After the Peeps photo session last week, I test drove my images with Tabitha (six years old).
Me: Which are there more of in this picture? Purple Peeps or pink?
Tabitha: Purple.
Me: How do you know?
T: It goes all the way to the top.
Piaget would be proud. Tabitha’s focus is on one dimension, rather than on overall quantity. So let’s test that hypothesis. Does she really believe that’s all that matters?
Me: What about in this picture?
T: Purple.
Me: But they both go to the top in this one.
T: This one (purple) has full rows, and this one (pink) has holes.
Me: Interesting. You know what I see? I see that if you moved that last bunny on the bottom row up to the next row, you’d have two rows of three and an extra bunny, while the purple has three rows of three.
T: Yeah.
Me: OK. One last one. What about this picture?
T: Purple.
Me: Because it goes to the top?
T: Yeah.
Me: Look carefully, though.
T: Pink.
Me: Why?
She proceeds to count 9 pink bunnies. I correct her and have her count over. She again counts 9 pink bunnies. I show her that if you move the two top purple bunnies into the second row, you would fill that row. She is uninterested and we move on to other things.
Overthinking my teaching 
“Me: Look carefully, though.”
“Pink.”
ALERT ALERT TEACHER-PROMPTED RESPONSE ALERT ALERT
Ha! For sure, joshg for sure.
I’m going to test these out with my son tonight.
I’ve turned these images into a very short presentation here: https://docs.google.com/presentation/d/1PQ6cX25Zd3ovADU9sOKH8e3rqRJWrTIGaCvaGGDrR3Y/pub?start=false&loop=false&delayms=3000 in case anyone else wants to do this same experiment, but has a child who can read (and might get some clues from this blog post).
Beautiful, David. The full set of Peeps photos is also available for download as a .zip file
“She is uninterested and we move onto other things” is a powerful lesson. You sometimes have a short window of time in which to get all of the mathy thoughts on the table, after which point you’re the only one interested in having the conversation.This reminds me of all those too-long lesson openings I’ve taught, when all kids wanted to do was, well, anything but keep listening to me.
Hawke took my quote! “She is uninterested and we move on to other things” is beautiful — perfect timing to let go of something and shows tremendous respect for each other’s space. It reveals to me a sweet understanding between you and Tabitha that you’ll return to this [math] conversation soon enough, within the hour, within the day, most likely about something else, so let’s not spoil it all in one sitting.
Pingback: Blog Entry #2 (Overthinking my Teaching) | Steph's Blogarithm