Preparing Urban Middle Grades Mathematics Teachers to Teach Argumentation Throughout the School Year

本项目是为在城市学区全面实施以数学论证为重点的数学教学改革而开展的一项重要的前期研究。这个完整的研究和开发项目的目标是开发资源、模型和工具（rmt），帮助在职的初中数学教师在整个学年中支持数学论证。数学论证是对数学猜想和论证的建构和批判，是学生往往无法掌握的数学基本学科实践。该项目在两项由美国国家科学基金会资助的短期课程单元中对项目方法的概念进行了验证，该项目扩展了该模型，以帮助教师全年支持数学论证。一个连贯的、便携的、为期一年的数学论证专业发展计划有可能增加全国学生接触数学论证的机会，特别是满足城市地区教师和学生的需求。在国家首都展示这个项目可能会吸引广泛的兴趣，并产生关于如何在城市环境中实施数学实践的重要知识。学校中越来越多的数学论证有可能对学生的成就和参与21世纪的工作场所做出巨大贡献。数学论证是学生运用数学权威，共同构建猜想和论证的丰富讨论。对许多教师来说，支持这样的话语是具有挑战性的；许多人对初始化-响应-评估类型的实践最为满意，并且/或者对内容理解不足。专业发展将教师培养成有纪律的即兴表演者——拥有工具、知识和实践工具包的专业人士，随着数学论证的展开，他们可以创造性地、反应性地进行部署。这门学科包括建立课堂规范和规划辩论课程。该模型的行动理论有四个设计原则：提供工具包，使用课堂模拟来练习即兴创作，支持关键内容的学习，以及为全年使用新实践提供嵌入工作的技术支持。为期三年的研究将涉及设计、可行性和前景。在研究1中，该团队与哥伦比亚特区公立学校的工作人员共同设计了rmt。研究2是一项可行性研究，旨在检查项目实施情况，确定障碍和促进因素，并告知改进措施。研究3是一项准实验试点，旨在测试实现预期结果的承诺：扩大教师对数学论证的内容知识和支持，提高学生在课堂上的数学论证和口语论证能力。这些研究将形成一个为期一年的专业发展计划，包括行动理论、设计决策、试验数据和仪器技术质量的文件。

The project is an important study that builds prior research to bring a comprehensive implementation of reform mathematics instruction focused on mathematical argumentation to an urban school district. The objective of this full research and development project is to develop resources, models, and tools (RMTs) that help inservice middle grades mathematics teachers support mathematical argumentation throughout the school year. Mathematical argumentation, the construction and critique of mathematical conjectures and justifications, is a fundamental disciplinary practice in mathematics that students often never master. Building on a proof of concept of the project's approach in short curriculum units from two prior NSF-funded studies, this project expands the model to help teachers support mathematical argumentation all year. A coherent, portable, yearlong professional development program on mathematical argumentation has the potential to increase access to mathematical argumentation for students nationwide and, in particular, to address the needs of teachers and students in urban areas. Demonstrating this program in the nation's capital likely attracts broad interest and produces important knowledge about how to implement mathematical practices in urban settings. Increasing mathematical argumentation in schools has the potential for dramatic contributions to students' achievement and participation in 21st century workplaces.Mathematical argumentation is rich discussion in which students take on mathematical authority and co-construct conjectures and justifications. For many teachers, supporting such discourse is challenging; many are most comfortable with Initiate-Respond-Evaluate types of practices and/or have insufficient content understanding. The professional development trains teachers to be disciplined improvisers -- professionals with a toolkit of tools, knowledge, and practices to be deployed creatively and responsively as mathematical argumentation unfolds. This discipline includes establishing classroom norms and planning lessons for argumentation. The model's theory of action has four design principles: provide the toolkit, use simulations of the classroom to practice improvising, support learning of key content, and provide job-embedded, technology-enabled supports for using new practices all year. Three yearlong studies will address design, feasibility, and promise. In Study 1 the team co-designs the RMTs with District of Columbia Public Schools staff. Study 2 is a feasibility study to examine program implementation, identify barriers and facilitators, and inform improvements. Study 3 is a quasi-experimental pilot to test the promise for achieving intended outcomes: expanding teachers' content knowledge and support of mathematical argumentation, and increasing students' mathematical argumentation in the classroom and spoken argumentation proficiency. The studies will result in a yearlong professional development program with documentation of the theory of action, design decisions, pilot data, and instrument technical qualities.