國中二年級學生一元二次方程式解題歷程分析之個案研究

• Main Author: 林千鑫
• Other Authors: 蕭龍生
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/98219178610553697287

碩士 === 國立高雄師範大學 === 數學系 === 102 === Abstract The main purpose of this study is exploring the eighth graders’ related concept development of quadratic equation with one unknown and analyzing the case by problem-solving processes, problem-solving strategies and the factors that determine success or failure of problem-solving. The study adopts the case research methodology of qualitative research methods to analyze the data that were collected from the case and explores the factor of low performance on mathematics. Based on the research result, we offered some conclusions and suggestions as below to be the reference on the further teaching of mathematical courses. 1. For problem-solving processes, &;lt;1> The key point of reading questions is based on whether the case can understand the description of the subject clearly or not, by catching the key words of the subject itself to know how to use which Factorization method or hypothesize a variable for unknown part to solve the problem gradually by clues. Some slight conditions always are missed when the case uses the careless attitude to solve the problem. &;lt;2>When practicing the strategy to solve the problem, the case has to have a certain degree of calculation ability on equation; after knowing how to hypothesize variable parallel formula is followed by the process of equation factorization calculation. The calculation mistake happens easily to the person with the poor calculation ability or over self-confidence and carelessness on solving the problem. 2. For problem-solving strategies, &;lt;1> Students rely on recollection and reciting strategies excessively when solving the application problem of Quadratic equation with one unknown, they only remember which kind of question can go with which hypothesis variable method and then the process of solving the problems will be lead to become an formalization without thinking why. Therefore, it will cause a great obstacle to solve the problem. &;lt;2>When facing the application and the calculation of the quadratic equation with one unknown at the same time, students fear for how to answer the questions systematically; therefore, if they can try to write down their thinking to suppose the unknown part and find the way to calculate from equality relationship, learn to accept trial and error and find out the core problems, it will strengthen the problem-solving ability due to the trial and error experiences. 3. For factors that determine success or failure of problem-solving, &;lt;1> Knowledge about mathematics: The establishment of the right schemes affects the students to answer the questions successfully or not a lot. Students have to make a connection with the past experience when facing the problem. With more abundant experience, the more clues will be adopted. Understanding the meaning of the question ,and knowing well the key words and then applying the related schemes to integrate systematically, the problem can be solved completely. &;lt;2> Meta-cognition: It is important if the case herself/himself understands the progress in solving the problem, knows the situation of solving the problem and is aware of her/his problem. The case must learn to superintend herself/himself to complete the answer to the question. &;lt;3> Affective attitude: That the case screws up the courage and confidence to solve the problems will influence the results greatly. Failure this time can be a preparation for the next challenge. Key Words: Problem-solving processes, Problem-solving strategies, Quadratic equation with one unknown