## Sunday, January 18, 2015

### Noticing and Wondering: A Sampler

It's hard for me to believe that I've spent most of my teaching career in complete ignorance of noticing and wondering.  This simple, elegant prompt has become an integral part of my practice, and its use is spreading throughout the school.  Here are some examples from the past few months:

 I snapped this picture in the teacher's lounge the Monday after Thanksgiving break.  Rich  put it up as a noticing and wondering math message.
It was clear that some of the responses were inspired by our continuing use of the pie-eating contest:
• How many degrees are eaten?  How much of the pie is left in an angle?
• How big is the missing piece?
• Is 75 degrees eaten?
But many took a different direction:
• How much did the pie cost?  What would be the unit cost for the one piece missing?
• How many ingredients were used?  How many teaspoons of sugar?
• How heavy is the pie?
• What's the perimeter of the pie?
• Could you divide it in equal pieces?  Can you make it into a fraction, like 1/6?
• Is it store bought? (Not overtly mathy, but I liked it!)
• Why does it look like pac-man?

The second grade teachers have done a wonderful job incorporating noticing and wondering into their math message routine.

Instead of asking the kids to fill in the diagram and solve the problem, Maggie provided the answers and let them have at it.  Here's what came up:
• In the two parts (45 and 25), the digits in the ones places are the same, while the digits in the tens places are different.
• The two parts are odd, but when you add them together the total is even.
• If you have a number and you add more to it, you get a higher number.
• The cents symbol looks like a "c" with a line through it.

Theresa and I have been spending time with the first grade teachers and students talking about the importance of subitizing.  It made me happy to walk into Jen's room one morning and see what she had chosen for a warm-up activity:

 I've been taking photos in the supermarket and downloading them into a folder on the school's shared drive for the teachers to use as subitizing prompts.
 Jen recorded their responses,  The kids are getting really good at this!

Last week I found myself staring down a guided group and a pile of  Magic Squares that I had found to help the kids practice adding fractions and mixed numbers.  I will admit that I had not put much thought into how I was going to present the task.

 As I showed them the model, it struck me.  How about a simple, "What do you notice?  What do you wonder?"
Asking the kids to notice and wonder allowed them all to enter the task at the ground floor.  They noticed the boxes, some empty and some filled; they noticed the two mixed numbers and the one whole number; they noticed the tic-tac-toe-like configuration.  They wondered what might be magical about the 40 1/2; they wondered whether some mathematical operations might be involved.  After only a few minutes of discussion, they were ready to go,

 I highly recommend this activity.  It hit some kind of 5th grade sweet spot.

Noticing and wondering has many benefits:

• It's easy for a teacher to remember and can be used in many situations.
• There are no right or wrong answers, and nothing to solve.  It's anxiety-free.
• It's a one-size-fits all prompt. It's as simple or challenging as the individual child that responds.
• It can be a valuable formative assessment tool, and a window into the minds of our students.
• It can be practiced, and kids can get better at it.
• Kids can utilize it as a protocol for understanding a problem before they go about deciding how to solve it.
Noticing and wondering is all the rage at my school.  How are you using it at your school?