Exploring the Nature of Numbers

I've written elsewhere in this blog about how I am remediating myself by learning math along with my currently five year old daughter.  I am a classic case of someone who probably would have LOVED math but instead got confused by a worksheet in kindergarten (something about bumblebees) and never fully recovered.  In high school I loved geometry so much that I was motivated to memorize all the theroms.  I was never able to apply what I learned, but I think it was the challenge and process of understanding interesting rules that caught my attention.  Plus, geometry is visual, which is my thing too. 

I really had to address my math phobia when I came up with the bright idea to integrate math with percussive dance, but what I realize now is that my love of geometry (which some people, I've heard, call the only 'real' math, but that's another argument conversation) has really served me in that effort.  And, the effort I've put in over many years to make sure I really understand the math the fits with percussive dance has also restored some of that natural mathematical curiousity which I lost back in kindergarten in the '70's.  I am really starting to see how math can be playful and full of interesting ideas and questions and it's own form of inquiry unto itself, just like being playful in the process of creating percussive patterns.  It's okay to ask questions that have more than one answer.  Not only that, it's FUN!

So, anyhow, this morning my daughter was teaching her toy cat Matilda her letters and some basic arithmetic.  They do other kinds of math in her kindergarten, but she seems taken with what numbers are and how they get bigger and smaller.  Here is a snapshot of our conversation this morning.  First she tells me:

"I'll write 100 really BIG because it's a BIG number and 1000 even BIGGER. And then a quadrillion."

This is really interesting to me, actually.  I do, despite what I've said so far, understand the concept of scale and size and amounts, etc.  But, I read somewhere that the whole 100 days of school project (which practically every kindergartener experiences) started back in the 1980's and I'm sorry I missed out!  On the 100th day of school this year she brought in 100 dried chickpeas in a little baggie.  I was surprised that it actually didn't look like very much.  She also, as a joke (and this was totally her idea) brought:

"One hundred pennies in the form of a dollar bill." 

My daughter has also had some questions about if the numbers ever end.  I think she was happy when we read a book called The Cat in Numberland which was about the Hotel Infinity where numbers keep moving in and there are always enough rooms for them, and it seemed to provide the answer she was looking for.  She still tells me she loves me 'to the end of the numbers' which is very sweet, even if it's not accurate!

In her kindergarten class she's been learning basic addition and subtraction.  She comes home and writes down little equations.  This morning she said, "Tell Matilda [her toy cat] what subtraction is."  I said, "What can you tell her?"  She answered, "When you take away a number to make a smaller one." 

Also on the subject of subtraction, at some point recently she started trying to take away a larger number from a smaller one, which led me to comment, "Did you know there are numbers smaller than zero?"  I tried to explain but I didn't know if I made sense or if she understood, until this morning.  She was writing down an equation for her cat.  This is what she said while she wrote it out:

"Three minus eight equals....zero!  And I'll put a minus sign on the zero because it's less than zero."

My response?

"I think I'll go out and get you a number line!"