【摘要】：在數學學習過程中,學生解題犯錯是正常的。但在教學過程中,教師希望幫助學生徹底理解數學知識,少犯錯或不犯錯,以提高學習的效率。近年來,解題錯誤的合理性逐漸得到人們的肯定,越來越多的人開始關注解題錯誤的教育價值。作為平面解析幾何的核心內容,圓錐曲線是高中生數學學習的重點和難點,也是高考考查的重點。對高二學生圓錐曲線解題錯誤的調查表明,學生在學習圓錐曲線時存在一定的問題,在解答與之相關的題目時出現了較多的錯誤。但國內外與解題錯誤相關的研究中缺少對圓錐曲線解題錯誤的調查研究。本研究主要采用問卷調查法、訪談法、試卷分析法,應用Excel進行數據處理,對高二學生解題錯誤做調查研究。本論文總共六章。第1章是引言。主要介紹了研究的背景、意義,本文要研究的主要問題及其基本結構。第2章是文獻綜述。通過對國內外有關解題錯誤的研究資料進行梳理與總結,為本文的寫作提供指南。第3章是研究的方法。主要對本文所選的研究對象、研究內容,采用的研究方法、研究工具進行了詳細說明,并介紹了數學解題錯誤的分析框架：知識性錯誤、邏輯性錯誤、策略性錯誤及疏忽性錯誤。第4章是高二學生圓錐曲線解題錯誤的調查與分析。這一章主要進行兩方面的調查研究：一方面是高二師生對解題錯誤認識的調查；另一方面,對高二學生在解決圓錐曲線相關問題的過程中出現的解題錯誤進行歸類統(tǒng)計,并分析了不同類型錯誤產生的原因。第5章是糾正高二學生圓錐曲線解題錯誤的原則和對策建議。針對高二學生圓錐曲線學習中存在的主要錯誤,教師在糾正學生錯誤時應遵循適時性、針對性和主體性三大原則,并提出幫助學生樹立恰當的錯誤觀、注重分析學生的錯誤、區(qū)別對待不同類型的解題錯誤、注重學生良好的解題習慣的養(yǎng)成、引導學生利用好錯題本這五條糾錯建議。第6章是結論與反思。這部分圍繞本論文研究的主要問題總結了研究的結論,并指出本研究的不足和今后研究的方向。
[Abstract]:It is normal for students to solve problems and make mistakes in the process of learning mathematics. But in the process of teaching, teachers hope to help students understand mathematics thoroughly and make fewer mistakes or no mistakes, so as to improve the efficiency of learning. In recent years, the rationality of problem-solving errors has been gradually affirmed, and more people begin to pay attention to the educational value of problem-solving errors. As the core content of plane analytic geometry, conic curve is the focus and difficulty of senior high school students' mathematics study, and also the key point of college entrance examination. The investigation of the problem solving errors in the conic curve of senior two students shows that there are some problems in learning conic curve, and there are many errors in solving the related problems. However, there is a lack of investigation and research on conic curve problem solving errors in domestic and foreign research. In this study, questionnaire, interview, test paper analysis and data processing with Excel were used to investigate the problem solving errors of the sophomore students. There are six chapters in this thesis. Chapter 1 is the introduction. This paper mainly introduces the background and significance of the research, the main problems and the basic structure of this paper. Chapter 2 is a literature review. This paper provides a guide for the writing of this paper by combing and summing up the research materials about problem-solving errors at home and abroad. Chapter 3 is the research method. This paper mainly introduces the research object, research contents, research methods and research tools adopted in this paper, and introduces the analytical framework of mathematical problem solving errors: knowledge error, logical error, and so on. Strategic and negligent mistakes. Chapter 4 is the investigation and analysis of conic problem solving errors. This chapter mainly carries on two aspects of investigation and research: on the one hand, it is the investigation of teachers and students' understanding of problem solving errors; on the other hand, it classifies the errors in solving problems related to conic curves in senior two students. The causes of different types of errors are analyzed. Chapter 5 is the principle and suggestion of correcting the problems of conic curve of senior two students. In view of the main mistakes in the learning of conic curve, teachers should follow the three principles of timeliness, pertinence and subjectivity in correcting students' errors, and put forward some suggestions to help students set up a proper view of mistakes and pay attention to the analysis of students' mistakes. Treat different types of problem-solving errors, pay attention to the cultivation of students' good problem-solving habits, and guide students to make good use of the five error-correcting suggestions. Chapter 6 is conclusion and reflection. This part summarizes the conclusions of the research around the main problems of this paper, and points out the shortcomings of this study and the direction of future research.
【學位授予單位】：陜西師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6

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本文編號：2149878