The Study of Open-ended Approach in Mathematics Teaching Using Jigsaw Method : A Case Study of the Water Beaker Problem<教育科学>

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The aim of study was to (1) create a lesson plan of an open-ended problem using jigsaw method (2) experiment the lesson plan in junior high school in Japan and (3) compare between expected and empirical result in class experiment. This study was conducted by reviewing the related literatures, creating the lesson plan and other instruments, experiment the lesson plan in junior high school in Japan and summarizing the result of teaching.The process of Mathematics teaching using the open-ended problem is the method that allows students to encounter Mathematics problems having the openness in processes, answers and developing of problem. The students will find the solution by using Mathematics knowledge based on their prior knowledge and their abilities. The jigsaw activity provides students learn to collaborate with others and improves their communication skills in order to explain the findings to others. The lesson plan about the water-beaker problem tilted with one fixed edge, was created along with jigsaw method which are as follows:(1) Expert activity was divided into 3 steps: 1.1) Brainstorming: Students are divided into groups to brainstorm what they want to examine the beaker from only one view (Front/Top/Side-view), 1.2) Sharing: Students regroup to share viewpoints of brainstorming group in own view, 1.3) Experiment: Students regroup to examine viewpoints by experiment in own view, (2) Jigsaw activity: Students regroup to group of all views (Front, Top, Side-view) to explain all findings. The lesson plan was tried out with students in 2nd year junior high school class of Saitama prefecture junior high school for 2 periods by Japanese teacher and the researcher.The results of experiment showed that students perceived the volume of water is constant and discovered a variation of water height which is the height of water at the tilted side increases but the opposite side decreases. Those are important foundation conditions to generate other amounts. Most students collected data in experiment by measuring so the teachers should encourage students draw a model of tilted beaker to help seeing the perspective in order to compute other amounts. It should be noted that the students were 2nd year junior high student and still have not study about irrational number such as square root of 2, Pythagorean theory. Therefore they could not find some exactly detail. On the other hand, they could find many changes about ratio, directly and inverse proportional which they have already studied. It means they could integrate their mathematical knowledge. Furthermore, most of them could not explain ideas clearly and accurately so the teacher should emphasize students to add more detail of change clearly.From this study, it shows that students’ thinking ability is satisfactory in flexibility but unsatisfactory in fluency and originality. They should be offered the improvement because these skills are important and beneficial effect on their lives. Teacher should pay attention to make familiar relationship with the students at the beginning and must be able to communicate with students naturally and explain simply in order that the learning process could be done smoothly and successfully. Communication skill is a very indispensable and important skill that teacher have to improve. About learning activities, the more openness of question teacher asked may be the greater of the challenge and interesting of question. Moreover, if teacher provided students make a condition of question by themselves, students will be engaged to the problem gradually and can understand the problem more deeply.

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