Teaching Mathematical Thinking through Space Exploration

* 9550493 Feurzeig这个为期三年的项目的目标是开发四个课程单元，以取代或补充当前的课堂材料在代数，几何，微积分和拓扑学的关键主题。这些单元将通过一系列高度图形化和交互式的计算机辅助探索，实验和游戏，向广大高中学生和教师介绍现代数学思想的一些最基本和最核心的理想。前三个单元可以在标准代数，几何或微积分课程中单独使用。作为一个整体，他们准备了一系列的探索之旅在世界上的一维，二维和三维空间形式，其中包括最后一个单元的具体主题。作为另一种选择，单位可以加入提供一个学期的课程，无论是在微积分预科或作为一个可选的第四年大学预科课程。这四个单元将支持10至18周的教学。该项目第一年的重点是活动和支持软件的开发和非正式试验;第二年继续编写材料、培养工作人员、课堂实施、试点试验和形成性评价;第三年是教师发展、实地测试、评价和传播。当地高中将参加试点试验和实地测试。研究，开发和教学将由数学家和数学教育顾问组成的跨学科团队进行，他们在课程开发和评估方面具有专业知识。项目团队将与ARISE的开发人员密切合作，ARISE是由数学及其应用联盟（COMAP）进行的NSF综合高中课程项目，在广泛分发的系列中发布项目材料，高中数学及其应用（HiMAP）。***

* 9550493 Feurzeig The goal of this three-year project is to develop four curriculum units to replace or supplement current classroom materials on key topics in algebra, geometry, calculus, and topology. These units will introduce some of the most fundamental and central ideals of modern mathematical thinking to a broad population of high-school students and teachers through a series of highly graphic and interactive computer-assisted explorations, experiments and games. The first three units can be used separately within the standard algebra, geometry or calculus courses. Taken as a whole, they prepare the way for a series of exploratory journeys in the world of one-, two-, and three-dimensional space forms, which comprise the specific subject matter of the last unit. As another alternative, units can be joined to provide a one-semester course, either in place of pre-calculus or as an optional fourth-year college preparatory course. The four units will support from 10 to 18 weeks of instruction. The first year of the project will focus on development and informal trials of the activities and supporting software; the second year on continued materials development, staff development, classroom implementation, pilot trials, and formative evaluation; the third year on teacher development, field testing, evaluation, and dissemination. Local high schools will participate in the pilot trials and field tests. The research, development, and teaching will be carried out by an interdisciplinary team of mathematicians and mathematics education consultants with expertise in curriculum development and evaluation. The project team will work closely with the developers of ARISE, the NSF Comprehensive high-school curriculum project underway by the Consortium for Mathematics and its Applications (COMAP), to publish project materials in the widely distributed series, High-school Mathematics and its Applications (HiMAP.) ***