การพัฒนาความสามารถในการแก้ปัญหาทางคณิตศาสตร์ของนักเรียนชั้นมัธยมศึกษาตอนปลายในชั้นเรียนที่สอนด้วยวิธีการแบบเปิด

Abstract

The objectives of this qualitative research were to (1) analyze mathematical problem solving abilities of upper secondary school students in classroom taught by open approach and (2) investigate teaching practices for developing mathematical problem solving ability of upper secondary school students in classroom taught by open approach. The target group consisted of 30 Mathayom Suksa 5 students at Hotpittayakom School, Hot district, Chaing Mai Province during the second semester of the 2012 academic year. The researcher developed 12 probability lesson plans and implemented them in real classroom teaching. All classroom teaching-learning activities were videotaped and later on analyzed by means of the protocol analysis using Schoenfeld’s mathematical problem solving behavior framework as a reference. Concurrently, data from classroom observations and students’ written works were also summed up and used as an additional information to support the protocol analysis. The research results were then presented in the form of analytical narrative. The research findings showed that a so-called open approach did have positive impacts on both students’ problem solving ability and teacher’s teaching techniques. Based on the protocol analysis, the students had progressively developed the mathematical problem solving ability throughout the learning unit of probability and the researcher also to a large degree, successfully developed teaching practices through the 4 steps of open approach. As for the students’ mathematical problem solving ability on probability, their learning had gradually developed through six episodes of problem solving behaviors. Students read and understood open-ended problem situation, then explored the problem through trial and error strategy and surveyed some conditions or prior knowledge needed for solving the given problem situation. In step of students’ self learning, the episode of analysis emerged through the use of representations and some principles concerning probability to model the problem such as drawings, symbolizing, drawing tree diagrams and using the fundamental rule of counting. In addition, students often showed planning behavior through collaborative problem solving within their small groups. Finally, the students carefully implemented their plan to solve the problem and performed verification behaviors through reviewing and checking their problem solving processes and solutions. As for teaching practices, the followings were teaching techniques employed. Using open-ended problem situations to stimulate students’ interest in reading and understanding the given problems, providing appropriate time for students to solve the problem freely, using periodic questioning to stimulate students’ application and verification behaviors on their own efforts, observing and surveying students’ mathematical problem solving behaviors in order to check their progress and keep it in mental notes for preparing whole-class discussion and comparison, selecting and sequencing the students’ written works for purposive presentations. Moreover, in step of whole-class discussion and comparison, the teacher proposed important ideas of problem solving emerging in class and extended the ideas through teacher’s representations. To conclude each lesson, the teacher summarized today lesson through presenting rules or principles of probability which correspond to the students’ problem solving ideas occurred throughout that lesson.