Implementing Lesson Study Summary

Monday - Friday, July 3 - 7, 2006

July 3, 2006

For this day, our main focus was to streamline our thought processes and the lesson plan. It is important to consider the fact that the standards are very broad concepts, but our lesson should have a very narrow focus. Students always seem to have some difficulty on remembering the formulas for the area of polygons. When they do remember the formulas, they may not understand exactly where the formula came from or how to use it. The driving factor behind this lesson is for students to discover the importance of the perpendicular measures of the parallelogram and not necessarily the measures of the sides. We would use this information to allow the students have a foundation so that they can build a way for students to find the area of triangles, trapezoids, kites, and regular polygons. We returned to our breakout groups and continued the work that we began on Friday.

July 5, 2006

On this day, rather then working in our breakout groups we worked together to iron out the details of the lesson. We agreed we were more concerned with finishing the writing of the lesson. We reviewed each other's work and provided feedback on how to change both the lesson and the rationale and goals. We spent some time discussing and decided who was going to teach the lesson. It was decided that James would teach the mock lesson on Friday and Jo would teach the actual lesson on Monday. We spent a great deal of time working on putting the lesson in the format of the lesson plan provided to us by Aki. This lesson was organized in a table with 4 different rows: Introduction to the problem, problem solving, class discussion and summing up. The rows were also divided into 3 columns: Learning activities, teacher's support, and points of evaluation. James took time to pull together the work from the group members and put them into this format. We also discussed in great length the anticipated student responses. Based on each of these responses, we discussed how we would handle the situation. We documented the types of questions we would ask students in order to help facilitate student discussion. We spent some time discussing what materials would be needed for the classroom and collected questions that would be beneficial to ask the teacher prior to the teaching of the lesson.

July 6, 2006

We spent more time today polishing the lesson. We decided not to use "placemat" after discussing some of the technical difficulties. James visited the classroom teacher in the morning and discussed the room arrangement, bulletin boards, white boards and seating charts. He found out that there were 12 students in the class. They bring food and eat during the class. The students are taught very traditionally without much discovery or hands-on approaches. The students have basic materials like calculators, writing utensils and paper.

As a group we discussed the materials we would need to bring to the practice lesson on Friday and the lesson on Monday. Various group members volunteered to help gather materials needed. We also spent time reading both the lesson and the lesson rationale pieces presented by group members and made some revisions.

July 7, 2006

Today we did a practice lesson. James taught the lesson while all the other group members and facilitators were present as observers. Also, several members of the learning from teaching cases group and other volunteers were posing as students. Some members of the international seminar also attended as observers. After running through this test lesson, we noticed a lot of difficulties that caused us to make revisions to the lesson. Some of the participants made a comment about the directions being unclear. One immediate revision that was agreed upon immediately was that we needed a visual representation of the rancher problem. There needed to be a place where the students could refer back to and read the problem. Receiving this information verbally once was not enough and caused a lot of questions that could have been avoided. Many students were still confused on the 5,8,5,8 constraints. Other participants questioned the purpose of giving students the "38" measure. To avoid this issue, our group decided to leave out the 38 measurement of area until later, after they came up with an area different from 40. We also discussed using different materials, perhaps spaghetti or straws, instead of strips of paper. The reasoning is students were overlapping strips and the lengths were changing as a result. Also, some groups were breaking up the fence into pieces.

We talked about removing the term "environmentally conscious" because it leads to some questionable ideas about cramming animals into confined spaces ! One major concern was that much time was spent in groups and not enough time pulling together as a class and having class discussion. We did not formalize the area of the parallelogram as a class.

At the end we divvied up responsibilities of how to prepare for Monday. We agreed that we would have a visual write-up on big paper of the two word problems. We will also create a large visual of the parallelogram worksheet.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.