Collaborative Research: Investigating Productive Use of High-Leverage Student Mathematical Thinking

该项目将考察中学数学教师如何在整个课堂讨论中回应和利用学生的思维。教师面临的一个持续挑战是如何在课堂讨论中充分利用学生新兴的数学思想。教师需要利用学生已经形成的思想来创造学习重要数学概念的机会。本研究将创建专门设计的任务，为教师创造机会，以学生的思维为基础，然后使用课堂观察和课堂视频分析来开发工具，以支持教师领导全班讨论。探索研究K-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具（rmt），显著提高pre -12学生和教师对科学、技术、工程和数学（STEM）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实证依据。该项目侧重于建立学生思维的教学实践，在这种实践中，教师让学生理解同龄人的数学思想，以帮助整个班级的数学理解向前发展。本研究考察了教师如何将这种实践融入中学课堂的数学讨论中，方法是设计任务，为教师创造机会，以学生的思维为基础，并研究教师如何围绕学生对这些任务的反应组织全班讨论。该项目让教师和研究人员共同探索建筑实践。教师研究人员将在他们的课堂上使用项目设计的任务，然后与研究团队一起对他们自己的教学进行循环分析。数据收集和分析将依赖于课堂视频分析，教师对任务制定的反思，以及在与教师研究人员召集的研究小组会议上收集的数据来分析实践。

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion. The Discovery Research K-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 (RMTs). 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.The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.