| Summary: | 碩士 === 國立高雄師範大學 === 數學系 === 107 === The purpose of this study is to explore the problem-solving process, problem-solving strategies and related knowledge in the application of the 8th graders in the arithmetic sequence.
Based on the three non-routine problems of the arithmetic sequence, this study was conducted on five students of the 8th graders in Taichung City. The thinking loud method was used to collect the problem-solving process of five students, and five students were asked to record the problem-solving history of the three non-routine problems of the arithmetic sequence. The Montague's problem-solving process model was used to analyze the problem-solving process and problem-solving strategies of the five students. The following conclusions were obtained as below.
First, in the process of solving the problem, when students face the non-routine problems of the arithmetic progression, they will not necessarily have all the problem-solving stages in the process of solving the problems. There are different problem-solving stages due to different topics. The order of the problem-solving process is also not in accordance with the Montague problem-solving process model, and the calculations are adjusted at any time as the thinking progresses.
Second, in terms of problem-solving strategies, most students will use the formula to solve problems. A few of students use their own regularity to solve problems because of forgetting the equations of the arithmetic sequence. Students often have incomplete answers to their ability to remember mathematical concepts, their ability to translate textual descriptions into mathematical symbols, and the ability to organize topics.
This study will discuss the research results and propose teachers' reference suggestions for the teaching of the arithmetic sequence in the future.
Keywords: arithmetic sequence, problem-solving process, mathematical problem-solving strategy
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