|Dr. Soledad A. Ulep|
UP NISMED Director
Since 2010, the HSM Group of NISMED has been working with the mathematics teachers of a public high school in Pasig City to promote the teaching of mathematics through problem solving using lesson study. A school-based and teacher-led professional development model for teachers which originated in Japan, lesson study enables teachers to research on their own teaching practices in order to improve students’ thinking and learning. Based on a long term goal that the teachers formulate, they collaboratively develop, implement then revise/improve a research lesson using pieces of evidence on students’ thinking and learning gathered during the actual implementation of the research lesson. In the partner school of NISMED in Pasig City, the long-term goal of the lesson study groups is to develop students’ mathematical thinking through problem solving. Their sub-goals are to represent real-life and mathematical situations, to give meaning to these representations, and to solve problems in different ways.
Graphs can visually represent functions. It is in Mathematics IV that students study functions. So, the NISMED team decided to work with the Mathematics IV teachers. The team realized that if the students were given a graph, they would most likely ask questions to make sense of what it meant. So, the team thought that the mathematical task which could be used in the research lesson should require the students to formulate questions whose answers could be found in the graph. The students would have to think much in generating questions because of the condition that the answers could be obtained from the graph. The task was open-ended since it could have many different correct responses (questions) from the students. Based on the various information that could be drawn from answering these questions, the students could form generalizations which they could find useful in making decisions on how to avoid experiencing the damage that earthquakes could bring.
The meeting of the NISMED team with the group of Mathematics IV teachers to do the lesson study was timely. The Mathematics IV classes were then studying polynomial functions. The teachers claimed that it would be their first time to use a natural disaster, namely, earthquake, as context for students to apply their knowledge and skills related to functions. They expressed their lack of confidence to teach the research lesson that the lesson study group (the Mathematics IV teachers and the NISMED team) would develop because of their lack of the science knowledge needed in understanding earthquakes. They also claimed that it would be their first time to give students a task that would require them to formulate their own questions. The teachers were apprehensive that the students would not be able to come up with questions. Initially, they asked the NISMED HSES Group staff many questions about earthquakes. When the science concepts became clear to them, the lesson study group collaboratively developed the research lesson. The teachers suggested that the students do the task in small groups; that during the whole-class discussion of the groups’ outputs, the questions should be arranged as easy, average, and difficult and that the questions formulated by a group should be answered by other groups; and that focus should be made on those questions that would lead to the desired generalizations so that there would be lesson closure.
Each teacher implemented the research lesson in one of their classes with the rest of the members of the lesson study group observing. The group conducted a post-lesson discussion at the end of each lesson. During each post-lesson discussion, the teachers expressed amazement at their students’ ability to formulate questions and answer them based on the graph. The observers noted that during the small group discussions, the students often referred to what they had learned in their previous science and mathematics lessons while doing the task. They observed that everyone contributed to the discussions. They found out during the whole class discussions that the students expressed similar ideas in the form of different questions. After the first implementation of the research lesson, the lesson study group decided that instead of asking the different groups to put together questions based on their difficulty level, they would ask them to put together questions that expressed the same ideas. As a result, it became easier for students to formulate the desired generalizations.
The teachers remarked that through lesson study they learned much from their new experience of using a science-related topic, earthquake, as context for their students to apply their mathematics knowledge and skills and to develop skills in question posing. They liked the research lesson because it provided the students the opportunity to realize the importance of the mathematics that they were learning in school in their lives. Indeed, much could be learned from natural disasters!