Technology-Enhanced Learning of Geometry in Elementary Schools

该项目将调查并记录技术增强课程如何以及在何种情况下允许K-5年级的学生参与学习挑战和实验，以支持重要几何概念和原理的发展和应用。该项目将重点关注几何思维的一个重要方面的相关子集：单位、图案和重复——图案和形状由单位的重复产生的方式；形状的变换；对称是特定组合和单位变换的结果。这些思想是理解传统的初等几何中许多主题的基础，也是理解数学、科学和艺术中其他主题的基础。技术增强的课程是研究的重点，包括概念性设计的微世界，旨在以适合年龄的方式体现特定的数学概念。该研究将在课堂环境中进行，整合与提高学生学习相关的几个因素：基于软件的活动、具体的操作、支持各种学习方式的活动、学生日常生活中的例子和应用，以及知识渊博的教师的有效指导。研究结果将包括记录这些课堂环境如何影响目标几何概念的学习；特别是软件的使用如何影响学生的学习；软件如何与其他学习活动互动；以及在技术增强的课堂环境中，几何概念的学习如何在K-5年龄段发展。研究课堂中的学生学习成果将与非参与课堂的学生学习成果以及与全国学生学习成果样本进行比较。这项研究的结果将为未来开发技术增强学习环境的努力提供信息，并为支持有效学习可能需要的教学法变革提供见解。此外，将作为研究的一部分开发的评估任务，以衡量学生几何理解的发展，将作为课堂评估任务使用。该项目将由三家机构的研究人员合作完成，这三家机构分别是教育发展中心（EDC）、威斯康星大学和纽约州立大学布法罗分校。这三家机构一直是几何思维发展研究和基础数学软件和课程开发应用研究的先驱。这三个合作组织将共同努力，在所有研究地点开发和实施连贯的研究设计，并将为18名参与的教师（每个地点6名）提供相同的培训和同等的持续支持。参与的学校有适当的技术基础设施，教师在课堂教学中使用技术方面经验丰富。研究中心将全面管理和协调研究工作。

This project will investigate and document how, and in which circumstances, technology-enhanced curricula allow students in grades K-5 to engage in learning challenges and experimentation that support the development and application of important geometric concepts and principles. The project will focus on a related subset of important aspects of geometric thinking: units, patterns, and repetition-the ways that patterns and shapes result from the repetition of units; transformations of shapes; and symmetries as outcomes of particular kinds of compositions and transformations of units. These ideas underlie understanding of many of the topics traditionally taught in elementary geometry and form the basis for understanding of other topics in mathematics, science, and the arts. The technology-enhanced curricula that are the focus of the research include conceptually designed microworlds designed to embody specific mathematical concepts in age-appropriate ways. The research will take place in classroom contexts that integrate several elements individually associated with improved student learning: software-based activities, concrete manipulatives, activities supporting a variety of learning modalities, examples and applications from students' daily lives, and effective instruction by knowledgeable teachers. The outcomes of the research will include documentation of how these classroom environments influence learning of the targeted geometry concepts; how use of the software in particular influences student learning; how the software interacts with other learning activities; and how learning of geometry concepts develops across the K-5 age ranges in technology-enhanced classroom contexts. Student learning outcomes in the research classrooms will be compared to student outcomes in non-participating classrooms and to a national sample of student outcomes. The results of this research will inform future efforts to develop technology-enhanced learning environments and provide insights about changes in pedagogy that may be needed to support effective learning. In addition, the assessment tasks that will be developed as part of the research to measure development of students' geometric understandings will be made available for use as classroom assessment tasks. The project will be a collaboration among investigators from three institutions-Education Development Center (EDC), Inc., University of Wisconsin, and State University of New York at Buffalo-that have been pioneers in research on the development of geometric thinking and in applied research leading to elementary mathematics software and curriculum development. The three partner organizations will work together to develop and implement a coherent research design across all research sites, and will offer the same training and equivalent ongoing support for the 18 participating teachers (6 at each site). Participating schools have the appropriate technical infrastructure, and teachers will be experienced in using technology in classroom instruction. EDC will provide overall management and coordination for the research effort.