Probability by Surprise: Animations and Simulations

学生开始学习概率和统计时，有强烈的、经常误导人的直觉想法。这个项目旨在直面学生的先入为主的观念，同时将其作为动力的来源。我们的方法使用概率中与直觉相反的一面来“吸引学生”--捕捉他们的想象力，迫使他们思考。我们正在开发一个网站，提供交互式的、基于Java的材料，可用于专家和非专家的概率和统计入门课程，从AP课程到高级大学课程。该网站将包括：模拟；动画场景；数学背景材料的链接；交互式维恩图、概率树和直方图限制的密度；与概率和统计有关的历史材料；以及图形动画。但该网站的核心将是一系列让学生感到惊讶和吸引他们的模块--“Gotcha！”概率论。我们利用了拉普拉斯的观察--“大脑就像视觉一样有幻觉；就像触觉纠正后者的幻觉一样，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，它识别了学生的先入为主的概念，以及他们为理解概率而制造的障碍。第二，它将指导开发通过网络可用的丰富的多媒体和交互技术的有效教育应用。

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.