Development of Meta Problem Types to Improve Problem-solving Power

문제 해결력 신장을 위한 베타 문제 유형 개발

In mathematics education we have focused on how to improve the problem-solving ability, which makes its way to the new direction with the introduction of meta-cognition. As meta-cognition is based on cognitive activity of learners and concerned about internal properties, we may find a more effective way to generate learners problem-solving power. Its means that learners can regulate cognitive process according to their gorls of learning by themselves. Moreover, they are expected to make active participation through this process. If specific meta problems designed to develop meta-cognition are offered, learners are able to work alone by means of their own cognition and regulation while solving problems. They can transfer meta-cognition to the other subjects as well as mathematics. The studies on meta-cognition conducted so far may be divided into these three types. First in Flavell(［3］) meta-cognition is defined as the matter of being conscious of one's own cognition, that is, recognizing cognition. He conducted an experiment with presschoolers and children who just entered primary school and concluded that their cognition may be described as general stage that can not link to specific situation in line with Piaget. Second, Brown(［1］, ［2］) and others argued that meta-cognition means control and regulation of one's own cognition and tried to apply such concept to classrooms. He tried to fined out the strategies used by intelligent students and teach such types of activity to other students. Third, Merleary-Ponty (1962) claimed that meta-cognition is children's way of understanding phenomena or objects. They worked on what would come out in children's cognition responding to their surrounding world. In this paper following the model of meta-cognition produced by Lester (［7］) based on such ideas, we develop types of meta-cognition. In the process of meta-cognition, the meta-cognition working for it is to be intentionally developed and to help unskilled students conduct meta-cognition. When meta-cognition is disciplined through meta problems, their problem-solving power will provide more refined methods for the given problems through autonomous meta-cognitive activity without any further meta problems.