利用概念图促进概率统计知识建构的探索

概率统计区别于学生先前所学的确定性数学,它属于不确定性数学,该课程中的结论形式往往会以"一定的概率成立"出现,如:参数θ的置信区间(θ,θ),它是指以一定的概率包含参数θ真值的随机区间,而不是一定包含参数θ真值的确定性区间.这与确定性数学有非常大的区别.学生学习概率统计,属于第一次接触不确定性数学,一时难以适从.学生不能很好地将所学的概念穿成串、结成网、变成结构化的知识铭记在脑海中,也不能很好地理解概念及概念间的关系,也就难于领会其中蕴含的概率统计思想,不能主动地形成概率思维和统计观念.一种认知工具--概念图恰好可以用来改善这一情状,促进学生的知识建构.     

概念图指向单元整体建构课的教学策略--“二次函数图象与性质”赛课观摩有感

概念图是课堂教学设计的有效工具.为了让学生对一个单元所学知识网络化,建构对单元知识和方法的整体理解,引导学生深度学习,研究者以观摩省赛课“二次函数图象与性质”为例,探究基于概念图的单元整体建构课的教学策略:知识建构,让思维痕迹可视化;方法统领,让思维品质高阶化;深度探究,让思维体验个性化.     

基于概念图的概率统计课程评价的实证研究

概念图评价的发端可以追溯到奥苏贝尔(Ausubel),特别是诺瓦克(Novak)及其同事在20世纪六、七十年代早期的工作,他们经过12年的研究得出概念图是有效的评估工具,2004年在西班牙召开的第一届概念图国际会议上探讨的第一个主题便是:概念图在教学中的评价.     

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.……     

概率统计与函数的交汇

概率统计与其他相关知识,特别是与函数的交汇应用问题是新课标高考数学的一大创新热点,借助一些特殊函数的基本性质、函数的思想方法等来解决概率统计中的一些应用问题,合理培养学生创新应用与创新意识等,引领并指导数学教学与复习备考.     

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.     

基于SPOC的概率统计课程建设研究

基于SPOC的教学模式结合了MOOC教学与传统教学,为当代教学改革提供了新思路.本文以概率统计课程为例,分析概率统计课程教学的现状,探讨SPOC教学模式的设计流程,提出概率统计课程改革的新思路和遇到的困难,分析该教学模式在提高教学质量的同时,对教师和学生提出更高的要求.     

关于高中教材中独立性检验知识呈现方式的思考

由于随机现象在现实生活中随处可见,因而描述其变化规律的统计概率知识在公民的知识构成中占有重要的地位,成为一个未来公民必备知识.为适应这种知识需求,普通高中<数学课程标准>(下简称为<课标>)增加了很多统计概率的知识内容,其中统计案例中的独立性检验内容对于教材编写者和教材使用者(教师)都是一个挑战.对于教材编写者的困难是如何能够在高中的知识背景之下,能够将独立性检验的思想完美地在教材中呈现;对于一线教师的困难是如何正确理解独立性检验思想,并将这种思想正确地传递给学生.笔者有幸参与人民教育出版社出版的普通高中课程标准实验教科书<数学选修1-2>(A版)和<数学选修2-3>(A版)(下分别简称为<选修1-2>和<选修2-3>)的编写,在这里谈谈独立性检验的编写与修订意图,供一线教师在组织教学中参考.     

数珠联袂 启智增慧——一年级数学教学中融合珠心算的实践探索

正数学的抽象特点使学生的学习有一定难度。算盘档位分明,示数直观,是最好的认数工具。具体与抽象相结合是《数学课程标准》规定的小学数学教学的重要原则。珠心算融入数学教学,可以把抽象的数学具体化,促进数形结合,全面提高学生数学能力。《数学课程标准》安排了四个部分课程内容:数与代数、图形与几何、统计与概率、综合与实践。珠算与这四个部分知识均有联系。现从这四个方面分析如下:一、数与代数     

数学知识的智力价值及其在教学中的体现

在数学教学中,同是一项数学知识,有的教师单纯地把它作为工具传递(奉送)给学生,而有的教师则把它作为磨炼学生智力的材料,使学生在逐步掌握知识工具的过程中,培养了能力,发展了智力。例如,同是一元二次方程的求根公式,有的教师把推导过程作为敷衍公事,急于让结论与学生见面,使学生毫不费力地得到它。而有的教师则把它作为培养学生“化新为旧”的数学基本功(例如把ax~2+bx+c=0转化     

基于概念图的大数定律教学

介绍概念图的内涵及其基本理论,并将其应用于概率论中关于＂大数定律＂的教学过程,通过学生小组合作制作概念图,以及师生合作完善概念图,来帮助学生理清脉络、加深理解,教学实践效果良好.     

