Computer-Based Integral Calculus for High Schools

这个项目解决了如何在高中微积分教学中使用符号计算工具的一般问题。多年来，已经出现了一些程序，如REDUCE、MASCYMA、SCRATCHPAD和MuMATH，它们可以执行微积分练习解所需的符号计算。但是这些强大的程序主要被纯数学和应用数学的许多领域以及实际工程应用的研究人员使用。REDUCE代数系统将适应教学目的，通过建立一套以计算机为基础的积分课程样本。这些课程，结合之前关于微积分的工作，将涵盖大学理事会推荐的大学先修微积分AB课程的所有标准材料。除了使用REDUCE作为“代数引擎”之外，课程充分利用了高分辨率图形，该软件旨在通过个人工作站交付给学生。最重要的是，用于解决问题和微积分练习的软件将能够跟踪学生所做步骤的有效性，并检测并通知学生不正确的步骤。整体环境是将代数和图形工具嵌入到有效数学推理框架中的环境。此外，这个项目正在开发一个交互式定理证明系统，在这个系统中，非常有能力的学生可以证明实分析的主要定理，这些定理与一年级微积分的概念有关。在1988- 1989学年期间，这些课程将由少数高中生进行测试。这些课程将于1990年1月提供，供更广泛地使用。

This project addresses the general problem of how the tools of symbolic computation can be used in the context of calculus instruction in high schools. For many years there have been programs, such as REDUCE, MASCYMA, SCRATCHPAD, and MuMATH which can perform symbolic computations that are required for the solutions of calculus exercises. But these powerful programs have been used mainly by researchers in many areas of pure and applied mathematics and in practical engineering applications. REDUCE algebra system will be adapted for instructional purposes by building a set of sample computer-based lessons in integral calculus. These lessons, combined with earlier work on the differential calculus, will cover all the standard material of the College Board's recommended curriculum for advanced placement calculus, AB. In addition to the use of REDUCE as an "algebra engine" the lessons make full use of high- resolution graphics, and the software is intended to be delivered to students on individual workstations. Most importantly, the software for problem-solving and calculus exercises will be able to keep track of the validity of the steps the student makes and detect and inform the student about incorrect steps. The overall environment is one in which algebraic and graphics tools are embedded in a framework of valid mathematical inference. In addition, this project is developing an interactive theorem proving system in which very able students can prove the main theorems of real analysis which are relevant to concepts in first-year calculus. During the academic year 1988-89 the lessons will be tested with a small number of high school students. The lessons will be available for wider use in January 1990.