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

该项目开发了一个教师专业发展干预，以支持学生适应乘法和分数推理教学法。其理念是课堂教学应该建立在学生当前的概念和经验之上。这项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，服务不足和低社会经济地位人口的学生，他们往往在小学年级落后，对中学数学准备不足。它包括一个夏季研讨会和学年的后续行动，包括教师合作。该项目提供了利用成功的校本研究的工具，以促进教师接受、采用和维持适应学生的教学法。该项目还包括测量学生对概念的理解。一项广泛的计划是为教师和教学教练分享工具和资源（可扩展到地区/州一级）以及研究工具和研究结果，这将促进与负责学生成长的广大利益攸关方（教师、行政人员、研究人员、家长、决策者）分享项目成果。这是DRK-12项目学习链中的一个完整设计开发项目。探索研究K-12计划（DRK-12）旨在通过研究和开发创新资源，模型和工具（RMT），显着提高学前班学生和教师的科学，技术，工程和数学（STEM）的学习和教学。DRK-12项目中的项目建立在STEM教育的基础研究以及之前的研究和开发工作的基础上，为拟议的项目提供理论和实证依据。该项目旨在实施和研究一种专业发展干预措施，旨在将小学高年级教师的数学教学转向建构主义方法，称为学生适应性教学法（AdPed），它根据学生的概念和经验来调整教学目标和活动。该项目的重点是乘法和分数推理-学生在中学数学的关键领域的成功至关重要（例如，比例、比例和功能）。本研究旨在设计一个教师实施AdPed的测量工具，一个学生乘法推理的临床访谈量表，然后分析教师的内容知识和专业发展后的AdPed实施情况。研究设计植根于一个创新的，有凝聚力的框架，整合了四个基于研究的组件：（一）数学学习和知识的模型，（二）学生的乘法和分数推理的进展模型，（三）教学模式（AdPed），以促进这种学习，和（四）数学教师发展连续体。利用丹佛大都会地区成功的初步努力，完善PD干预和学生自适应工具，挑战和改变目前的做法，该项目将首先验证和测试工具，以衡量（a）教师对自适应教学法的发展和（B）学生在乘法推理的增长。利用这些新的工具，沿着现有的措施，该项目将在一个有大量得不到充分服务的学生的城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做法和学生成果的好处。混合方法研究包括基于课堂的数据（例如，录像分析，课堂观察，教师访谈）和测量学生的乘法推理具体和数学理解一般。

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.