Thursday, January 28, 2010

Focus on the 20%

I had a fascinating conversation with a friend, an educator of Math educators,who is getting frustrated with the educators she is educating, and would like to bypass them, and go straight to the point, the mathematics students!  We started talking about big ideas in mathematics: those that give the most bang for the buck, the most benefit for the effort.  She feels that there are relatively few, and when they are mastered and expanded upon, bring enjoyment and satisfaction in most mathematics education. Unfortunately, she says, most teachers and students spend much of their time focused on the smaller ideas, which,by themselves can seem quite irritating and irrelevant.  This leads to math frustration and many people,  faced with some differentiation or imaginary numbers, decide that mathematics is just not for them.

I was pretty excited at this insight.  What are these big ideas in mathematics?  I certainly didn't know them and I taught math grades 7-12 and first year college level algebra and probability theory.  I can be really good at following an algorithm, no understanding necessary (I spent many years thinking about whether computers can demonstrate intelligence, the Turing Test and ELIZA).

 Now that I'm doing second and third grade math with Simonne, I'm really fascinated by how much I'm learning!  Now, if I could get a handle on what these big ideas are....  I asked my friend,and she rattled off a few.  I only caught one.  She said that if a child becomes comfortable with the concept of complements, large chunks of mathematical processing become easier.

For example, the complements in 10 are 9 and 1, 8 and 2,7 and 3 and all the other pairs of numbers that add to 10.  The picture shows how a very small child would become comfortable with this idea by building a wall with cuisenaire rods such that every row has only 2 rods, except for the first row,which has the orange rod (the orange rod represents something 10 units long).  Even before a child knows that 7+3 = 10, he understands that the orange rod is the same as the black rod and the light green rod put together.

One possible expansion of the idea of complements is in finding change from $1 (or $10 or $100...any other) can be done easily by knowing the complements in 10 for the rightmost digit,and the complements in 9 for all the others!  Try it.  What change would you give me if I gave you $100 for a $67 item?

Ok,what has this to do with the 20%?  It's from that guy Parento and his notion that 20% of causes lead to 80% of the effects.  I'm already doing this in a few areas:

  • In Jay's home program, I decided that being able to relate and communicate was the 20% that I was going to make really big.  I decided that the other skills, like being able to write his name, though useful,would fall into the 80% that wouldn't really go far in getting me what I wanted for Jay.
  • In business, I decided that being able to connect with people and be helpful is my continuously expanding 20%,vs the 80% of product specific knowledge
  • In my relationship with Isaiah, I notice we experience the jet stream when we pay attention to the big things that are so big,they seem invisible, like the things we enjoy experiencing, our common passions and visions.  I try out hyper focussing on the small stuff that I allow to take up space, but don't add value.  I haven't found that useful.
  • I'm on a quest to figure out what the 20%  is in Mathematics, so my kids can really learn something, instead of fronting,the way I did for so many years.  
So, as I experience my life every day, I'm starting to ask myself, Is this in the 80% or in the 20%?  Is this bringing me value,or just taking up energy and space?  Just asking myself the question illuminates my choice to  focus on things that take me closer to where I want to go!  Focus on the 20%

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