高中生三角函数学习中认知错误及纠正的案例分析

发布时间：2019-06-19 05:30

【摘要】：三角函数是学生在高中阶段应该掌握的一类基本初等函数,是高中数学中的重要知识,三角函数有广泛的应用,可见其重要性。本研究从高中生学习三角函数的认知特点出发,了解和掌握高中生在三角函数学习中可能出现的认知错误及成因,并对典型性错误的案例进行详细分析,寻求纠正错误的有效方法。本研究以文献分析、访谈、调查、教学实践研究等方法进行,通过编制三角函数错误类型测试卷,对2014-2015第一学期我校六个班级236名学生实施测试,针对测试结果,选取部分测试者进行非标准化访谈,再将测试和访谈结果进行归纳、总结、研究,发现高中生学习三角函数在概念和运算等方面出现的错误类型,总结、概括为四大类：(1)三角函数概念方面的错误；(2)三角函数图象、性质方面的错误；(3)基本公式运算方面的错误；(4)忽视条件限制方面的错误等。从高中生的认知结构出发,分析各种错误的成因,得出学生出现的错误多属于知识性错误和认知策略性错误,总结出以下四种错误成因：(1)认知原因；(2)思维原因；(3)缺少反思；(4)其他原因,例如原有基础知识不牢固、新知识体系不完善、新旧知识体系混淆、不良学习习惯的影响、思维定势的消极作用,以及学生的畏难情绪等等。通过“防错”与“纠错”的实际教学案例,汇总学生在三角函数学习中容易出现的一些错误,并针对这些错误进行分析和更正,弥补知识上和心理上的不足,避免再次出错。针对研究结果,结合高中生的特点提出了对三角函数这部分内容在教学方面的一些建议,希望能通过三角函数的学习,有效地提高学生的探究能力和数学水平,能为一线教师积累一些经验,提供一些参考。
[Abstract]:Trigonometric function is a kind of basic elementary function that students should master in senior high school. It is an important knowledge in senior high school mathematics. Trigonometric function has a wide range of applications, so it can be seen that it is important. Based on the cognitive characteristics of senior high school students learning trigonometric functions, this study understands and grasps the possible cognitive errors and causes in trigonometric function learning of senior high school students, and analyzes the cases of typical errors in detail, so as to find an effective way to correct the errors. This study is carried out by means of literature analysis, interview, investigation and teaching practice research. 236 students from six classes in our school in the first semester of 2014 / 2015 are tested by compiling trigonometric function error type test paper. according to the test results, some testers are selected for non-standardized interviews, and then the test and interview results are summarized, summarized and studied. This paper finds out the types of errors in the concept and operation of trigonometric functions in senior high school students, and summarizes them into four categories: (1) the errors in the concept of trigonometric functions; (2) the image of trigonometric function, the error of property, (3) the error of basic formula operation, (4) the error of neglecting the limitation of condition, etc. Starting from the cognitive structure of senior high school students, this paper analyzes the causes of all kinds of errors, and concludes that most of the mistakes made by students belong to intellectual errors and cognitive strategic errors, and the following four causes of errors are summarized: (1) cognitive causes, (2) thinking reasons, (3) lack of reflection, (3) lack of reflection, (2) thinking reasons, (3) lack of reflection, and (3) lack of reflection. (4) other reasons, such as the original basic knowledge is not firm, the new knowledge system is not perfect, the new and old knowledge system is confused, the influence of bad learning habits, the negative effect of thinking stereotype, and the students' fear of difficulties and so on. Through the actual teaching cases of "error prevention" and "error correction", this paper summarizes some mistakes that are easy to occur in trigonometric function learning, and analyzes and corrects these errors, so as to make up for the lack of knowledge and psychology and avoid making mistakes again. According to the research results, this paper puts forward some suggestions on the teaching of trigonometric function according to the characteristics of senior high school students. It is hoped that through the study of trigonometric function, the students' inquiry ability and mathematics level can be effectively improved, and some experiences and references can be accumulated for front-line teachers.
【学位授予单位】：天津师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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