Probability by Surprise: Animations and Simulations

惊喜概率：动画和模拟

• 批准号: 9752559
• 负责人: Susan Holmes
• 金额: $ 10万
• 依托单位: Cornell Univ - State: AWDS MADE PRIOR MAY 2010
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-01-01 至 1999-04-12
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9752559&HistoricalAwards=false
• 关键词: Probability; Surprise; Animations; Simulations

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.

学生以强烈且常常误导性的直觉想法开始概率和统计的学习。 该项目旨在面对学生的先入之见，同时将其作为动力的来源。 我们的方法利用概率反直觉的一面来“吸引学生”——捕捉他们的想象力并迫使他们思考。 我们正在开发一个基于 Java 的交互式材料的网站，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、概率树和密度作为直方图的限制；与概率和统计相关的历史材料；和图形动画。 但该网站的核心将是一系列让学生感到惊讶和吸引的模块——“陷阱！”的概率。 我们利用拉普拉斯的观察——“心灵，就像视觉一样，有它的幻觉；正如触觉纠正后者的幻觉一样，思想和计算纠正前者。认知心理学家最近的工作以两种方式为这个项目提供信息。首先，它确定了学生的先入为主的观念以及他们为理解概率而设置的障碍。其次，它将指导丰富的多媒体和交互技术的有效教育用途的发展 可通过网络获取。