During the fall of my student teaching year I was involved in two lesson studies and then two more during the spring of my student teaching. For one of them, the final results were compiled as a poster and presented at a poster fair at Michigan State University in late fall of 2012.
After completing the lesson task students were able to engage in dialogue related to the work they had just completed. In revising the lesson structuring the chart so that some examples had variables in them for students to work with and possibly eliminating some of the examples. This would allow for students to start conceptually thinking about the material earlier in the task. Asking students to explain their thinking and then reach a symbolic pattern in two separate questions in an effort for each student to come up with both representations. Keeping a timer at the front of the class to help pace the students and teacher on the material to leave more time for the final discussion. This would help keep the momentum of the classroom and leave extra time for full discussion and wrap-up of the lesson.
During the spring of my student teaching I was again part of two lesson studies where I was the lead teacher and then part of the observation party. The lesson study I was the teacher for was again written up and presented at a poster fair at MSU in the spring of 2013. Over the course of the study there were areas of effectiveness and areas where improvement could be made. It was evident from the student discussion that a majority of the students were clear on the difference between arithmetic and geometric sequences. Students were able to identify when adding or multiplication was needed to generate the sequence. Students were selected and brought to the board to display and explain their work. The following day the students had their homework completed and thoughtful questions about it. However, when looking at student work about recursive formulas there were some problems. Not all students caught on to exactly how the formula worked and how to use it. This was not a goal of this specific lesson rather a goal across a few of the lessons. After looking at student work around recursive formulas there was a need for some revision in the task to aid the students in understanding. On the other hand, students across the board succeeded in creating and using the explicit formula. Looking at the geometric mean some students had trouble differentiating it from the arithmetic mean. After reviewing notes and looking at student work it was agreed that the lesson was effective.
After implementing the task we decided to revise it by restructuring questions. Instead of explicitly asking for a recursive and explicit model the questions were restructured into to asking for two different models to represent the situation. This revision would hopefully yield a more diverse answer base and hopefully lead to a stronger discussion. Another revision to the task would be to ask. “If the copier was stuck on a 150% enlargement how would your models change? Explain.” Adding this question would serve as an assessment check for the teacher. In addition to clarifying differences between the geometric and arithmetic means an extra note will be given by the teacher to remind the students that they are looking for a different relationship than what they found the previous day.
The other lesson study I was involved in I was part of the observation team. I aided in the planning of the lesson and then took field notes as I watched a fellow intern teach the lesson. After notes were compared and then discussion around how to better execute the task was held. Reflecting on the lesson study process I enjoyed getting to plan a lesson together. Discussing misconceptions together brought out some thinking about the task that may not have happened if we were working alone. I also really value observing others to help me with my own teaching practice. During student teaching, I was able to observe my mentor teacher every day but we do not always get the option to observe our peers. When Kevin was leading discussion I focused more on his moves and less on the student response. During the student work time, I focused on the students he was working with and did not really focus much on what the students were doing when he was not with their group. In the lesson planning process, I want to plan out more student misconceptions. Overall this experience left me hopeful for our future lesson studies.