The study of promoting the abilities of solving problems about law of sine and law of cosine in twelve grade student - using triangle congruence strategies

• Main Authors: Wei-chun Chang, 張惟淳
• Other Authors: none
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/62760863741738027681

碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 100 === This study is focus on reviewing of lessons. Under learning and teaching in the frame of metacognition, we can encourage students to relational understanding, discovering the relationships of laws sine, law of cosine and congruence of triangles. And then, we trained strategies of problem solving of students, to improve their ability as they faced to several kinds of problems. Self-regulation, the theory of a master of psychology, Piaget (1964, 1971), told us that human learns in two ways, assimilation and accommodation. Learning is a procedure that assimilation and accommodation occurs repeatedly. Understanding the reasons behind the theories can make students bring their knowledge into their schema. What teachers can do is help them learning meaningful, which called relational understanding by Skemp (1987, 2007). And besides, we need learning and teaching under metacognition, students look back how they know after learning, teachers monitor the procedure and adjust their methods as they teaching. There were 3 phases in this study. First: Linking of laws sine, law of cosine and congruence of triangles. We begun with 5 concepts of congruence of triangles, students learned how to match laws sine, law of cosine with congruence of triangles by the idea “known and unknown information build up formula.” Second: Thinking of procedure problems. Using complex problems to build up the concept “congruence of triangles is the condition that a triangle can be defined uniquely,” thus students can begin with finding out congruence of triangles as they solving problems. Final: Go further, problem solving. We researched much more difficult problems here, solving with the strategies of problem solving of Polya (1945), to improving the abilities in thinking, problem solving and applications.