I have found that when my pursuit of a question focuses more on the answer than on the learning itself, the results are lifeless. The answer becomes a check next to my bulleted list, nothing more. But when there is a process for crafting and chasing down a question, I land deep in a cycle of learning. Lesson Study is one such process.
I have been working with a first grade team for the last two years as an instructional coach. We meet weekly to discuss mathematics, specifically problem solving. We have dug in and challenged each other to develop and clarify our beliefs about mathematics instruction.
- How do you define problem solving?
- What role does novelty play in problem solving?
- How do you assess problem solving?
- How do you ensure you are assessing problem solving and not computation?
The conversations are involved and passionate.
At the same time I was participating in Lesson Study facilitator training. At one point during the training, I realized that Lesson Study was the perfect tool with which to answer our questions about problem solving. I discussed my concept with the team and they decided they would be interested in participating in a Lesson Study cycle. I invited the school’s gifted resource teacher and the Math Vertical Team leader from central office to join our team. We set up our first Lesson Study cycle.
Throughout our conversations about problem solving we had struggled with the role of the teacher.
- How much information do we give our students?
- What should strategy instruction look like?
- How do we honor the process as well as the answer?
As a part of our Lesson Study we named the qualities of an excellent problem solver. We also talked about the current state of problem-solving in the first grade classrooms. From there we decided our research theme would be “What is the role of the teacher in helping students to mature as problem solvers?”
We went about examining a lesson with this question in mind. We had chosen to do a Marilyn Burns lesson involving measurement. Each team of students was given a box and they were to determine the length of ribbon they would need to wrap around the box twice and tie a bow at the top. We knew that the teams who made a plan would be more successful with the problem. We decided however that we would not state this at the beginning of the lesson because this was part of the learning that needed to take place.
Craig Dommer’s (our Lead Instructional Coach and Math Vertical team leader) name was drawn from the hat to teach the lesson. The rest of us were to collect data as we observed the lesson. The lesson started by providing a context. The students were to be employees at a store that wrapped customer purchases. They were to decide the amount of ribbon they would need. Too much and they would waste the shop owner’s money. Too little and the first piece of ribbon would be wasted, requiring a second piece to tie up the present. To build some experience we asked the students to start by tying a piece of ribbon into a bow around a pencil and to measure the length of the ribbon. In planning this part of the lesson we thought the students would use non-standard units with which to measure because that was what they were accustomed to using in their classroom. Instead, as soon as they heard the word measure, one group shot up and grabbed a ruler (available in the room for the use of a straight edge) and all the rest followed. It was a classic example of use and confuse.
When the teams got their boxes they each decided to continue to use the ruler. The adults in the room were looking at each other with wide eyes. We had decided during the planning not to intervene during this stage of the lesson. Instead, the teacher was to look for the different approaches of the teams. These observations would be used to frame the closing discussion of the lesson. Not one of the teams was able to solve the problem. If we had ended the lesson here it would have been a wash. But we didn’t. We had planned for a closing meeting and the teacher convened the teams on the rug.
We pretended we were wrappers in a store. But this is really math and this was a problem solving lesson. Whether or not you tied the package successfully is important, but it is most important to share how we worked together to try and solve the problem.
Next the teacher asked the teams a series of questions, recording their answers on the board. We had decided the teacher would ask the teams to share sequentially from least sophisticated to most sophisticated approach.
- What did you first do when you got your box?
- How did you decide on the length of your ribbon?
- What happened when you tested your estimate?
And after everyone shared the teacher asked:
It seemed to go better for these groups (pointing to the responses from the last two teams who were very close to solving the problem). What do you notice about the work of these teams?
There was a long silence and the adults all held their breath. One child called out, They understood the problem and started with a plan.
The children decided that one thing they learned is that for future problem solving they would be sure to understand the problem and make a plan for how to solve it.
The lesson ended and the team furiously ran back to debrief.
How would this lesson have been different if up front we had said, “Good problem solvers plan. Today we are all going to make a plan before we start the problem.”
Looking at our data, and the failures and triumphs of the lesson we went back to our original question, what is the role of the teacher in helping students to mature as problem solvers?
We decided to list the beginnings of our answer.
A teacher helps students to mature as problem solvers by:
- Guiding students to discover the learning on their own
- Putting the questions back on the students
- Asking questions during the debrief that get at the “look fors” of the lesson
- Asking reflective questions during the problem solving to “unstick” the students or to facilitate their own reflection and thinking
We also listed the attributes of a good problem-solving lesson:
- Have an open-ended process (there are different ways to approach the problem successfully)
- Clearly state what should be known about the problem
- Include time for the teacher to monitor and observe students during the lesson-gathering data for the debrief
- Have clear qualities or “look fors”
- Have the debriefing or closure questions already written
- Include a closure piece with a comparison of students’ methods and identification of strategies.
- Have the learning take place at the end
This Lesson Study gave us the process and opportunity to get inside a question that we had been trying to answer. We chased down our question and along the way had many more. It gave us a common experience by which we can reference in our future conversations and on which we can build our future inquiries.