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

合作研究：利用 MIPO：发展学生数学思维的有效利用理论

• 批准号: 1220357
• 负责人: Shari Stockero
• 金额: $ 22.99万
• 依托单位: Michigan Technological University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-10-01 至 2017-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1220357&HistoricalAwards=false
• 关键词: Collaborative; Research; Leveraging; MIPOs; Developing

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.

利用MOSTs（数学上重要的教学开放来建立在学生思维上）是杨百翰大学、密歇根理工大学和西密歇根大学之间的一个合作项目，重点是通过提高教师在教学中利用学生思维来发展数学概念的能力来改善中学数学教学。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)教师如何在教学中运用学生的思维？这种运用背后的目标、取向和资源是什么？(3)有效运用学生思维的教学实践的学习轨迹是什么？(4)可以提供哪些支持来推动教师沿着学习轨迹前进？该项目正在开发一种学生数学思维的有效运用理论（PUMT理论），该理论阐明了有效运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。设计研究方法的基础是四个相互关联的阶段的工作：(1)学生思维-通过扩展现有的课堂演讲视频数据集来测试和完善初步框架，以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，以及他们如何决定追求哪种思维；(3)教师对学生思维的了解——通过一系列教师发展实验，提高教师在教学中有效利用学生数学思维的能力；(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进一步改进。数据包括课堂教学录像（以确定大多数和教师对他们的反应），教师访谈（了解他们对学生思考实例的反应），教师发展会议和研究人员关于教师发展的讨论记录（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总结性两部分，重点关注项目开发PUMT理论和相关工具和专业发展过程的质量，以及最终产品的质量。利用most为教师、教师教育工作者和研究人员提供了重要的资源，包括理论、框架和假设的学习轨迹，这些资源使有效利用学生数学思维这一通常抽象但基本的目标更加具体化。该项目增强了该领域对以下方面的理解：(1)教师在课堂上可以使用的most，以及它们在不同背景下的差异；(2)教师在教学过程中对学生思维的认知和有效利用；(3)教师学习学生思维的轨迹，以及如何最好地支持沿着这一轨迹的运动。有效地利用学生的思维是有效教学的基石，因此该项目产生的PUMT理论和相关支持对于数学教育和其他领域的人员来说是宝贵的资源。