基于概念教与学理论的高中函数概念教学研究

发布时间：2018-11-04 16:45

【摘要】：在高中数学课程中,函数作为一条主线贯穿整个高中课程。然而由于函数具有高度抽象性与复杂性,致使函数教学现状不是很乐观。此外,函数在教学方面的研究主要集中在教学设计、思想方法、信息技术以及解题技巧方面。大多比较注重解题而忽视了概念形成、注重理论而忽视了实践研究。所以本研究选择高中函数的概念进行教学研究。本研究以数学概念教与学的理论为基础、结合新课程标准要求；分析函数概念教学中存在的优势和不足,并对现状出现的原因做分析；最后根据以上分析对函数概念教学设计做改进,并将改进后的教学设计进行课堂实施,以检验教学效果。具体研究内容如下：首先,通过文献分析法对指导函数概念教学的理论做分析,主要分析了两方面内容：(1)函数概念教与学的理论分析,为后文提供理论依据。(2)对函数内容进行分析,为教学设计改进提供参考和依据。其次,在理论基础上,通过对收集到的教学设计案例进行分析,发现高中函数概念教学存在许多优点,主要表现在：概念理解方面剖析透彻；概念应用方面由易到难,逐步加深,符合学生认知规律。但笔者也发现存在一些不足,主要表现在以下三个方面：(1)概念引入方面忽视概念形成过程；(2)沿用教材三个例子解释函数变量对应关系,学生不能很好的理解；(3)概念系统化过程没有得到体现。出现以上教学现状的原因主要是：应试教育以高考为中心,导致教师自动屏蔽不考内容；新课标提出教学要回归教材,所以一切以教材内容为主；大部分教师误认为概念系统化过程浪费了课堂时间。再次,在理论与现状的基础上,笔者对函数概念教学设计从以下几个方面进行改善：概念引入上选择形成和同化相结合的方式,这既没有忽视概念形成过程,也不会浪费太多的课堂时间,达到更理想的学习效果；选择两个简单一次函数,通过列表、图像、解析式的方式引导学生分析函数变量对应关系特点,这使得学生在原有认知结构上更容易理解新内容；概念系统化过程不可少,帮助学生将新概念纳入到原有认知结构中去。最后,将改进后的教学设计进行课堂实施,通过课堂观察、教师评课、学生访谈等方式进行评价,综合结果发现：学生对概念的形成过程清晰、理解比较透彻、应用比较灵活；整节课学生学习积极性高,主体性体现到位,学生经过类比、思考、讨论、探究等过程,培养了学生观察、类比、推理的能力。
[Abstract]:In high school mathematics curriculum, function runs through the whole high school curriculum as a main line. However, due to the high abstraction and complexity of function, the present situation of function teaching is not very optimistic. In addition, the research of function in teaching mainly focuses on teaching design, thought method, information technology and problem-solving skills. Most of them pay more attention to solving problems and neglecting the formation of concepts, paying attention to theory and neglecting practical research. Therefore, this study chooses the concept of high school function for teaching research. This study is based on the theory of mathematics concept teaching and learning, combined with the requirements of the new curriculum standard, analyzes the advantages and disadvantages of the function concept teaching, and analyzes the reasons for the present situation. Finally, the function concept teaching design is improved according to the above analysis, and the improved teaching design is implemented in class to test the teaching effect. The specific research contents are as follows: first, through the literature analysis to guide the function concept teaching theory to do the analysis, mainly analyzed two aspects content: (1) the function concept teaching and learning theory analysis, (2) analyzing the content of function and providing reference and basis for the improvement of teaching design. Secondly, on the basis of the theory, through the analysis of the teaching design cases collected, we find that there are many advantages in the teaching of the concept of function in senior high school, mainly in the following aspects: thorough analysis of the concept understanding; Concept application from easy to difficult, gradually deepened, in line with the law of students' cognition. However, the author also finds that there are some shortcomings, mainly in the following three aspects: (1) the concept introduction neglects the concept formation process, (2) using the three examples of textbooks to explain the corresponding relationship between functional variables, students can not understand very well; (3) the process of conceptual systematization is not reflected. The reasons for the above teaching situation are as follows: examination-oriented education takes the college entrance examination as the center, which leads the teachers to automatically block the content of the examination, and the new curriculum standard proposes that the teaching should return to the teaching material, so all the contents of the teaching materials should be given priority to; Most teachers mistakenly believe that the conceptual systematization process is a waste of classroom time. Thirdly, on the basis of theory and present situation, the author improves the teaching design of function concept from the following aspects: the combination of formation and assimilation is chosen in the introduction of concept, which does not neglect the process of concept formation. Also will not waste too much classroom time, achieves the more ideal study effect; Selecting two simple one-degree functions to guide students to analyze the corresponding characteristics of function variables through lists, images and analytic methods, which makes students understand the new content more easily in the original cognitive structure; The process of conceptual systematization is indispensable to help students incorporate new concepts into their original cognitive structures. Finally, the improved teaching design is implemented in class, and evaluated through classroom observation, teacher evaluation and student interview. The comprehensive results show that the students have a clear process of concept formation, a thorough understanding and a flexible application; The students in the whole class have high enthusiasm for learning and their subjectivity is in place. Through the process of analogy, thinking, discussion and exploration, the students' ability of observation, analogy and reasoning has been cultivated.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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