How Pete the Cat got me thinking about Zero

Hello Friends,

I have been thinking about Ari telling me that learning to read is kind of like counting.   I pontificated at length on a blog or two about how amazing she was to construct the idea that a written word must match a just right spoken word,  I think the idea of conservation of numbers and the matching of one word to one spoken word came up. 

But that whole idea resulted in  me  tossing and turning all night long over a  bigger harder question....Just how do the very young learn to count?

Hmm... You gather  some buttons and place in front of your short friend.  Then you select a button and encourage her to say one...Then add another one and hope that she  will utter the word two, then add another button and try for the word "three".  This goes on until the child gets the idea that every time you add a button a new number name is expected.

Ten apples on Top by Dr Seuss has a dog, a tiger, and a lion, compete to see how many apples they can balance on their head and  Frogs,Frogs, Frogs, by Brenda Boreham matches counting with increasing numbers of frogs shown  on each page. 
A Very Hungry Caterpillar by Eric Carle features counting to five and days of the week.    In Went Mouse by moi, simply has fun with the idea of  one more animal choosing to use the maple tree as its home results in a very full house.

Counting books are everywhere and they are very engaging.  I wonder why?


 I think the child gets the basic counting concept by induction, but I wonder what is the concept they are getting?
It seems to me  you have to figure out that you only need to memorize twelve names...(one, two...eleven twelve) after which you can work out, construct or predict  how this list of names thing works.
Is the aha moment when the pattern is understood that a new name is required when we add one to the existing number?  Is all of mathematics founded on this foundation of finding a predictable pattern? 

 But the names of numbers are words that are part of our language, however, they are not quite like our language.  There is no dictionary entry for the word forty-five that is consistent with how a dictionary talks about the definition of "apple".

 And back to those  button we  placed in front of our short friends.    The one to the right might get the name two, but not the one to the left. (and besides, it has a name called "button").

 The counting rule is what is the big deal when looking at the buttons, not the series of phonemes represented by b u t t o n . Are these two systems aliens?

 And Oh my, how do the very young handle the concept of ZERO?  And is NONE really a number?







Oliver Jeffers has Huey asking
"How many lumps of chhse do see just there?"
"Um...I don't see any."
"That's because there are none!"
"Is none a number?"
"Of course.  It's one less than one."
"I see.  So one more than none is one?
"That's right...






And then there is the whole concept of subtraction.




  And that is where Pete the Cat and his Four Groovy Buttons comes into this discussion. 

 When all Pete's  buttons popped off he wasn't sad...Oh goodness no!...He still had his belly button.   

And that is a funny ending and thinking about zero has really not been all that funny. 

 So I am not going to try and figure out:

 "Before the arrow can reach its target, it must get half-way there; before it can get half way it must get a quarter of the way; and so forth: 1/2, 1/4,...1/2N, 1/2(N+1),...If we grant that the series of markers it needs to pass on its waay to the target in infinitely long, then how can the arrow ever get there?" (dark possibilities at the heart of the paradoxes of Zeno)

But I am going to continue to celebrate and share the brilliant picture books with number content as a play-based, fun-filled approach to supporting our shorter friends efforts to construct number theory.

As always, In friendship,
Donna
aka The Book Lady