The Brain Board

We've been plodding along with math at a slow and steady pace for about 7 years now, and I'm starting to get the hang of it.

My original thought was if reading each day helps reading, wouldn't a child need to exercise math each day in order to be adept at math?  This was before I knew that reading alone teaches all thinking skills, although too gradually to pass a GAT test before 3rd grade.   This was before I realized that core thinking skills and working memory are much more important to math.  This was before I enumerated cognitive skills.

I generally spend half the year doing thinking related at home work, and the other half of the year applying that thinking to math.   The the other half of the year doing way too hard math at a slow and steady pace.  That makes 18 months in a year for us.

As I mentioned a few months ago, the soon-to-be-3rd-grader and I are covering fractions.  I decided to do decimals as well.   I give him a single problem every other day, and make him do the ridiculously mind taxing working memory problems from Test Prep math the other days.   For his fraction problem, we talk through it.  We might talk through a problem and solve it a few different ways over a 20 or 30 minute period.  I've found that 30 problems on a worksheet are useless, but a single good problem teaches a lot.  6 problems for younger children is also good, which is what Every Day Math does.

I can now fully appreciate the Every Day Math curriculum.   When we break down pre-algebra problems, there isn't a single step or skill that wasn't taught in the EDM books.    Curriculum is moving toward a problem based approach, and away from the type of practice in EDM.  I know this is a good idea, but this is going to frustrate educators and parents and the pendulum will probably swing back in the next paragraph.

Last year, my son was supposed to memorize his multiplication math facts, but at my suggestion, he didn't, or what he learned he has already forgotten because I think math facts are a way to teach bad habits and I was openly negative about the task.   We can't really do fractions without math facts, and pre-algebra is impossible.   If your child is getting killed in pre-algebra, you should start with math facts, even if it means taking a Kumon course or doing worksheets or flash cards.

He needs his multiplication facts for next year's curriculum, so the last month in summer will include this exercise:  For each multiplication problem 2 to 12, devise a rule and apply it.  No memorization. I may hold up flash cards and have him shout out his transformation.

To prove my point, I asked him to add 6 + 7.  He said 13 immediately.  Then I asked him to multiply 6 x 7 and after about a minute, he said 48.   I know he was adding 6 over and over again.

Then I asked him how he added 6 + 7.  I expected something like 6 + 6 +1.  He replied, "I put 7 tick marks on my brain board, and then 6 more tick marks, and then I count.  That's why I stare or close my eyes."  Holy cow.  What kind of mutant wierdo method is that?

When we first started to learn math, back at age 3, I used 2 groups of blocks (like 2 blocks and 4 blocks, for example) and told him to tell me what changed.   I call this Pre-COGAT.  I noticed that he would assign personalities to the blocks.  I recommend doing this once a child learns some numbers, like 3 or 4.  It builds an internal visualization of numbers, and this will be very useful in graduate school in a variety of fields.

When I was learning 3 + 5, my mother showed me how to draw three little points with the pencil, and then 5 little points, and count them.  Both I and my sister did this during the SAT in high school.  I don't recommend this, but it's no different than the brain board.  

With the older one going into 6th grade next year, you might be wondering how we could consistently work on math all year long without giving up at some point.  One answer might be that I vary the material constantly and have a minimum of 2 books for them to choose from.  One answer might be that we spend a lot of time looking at each problem and talking about it, and it's not really boring.  The real answer is video games.   I don't like them playing video games each day, so I made a rule - no video games unless you do your math for that day and practice your instrument.  I think if I had daughters instead, I would get time either iPhones or Facetime on an iPad or something similar.