Case-Based Reasoning for Engineering Statistics

利用认知科学的发现，一种智能教学系统(ITS)的原型正在开发中。它利用基于案例的推理(CBR)来支撑工科本科生学习概论概率和统计学。这个脚手架过程是基于这样一个原则，即成功的问题解决者和专家通过在到达死胡同或看到新的方法来制定问题时来回移动，从而更好地掌握潜在的问题结构。具体地说，学生学习以下三个步骤：1)情境概念--用日常语言理解问题；2)数学化情境概念--创建数学表征；3)解决方法概念--执行数学程序。现有的商业软件和成熟的基于研究索引的CBR和基于规则的专家系统被用来支持研究生在课程中向本科生介绍ITS。对ITS的评估是为了检验两个假设：1)ITS是否增加了学生对关键概念的内化？2)ITS是否提高了学生表征和解决问题的自主性？此外，评估是通过比较ITS学生和非ITS学生在与假设相关的问题上的表现来进行的。从将ITS与现有的工程统计课程相结合的角度对ITS进行的初步评估，允许同样提供工程统计课程的其他大学参与一个联合的长期项目，以实现完全功能的ITS。此外，与其他大学的合作提供了一种工具，可以将智能交通系统嵌入到其他课程中，在这些课程中，同样的认知和教学原则是适用的。最终产品--一个更全面功能的智能交通系统的原型和建议--将：1.帮助学生从说明整个工程学科范围的工程统计问题中提取潜在的共同结构；2.允许学生生成、定制和更改虚拟的无限练习集合，这些练习可以在智能交通系统的帮助下解决。学生可以探索不同参数变化的效果，以及这些变化对解决方案的影响；帮助学生形成和解决实际问题和开放式问题。最终产品将保存在光盘上，并将通过工作坊进一步传播。关键词：基于案例的推理，智能辅导系统

Using findings from cognitive science, a prototype of an intelligent tutoring system (ITS) is being developed. This ITS utilizes case-based reasoning (CBR) to scaffold undergraduate engineering students in their learning of introductory probability and statistics. This scaffolding process is based on the principle that successful problem solvers and experts gain a better grasp of the underlying problem structure by moving back and forth as they reach dead-ends or see new ways to formulate the problem. Specifically, the students learn the following three steps: 1) situation conception--understand the problem in everyday language; 2) mathematized situation conception--create a mathematical representation; and 3) solution method conception--carry out the mathematical procedures. Existing commercial software and well-established research index-based CBR and rule-based expert systems are used to support the presentation of ITS by graduate students to the undergraduate students in the course. The assessment of ITS is to test two hypotheses: 1) Does the ITS increase the internalization of key concepts by the students? and, 2) Does the ITS increase the student independence in representing and solving problems? Also, assessments based on comparing the performances on questions related to the hypotheses for ITS-students and non-ITS-students. This initial evaluation of ITS from the standpoint of integrating it with an existing engineering statistics course, allows the participation of other universities who also offer the engineering statistics course to participate in a joint, longer term project to realize a fully functional ITS. Also, the partnership with other universities provides a vehicle for embedding ITS into other courses where the same cognitive and instructional principles are appilcable.The final product--a prototype and recommendations for a more fully functional ITS-- will:1. Assist students in extracting the underlying common structure from engineering statistics problems that illustrate the full range of engineering disciplines;2. Allow the student to generate, customize, and change a virtual infinite collection of exercises that can be solved with the assistance of the ITS. The students can explore the effect of changes to different parameters and how those changes influence the solution; and3. Help students formulate and solve practical and open-ended problems.The final product will be kept on CD-ROM, and further dissemination will be via workshops.Keywords: Case-based reasoning, intelligent tudoring system