Collaborative Research: Social Organization, Learning Technologies & Discourse: System Features for Facilitating Mathematical Reasoning in PreK-3 Students

本研究将探讨社会组织、学习技术及其相互关系对学前三年级学生几何推理的影响。社会组织在这里的运作是将学生分成三合会，参与协作解决问题的战略小组。学习技术在这里被操作为物理和虚拟操作类型(探戈、五角星、地理板)，以及旨在帮助学生获取数学知识的支持软件。基于这一领域的初步工作结果，有人提出，学习技术允许同行之间的流体交换，以及物理和虚拟操作之间的转换，从而显著增强几何推理。目前的项目提出了一个强大的研究和设计框架，将课堂上实地研究的迭代周期与实验室中的开发和实验相结合。其目标是设计、开发和制作一种桌面计算机界面，允许学生之间进行前所未有的交流，并在操纵型之间进行转换。桌面界面将首先用作促进实验操作的设备，然后通过迭代改进用作学习技术平台，学生通过该平台获得数学知识。目前的工作提出的进步是，它将所有的交互放在水平桌面上。这一点至关重要，因为它消除了先导研究结果中不同座位和屏幕方向的混淆影响。几何人工制品的操作沿着研究问题的两个维度展开：社会互动和学习技术对几何推理的影响。1)儿童发展--从学习轨迹上理解儿童数学推理的发展；2)数学教育--理解教师在课堂教学中使用高级学习技术和角色，以及儿童使用高级学习技术进行数学学习；3)学习科学--分析、设计和开发高级学习技术的精炼技术；4)人机交互-设计有助于学习的界面，包括手势交互、有形操作和水平展示；以及5)心理语言学-课堂环境中其他领域发展的概念基础。这项研究的结果也将对女孩参与数学课堂产生很大影响，目标是鼓励所有学生进行丰富的话语。此外，发达的技术可能会对特殊需要儿童的教育产生影响，因为可以修改和重新配置教学接口，以满足这一人数不足的群体的不同需求。这些学科之间合作的一个重要成果将是为博士生提供尖端研究机会，并为建立新的课程和可能的学位课程奠定基础。

This research project will investigate the effects social organization, learning technologies, and their interrelationships, have on the geometric reasoning of PreK-3 students. Social organization is operationalized here as the strategic grouping of students into triads to engage in collaborative problem solving. Learning technologies are operationalized here as physical and virtual manipulative types (tangrams, pentominoes, geoboards) together with supporting software designed to facilitate students in accessing their mathematical knowledge. Based on findings from preliminary work in this area, it is proposed that learning technologies allow for fluid exchanges between peers, and transitions between physical and virtual manipulatives, significantly enhancing geometric reasoning. The current project presents a robust research and design framework that combines iterative cycles of field studies in the classroom with development and experimentation in the lab. The goal is to design, develop and prototype a tabletop computer interface that allows for unprecedented exchanges among student peers and transitions between manipulative types. The tabletop interface will serve first as the apparatus that facilitates experimental manipulations, later being used, through iterative refinement, as the learning technology platform by which students gain access to mathematical knowledge. The advancement proposed by the current work is that it places all interaction on the horizontal tabletop. This is critical in that it removes confounding effects of different seating and screen orientations from pilot study findings. Manipulations of geometric artifacts reside along two dimensions of research questions: the effects of social interaction and of learning technology on geometric reasoning. Hence, the proposed studies will allow investigation of different transitions between fully functional and fully operational thinking, functional and qualitative operational thinking, and qualitative and quantitative parametric thinking with the same interaction morphologies.The proposed research has the potential to make significant contributions to the following intellectual domains: 1) child development -understanding children's development of mathematical reasoning in terms of learning trajectories 2) mathematics education - understanding teachers' use of advanced learning technologies and role in classroom instruction, and children's learning of mathematics using advanced learning technologies; 3) learning sciences - refining techniques for the analysis, design, and development of advanced learning technologies in use; 4) human-computer interaction -design of interfaces that aid learning to include gestural interaction, tangible manipulation, and horizontal displays; and 5) psycholinguistics - grounding of concepts developed in other domains in the classroom environment. Results from the research will also have much to say about the participation of girls in the mathematics classroom, a goal being to encourage rich discourse of all students. In addition, developed technologies may have implications for the education of special needs children as instructional interfaces can be modified and reconfigured to meet the diverse needs of this underrepresented group. A significant outcome of collaboration among these disciplines will be cutting-edge research opportunities for doctoral students and groundwork for the establishment of new curricula and, possibly, degree programs.