noticing and wondering, and while I've applied the Noticing and Wondering formula (which is anything but formulaic, once you get past the initial questions) to every other piece of curriculum in the classroom, I realize that I've been leaving math out.
You can watch the video that I found mind-changing at that staff development meeting here:
Our staff has met twice more to consider and discuss (only very briefly; seven minutes isn't near enough time for in-depth conversations) this approach to math education and to try to link it--of course--to the new Common Core Standards and to the Five Strands of Mathematical Proficiency, UCARE. (Yes, I care about math; it just doesn't come as naturally to me!)
Earlier this week one of my colleagues shared, valuably, her experience with a less-is-more inquiry approach which begins with a lot of TIME. To start, she has been offering her students plenty of time to sit and look at a new math concept, such as a fraction and its reduced version, in order to notice and wonder about the two numbers and their possible relationships. Perhaps they attempt to represent their ideas on paper or whiteboards.
Once they have begun to have some ideas about what might be going on (and my favorite feature of the "What do you notice?" launch is that everyone can notice, whether or not they have an inkling of what the end point or "correct answer" might be), the children have seven whole minutes to talk through their thoughts with a partner, to express their notions of the problem in words. This is wait time with a capital W.
My colleague spoke about her strong tendency to feel that this might be a waste of time, compared to simply teaching the class the logarithm for reducing fractions straightaway, and how she has had to persevere in permitting herself to allow time for ambiguity, for process. She described observing the children's initial delving into what the problem might be, and how understanding comes in fits and starts that often begin with "flashes of maybeness."
This is a feeling I know well, having been a child who struggled with math although I had a fairly good sense of "reasonable." Now I know that not understanding place value until I was offered base 10 blocks in a Math for Teachers course at age 22 makes me a more effective and sympathetic teacher for children (unlike my own!) who need substantial time to reach true comprehension of math concepts. I'm grateful for the lead toward honoring all those flashes of maybeness.
there's a ticklish
in your eyebrows
that zaps through
your backbone and lungs
a breath and then
flashes of maybeness
bubble your brain:
the eye in your mind opens wide
starts to see
and any day now
your mouth will catch up
Heidi Mordhorst 2012
all rights reserved
Many thanks to my colleague Stephanie Cromwell for giving me this week's poem, and to Joelle Thompson, the staff development teacher who has been leading these meetings. The round-up this Poetry Friday is with Laura Purdie Salas (and her guest David Harrison) at writing the world for kids.