การพัฒนาความเข้าใจเชิงความคิดรวบยอดทางคณิตศาสตร์ของนักเรียนชั้นมัธยมศึกษาตอนปลายในชั้นเรียนที่สอนด้วยวิธีการแบบเปิด

Abstract

The purposes of this qualitative research were to 1) analyze mathematical conceptual understanding of upper secondary school students in classroom taught by open approach, and 2) investigate teaching practices that support developing mathematical conceptual understanding of upper secondary school students in classroom taught by open approach. The target group consisted of 28 Mathayom Suksa 5 students at Lampang Kanlayanee School, Muang District, Lampang Province during the second semester of the 2012 academic year. The researcher developed 10 graph theory lesson plans and implemented in real classroom teaching. All classroom teaching-learning activities were videotaped and later on analyzed by means of the protocol analysis using Pirie and Kieren’s levels of conceptual understanding as a frame of reference. Concurrently, data from the student’s behavior observation form and students’ written works were also summarized using descriptive analysis. The research findings were then presented in the form of analytical narrative. The research findings showed that the students had gradually developed the mathematical conceptual understanding at different levels and the researcher also successfully developed teaching practices through the 4 steps of open approach. Based on the protocol analysis, the students achieved the first five levels of mathematical conceptual understandings throughout the learning unit of graph theory. The students had the mathematical conceptual understanding at level of primitive knowing regarding the use of graph to solve problems which is a prior knowledge for building up the higher levels of mathematical conceptual understanding. Image making occurred while the students creating models by means of graph on their own in order to solve the open-ended problem situations. Image having was developed when the students used mental construct with their own made images. Property noticing emerged after students recognized connections between their various solutions. Moreover, the students developed the conceptual understanding at the level of formalizing through making formulas which representing some rules and theorems of graph theory. As for teaching practices, the followings are the techniques used for developing students’ mathematical conceptual understanding in classroom taught by open approach. Posing an open-ended problem situation for students to solve and encourage them to see the significance of the conceptual understanding at the level of primitive knowing, using periodic questioning to enhance the students’ conceptual understanding up to higher levels, selecting and sequencing various students’ written works which revealed their conceptual understanding at the level of image having for the purposive presentations. In step of whole-class discussion and comparison, the teacher clearly proposed some issues regarding mathematical conceptual understanding at the level of image having through re-voicing and asking the “what”, “how” and “why” types of questions to enhance the level of property noticing and formalizing. To sum up the lesson, the teacher connected students’ various levels of conceptual understanding by means of presenting definitions or principles concerning graph theory in the form of mathematical formulas.