基于APOS理论对概率概念教学方式的探究

发布时间：2018-01-21 00:13

本文关键词： APOS理论概率概念建构　出处：《陕西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：美国数学教育家杜宾斯基在建构主义理论的基础上提出了APOS理论,主要针对数学概念学习的过程研究。他指出学生学习新的数学概念要经过思维的活动(Action)、过程(Process)、对象(Object)和图式(Scheme)四个阶段。该理论强调在数学概念学习中,要以社会现实为背景,根据学生的已有知识经验,让学生亲身体验老师所设计的数学活动,经过反思与归纳,逐渐建构自己内在的知识体系。本文以北师大版教材数学必修3的概率概念为切入点,主要研究下面的三个问题：(1)高中学生对概率概念重要性的认识；(2)高中学生对概率概念的认知水平和学习中所存在的困惑；(3)讨论基于APOS理论指导下的概率概念教学设计。为了解高中学生的概率概念学习的现状和存在的问题,我们对安康市某高级中学的高二13班与14班学生进行了调查,并对他们和该校的高中数学老师进行了访谈。结合教育实践积累的教学经验和教学案例,我们还了解到,目前的数学课堂针对高中概率概念所使用的基本教学方法。据此,我们从学生认知过程出发,在APOS理论指导下分别对“频率和概率”、“古典概型的特征和概率计算公式”以及“模拟方法——概率的应用”三节内容进行了课堂教学设计。我们的实践表明,APOS理论对概率概念教学具有重要的指导意义。运用APOS理论有助于改进教学方法,提高课堂的教学效果。能够更好地帮助学生建构概率概念的知识体系,让学生更深入的理解概率概念,并把概率概念以一种综合的心理图式储存于认知结构中。APOS理论指导下的教学设计与传统教学设计的区别主要在于：APOS理论指导下的数学概念教学设计突出了学生的主体地位,重视学生对课堂活动的参与。设计过程分为四个阶段,每个阶段都有学生的活动,学生通过亲身体验,在教师的引导下,对问题进行反思与归纳,主动探究概念的形成过程。传统教学设计突出的是教师的讲,学生完全处于一种被动接受知识的状态,参与课堂活动和自主思考的时间较少。为了在教育实践中更好的应用APOS理论,建议：(1)教学中多增加生活实例,让学生感知数学的实际价值；(2)创造性地使用教材,精心设计教学内容；(3)适当运用多媒体技术；(4)概念教学要注重探究过程；(5)注重数学思想方法的渗透。
[Abstract]:On the basis of constructivist theory, American mathematics educator Dobinsky put forward APOS theory. He points out that students learn new mathematical concepts through the activities of thinking, action, process). The theory emphasizes that in the study of mathematical concepts, the social reality should be the background, according to the students' existing knowledge and experience. Let students experience the mathematics activities designed by the teacher, through reflection and induction, gradually build their own internal knowledge system. This paper mainly studies the following three questions: 1) the understanding of the importance of the concept of probability among senior high school students; (2) the cognitive level of high school students on the concept of probability and the confusion existing in their study; 3) discuss the teaching design of probabilistic concept based on APOS theory. In order to understand the present situation and existing problems of probabilistic concept learning for senior high school students. We investigated the students of Class 13 and Class 14 in a senior middle school in Ankang City, and interviewed them and the high school math teachers, combined with the teaching experience and teaching cases accumulated in educational practice. We also understand the basic teaching methods used in the current mathematics classroom for the concept of high school probability. According to this, we set out from the cognitive process of students, under the guidance of APOS theory, respectively "frequency and probability". "the characteristics of classical probability type and the formula of probability calculation" and "the application of simulation method-probability" are designed for classroom teaching. Our practice shows that. APOS theory is of great significance to the teaching of probabilistic concepts, and the application of APOS theory is helpful to improve the teaching methods. Improve the teaching effect of classroom. It can help students to construct the knowledge system of probability concept, and let students understand the concept of probability more deeply. The difference between the teaching design guided by the theory of .APOS and the traditional teaching design is that the concept of probability is stored in a comprehensive psychological schema in the cognitive structure. Under the guidance of APOS theory, the teaching design of mathematics concept highlights the main position of students. Emphasis on the participation of students in classroom activities. The design process is divided into four stages, each stage has students' activities, students through personal experience, under the guidance of teachers, to reflect on the problems and induction. The forming process of active inquiry concept. The traditional teaching design is the teacher's speaking, students are in a state of passive acceptance of knowledge. In order to better apply APOS theory in educational practice, it is suggested that more living examples be added in teaching, so that students can perceive the practical value of mathematics. 2) creative use of teaching materials and careful design of teaching contents; 3) proper use of multimedia technology; (4) Conceptual teaching should pay attention to the process of inquiry; Pay attention to the infiltration of mathematical thought and method.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【相似文献】