Sunday, January 11, 2015

Joyful Learning - Vignette 1

I am currently part of a group of teachers who are investigating joyful learning. The essential questions of our group are as follows:
  • What does the “pursuit of joyful learning” mean to us-- as learners and as educators? Why is it important?
  • What does it mean to teach with “joy” in mind? (students owning, driving and expressing joys of learning?)
  • What does joy sound like and look like? 

As part of our investigation, we have done some writing about experiences of joy in our own learning. Here is my response to the prompt: 
What is one salient memory or example (recently or as far back as childhood) where you were both driven and excited about learning something hard? 
To give some context, this learning experience took place during the math content methods class I took as a preservice teacher. I was student teaching Monday through Thursday and then we met for three hours on Thursday evening.

It was Thursday afternoon after a full week of teaching and we were sitting in content methods class. Our teachers had realized early in the year that what gave us energy in this class was doing math. And so like most weeks, we started class with a math problem that was related to whatever we were learning about that day.

We were focusing on geometry that week and they selected the following math problem:
You have a cake that is a rectangular prism with a square base. It is frosted on the top and each of the four sides. You want to split the cake into seven equal sections, where each section has the same amount of frosting and the same volume of cake.
We started working individually, each on our own separate piece of chart paper. On the paper, we were documenting our thinking, rather than trying to make a presentable product. This was a habit that we had gotten into over the course of the year and one that we wanted our students to do as well. The problem, though fairly straightforward in its set-up, was hard. The challenge and interest came from the corners and the frosting on the sides of the cake. Although I don’t remember exactly what I did during that initial private think time, I likely chose dimensions for the cake and calculated the volume as well as the surface area of the frosting. I probably thought about a circle and how much simpler (and more boring) the problem would be if it were a circular cake.

After some time to grapple with the problem on our own, we started working in partners. Again, I don’t remember the specific details of what my partner or I said or did. But based on how partner work generally went in that class, I would guess that we both shared what we had worked on so far, and asked questions of each other in order to both understand and probe each others’ thinking. This then gave each of us a direction to keep working or something new to try. We probably then continued to work individually, but would periodically check in, because sharing our ideas helped us thinking more clearly and creatively. Our teachers watched what we were doing. They also asked us questions so that they could understand. In talking with them, it pushed our thinking, just like talking to our partners. They, however, did not indicate how they had solved the problem, or if we were on the “right track.” We were the ones who were doing the heavy lifting of thinking.

There are particulars that I do remember from this day, though, that made it stand out from the other content methods classes. This is the only problem from the whole year that I did not come up with a solution for during class. Our teachers had us share out specific parts of our strategies to the rest of the class. One of my classmates, who taught under the same mentor teacher as me, had figured out a solution. I remember her being so proud and borderline smug (we all knew each other well enough at this point that it was allowed to be borderline smug) that she had come to a solution. I remember being annoyed and jealous that I hadn’t been able to figure out a reasonable solution in the time that we were given.

The feelings that we had were not destructive or harmful to the learning or the relationship we had with each other, though. They were part of friendly competition that rested on the solid foundation that we had set up as a community. I trusted everyone in that room to know that I was trying my best and that I did have interesting/useful ideas about math and teaching. I know that I believed that of everyone else in the room. I also knew that they were there to support me no matter what. Throughout the year, they had seen me at my lowest points, just as I had seen them. In those times, they had helped me figure out how to pick myself back up and keep going. So we could have a little friendly competition and boasting because of that.

The last thing that I remember clearly about that problem and that day was that even though one person had figured out a solution, none of us were satisfied at the end. The solution was inelegant. It brute-forced a way for everyone to get the same amount of cake and the same amount of frosting. We were all convinced that there was a more elegant way to split that cake into 7 equal pieces. Despite having a solution, we wanted to keep working on the problem in order to find a better one.

Looking back at what I remember from this class, there are so many elements that made us both driven and excited to work on this problem. Here are the elements that I notice that I want to work towards in order to foster joy in learning mathematics in my own classroom:
  1. Our teachers intentionally structured class to start with something they knew was engaging and gave us energy.
  2. The problem we were looking at was simple to understand but challenging to solve.
  3. We all had some time to start the problem on our own.
  4. We weren’t trying to make a final product as we were solving. The documentation we did was a record of our thinking.
  5. My partner and I both found it useful to talk to each other about our work because explaining our own work and hearing someone else’s ideas pushed our thinking on the problem.
  6. We had the freedom and the self-regulation skills to move back and forth between individual thinking and discussing our work with partner.
  7. We, the students, did the majority of the thinking. Our teachers supported us, but I still have no idea how they solved the problem, or if they knew a more elegant solution than anything we came up with.
  8. I was interested in what the other groups had tried. This was facilitated by what our teachers had us share with the whole group, but was primarily because everyone shared a different idea that as a class pushed us closer to a solution.
  9. We all trusted and respected each other. We had built relationships where every single person was valuable to the group.
  10. The competition that we felt with each other pushed us all to do our best.
  11. Despite having found an answer, we still wanted to work on the problem. We valued other parts of the solving process (elegance, succinctness, being able to articulate ideas) more than having a solution.

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