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題名:不同程度國中生代數解題之研究
作者:顏錦偉
作者(外文):YIAN,JIIN-WAY
校院名稱:國立高雄師範大學
系所名稱:科學教育暨環境教育研究所
指導教授:柳賢
學位類別:博士
出版日期:2016
主題關鍵詞:代數問題解題成分Algebraic ProblemProblem-Solving Component
原始連結:連回原系統網址new window
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本研究採質性分析方式,透過檢視與晤談來詮釋國中生在解答代數問題歷程的「解題成分」表現情形,與探討不同程度國中生在解答代數問題的「解題成分」表現情形。關於解答代數問題的「解題成分」研究結果:
一、學生對條件充足的問題情境容易理解;問題表徵需要基模知識;解題歷程是基模知識的整合過程;概念和程序知識彼此存在相依關係。
二、系統分析問題訊息產出解題策略;學生可以接受解題策略遷移;忽略程序知識會影響整體解題結果表現;不同的基模知識呈現不同的表現方式;代數問題解題的符號表徵優於文字表徵。
三、洞察問題關鍵條件是詮釋問題的核心;解題歷程是一個監控與詮釋的過程。
關於不同程度學生解答代數問題的「解題成分」研究結果:
一、不分程度高低的學生對「給定已知條件」的問題容易理解;高程度學生擁有閱讀思考的能力與穩固的基模知識,低程度學生閱讀慢,缺乏基模知識。
二、高程度學生應用與分析數學原理,計算書寫過程表現佳。中、低程度學生採直觀方式解題,計算能力薄弱。
三、高程度學生能進行解題歷程自我監控的動作,洞察解題關鍵條件;低程度學生檢驗與說明能力不佳。
根據結論對國中數學教學、學生學習和未來進一步研究提出建議。
關鍵字:代數問題、解題成分
This research uses the qualitative analysis way, through interviews with a review to the interpretation of the junior high school students' "problem-solving component" performance on the algebraic problem solving process, and explore to various levels of junior high school students' "problem-solving component" performance on the algebraic problem solving. The first results of research:
1.The students sufficient condition problem situation is easy to understand; problem representation requires the knowledge of schema; the course of solving the integration process is the knowledge of schema; knowledge of the concepts and procedures exist dependencies to each other.
2.The system analysis of the problem solving strategies message output; the student can accept migration problem solving strategies; ignore knowledge of the procedures will affect the overall problem solving performance results; knowledge of different archetypes show different expressions; algebraic problem solving symbolic representation than text characterization.
3.The key condition for insight is the core problem of interpretation; problem solving course is a process monitoring and interpretation.
The second results of research:
1.Regardless of the level students, "given the known conditions" of the problem is easy to understand; that high level of students' have ability to think and to read, with a strong knowledge of schema, the low level of students' reading slow, lack of the knowledge of schema.
2.High degree students to apply mathematical principles and analysis, performance calculation process of writing good. The low level of student problem solving mining in an intuitive way, computing capacity is weak.
3.The high level of problem-solving course students can operate self-monitoring, problem solving insight into the key conditions; the low level of student to testing and explanation ability is not good.
According to the conclusion at junior high school of mathematics teaching, the student study and the future will further study puts forward the suggestion.
Key words: Algebraic Problem, Problem-Solving Component.
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