Investigating Mathematical Modeling, Experiential Learning and Research through Professional Development and an Integrated Online Network for Elementary Teachers

数学建模，即应用数学来解决实际问题，是一种数学实践，由数学家使用，并在共同核心国家数学标准中规定。改善初级数学教与学的必要性是有据可查的。此外，对如何在早期年级教授数学建模的关注也非常有限。这种将数学应用于实际问题的数学实践的重要性在《国家数学共同核心标准》中得到了承认，是所有数学家使用的基本工具。该项目将为小学数学教师设计和提供专业发展，并将产生以小学数学建模为重点的课程模块。该项目基于在劳动力中实践的数学建模，并将产生关于教师如何学习和实施建模过程的研究结果。该项目将提供一个在线资源库，作为制作材料的交换中心，并提供一个虚拟界面，帮助教师就数学建模的教学、学习和实践进行对话。这项研究的核心问题是：有针对性的数学建模专业发展如何影响教师实践？该项目是一个机构伙伴关系，合作伙伴包括：乔治梅森大学、哈维穆德学院和蒙大拿州立大学，以及各自的三个合作学区：费尔法克斯县公立学校、波莫纳联合学区和博兹曼公立学校。该项目将通过一个注重内容的暑期学院和通过后续课程研究进行协作辅导，在数学建模方面提供高质量的教师专业发展。这项工作将产生广泛的影响，因为它涉及小学(2-6年级)数学教师、特殊教育工作者和英语水平有限学生的教师，重点是：a)根据共同核心数学内容、课堂策略和学生评估标准对数学思想进行建模；b)为小学数学建模开发基于问题的评估和基于表现的任务；c)创建活动，区分教学和并行任务，丰富21世纪的建模技能(交流、协作、创造力和批判性思维)，旨在提高不同人群(特殊教育、天赋、有限的英语水平和经济困难)的学术成就；以及d)开发基于需要的现场和在线网络学习专业资源和课程资源(示范课程的视频剪辑、现实生活中的数学联系和使用虚拟操纵法模拟的概念)。专业发展网络资源和工具将提供给各个伙伴州的学校部门，因为它们正在开发，然后在全国范围内传播。该项目将采用三级评价：一名外部评价人将对项目文件进行年度审查，包括研究方案和数据分析方法、咨询委员会会议议程和补充材料以及向供资机构提交的报告；由一名具有评价专业发展模式经验的小组成员进行内部审查；由专家咨询委员会进行同行审查。这种三阶段评价模式将最大限度地利用项目资源和专业知识。

Mathematical modeling, in which mathematics is applied to solve real problems, is a mathematical practice, used by mathematicians and specified in the Common Core State Standards for Mathematics. The need to improve the teaching and learning of mathematics at the elementary level is well documented. Moreover, very limited attention has been paid to how to teach mathematical modeling in the early grades. The importance of this mathematical practice, in which mathematics is applied to real problems, is recognized in the Common Core State Standards for Mathematics and is a foundational tool used by all mathematicians. This project will design and deliver professional development for elementary grades mathematics teachers and will result in curriculum modules that focus on mathematical modeling in the elementary grades. The project is based on mathematical modeling as it is practiced in the workforce and will yield research results regarding how teachers learn about and implement the modeling process. The project will offer an online repository as a clearinghouse for materials produced as well as a virtual interface to help facilitate a dialogue among teachers about the teaching, learning and practice of mathematical modeling.The research question at the heart of this study is: How does targeted professional development in mathematical modeling affect teacher practice? The project is an institutional partnership, with collaborating partners including: George Mason University, Harvey Mudd College and Montana State University with three respective collaborating school districts, Fairfax County Public Schools, Pomona Unified School District and Bozeman Public Schools. The project will provide high-quality teacher professional development in mathematical modeling through a content-focused summer institute and collaborative coaching through follow-up Lesson Study. The work will have broad impact as it engages elementary (grades 2-6) mathematics teachers, special educators, and teachers of students with Limited English Proficiency, to focus on: a) modeling mathematics ideas aligned to the Common Core mathematics content, classroom strategies, and student assessment standards; b) developing problem-based assessment and performance-based tasks for mathematical modeling in elementary grades; c) creating activities to differentiate instruction with parallel tasks that enrich 21st century skills in modeling (communication, collaboration, creativity and critical thinking) aimed at increasing the academic achievement of diverse populations (special education, gifted, Limited English Proficiency and economically disadvantaged); and d) developing need-based on-site and online web-learning professional and curricular resources (video clips of exemplar lessons, real-life math connections and concepts modeled using virtual manipulatives). The professional development web resources and tools will be available to school divisions across the respective partnering states as they are being developed and then disseminated nationally. The project will use three levels of evaluation: an external evaluator who will conduct an annual review of project documents, including research protocols and data analysis methods, advisory board meeting agendas and supplementary materials, and reports to the funding agency; an internal review by a team member experienced with models for evaluating professional development; and peer review by an expert Advisory Board. This tri-phase model of evaluation will maximize project resources and expertise.