Computer-Based Integral Calculus for High Schools

这个项目解决了如何符号化工具的一般问题 计算可以用在高微积分教学的背景下， 学校 多年来，一直有一些方案，如减少， MASCYMA、SCRATCHPAD和MuMATH可执行符号计算 微积分练习题的答案。 但这些 强大的程序主要被研究人员用于许多领域， 纯数学和应用数学以及实际工程应用。 REDUCE代数系统将通过以下方式适应教学目的： 建立一套基于计算机的积分学课程样本。 这些教训，结合早期的工作微分， 将涵盖大学理事会推荐的所有标准材料 高级微积分课程，AB。 除了使用 REDUCE作为“代数引擎”的经验教训充分利用高- 分辨率的图形，并且该软件旨在交付给 学生个人工作站 最重要的是，解决问题和微积分的软件 练习将能够跟踪步骤的有效性， 学生制作并检测并告知学生错误的步骤。 整个环境是一个代数和图形工具， 嵌入在有效的数学推理框架中。 此外，本发明还提供了一种方法， 这个项目正在开发一个交互式定理证明系统， 非常有能力的学生可以证明真实的分析的主要定理 这与一年级微积分的概念有关。 在一九八八至八九学年，我们会以一个小型的 高中生人数。 这些课程将提供给更广泛的 1990年1月使用。

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.