while_you_were

While you were learning

 
On Friday afternoons when most classes are finished for the week, a
friend and I get together to review the week.   This week was on the
phone. Now the way we have been doing this of late may be different
from the usual,  so first a word of explanation.  
 
 We share special learnings we have had during the week.  
 You know the sort of little gems one picks up and momentarily
admires.   Sharing them gives them a polish of appreciation that
preserves the learning in them.  Hey,  It's a nice habit to get into.
 
 
Well, this Friday my friend asked if I knew why art teaches suffer
less from burnout than the rest.   The answer was so simple once you
knew that rather than guessing he suggested we just let it lie for a
bit while I told him how my day had gone.  
 
As it happened I'd had an interesting morning teaching a basic
numeracy class.    We both teach math.  My friend university papers,
me basics for science and engineering.    My class had been engaged in
self paced learning doing fractions etc.   My role as a teacher here
is largely getting our of their way and letting them get on with it.
I started reading another chapter in a book The Crest of the Peacock.
about non-European roots of mathematics.  I noticed how really excited
I felt as I had a sudden revelation.about Egyptian arithmetic.  
 
They did multiplication and division by doubling.   
Doubling and addition were their fundamental arithmetic processes.
For the _first_  time I understood why their 2/n tables were so
important to them.      I was fair oozing enthusiasm.    
 
"Is that a good book, or what?"  asked one of the students confident
in his assumption of reading my state of enjoyment.  
 
"Yes, it is.   While you have been learning one arithmetic, I have
been learning another, Egyptian arithmetic, where they used the
process of doubling to do division and multiplication."   
 
I showed them some examples.   "For the first time I understand why
they almost worshipped their 2/n tables.   They used them to double
fractions. "
 
eg           2/7 = 1/4 + 1/28. 
 
For them it was 
 
"To double a seventh add a quarter and a twenty eighth." 
 
Almost  7" = 4' + 28'
 
"We can do that with the fraction buttons on our calculators."  
 
         My jaw dropped. 
 
"Yeah,  There's this key  [a  b/c]  that does fractions." 
they continued.  
 
They showed me,  1 [a b/c] 4 +  1 [ a b/c] 28 =  2/7. 
 
(I'll be using that with some other classes come Monday I tell you.)  
 
...
 
I'll swear I could hear my friend smiling on the other end of the phone.
 
 
"Well this weeks little gem is going to be easy, isn't it.   
Why _do_ art teachers outlast other teachers?"     
 
 
I think we answered that one together.  
Who said what doesn't matter.    It all just tumbled out. 
 
They get a chance to paint while their students paint.  
 
When they enter a learning state their students learn about learning
states by example.   The learning state itself is generative, wontonly
enthusiastic and personal.    More over the motivation is real and
unforced.    
 
Reminds me of a thread here long ago on a.p.nlp about the meaning of
the phrase, " Going first. " 
 
Well that was my Friday. 
  
Its Sunday morning and the family is off to have breakfast somewhere. 
 
Go learn something and let your face know it.