to implement it for older kids, but it's basically the same approach.

Ages 4 -5 I use fun workbooks like Kaplan or Sylvan K math, and concentrate on building a huge vocabulary of any word that can be visually described.   "Rectangular Prism" qualifies, for example, but "arc tangent" and "prime number" do not.

Optionally, if the kid is ahead, I'll pick a 1st grade math work book next.  Something condensed.

During Christmas break of Kindergarten, we start 2nd Grade Math, one page a day.  I use the Every Day math because if the child does every single page, he can begin to teach himself new concepts.  I expect Common Core books to be similar.   (No text book, just the work book.)  What I'm really looking for during this phase is to make the child comfortable working with problems, vocabulary and concepts beyond his abilities.  I'm also looking for some days where the kid gets every problem wrong, and some days where the work takes a ridiculously long time.

For older kids - I just pick material 2 years advanced and am prepared to backtrack as needed to fill in missing skills.   It is important to work through material that is advanced.   The kids will eventually pick up all of the concepts, but without advanced material they lose out on a lot of ancillary skills.

Since I teach the kids, I keep the Poyla problem solving guide handy (see my math chapter at the bottom).  If he is stuck on anything, I walk through the problem solving steps with him until one of the solution techniques clicks with him.   I'm not sure which one will work, so we may try them all.

I will demonstrate to the child that he did every single problem in the work book (except the group exercises) and he has nothing to blame for his achievement but his own hard work.

In first grade, I just supplement the school math with some addition and subtraction worksheets, and move up to multiplication and division during second grade.  Think of Kumon here.  In my case, the children are taking accelerated math, so I can do this.  If the school doesn't provide accelerated math, I would do it at home instead of Kumon worksheets.  During school, I encourage my kids to take a break with material already covered - just do it fast, practice it, and then do something else like spelling or science.

If this goes well, the child can't help but notice that he is ahead through his own prior hard work.  This is the kind of confidence and self esteem is earned.  In other words, the right kind.

Next, I take a whole year off (in this case, starting around fall of grade 2) and let him sink, swim, advance, or slide back on his own.  This is the hardest part for me but teaches the most valuable lessons.

In third grade and beyond, one or 2 days a week he has to do a page from a 6-8 eight grade algebra book.  Sometimes this is ridiculous, but at this point, I've got a kid with the following skills:
  1. Hard work
  2. Ability to focus and concentrate
  3. Comfort with really difficult material that he doesn't understand
  4. Patience doing work until he gets it
  5. Not frustrated by wrong answers and mistakes
  6. Exposed to problem solving techniques
  7. Used to applying examples without 100% understanding
  8. Complete lack of fear
The payoff - the real surprise to me - is that I've got a soon-to-be 4th grader that learns really quickly.  I didn't expect this.

A few weeks ago we did exponent operations (multiplication and division primarily).  This didn't go well, and when I explained things I wasn't sure if any of them made sense even to me.  After a few weeks off, he did the test and got everything right.   It took me a while to calculate things and grade them.  An adult I know who will remain nameless got the sample problems wrong.

I can clearly see him applying his learned skill set to this exercise. 

I'm now trying to transition this approach to reading comprehension exercises.   This skill set listed above is not automatically working yet in its entirety , but we're making progress.  For example, he'll read a passage he doesn't fully understand and then get stuck on the questions.  I point out that he doesn't have to understand it, but just copy the sentences into the answer that address the question.   We can both do this with math.  But it doesn't work so well with reading. 


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