Teaching Amidst Uncertainty: Developing Mathematics Teachers' Groupwork Monitoring Practices

几十年的研究表明，当学生有机会谈论数学时，学生学习最好，教学更具包容性。出于这个原因，许多以概念为导向的数学教学方法强调对等讨论。然而，围绕教师应该如何管理这种讨论的问题，研究存在分歧。这种教学实践被称为小组监控。在教师参与的问题上，存在着相互矛盾的指导：教师是应该退后支持学生的自主，还是应该经常参与进来，支持富有成效的耸人听闻的创作？本研究探讨了与小组活动监控相关的数学教育和教师学习研究中的两个公开问题。第一个问题集中在小组活动监控本身：教师如何在学生中培养富有成效的数学对话？第二个问题涉及教师教育中一个不发达的话题：教师准备和专业发展可以以什么方式支持教师学习，有效地进行小组工作监督。许多教师教育策略--如排练例行公事或学习课程--旨在让教师学习结构良好、可预测的教学方面，但没有明确的方法来帮助教师学习支持数学教学中更具互动性和新颖性的方面。这一设计与开发项目通过研究大型城市学区有经验和有成就的中学数学教师对小组活动监控的学习来应对这些挑战。使用现代信息可视化技术和开源工具，以及基于视频的辅导活动，教师将a)分析以小组数学讨论为特色的课堂视频记录，b)发现和调查他们与学生群体的具体互动，以及他们在这一重要课程阶段的总体方法。通过这些工具，教师将发展对有效的小组活动监控策略的战略性和整体性的理解。作为这项工作的结果，教师和研究人员将能够更好地将教师的监控选择与学生的点对点数学对话联系起来。为了调查经验丰富的中学数学教师是如何了解小组监控的，该项目将开发丰富的可视化工具来分析课堂讨论，让教师参与分析活动，并研究结果教师和学生的学习。在第一阶段，项目团队将建立在现有可视化工具的基础上，开发高效的监控交互可视化流程，提供将课堂视频与教师整体互动模式联系起来的新方法。在第二阶段，六个校本小组的12至16名有经验的中学数学教师将在为期两年的时间内参与教师专业发展，以加强他们对个人和团队监测的认识。增强的视频反馈系统将允许教师指导、记录和调查他们不断演变的感官创造。在第三阶段，将从丰富的课堂和教师感知数据语料库中开发出个人和团队学习产出性数学谈话的肖像。同时，对语料库进行了量化分析，以考察不同教师监控策略对学生产出性数学话语的支持或阻碍情况。主要的研究成果将是：1)新的、开放源码的工具，它动态地可视化教师对一节课的监控工作，并与具体的教师-小组互动相协调；2)数学教师监控的框架；3)关于教师学习响应性和情境性实践的理论，其中监控是一个例子；以及4)更有力的实证证据来指导数学教师的监控实践。探索研究PREK-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具，显著提高Pre-K-12学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和经验上的证明。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Decades of research shows that students learn best and instruction is more inclusive when students have opportunities to talk about mathematics. For this reason, many conceptually-oriented mathematics instructional approaches emphasize peer-to-peer discussion. Yet research diverges around questions of how teachers should manage such discussions, an instructional practice referred to as groupwork monitoring. There is contradictory guidance on issues of teacher involvement: should teachers stand back to support student autonomy or involve themselves frequently to support productive sensemaking? This study addresses two open questions in mathematics education and teacher learning research related to groupwork monitoring. The first question centers on groupwork monitoring itself: How can teachers foster productive mathematical talk among students? The second question touches on an underdeveloped topic in teacher education: in what ways can teacher preparation and professional development support teachers in learning effective group work monitoring. Many teacher education strategies –– such as rehearsing routines or learning curriculum –– aim for teachers to learn well-structured, predictable aspects of instruction, yet there are not clear approaches in helping teachers learn to support more interactive and emergent aspects of mathematics teaching. This Design and Development project addresses these challenges by studying experienced and accomplished secondary mathematics teachers’ learning about groupwork monitoring in a large urban school district. Using contemporary information visualization techniques and open-source tools , alongside a video-based coaching activity, teachers will a) analyze classroom video records featuring group math discussions and b) uncover and investigate their specific interactions with student groups as well as their overall approach to this important phase of their lessons. Through these tools, teachers will develop strategic and integrated understandings of effective groupwork monitoring strategies. As a result of this work, teachers and researchers will be able to better connect teachers’ monitoring choices to students’ peer-to-peer math talk.To investigate how experienced secondary mathematics teachers learn about groupwork monitoring, the project will develop rich visualization tools to analyze classroom discussions, engage teachers in analytical activities, and study resultant teacher and student learning. In Phase 1, the project team will build on existing visualization tools to develop efficient processes for producing interactive visualizations of monitoring that provide new ways to link classroom video to teachers’ overall interactional patterns. In Phase 2, 12-16 experienced secondary mathematics teachers in six school-based teams will engage over a two-year period with teacher professional development designed to enhance their sensemaking about monitoring, both individually and in teams. The enhanced video feedback system will allow teachers to guide, document, and investigate their evolving sensemaking. In Phase 3, individual and team learning portraits of productive math talk will be developed from the rich corpus of classroom and teacher sensemaking data. At the same time, the corpus will be analyzed using quantitative methods to investigate the conditions under which different teacher monitoring moves support or impede students’ productive math talk. The primary research products will be: 1) novel, open-source tools that dynamically visualize teachers’ monitoring work over a lesson, coordinated with specific teacher-group interaction; 2) a framework for mathematics teachers’ monitoring; 3) a theory about teachers’ learning of responsive and situated practices, of which monitoring is an example; and 4) stronger empirical evidence to guide mathematics teachers’ monitoring practices. The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.