Intelligent Tools for Mathematical Inquiry

该项目的目的是为中学生设计，实施，评估和传播数学课程序列，旨在向他们介绍数学思维的概念和艺术，并培养数学探究的基本技能。这部分将通过以数学设计活动为中心的实验室演示来完成，这些活动跨越了丰富多样的引人注目的项目，部分通过使用智能工具来支持和指导建设性的探索和设计任务。该序列将包括代数，初级功能分析和数学建模领域的模块。数学内容的发展将支持探究活动的需要和目标。将开发三种主要类型的工具，对应于为开放式探究活动嵌入智能支持的质量不同的方式。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原型的开发，并在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该方法，并将其建立为未来数学课程的国家模式。

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.