元认知理论下初中生反比例函数出错归因与对策
发布时间：2019-04-04 19:39
【摘要】：初中阶段在学生整个学习生涯中占有重要的地位,学习内容也越来越偏向于抽象化,是学生由具体形象思维走向抽象概括思维的重要时期。在此阶段函数的学习也越来越深入,其中反比例函数在这一时期占有重要地位,同时也是中考重要考点之一。反比例函数概念较抽象,性质方面涉及的知识也较多,并与其他内容结合性强,这就导致了学生在学习反比例函数的过程中,容易出现各种各样的错误,并且这些出错的类型是每届学生都会产生的。由此,如果可以对反比例函数中经常出错的题目进行整理,找出出错的类型及原因,并在此基础之上,提出恰当并有实践意义的教学策略,就可以有效的减少错题的产生,使学生找到适合自己的学习方法和学习策略,增强学生学习数学的信心,并为他们升入高中学习更加复杂的函数打下坚实基础。因此,笔者认为研究反比例函数出错的归因是很有意义的。本文主要的内容:笔者首先通过文献阅读的方法,在大量阅读相关文献的基础上,整理分析了国内对数学错误和反比例函数的相关研究,并给出了文献综述。通过阅读文献,参考别人的定义方式方法,给出了数学错误以及归因理论的概念界定。在元认知理论下,以元认知知识、元认知体验以及元认知监控理论,来对反比例函数出错的归因进行深入的探讨和研究,并在此基础之上辅助以建构主义理论、行为主义理论的相关知识,对反比例函数学习中出错的归因给出相关的指导。在确定出错类型时,通过对教师和学生进行访谈,找到出错的大致类型,并根据访谈的结果编制测试卷,对学生出错的类型进行测试,以确保访谈的真实性和有效性。访谈与测试结果得出,针对初中生反比例函数学习中出错的题目,分为1.反比例函数概念错误;2.反比例函数性质错误;3.反比例与一次函数结合应用错误;4.反比例函数与几何结合应用错误,这四项具体的出错类型。笔者在找出学生反比例函数学习中出错的大致类型后,针对这些确定的出错类型,利用编制出的调查问卷,进行分因素的调查,由此来确定学生归因的主要方向,并根据这些归因结果给出针对性的教学对策。通过对初中生进行调查,得到相关的数据,调查问卷的数据分析主要结果为:本文利用问卷调查的方法抽取部分初中生进行调查,详细了解初中生不同群体在反比例函数学习过程中出错的归因,并对不同群体在归因上差异性进行比较分析。反比例函数出错的归因上,通过调查数据结果分析得出:在反比例函数概念上出错主要归结于教师讲解清晰度上;在反比例函数的性质方面出错主要归结于学习兴趣;在反比例函数与一次函数相结合的题目中出错主要归结于学习方法;最后在反比例函数与几何相结合题目产生错误主要归结于学习能力。针对归因的结果,对每类出错类型提出了针对性的教学策略。
[Abstract]:The junior high school stage plays an important role in the whole learning career of students, and the learning content is more and more inclined to abstract, which is an important period for students to change from concrete image thinking to abstract generalizing thinking. In this stage, the learning of the function is getting deeper and deeper, in which the anti-proportional function plays an important role in this period, and it is also one of the important examination points in the middle school entrance examination. The concept of anti-proportional function is more abstract, and it involves more knowledge in nature, and has a strong combination with other contents. This leads students to make a variety of mistakes in the process of learning anti-proportional function. And these types of errors are produced by every student. Therefore, if we can sort out the problems that are often wrong in the anti-proportional function, find out the types and reasons of the errors, and on this basis, put forward appropriate and practical teaching strategies, we can effectively reduce the occurrence of the wrong questions. So that students can find suitable learning methods and learning strategies, enhance students' confidence in learning mathematics, and lay a solid foundation for them to enter high school to learn more complex functions. Therefore, the author thinks that it is meaningful to study the attribution of the error of inverse proportional function. The main contents of this paper are as follows: firstly, through the method of literature reading, on the basis of reading a large number of related documents, the domestic research on mathematical errors and inverse proportional function is analyzed, and the literature review is given. The definition of mathematical errors and attribution theory is given by reading the literature and referring to other people's methods of definition. On the basis of metacognitive theory, metacognitive knowledge, metacognitive experience and metacognitive monitoring theory, the attribution of errors in inverse proportional function is deeply discussed and studied, and on this basis, the theory of constructivism is assisted. The related knowledge of behaviorism theory provides relevant guidance to the attribution of errors in the learning of anti-proportional functions. In order to ensure the authenticity and validity of the interview, the teachers and students are interviewed to find out the general types of errors. According to the results of the interviews, the test papers are compiled to test the types of errors made by the students in order to ensure the authenticity and validity of the interviews. The results of interview and test show that the problem of error in anti-proportional function learning of junior high school students is divided into 1. The concept of inverse proportional function is wrong; 2. The nature of inverse proportional function is wrong; 3. Application error in combination of inverse scale and primary function; 4. Anti-proportional function combined with geometry application errors, these four specific error types. After finding out the general types of errors in students' anti-proportional function learning, according to these definite types of errors, the author uses the compiled questionnaire to carry out the investigation of different factors to determine the main direction of students' attribution, so as to determine the main direction of students' attribution, and then find out the main direction of students' attribution. According to these attribution results, the author puts forward the corresponding teaching countermeasures. Through the investigation of junior high school students, the relevant data are obtained. The main results of the data analysis of the questionnaire are as follows: in this paper, some junior middle school students are selected by the method of questionnaire survey for investigation. The attribution of errors in learning anti-proportional function among different groups of junior high school students was studied in detail, and the differences in attribution of different groups were compared and analyzed. On the attribution of the error of anti-proportional function, through the analysis of the results of the survey data, it is concluded that the error in the concept of the anti-proportional function is mainly attributed to the clarity of the teacher's explanation, the mistake in the nature of the anti-proportional function is mainly attributed to the interest in learning. In the problem of the combination of inverse proportional function and primary function, the error is mainly attributed to the learning method; finally, the error caused by the combination of inverse proportional function and geometry is mainly attributed to the learning ability. Aiming at the result of attribution, this paper puts forward some teaching strategies for each type of error.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
