Goodness! Time flies when you’re having fun. It’s been some busy times here at Undercover Calculus; I need to buckle down and write more. Thanks for being a patient fan!
In my last post, I started talking about a clothesline math activity I facilitated with several elementary math coaches during a recent PD. And now that I have a moment, I’d like to share more about my professional learning from the experience. And just because I love acronyms, we’ll call these PLMs for Professional Learning Moments.
If you missed part 1, scroll down to the next post or click here. Just to recap, I had asked participants to make a “too low,” “too high,” and “just right” estimate for the number of Skittles in a bag. Then, in two groups of four, they were asked to put their numbers on a clothesline “in a way that makes sense to you.” While they worked, I tried to facilitate two conversations by popping back and forth in an effort to set up a compare and contrast reflecting conversation as a whole group.
I had asked the group that made the clothesline (pictured above) to think about ways to make their clotheslines more accurate. I was trying to get them to think about scale and attending to precision. (I wish I had known about Andrew Stadel’s “Place, then Space” language to frame the question. But now I’m ready for next time! Thank you Chris Shore!)
Then I approached the other group who made the number line pictured below, took a peek at what they had done, and started to move some of their numbers around in an effort to simplify their clothesline for our debrief conversation.
“Whoa whoa whoa!! What are you doing?” they decried! Clearly, they had become protective of their clothesline and they reminded me that I had asked them to put them in order “that made sense to them” and that their order does indeed make sense if I would get out of the way to let them explain.
PLM #1: When asking open questions to learners, I need to keep open perspectives about their answers…and I need to do this intentionally and mindfully at all times. I had judged to0 quickly because I didn’t see something that made sense to me. And I almost missed a chance to learn.
PLM #2: Individuals and groups naturally become protective over their work if given the opportunities to take pride and ownership over the space in which their work occurs. This protective pride can happen with the clothesline activity. I’ve seen elementary students show more care and motivation in their learning because they come to see the clothesline as their space to show their work and something worth being proud of. The same was true with these educators. They liked the way they represented their reasoning and they were eager to defend their arguments from critique.
Like the other group, they clumped their too lows, just rights, and too highs into clusters on the clothesline. But if you notice, their numbers don’t go in order. They had discussed changing it, but the more they talked the more they liked what they had created. They wondered aloud, “Does putting them in number order make our reasoning any clearer? In fact, isn’t our chosen way clearer?” Fair point.
Eventually both groups merged together in front of this number line and we continued to reflect about our learning and implications for our work teaching students. Some key pieces of learning and wondering from the discussion:
- They liked that each group member had a different colored marker. And that you could see the order they went in for each category of estimates. This allowed them to see patterns in their thinking.
- They also asserted the notion that the clothesline wasn’t necessarily a number line. It was physical model that they could manipulate how they wanted.
- That this representation was more useful than just putting them all in number order and calling it finished. It was about making choices that made sense and explaining them.
- We wondered how best to ask for the low and high estimates to avoid answers like 1 and 1,000,000,000. The best we came up with: “Give a low/high estimate that you’re pretty sure is too low/high.” If you have some input, please let us know in the comments.
- This activity is great for students who need to move in order to learn.
- Clotheslines are great for fostering student discourse in the classroom for learners at all levels.
And penultimately, PLM #3: I need to be aware of my own lens as a facilitator and an instructor if I want to focus on people’s reasoning, not just their answers.
And finally, PLM #4: Finding ways to add “…in a way that makes sense to you…” to questions or directions opens up learning opportunities for all learners and puts the focus on explaining sense making rather than just getting answers.