The other day, Ava grabbed her Russian dolls from the toy cupboard that she hadn’t played with in months. I guess the novelty of fitting the smaller dolls in the larger ones wore off and there was nothing else to learn about them. However, this time she decided to do something different with the dolls and she wanted to build a Russian doll tower using all of the pieces. Initially, she attempted to balance some of the flat bottom pieces on the rounded top pieces. This resulted in a lot crashing of pieces and failed attempts at building the tower, which led to a lot frustration. I left Ava to her own devices to figure things out and persevere with her self-directed activity. Thirty minutes later, I had a very proud daughter with her very own Russian doll tower (using all the pieces). Of course, I had to document this learning accomplishment and whipped out my iPhone to record. However, as I tried to get Ava to orally communicate her strategy, I found it very difficult not to explain it for her. Therefore in the video, you’ll hear me struggle with my questioning because I wanted Ava to explain her strategy without me giving her the words.
I could’ve immediately praised Ava for turning the bottom pieces upside down to create a more stable and flat surface however, I wanted to her to make the connection and verbalize it. After watching the video, I wonder if I funnelled her to what I wanted her to say or if I worked with her as she explained. I would love to hear some feedback on this.
I also didn’t expect Ava to ask me if I wanted her to make a different tower. This reminded me as a parent/educator to always set high expectations for our children and students and look for opportunities to extend their thinking. I was fully satisfied with Ava making one tower and didn’t even think to ask if she could build it in a different way (something I always encourage math teachers to ask their students).
Here’s what Ava produced afterwards:
Roflections 
Interesting and enjoyable video, Thomas, though I got the impression that Ava preferred making the tower and figuring out how to make it stand than trying to verbalize her thinking. I felt your frustration as you tried to elicit responses from your daughter; I remember doing that when our kids were young. I think that at a young age, children don’t have the verbal skills to express their thinking clearly, though they may be able to “show you what they are thinking”, as Ava did.
Thanks for sharing!
Thanks for commenting Peter. As a watched the video again, I agree that Ava was trying to explain her strategy by showing with actions and using statements like, “It can’t go up unless it’s down” (referring to turning the upside down pieces upside down). But I also try to give her opportunities to think out loud. In this case, I guess I’m wondering if I should have probed further to see if she could make the connection to the term, ‘flat’ in our discussion of her tower. In hindsight, I think I was so focused on her trying to make the connection that I forgot to really listen/see how she was explaining using her own understanding. She ended up making the connection through my repeated questioning but did it come at the expense of her trying to explain and demonstrate in her own way? Did she really need to say the word, ‘flat’ or did I just need to hear it?
Thomas, I absolutely love this post of yours! As I do more problem solving in the classroom, I’m running into the same problem that you discussed here. How do I have my students explain their thinking, without directing them, when they’re getting stuck? I really like how you started with very open-ended questions and then changed your approach when you could tell that Ava was struggling. You never came out and told her that the piece was flat, but you helped her as she came to this conclusion. I’ll be interested in following the comments here and seeing what others think.
You and your daughter actually inspired me. My Grade 1’s and 2’s complete a unit on structures later on in the year, and I think that I’m going to try the Russian doll challenge with them. I wonder if they can make a Russian doll tower together. I’m curious to see if their understanding of structures that’s gained through the unit also helps them articulate why certain towers work and other towers don’t. I think it’s time to start collecting and/or looking for Russian dolls. 🙂
Thanks for the inspiration! Thank you too for posting your video here. Hearing the discussion between the “math facilitator” and the “student” really helps me figure out new ways to get my students to explain their thinking in math. I’m glad that I could have some insight into your conversation!
Aviva
Thanks Aviva! I appreciate your comments and your feedback. I read a great blog post (http://www.blog.republicofmath.com/archives/4708) by Gary E. Davis (@republicofmath), a Professor of Mathematics at the University of Massachusetts Dartmouth. In his post, he coins the term “cognitive theft” and describes it as the “instructional interference with a student’s thought process”. He encourages teachers to focus less on their own understanding and listen more to the students’ understanding. Although I was trying to focus on my questioning to get Ava to make the connection between the word, ‘flat’ and her strategy without telling her it was flat, I still feel like I was leading her to what I wanted her to say. I don’t know if I was really listening to Ava’s own understanding of her strategy. I’m still working on how I question to extend thinking. Next time I going to try to focus more on what Ava understands and base my questions off to that. Looking forward to see how your structures challenge turns out!
Thanks Thomas! I read your earlier comment to Peter about this too, and I’ve actually been thinking about this for a while today. I know that my biggest challenge when teaching math is to get students to where I think they should be without leading them there. This gives a whole new perspective. Maybe I need to worry less about what I want them to say, and instead focus more on what they do say. You’ve given me a new outlook … and just in time for our Math Week starting on Monday. I can’t wait! 🙂
Aviva
Great post Thomas. I have started taping myself more and as I reflect on what I see, I can pick out the points where I am sometimes too leading. I thought I wasn’t leading but sometimes I do. It is hard to not push them to where you want them to go, even when you know you are not supposed to do it.