Collaborative Research: Leveraging MIPOs: Developing a Theory of Productive Use of Student Mathematical Thinking

利用MOSTS(数学上重要的教学机会建立在学生思维的基础上)是杨百翰大学、密歇根理工大学和西密歇根大学合作的项目，重点是通过提高教师在教学过程中使用学生思维发展数学概念的能力来改善中学数学的教学。该项目的核心研究问题是：(1)教师在课堂上提供给他们的高杠杆学生思维的本质是什么？(2)教师在教学中如何使用学生思维，这种使用的目标、方向和资源是什么？(3)有效利用学生思维的教学实践的学习轨迹是什么？以及(4)可以提供什么支持来推动教师沿着这条学习轨迹前进？该项目正在开发一种有效利用学生数学思维的理论(PUMT理论)，阐述了有效利用学生数学思维的实践是什么样子的，如何发展这种实践，以及如何促进这种发展。设计研究方法论支持四个相互关联的阶段的工作：(1)学生思维-测试和完善初步框架，通过扩展现有的课堂话语视频数据集，包括更多不同的教师和学生群体；(2)教师与学生思维的互动-评估教师对使用学生思维的看法，以及他们如何做出关于追求哪种思维的决定；(3)教师对学生思维的学习-利用一系列教师发展实验来提高教师在教学中有效地使用学生数学思维的能力；以及(4)可共享的产品-创造有用的产品，这些产品的形式鼓励反馈，以便进一步完善。数据包括课堂教学的录像带(以确定MOST和教师对他们的反应)、教师访谈(以了解他们对学生思维的反应的决定)，以及教师发展会议和研究人员关于教师发展的讨论的记录(为教师发展实验和未来的专业发展活动提供信息)。项目评估包括形成性和终结性两个部分，重点关注项目开发PUMT理论和相关工具的过程的质量和专业发展，以及结果产品的质量。利用MOST为教师、教师教育工作者和研究人员提供关键资源-包括理论、框架和假设的学习轨迹-使经常抽象但基本的目标更加明确，即有效地使用学生的数学思维。该项目加强了实地对以下方面的了解：(1)教师在课堂上可以获得的最多知识，以及这些知识在不同背景下是如何变化的；(2)教师在教学过程中对学生思维的感知和有效利用；(3)教师学习学生思维的轨迹以及如何最好地支持沿该轨迹进行的活动。有效地使用学生的思维是有效教学的基石，因此，该项目产生的PUMT理论和相关支持对参与数学教育的人以及其他领域的人来说都是宝贵的资源。

Leveraging MOSTs (Mathematically Significant Pedagogical Openings to build on Student Thinking) is a collaborative project among Brigham Young University, Michigan Technological University and Western Michigan University that focuses on improving the teaching of secondary school mathematics by improving teachers' abilities to use student thinking during instruction to develop mathematical concepts. The core research questions of the project are: (1) What is the nature of high-leverage student thinking that teachers have available to them in their classrooms? (2) How do teachers use student thinking during instruction and what goals, orientations and resources underlie that use? (3) What is the learning trajectory for the teaching practice of productively using student thinking? and (4) What supports can be provided to move teachers along that learning trajectory? The project is developing a theory of Productive Use of Student Mathematical Thinking (PUMT Theory) that articulates what the practice of productively using student mathematical thinking looks like, how one develops this practice, and how that development can be facilitated.Design research methodology underlies the work of four interrelated phases: (1) Student thinking - testing and refining a preliminary framework by expanding an existing data set of classroom discourse video to include more diverse teacher and student populations; (2) Teachers' interactions with student thinking - assessing teachers' perceptions of using student thinking and how they make decisions about which thinking to pursue; (3) Teachers' learning about student thinking - using a series of teacher development experiments to improve teachers' abilities to productively use student mathematical thinking during instruction; and (4) Shareable products - creating useful products that are in forms that encourage feedback for further refinement. Data include video recordings of classroom instruction (to identify MOSTs and teachers' responses to them), teacher interviews (to understand their decisions in response to instances of student thinking), and records of teacher development sessions and the researchers' discussions about the teachers' development (to inform the teacher development experiments and future professional development activities). Project evaluation includes both formative and summative components that focus on the quality of the project's process for developing a PUMT Theory and associated tools and professional development, as well as the quality of the resulting products.Leveraging MOSTs provides critical resources - including a theory, framework, and hypothetical learning trajectory - for teachers, teacher educators, and researchers that make more tangible the often abstract but fundamental goal of productively using students' mathematical thinking. The project enhances the field's understanding of (1) the MOSTs that teachers have available to them in their classrooms, and how they vary in diverse contexts; (2) teachers' perceptions and productive use of student thinking during instruction; and (3) the trajectory of teachers' learning about student thinking and how best to support movement along that trajectory. Using student thinking productively is a cornerstone of effective teaching, thus the PUMT Theory and associated supports produced by the project are valuable resources for those involved in mathematics education as well as other fields.