SBIR Phase II: Sketchpad for Young Learners of Mathematics - Dynamic Visualization Software in Grades 3-8

这个小企业创新研究（SBIR）第二阶段项目旨在克服在小学和中学数学课上有效使用the Geometer’s Sketchpad软件的障碍，并发挥该软件在这些层面上改变教育的潜力。这种基于研究的教育技术工具及其“动态几何”交互范例在中学和高等教育中因其培养数学可视化和探索能力以及增强学生学习能力而闻名。该项目响应了教师、课程开发和研究团体以及国家数学教师委员会（NCTM）等标准机构对软件应用和适应低年级的明确呼吁。由创建和维护Sketchpad的团队领导的拟议研究，首先确定并原型修改软件，以增加范围和年龄相关的功能，并为年轻学习者消除访问障碍；第二，通过动态几何技术，开创了新的课堂活动——结构、材料和工具——以支持和扩展3-8年级的基于标准的课程。所提议的活动的智力价值反映了(a)该活动对小学和中学水平动态几何技术的感知教学需求（如引用的NCTM原则和标准2000）的响应程度；(b)有机会将中学阶段关于动态几何的广泛研究基础和文献扩展到更早的年级水平（特别是关于有效的动态几何活动设计和动态几何对早期学生情感和认知的影响）；(c)该提案为如何最好地将有效的、基于标准的课程（在本例中是互联数学项目、日常数学和数学研讨会课程项目）与有效的、基于标准的技术相结合这一问题提供的资源。该项目汇集了课程和软件设计方面的研究经验；项目人员包括Sketchpad的作者，项目顾问包括每个指定课程的作者团队。该项目达到其目标的更广泛的影响将是在小学和初中创造和提供适合年龄的动态几何数学教育技术和支持课程，类似于在中学阶段定义Sketchpad的课程，该软件被全国数学教师认为是“对学生最有价值的软件”（Becker, 1999）；以及研究驱动的解决方案，以应对用教育技术有效地支持基于标准的课程的挑战。

This Small Business Innovation Research (SBIR) Phase II project aims to overcome barriers to the effective use of The Geometer's Sketchpad software in elementary and middle school math classes, and to deliver on the software's potential for transforming education at these levels. This research-based educational technology tool and its "Dynamic Geometry" interaction paradigm are well known at the secondary and higher level for their ability to foster visualization and exploration in mathematics and to enhance student learning. This project responds to clear calls for the software's application and adaptation to younger grades coming from teachers, from curriculum development and research communities, and from standards bodies such as the National Council of Teachers of Mathematics (NCTM). The proposed research, led by the team that created and maintains Sketchpad, first identifies and prototypes modifications to the software to add scope and age-relevant functionality and to remove barriers to access for young learners; and second pioneers new classroom activities-structures, materials, and vehicles-for supporting and extending standards-based curricula in grades 3-8 through the agency of Dynamic Geometry technology. The intellectual merit of the proposed activity reflects (a) the degree to which the activity responds to perceived pedagogic need (as cited, e. g., in the NCTM Principles and Standards 2000) for Dynamic Geometry technology at the elementary and middle school level; (b) the opportunity to extend the broad base and literature of research that exists on Dynamic Geometry at the secondary level to significantly earlier grade levels (particularly with respect to effective Dynamic Geometry activity design and Dynamic Geometry impact on student affect and cognition in the early grades); and (c) the resources this proposal brings to the question of how best to integrate effective, standards-based curriculum (in this case, the Connected Mathematics Project, Everyday Mathematics, and Math Workshop curricular programs) with effective, standards-based technology. The project brings together research experience in both curricular and software design; project staff includes Sketchpad's authors and project consultants include the author teams of each of the named curricula.The broader impact of this project reaching its objectives will be the creation and availability, in primary and middle grades, of age-appropriate Dynamic Geometry mathematics education technologies and supporting curriculum similar to those which define Sketchpad at the secondary level, where the software is considered the "most valuable software for students" (Becker, 1999) by mathematics teachers across the country; and of research-driven solutions to the challenge of supporting standards-based curricula effectively with educational technology.