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，明确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。这将部分通过实验室演示来完成，该演示以跨越各种各样引人注目的项目的数学设计活动为中心，部分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。该序列将包括代数，初等函数分析和数学建模领域的模块。数学内容将被开发，以支持调查活动的需求和目标。将开发三大类工具，分别对应于为开放式调查活动提供智能支持的不同方式。这项工作建立在一个试点项目，导致开发这些工具的原型和他们的成功的课堂试验在介绍代数课程。本项目的目标是扩大和深化这一方法，并将其确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.