Proof-of-Concept of Computer-based Calculus Course

一门涵盖AB高等学分教学大纲中标准材料的完整电脑课程的概念验证测试，将在两种情况下进行，在这两种情况下，相同的电脑技术可以作为不同问题的解决方案。(1)有数学早熟学生的中学。(2)学生使用计算机程序解决问题和辅导帮助的学院或大学。这门以计算机为基础的课程广泛使用图形、交互式在线问题解决以及与微积分的水平和复杂程度相适应的交互式解释技术。在线问题解决和练习由称为方程推导系统的符号计算环境支持，在该环境中，学生使用自然的数学运算一步一步地构建问题的解决方案。本程序使用Reduce型计算机代数系统作为内部代数引擎。将对课程的这些主要组成部分的有效性进行评估。该程序在基于Unix的彩色图形工作站上运行。

Proof-of-concept tests of a complete computer-based course covering the standard material in the AB Advanced Placement Calculus Syllabus will be undertaken in two settings where the same computer-based technology can be used as solutions to different problems. (1) Middle schools with mathematically precocious students. (2) Colleges or Universities where students use the computer program for problem solving and tutorial help. The computer-based course makes extensive use of graphics, interactive on-line problem solving, and interactive expository techniques appropriate to the level and complexity of the calculus. On-line problem solving and exercises are supported by a symbolic computation environment called the Equational Derivation System in which students construct solutions to problems step by step using natural mathematical operations. The REDUCE computer algebra system is used as an internal algebra engine by this program. The effectiveness of these main components of the course will be evaluated. The program runs on UNIX-based color graphics workstations.