中学“统计与概率综合内容”的设计与思考

概率是研究随机现象及其规律的科学,统计则研究如何合理收集、整理、分析数据,并从数据中获取信息,它们都可以为人们制定决策提供依据和建议.概率和统计来源于现实生活,许多实际问题都可以用概率和统计的相关知识加以解决.在中学阶段,由于受学生所学知识所限,综合应用统计概率解决实际问题的内容并不多见,出现的应用问题大都比较简单和直接,对学生几乎没有挑战性,也难以让学生对其产生兴趣.在教材实验过程中,我们尝试借助"数学期望"的相关思想和素材,在中学阶段设计统计与概率的综合内容,以帮助学生更好地理解统计与概率的思想,并切实感受它们在生活中的广泛应用.下面谈谈这方面的一些探索和思考.     

利用人工智能案例推动概率统计课程教学

人工智能的迅猛发展离不开概率统计的支持,在概率统计的日常教学中,融入人工智能案例的介绍,能够促进学生的学习兴趣,提高教学质量.以举例的方式说明了概率统计的理论知识和人工智能技术的结合,为利用人工智能案例推动概率统计的课程教学提供了示例.     

改进教学方法培养学生良好的学习习惯和创新能力

结合自己的教学实践对概率统计的教学方法进行了探讨,通过实例说明了在概率统计的教学中如何激发学生的学习兴趣,如何培养学生的良好学习习惯和创新能力.     

课改后统计与概率内容考查研究

1 引言 统计与概率在工农业生产和社会生活中有着广泛的应用.在生产、生活和科学技术飞速发展的当今社会,它的应用已渗透到整个社会的方方面面,从而使统计与概率的基础知识成为一个普通公民的必备常识.由于统计与概率的学习对于培养和提高学生的数学思维能力方面发挥着特有的作用,因此国外许多国家很早就将其列为中、小学数学教学的内容和目标的一部分.如美国在1989年出版《中小学数学课程与评估标准》中规定了统计与概率,并且强调统计和概率的思想方法[1];前苏联在1990年颁布的教学大纲中就包涵概率与统计理论的教学内容,包括概率的加法与乘法,条件概率,独立事件,伯努利公式,随机变量,数学期望等内容知识.     

略谈概率统计课的育人价值

基础教育新课程中,从小学阶段就引入了对随机事件的认识,初中、高中阶段也将概率统计的初步知识作为必学内容.然而由于传统教学中只重视概率论与数理统计的科学工具性价值,看到的只是它在技术层面的功能,不注重挖掘概率统计的其它育人功能,没能使学生很好地掌握概率统计的思想和方法.本文试从概率统计科学工具性价值之外的角度,探讨概率统计的育人价值,以推动这门课的教学改革,充分发挥它的育人功能.……     

用数形结合法求解连续型随机变量的函数分布问题

针对概率统计课程教学中的关于"连续型随机变量函数的分布"这类难点,利用数形结合的思想,巧妙的通过一副图形完全涵盖了这一类问题所需的概率知识点,且帮助了学生后续积分的计算.表明数形结合法是一个值得在概率统计教学中推广的好方法.     

面向能力培养的教学模式探讨——以工科概率统计课程为例

以工科概率统计课程为例探讨面向能力培养的教学模式.概率统计是高等院校工科专业一门重要的公共基础课程.文章分析了概率统计课程的教学现状,指出其在教学理念、教学方法上必须进行适度改革,以深化其教育功能;分析了概率统计教学平台在培养学生能力上的不可替代的重要作用;探讨了落实概率统计课程教育功能可以采取的教学方法.     

高三数学新教材"概率与统计"简介

《全日制普通高级中学教科书(试验修订本)数学》第三册(选修Ⅱ)第一章是“概率与统计”。教科书是根据《全日制普通高级中学数学教学大纲》选修Ⅱ的第1部分“概率与统计”编写的。 在教学内容中增加概率与统计的初步知识,是《大纲》教学内容改革的重要组成部分。本章的教学内容是学生在初中学习“统计初步”和高中必修课的“概率”基础上学习的,内容分为“随机变量”和“统计”两部分。主要内容如下:     

概念图——概率统计教学的新途径

简述了概念图的起源、国内外发展现状,介绍了概念图的三个组成部分:结点、连线和连接语词,指出了相对于传统教学的概念图教学,在概率统计教学中的突出之处:概念图可作为教师教学的先行组织者;可作为学生复习时整理知识的工具;可作为教师检测学生学习的工具,提出了概率统计知识概念图制作的策略,并用实例说明了概念图应用于概率统计教学中的良好效果.     

中美高中阶段数学课程标准对统计与概率要求的比较研究

《高中数学课程标准》对统计与概率的重视程度是空前的,统计与概率作为必修模块中的内容,在《高中数学课程标准》中被强调为“一个未来公民的必备常识”,而整个数学课程改革的基调之一就是“培养未来公民的数学素养”,其对统计与概率之重要性的彰显可见一斑.事实上,在经济发达国家,对统计与概率也是比较重视的.各国都意识到,统计和概率知识在信息社会里显得越来越重要,工作、生活在2 1世纪里的现代学生必须很好的加以掌握.本文就《高中数学课程标准》(下称《标准》)和NCTM(美国数学教师协会)发表的《国家数学课程标准》(下称《标准》)中对…     

高级统计学的教学实践与思考

基于教学实践和调查问卷对研究生高级统计学的各个教学环节进行了探讨和分析.区别于本科生的统计学教育,在研究生的统计教学中,不仅要介绍统计方法,而且还要通过更加有效的手段加强研究生对统计分析方法的整体认识和应用能力.教学实践和对调查问卷的统计分析结果表明:将传统的解释性教学和演示性教学与现代的具有建构主义特征的发现学习相结合将有助于培养研究生的学习能力和科研能力.     

Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.     

概率统计类课程多维立体教学的实践与认识

针对概率统计类课程不同于其它确定性数学的特点,作者从教学内容及教学方法两个方面进行了探索与实践.在教学内容上,强调点面结合,拓展一些现代的与本学科密切有关的面上知识.在教学方法上,强调多维立体教学方式,即结合多媒体课件,案例教学,软件演示,实验教学,实现以教师为主导,学生为主体的主客体相结合的教学思想,以期达到使学生受益最大化的目标.     

概率论与数理统计课程改革的创新机制

针对课程改革的目的,结合教学实践,就概率统计课程建设和教学改革的必要性进行综合分析并主张：通过讲述概率统计理论发展史,引导学生明确学习重点;借助多媒体教学,整合教学大纲内容,系统教学;将理论与实际相联系,激发学生学习兴趣;立足基本理论,开设统计学软件实验课程．     

Kaizen teaching and the learning habits of engineering students in a freshman mathematics course

Which are the teaching methods that actually contribute to the learning of mathematics? The answer to this certainly is the holy grail of didactic and pedagogy, and should be supported by large scale statistical evidence. Our article aims at providing an initial step into this direction by first illustrating a teaching paradigm that is suited for the generation of large scale data sets: based on industry best practice quality assurance standards we introduce the Kaizen teaching paradigm which enforces Kolb’s reflective learning cycle on the students’ side. Second, we present and analyze the data we obtained through our pilot implementation at a engineering freshman mathematics course in the Sultanate of Oman. These emphasize the effectiveness of Kaizen teaching and once again show the necessity of continuous learning. A practice that seems to be forgotten in traditional university engineering courses due to the mere size of the audience. In particular it seems that a Markovian estimator for students’ performance may have to be considered.     

Electronic Resources: The Ohio State University EESEE Project

Electronic resources aid in the teaching and learning of statistics by providing data that may be used interactively by teachers and students. By interacting with the data students are encouraged to discover knowledge and thereby gain a deeper understanding of statistical concepts. The Electronic Encyclopedia of Statistical Examples and Exercises (EESEE) is an electronic resource that includes over 80 'real-world' examples about the uses and abuses of statistics. These examples are drawn from published and printed media and the diverse range of subject-matter areas make it suitable for use in any statistics course.     

An applied statistics course for systematics and ecology PhD students

Statistics education is under review at all educational levels. Statistical concepts, as well as the use of statistical methods and techniques, can be taught in at least two contrasting ways. Specifically, (1) teaching can be theoretically and mathematically oriented, or (2) it can be less mathematically oriented being focused, instead, on application and the use of data to solve real-world problems. The second approach is growing in practice and new goals have recently emerged. At present, statistics courses stress probability concepts, data analysis, and the interpretation and communication of results. Understanding the process of statistical investigation is established as a way of improving mastery of statistical reasoning. In this context, a project-based approach allows the design and implementation of participating learning scenarios in order to understand the statistical methodology and, as a consequence, improve research. This approach points out that statistics is a rational methodology used to solve practical problems. The purpose of this paper is to present the design and results of an applied statistics course for PhD students in ecology and systematics using a project-based approach. Examples involving character coding, species classification, and the interpretation of geographical variation, which are the principal systematic analyses requiring statistical techniques, are presented using the results from student projects. In addition, an example from conservation ecology is presented. Results indicate that the students understood the concepts and applied the systematic and statistical techniques accurately using a data oriented approach.     

Exploring Students' Conceptual Understanding of the Averaging Algorithm

Conceptual understanding of arithmetic average includes both an understanding of the computational algorithm and the statistical aspects of the concept. This study focused on the examination of 250 sixth-grade students' understanding of the arithmetic average by assessing their understanding of the computational algorithm. The results of the study showed that the majority of the students knew the “add-them-all-up-and-divide” averaging algorithm, but only about half of the students were able to correctly apply the algorithm to solve a contextualized average problem. Students were able to use various solution strategies and representations to solve the average problem. Those who used algebraic and arithmetic representations were better problem solvers than those who used pictorial and verbal representations. This study not only suggests that the average concept is more complex than the simplicity suggested by the computational algorithm, but also indicates the need for teaching the concept of average, both as a statistical idea for describing and making sense of data sets and as a computational algorithm for solving problems.     

Characterizing Key Developmental Understandings and Pedagogically Powerful Ideas Within a Statistical Knowledge for Teaching Framework

A hypothetical framework to characterize statistical knowledge for teaching (SKT) is described. Empirical grounding for the framework is provided by artifacts from an undergraduate course for prospective teachers that concentrated on the development of SKT. The theoretical notion of “key developmental understanding” (KDU) is used to identify landmarks in the development of SKT subject matter knowledge. Sample KDUs are given for the subject matter knowledge categories of common content knowledge, specialized content knowledge, and horizon knowledge. The theoretical notion of “pedagogically powerful idea” is used to describe how KDUs must be transformed to become useful in teaching. Examples of pedagogically powerful ideas for the pedagogical content knowledge categories of knowledge of content and teaching and curriculum knowledge are provided. Knowledge of content and students is hypothesized as a basis for the development of pedagogically powerful ideas.