Development of Instructional Models for Problem Solving in Quadratic Functions and Ellipses

이차함수와 타원의 문제해결 지도를 위한 멀티미디어 학습자료 개발

Recently, most classrooms in Korea are fully equipped with multimedia environments such as a powerful pentium pc, a 43″large sized TV, and so on through the third renovation of classroom environments. However, there is not much software teachers can use directly in their teaching. Even with existing software such as GSP, and Mathematica, it turns out that it doesn####t fit well in a large number of students in classrooms and with all written in English. The study is to analyze the characteristics of problem-solving process and to develop a computer program which integrates the instruction of problem solving into a regular math program in areas of quadratic functions and ellipses. Problem Solving in this study included two sessions: 1) Learning of basic facts, concepts, and principles; 2) problem solving with problem contexts. In the former, the program was constructed based on the definitions of concepts so that students can explore, conjecture, and discover such mathematical ideas as basic facts, concepts, and principles. In the latter, the Polya#s 4 phases of problem-solving process contributed to designing of the program. In understanding of a problem, the program enhanced students#### understanding with multiple, dynamic representations of the problem using visualization. The strategies used in making a plan were collecting data, using pictures, inductive, and deductive reasoning, and creative reasoning to develop abstract thinking. In carrying out the plan, students can solve the problem according to their strategies they planned in the previous phase. In looking back, the program is very useful to provide students an opportunity to reflect problem-solving process, generalize their solution and create a new in-depth problem. This program was well matched with the dynamic and oscillation Polya#s problem-solving process. Moreover, students can facilitate their motivation to solve a problem with dynamic, multiple representations of the problem and become a powerful problem solve with confidence within an interactive computer environment. As a follow-up study, it is recommended to research the effect of the program in classrooms.