【作者】 王杰；

【导师】 熊惠民；

【作者基本信息】 华中师范大学 ， 学科教学（数学）（专业学位）， 2021， 硕士

【摘要】 函数是贯通整个中职数学的主线之一,它可以看作两个数集之间的对应关系,也蕴含数形结合的思想。函数的概念高度抽象、函数的类型多种多样、函数章节与其他章节内容联系密切。函数既可以解决生活生产中的实际问题,也是连接高等数学系列课程的桥梁。如果函数单元教学设计能够精心设计,一堂“好课”不仅仅让中职学生对知识的掌握和分数的提高,更能让中职学生对于数学其他章节知识、生产生活、高等数学有更深入的了解。单元教学设计是一种整体教学观念,通过构建单元知识体系,根据中职学生的基础知识和已知经验,对单元教学内容进行调整和设计,在数学课堂上引导学生进行思考、计算、创造、想象,从而落实数学核心素养。本文采用文献法通过查阅文献目前有关核心素养的研究的现状与趋势;采用问卷调查法,调查中职学生在学习函数章节中的知识储备以及学习障碍;采用观察法、访谈法对中职函数教学进行客观评析和分析;采用案例研究法跟踪某个班级,采取主题单元教学设计下的课堂教学,分析其核心素养的落实。最后给出具体的函数的单元教学设计,并调查学生在学完函数章节之后的素养提高情况,探究函数单元的教学对数学核心素养积极作用。研究的主要结论为:(一)有关函数单元的学习,中职学生在不同的阶段表现出不一样的学习特征。中职一年级学生注重函数概念性理解,呈现死记硬背现象;中职二年级学生追求函数思想方法的运用,轻概念重应用;中职三年级学生渴望将函数与数列、导数等章节结合,深入到高等数学领域。同时,大部分中职学生对函数的本质存在认识不到位现象。(二)在实际教学中可以将教科书中呈现的“函数”课时安排进行调整,如果将函数的应用拆分为若干生活实例,并作为情境对新课进行导入,能够吸引学生的学习兴趣。(三)中职教师不关注函数单元教学目标及单元框架,在课堂教学中对学生的关注点停留在概念的理解和知识的运用层次,没有引导学生参与到函数单元的构建中,这对学生核心素养的落实及其不利。(四)一堂精心设计的函数单元教学设计有利于中职学生对于函数章节的理解。更多还原

【Abstract】 Function is one of the main lines of the whole Secondary Vocational School.It can be regarded as the corresponding relationship between two aggregates,and it also contains the idea of Combination of Data and Shape.The concept of function is highly abstract,and the types of functions are various,and the function chapters are closely related to other chapters.Function is used to solve the everyday problems in our life and production,and it also connects t higher-level math.If the teaching design of function unit can be designed carefully,a "good class”will be produced and the students’knowledge mastery and score will be improved.It also can make students have a deeper understanding of other chapters of mathematics knowledge,production and life,and advanced mathematics.Unit Instructional Design is a kind of overall teaching concept.We can build the construction of unit knowledge system by according to the students’ basic knowledge and the students’ known experience.If we adjust and design the unit teaching content,students can be guided to think,to calculate,to create and to imagine in the mathematics classroom.So the key competencies of math can be achieved by the Unit Instructional DesignIn this paper,I analysis that the key competencies of math in primary and secondary schools by the literature method.I conduct inspections to know the students’ knowledge reserve and learning disabilities in the chapter of learning function by questionnaire survey.I analysis the high school function teaching by observation and interview.I analyze the implementation of key competencies of math,throughing the use of case study method to track a class.Finally,I give the specific function unit teaching design,and investigate the improvement of students’ literacy after learning the function chapter,and explore the positive effect of function unit teaching on mathematics core literacy.The main conclusions of the study are as follows:(1)Students show different learning characteristics in different stages about learning function units.The students of senior high school pay attention to the conceptual understanding of function and show the phenomenon of memorizing hard;the second grade students pursue the application of functional thinking method,and emphasize the application of concept;senior three students are eager to combine functions with the chapters of sequence and derivative to further the field of higher mathematics.At the same time,most students have not fully understood the nature of function.(2)In the actual teaching,we can adjust the "function" class schedule presented in the textbook.If the application of function is divided into several life examples and introduced into the new class as a situation,students’ interest in learning can be attracted.(3)Middle school teachers do not pay attention to the teaching objectives and unit framework of functional units,and their focus on students in classroom teaching stays at the level of understanding of concept and the application of knowledge,and does not guide students to participate in the construction of functional units,which is not conducive to the implementation of students’ core literacy.(4).A well-designed teaching design of function unit is helpful to students’ understanding of function chapters.更多还原