本文编号：2454104
[Abstract]:The junior high school stage plays an important role in the whole learning career of students, and the learning content is more and more inclined to abstract, which is an important period for students to change from concrete image thinking to abstract generalizing thinking. In this stage, the learning of the function is getting deeper and deeper, in which the anti-proportional function plays an important role in this period, and it is also one of the important examination points in the middle school entrance examination. The concept of anti-proportional function is more abstract, and it involves more knowledge in nature, and has a strong combination with other contents. This leads students to make a variety of mistakes in the process of learning anti-proportional function. And these types of errors are produced by every student. Therefore, if we can sort out the problems that are often wrong in the anti-proportional function, find out the types and reasons of the errors, and on this basis, put forward appropriate and practical teaching strategies, we can effectively reduce the occurrence of the wrong questions. So that students can find suitable learning methods and learning strategies, enhance students' confidence in learning mathematics, and lay a solid foundation for them to enter high school to learn more complex functions. Therefore, the author thinks that it is meaningful to study the attribution of the error of inverse proportional function. The main contents of this paper are as follows: firstly, through the method of literature reading, on the basis of reading a large number of related documents, the domestic research on mathematical errors and inverse proportional function is analyzed, and the literature review is given. The definition of mathematical errors and attribution theory is given by reading the literature and referring to other people's methods of definition. On the basis of metacognitive theory, metacognitive knowledge, metacognitive experience and metacognitive monitoring theory, the attribution of errors in inverse proportional function is deeply discussed and studied, and on this basis, the theory of constructivism is assisted. The related knowledge of behaviorism theory provides relevant guidance to the attribution of errors in the learning of anti-proportional functions. In order to ensure the authenticity and validity of the interview, the teachers and students are interviewed to find out the general types of errors. According to the results of the interviews, the test papers are compiled to test the types of errors made by the students in order to ensure the authenticity and validity of the interviews. The results of interview and test show that the problem of error in anti-proportional function learning of junior high school students is divided into 1. The concept of inverse proportional function is wrong; 2. The nature of inverse proportional function is wrong; 3. Application error in combination of inverse scale and primary function; 4. Anti-proportional function combined with geometry application errors, these four specific error types. After finding out the general types of errors in students' anti-proportional function learning, according to these definite types of errors, the author uses the compiled questionnaire to carry out the investigation of different factors to determine the main direction of students' attribution, so as to determine the main direction of students' attribution, and then find out the main direction of students' attribution. According to these attribution results, the author puts forward the corresponding teaching countermeasures. Through the investigation of junior high school students, the relevant data are obtained. The main results of the data analysis of the questionnaire are as follows: in this paper, some junior middle school students are selected by the method of questionnaire survey for investigation. The attribution of errors in learning anti-proportional function among different groups of junior high school students was studied in detail, and the differences in attribution of different groups were compared and analyzed. On the attribution of the error of anti-proportional function, through the analysis of the results of the survey data, it is concluded that the error in the concept of the anti-proportional function is mainly attributed to the clarity of the teacher's explanation, the mistake in the nature of the anti-proportional function is mainly attributed to the interest in learning. In the problem of the combination of inverse proportional function and primary function, the error is mainly attributed to the learning method; finally, the error caused by the combination of inverse proportional function and geometry is mainly attributed to the learning ability. Aiming at the result of attribution, this paper puts forward some teaching strategies for each type of error.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
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