Intelligent Tools for Mathematical Inquiry

该项目的目的是设计、实施、评估和传播一个专为中学生设计的数学课程序列，旨在向他们介绍数学思维的概念和艺术，并发展数学探究的基本技能。这部分将通过以跨越各种引人注目的项目的数学设计活动为中心的实验室演示来实现，部分将通过使用旨在支持和指导建设性探索和设计任务的智能工具来实现。这一系列课程将包括代数、初等泛函分析和数学建模领域的模块。将开发数学内容，以支持探究活动的需要和目标。将开发三种主要类型的工具，与嵌入对不限成员名额查询活动的智能支持的不同方式相对应。这项工作建立在一个试点项目的基础上，该项目导致了这些工具的原型的开发，并在一门代数入门课程中成功地进行了课堂试验。本项目的目标是扩展和深化这一方法，并将其确立为未来数学课程的全国范本。

The purpose of the project is to design, implement, evaluate, and disseminate a mathematics curriculum sequence for middle school students expressly designed to introduce them to the notions and arts of mathematical thinking and to develop foundational skills of mathematical inquiry. This will be accomplished partly through a laboratory presentation centered on mathematical design activities that span a rich variety of compelling projects, and partly through the use of intelligent tools designed to support and guide constructive exploration and design tasks. The sequence will comprise modules in the areas of algebra, elementary functional analysis, and mathematical modeling. The mathematical content will be developed to support the needs and goals of the inquiry activities. Three major types of tools will be developed, corresponding to qualitatively different ways of embedding intelligent support for open-ended inquiry activities. This work builds on a pilot project which led to the development of prototypes of these tools and their successful classroom trial in an introductory algebra course. The goal of the present project is to extend and deepen the approach and to establish it as a national model for future mathematical curricula.