Theorizing and Advancing Teachers' Responsive Decision Making in the Domain of Rational Numbers

该项目满足了日益增长的研究需求，以支持教师发展响应性决策方面的专业知识，教师在教学过程中引导并建立儿童的数学思维。具体目标包括表征3-5年级教师在有理数领域的响应性决策，调查专业发展如何支持这种教学专业知识的发展，并探索教师响应性决策程度与学生学习之间的关系。本项目的理论和实践贡献解决了该领域产生关于儿童思维的研究性知识的能力与提供获取和有效利用这些知识的资源之间的差异。主要组织是奥斯汀的德克萨斯大学，主要合作组织包括格林斯博罗的北卡罗来纳大学、SRI国际和教师发展组织。在这项专业发展设计研究中，研究人员让大约100名教师参与了长达三年的专业发展，旨在使教师能够在基于研究的儿童有理数思维框架的指导下做出教学决策，重点是儿童分割数量的非正式想法，以及他们对运算和平等基本属性的理解。数据来源包括对工作坊和教师课堂的直接观察，以及教师的表现和对各种评估的反思。基于从这些来自3个教师群体的多个数据源中所学到的知识，研究人员将迭代地建立和完善响应性决策模型，并确定这一专业知识发展的关键特征。此外，研究人员使用了大约一半的样本，收集了学生的数据，以检验反应性决策与学生学习机会增加有关的猜想。该项目产生的发现、评估和专业发展将有助于该领域应对如何支持教师在教学中接受并有效利用儿童数学思维知识的关键挑战。预期的智力成果包括有理数领域的教师响应性决策模型、教师响应性决策发展的标志和障碍的识别，以及教师响应性决策专长与学生学习之间关系的知识。预期的专业发展产品包括一个基于网络的工具，以支持教师自主指导的协作探究，以及一个明确的、可扩展的教师专业发展课程，并通过教师发展小组正在进行的工作直接传播。

This project addresses the growing need for research to support teachers in developing expertise in responsive decision making in which teachers elicit and build on children's mathematical thinking in the midst of instruction. Specific objectives include characterizing grades 3-5 teachers' responsive decision making in the domain of rational numbers, investigating how professional development can support the development of this form of teaching expertise, and exploring the relationship between degree of teachers' responsive decision making and student learning. Theoretical and practical contributions of this project address the discrepancy in the field's capacity to produce research-based knowledge about children's thinking versus provide resources to take up and effectively use this knowledge. The primary organization is The University of Texas at Austin, and major partner organizations include the University of North Carolina at Greensboro, SRI International, and Teachers Development Group. In this professional development design study, researchers engage approximately 100 teachers in up to three years of professional development designed to empower teachers to make instructional decisions guided by a research-based framework of children's thinking about rational numbers, with an emphasis on children's informal ideas of partitioning quantities and their understanding of the fundamental properties of operations and equality. Data sources include direct observation of workshops and teachers' classrooms as well as teachers' performance and reflection on a variety of assessments. On the basis of what is learned from these multiple data sources across 3 cohorts of teachers, researchers will iteratively build and refine a model of responsive decision making and identify critical features of the development of this expertise. Further, using approximately half the sample, researchers collect student data to test the conjecture that responsive decision making is related to increased opportunities for students to learn.The findings, assessments, and professional development generated by this project will help the field respond to the critical challenge of how to support teachers to take up and effectively use knowledge of children's mathematical thinking in instruction. Anticipated intellectual products include a model of teachers' responsive decision making in the domain of rational numbers, identification of landmarks and obstacles in teachers' development of responsive decision making, and knowledge about the relationship between teachers' expertise in responsive decision making and student learning. Anticipated professional development products include a web-based tool to support teachers' self-guided collaborative inquiry and a well-specified, scalable professional development course for teachers with an immediate outlet for dissemination through the ongoing work of Teachers Development Group.