Effect of self-constructed concept map with peer feedback on chemistry learning outcome

Concept mapping remains widely used in education. However, little is known about how self-constructed concept maps and peer feedback can improve student learning outcomes in chemistry. We investigated the effects of peer feedback on concept mapping and how it improves students' learning performance in a large second-semester, introductory chemistry course. Three hundred and twenty students were randomly assigned to one of two concept mapping conditions: self-constructed concept map with peer feedback and self-constructed concept map without peer feedback. Each group constructed concept maps that depicted the relationship between concepts on the topic of intermolecular force. The results showed that students in the self-constructed concept map with peer feedback condition outperformed students in the no peer feedback condition in chemistry learning outcome. Overall, this study demonstrates that peer feedback enhances the effectiveness of learning with generative concept maps. The implications and future directions are discussed.     

Using Concept Maps and Interpretive Essays for Assessment in Mathematics

This study explored the use of student-constructed concept maps in conjunction with written interpretive essays as an additional method of assessment in three undergraduate mathematics courses. The primary objectives of this study were to evaluate the benefits of using concept maps and written essays to assess the “connectedness” of students' knowledge; to measure the correlation between students' scores on the concept maps and written essays, course exams, and final grade; and to document students' perception of the effect of this approach on their mathematical knowledge. Results indicated that concept maps, when combined with written essays, are viable tools for assessing students' organization of mathematical knowledge. In addition, students perceive this approach as enhancing their mathematical knowledge.     

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.     

Exploring college students’ mental representations of inferential statistics

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students’ representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students’ partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.     

A Bayesian network approach to making inferences in causal maps

The main goal of this paper is to describe a new graphical structure called ‘Bayesian causal maps’ to represent and analyze domain knowledge of experts. A Bayesian causal map is a causal map, i.e., a network-based representation of an expert’s cognition. It is also a Bayesian network, i.e., a graphical representation of an expert’s knowledge based on probability theory. Bayesian causal maps enhance the capabilities of causal maps in many ways. We describe how the textual analysis procedure for constructing causal maps can be modified to construct Bayesian causal maps, and we illustrate it using a causal map of a marketing expert in the context of a product development decision.     

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.     

Examining the Conceptual Organization of Students in an Integrated Algebra and Physical Science Class

The cross-disciplinary context of density and slope was used to compare the conceptual organization of students in an integrated algebra and physical science class (SAM9) with that of students in a discipline-specific physical science class (PSO). Analyses of students' concept maps indicated that the SAM9 students used a greater number of procedural linkages to connect mathematics and science concepts on the SAM9 students' maps than did the PSO students. The maps produced by SAM9 students also tended to show a more compartmentalized approach to thinking about the content of the two disciplines, a finding contrary to the researcher's original assertion. Traditional teaching territories and conceptual complexity were examined as possible explanations for the discrepancy between the predicted and actual outcomes.     

Scoring Concept Maps: An Expert Map‐Based Scheme Weighted for Relationships

The use of student‐constructed concept maps in assessment is congruent with the changing emphases set forth by the National Science Education Standards. Authorities have expressed concern about concept map scoring systems and their associated validity and reliability. They favor methods that employ expert/criterion maps as referents and emphasize the use of accurate concept relationships in deriving scores, which have been found to correlate with performance on standardized tests. In this study, student constructed concept maps (n= 17) that emerged from post‐instructional interviews about chlorofluorocarbons were scored against a teacher‐expert map using a scheme weighted for relationships. Interrater reliability for the scoring scheme was high (r= .959). Students' map scores correlated highly with their scores on the California Achievement Test component total (r= .729) and moderately with their Pathfinder index (r= .474), the latter believed to be an excellent measure of structural knowledge. A revised map score, derived only from relationships containing one or more of the concepts employed in Pathfinder analysis, was a statistically significant (p= .031) predictor of the Pathfinder index. The findings of this study support the recommendations of others to use expert referents and emphasize concept relationships in assessing concept maps.     

浅谈蒙特卡罗法在概率统计教学中的应用

在概率统计教学中利用蒙特卡罗法设计适当的模拟实验,结合多媒体在课堂教学中实时演示,能很好地加深学生对概率统计概念、思想的理解,进而培养学生的统计思维能力.