Student-Adaptive Pedagogy for Elementary Teachers: Promoting Multiplicative and Fractional Reasoning to Improve Students' Preparedness for Middle School Mathematics

该项目开发了一种教师专业发展干预措施，以支持学生适应乘法和分数推理的教学法。其理念是课堂教学应该建立在学生当前的观念和经验之上。该研究的背景是奥罗拉公立学校3-5年级的教师。它的重点是来自城市、缺乏服务和低社会经济地位人群的学生，他们在小学阶段往往落后，在中学数学方面准备不足。它包括夏季研讨会和学年后续活动，包括教师合作。该项目为利用成功的校本研究提供了工具，以促进教师对学生适应教学法的认同、采用和维持。该项目还包括测量学生对概念的理解。为教师和教学教练共享工具和资源（可扩展到地区/州级别）以及研究工具和成果的广泛计划，将促进与负责学生成长的广泛利益相关者（教师、管理人员、研究人员、家长、政策制定者）共享项目成果。这是DRK-12项目学习链中的一个完整设计和开发项目。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。本项目旨在实施和研究一种专业发展干预，旨在将小学高年级教师的数学教学转向一种建构主义的方法，即学生适应教学法（AdPed），它根据学生的概念和经验来适应教学目标和活动。该项目侧重于乘法和分数推理，这对学生在中学数学的关键领域（如比率、比例和函数）的成功至关重要。本项目旨在设计一个测量教师实施AdPed的工具，一个学生乘法推理的临床访谈题，然后分析教师的内容知识和专业发展后AdPed的实施情况。研究设计植根于一个创新的、有凝聚力的框架，它整合了四个基于研究的组成部分：(i)数学学习和认识的模型，（ii）学生乘法和分数推理的进展模型，（iii）促进这种学习的教学模型，以及（iv）数学教师发展的连续体。利用丹佛地铁地区成功的初步努力，改进PD干预和学生适应工具，挑战和改变当前的做法，该项目将首先验证和测试工具，以衡量(a)教师向适应性教学法的成长和(b)学生在乘法推理方面的成长。利用这些新工具和现有措施，该项目将在拥有大量得不到充分服务的学生群体的城市地区的多所学校促进全校教师专业发展（3-5年级），并研究专业发展对教师实践和学生成果的好处。混合方法研究包括基于课堂的数据（例如，视频分析、课堂观察、教师访谈）和学生乘法推理的具体测量和数学理解的一般测量。

The project develops a teacher professional development intervention to support student-adaptive pedagogy for multiplicative and fractional reasoning. The idea is that classroom instruction should build on students' current conceptions and experiences. The context for the study is grades 3-5 teachers in Aurora Public Schools. It focuses on students from urban, underserved and low-socioeconomic status populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics. It includes a summer workshop and academic year follow-up including teacher collaboration. The project provides tools for capitalizing on successful, school-based research for promoting teachers' buy-in, adoption, and sustaining of student-adaptive pedagogy. The project also includes measurement of student understanding of the concepts. An extensive plan to share tools and resources for teachers and instructional coaches (scalable to district/state levels) and of research instruments and findings, will promote sharing project outcomes with a wide community of stakeholders (teachers, administrators, researchers, parents, policy makers) responsible for students' growth. This is a Full Design & Development project within the DRK-12 Program's Learning Strand. 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 aims to implement and study a professional development intervention designed to shift upper-elementary teachers' mathematics teaching toward a constructivist approach, called student-adaptive pedagogy (AdPed), which adapts teaching goals and activities based on students' conceptions and experiences. The project focuses on multiplicative and fractional reasoning--critical for students' success in key areas of middle school mathematics (e.g., ratio, proportion, and function). The project seeks to design an instrument for measuring teachers' implementation of AdPed, a clinical interview rubric for students' multiplicative reasoning and then an analysis of teachers' content knowledge and the implementation of AdPed following the professional development. The research design is rooted in an innovative, cohesive framework that integrates four research-based components: (i) a model of mathematics learning and knowing, (ii) models of progressions in students' multiplicative and fractional reasoning, (iii) a model of teaching (AdPed) to promote such learning, and (iv) a mathematics teacher development continuum. Capitalizing on successful preliminary efforts in the Denver Metro area to refine a PD intervention and student-adaptive tools that challenge and transform current practices, the project will first validate and test instruments to measure (a) teacher growth toward adaptive pedagogy and (b) students' growth in multiplicative reasoning. Using these new instruments, along with available measures, the project will then promote school-wide teacher professional development (grades 3-5) in multiple schools in an urban district with large underserved student populations and study the professional development benefits for teacher practices and student outcomes. The mixed methods study includes classroom-based data (e.g., video analysis, lesson observations, teacher interviews) and measures of students' multiplicative reasoning specifically and mathematical understanding generally.