Now that we're not homeschooling, I've started volunteering in my daughter's 3rd/4th grade classroom during math time, 30 minutes with each group, and every time I volunteer I leave abuzz with energy. I am not a math teacher, per se, but in addition to my work with Math in Your Feet I've spent the past few years with my daughter focusing on mental and conversational math; essentially, learning math through games, making projects, and finding examples of math in the real world. Now that she's in school I am still so curious about what comes next and about how kids other than my daughter make mathematical sense of the world.
Here's a confession: I used to be afraid of numbers. Every time numbers would come up in conversation I'd get a tight, anxious feeling in my chest and do my best to change the subject. After a couple years of remediating myself by learning math along with my daughter, I have found that whole numbers are actually funny little friends who I might actually understand. I like having new friends, so this is a fabulous turn of events.
Earlier this month I made an investment in some math ed books including one called Number Sense Routines. I didn't think I'd have a chance to use it, I was just curious, mostly because I like reading about helping kids learn math. Then I got wind of Sadie Estrella's work (she's @wahedahbug on Twitter) with counting circles. I read her stuff and made the connection between what she is doing and my new book. It's great to have both -- I love watching Sadie teach and it really helped me jump right into my very first counting circle today!
One of the points made in the book (it's called 'count around the circle' there) is that ground rules are important to make sure the quick thinkers don't take over the activity. I reminded my kids that we needed to all wait until it was our turn, that we should count along in our heads, and to allow someone 'think time' if they needed it. Also, that we would be doing a counting circle every time we get together.
Oh. My. Gosh. Not only was it an incredibly focused, almost meditative, experience but after five minutes of what seemed like a very simple task, it was like a light came on and I could actually see where the kids are on their own paths to numeracy.
First, since we we've been working on making our own Sierpinski Triangles we've been talking a lot about infinity and the powers of three. So, I thought for my first counting circle I'd do something with intervals of three. From previous interactions, I figured the kids could already do the normal kind of skip counting by threes (3, 6, 9...) so I decided instead to start at 7. For both of the groups, things went very well until we reached the transition between 19 and 22, and at every similar transition up to 60. This is where I was able to closely observe kids' strategies for figuring it out. If they didn't know the next interval, most counted on their fingers or whisper counted by ones. For one of the groups, as you can see in the picture, I had to visually draw individual 'jumps' and talk out the adding. For example: "We're on 39, let's count...40, 41, 42 [drawing each individual jump as I spoke]."
In general, the counting was okay up to about 19 but required some real thought after that. Assessment wise, it showed me clearly that many of them have not yet internalized number bonds to 20, let alone transferred and generalized that knowledge to larger numbers. This is thrilling news for me. In part because I got such a interesting picture of where their numeracy is in a way I would have never have seen otherwise. And, frankly, also because although I'm not really a math teacher, I LOVE TEACHING MATH! It is so fascinating to watch kids learn math.
I have a lot more to say about my hour or so at school today but I'll end with one small vignette. There was one boy who was quiet during the counting circle but when it came to his turn (small groups meant everyone could have at least three turns) it was clear he was not following along. After counting, we went on to our Sierpinski triangle project. Here's what he did:
I know it's not what you were expecting, but I see so much thinking in this picture. First of all, he was a natural at approximating midpoints. Second, when he first drew the little blue triangle at the top I had no idea what he was doing. I initially tried to redirect him toward dividing each iteration in the order we had discussed but while I was talking he drew a line across and just under the top little blue triangle and all of a sudden I saw what he saw. I encouraged him to continue on his line of inquiry and this is what resulted.
I was so thrilled and told him I never would have seen that kind of structure or pattern if not for him. He told me he wanted to be an inventor when he grew up and I said, well, that's part of what inventors do -- they take things we think we know and turn them into something new. It might be cliche to say it this way, but he was so proud of himself that he practically threw off sunbeams.
I think maybe next time he'll give the counting circle a go.
Are you going to cut out their triangles, and hang them together as one giant ST?
ReplyDeleteHi Becca - Yes! At least all laid out on the floor, but I hope we can find a place to mount and hang it so we can have a view of infinity and self-similarity for the entire school year. :-)
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