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

该项目是一项重要的研究，旨在为城市学区全面实施以数学论证为重点的数学教学改革奠定基础。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)，帮助在职中学数学教师在整个学年支持数学辩论。数学论证，即对数学猜想和论证的建构和批判，是数学中的一项基本的学科实践，学生往往永远不会掌握。基于之前两项由NSF资助的研究中对该项目在短期课程单元中的方法的概念证明，该项目扩展了该模型，以帮助教师全年支持数学辩论。一个连贯的、可移植的、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。在首都展示这一项目可能会引起广泛的兴趣，并产生关于如何在城市环境中实施数学实践的重要知识。在学校里，越来越多的数学辩论对学生的成就和参与21世纪的工作做出了巨大贡献。数学辩论是一种丰富的讨论，学生在讨论中挑战数学权威，共同构建猜想和论证。对于许多教师来说，支持这样的话语是具有挑战性的；许多教师最习惯于启动-回应-评估类型的做法和/或对内容理解不足。专业发展将教师培养成有纪律的即兴演奏者--拥有工具、知识和实践工具包的专业人员，可以在数学论证展开时创造性地和负责任地进行部署。这门学科包括建立课堂规范和为辩论安排课程。该模型的行动理论有四个设计原则：提供工具包，使用模拟课堂练习即兴创作，支持关键内容的学习，为全年使用新实践提供工作嵌入和技术支持。为期三年的研究将涉及设计、可行性和承诺。在研究1中，研究小组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，目的是检查计划的实施情况，找出障碍和促进者，并提出改进意见。研究3是一项准实验试点，旨在检验实现预期结果的承诺：扩大教师的内容知识和对数学论证的支持，提高学生在课堂上的数学论证和口语论证能力。这些研究将导致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档记录。

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.