Probability by Surprise: Animations and Simulations

学生们在开始学习概率和统计时，往往带有强烈的、容易误导的直觉观念。这个项目试图面对学生的先入之见，同时把它们作为动力的来源。我们的方法是利用概率反直觉的一面来“拴住学生”——抓住他们的想象力，迫使他们思考。我们正在开发一个网站，其中包含基于java的交互式材料，可用于专家和非专业人士的概率和统计入门课程，从AP课程到高等大学课程。该网站将包括：模拟；动画场景;链接到数学背景材料；交互维恩图、概率树和密度作为直方图的极限；与概率和统计有关的历史资料；还有图形动画。但该网站的核心将是一系列让学生感到惊喜并吸引他们的模块——概率的“抓到你了”。我们利用拉普拉斯的观察——“心灵，像视觉一样，有它的幻觉；就像触摸能纠正后者一样，思考和计算也能纠正前者。认知心理学家最近的工作从两个方面说明了这个项目。首先，它确定了学生的先入之见以及他们为理解概率所造成的障碍。第二，它将指导通过网络提供的丰富的多媒体和交互技术的有效教育用途的发展。

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.