Probability by Surprise: Animations and Simulations

学生开始他们的概率和统计的研究与强大的，往往误导直观的想法。 该项目旨在直面学生的先入之见，同时将其作为动力来源。 我们的方法使用概率的反直觉的一面来“吸引学生”-捕捉他们的想象力并迫使他们思考。 我们正在开发一个网站与互动，基于Java的，材料，可用于介绍概率和统计类的专家和非专家，从AP课程到高级大学课程。 该网站将包括：仿真;动画场景;链接到数学背景材料;交互式维恩图，概率树和密度作为直方图的限制;与概率和统计有关的历史材料;和图形动画。 但该网站的核心将是一个模块的集合，惊喜和吸引学生-“Gotcha！“概率。 我们利用了拉普拉斯的观察--“心灵，就像视觉一样，也有它的幻觉;就像触摸纠正了后者的幻觉一样，思想和计算也纠正了前者。 认知心理学家最近的工作从两个方面为这个项目提供了信息。 首先，它确定学生的先入之见和他们创造的理解概率的障碍。 第二，它将指导如何有效地在教育上利用通过网络提供的丰富的多媒体和交互技术。

Students begin their study of probability and statistics with strong and often misleading intuitive ideas. This project seeks to confront students' preconceptions and at the same time use them as a source of motivation. Our approach uses the counter-intuitive side of probability to "rope students in" - to capture their imagination and force them to think. We are developing a Web site with interactive, Java-based, material that can be used in introductory probability and statistics classes for both specialists and non-specialists, from AP courses through upper level college courses. The site will include: simulations; animated scenarios; links to background material in mathematics; interactive Venn diagrams, probability trees, and densities as limits of histograms; historical material related to probability and statistics; and graphical animations. But the heart of the site will be a collection of modules that surprise and engage students - the "Gotcha!" of probability. We exploit the observation of Laplace -- "The Mind, like the sense of sight, has its illusions; and just as touch corrects those of the latter, so thought and calculations correct the former. Recent work of cognitive psychologists informs this project in two ways. First, it identifies students' preconceptions and the barriers they create for understanding probability. Second, it will guide the development of effective educational uses of the rich array of multimedia and interactive technologies available via the Web.