Making Upper Division Mathematics Courses More Relevant for Future High School Teachers: The Case of Inquiry-Oriented Dynamical Systems and Modeling

该项目旨在通过创建和调查一门高级选修课--面向未来中学数学教师的探究性动力系统与建模--的影响，为国家利益服务。为此，NSF IUSE：EDU参与的学生第二级学习项目旨在解决高年级数学课程与未来中学教师需求之间有充分证据的脱节问题。这个项目将包括开发一个为期一学期的开源课程，其中建模应用程序将包括学生感兴趣的各种环境、生态、可持续发展和社会问题，并将与高中数学主题密切相关。课程将包括学生任务以及教师资源和教学策略。该项目将探讨在专门为未来中学教师开设的以探究为导向的动态系统和建模课程中，中学数学内容与教学之间建立深入和有意义的联系的前景和可能性。该项目将得到来自多所大学的不同研究人员团队以及来自数学教育、数学和中学教育的顾问的支持。国家专家咨询委员会将就项目小组的核心工作向其提供咨询意见，并将评估项目的成功。该项目有可能显著影响本科数学教育，并通过课程和计划向数学界传播工作来间接影响中学数学教育。该项目的三个主要目标是：(1)创建包括学生任务和教师资源在内的开放源码课程，(2)研究与未来教师的教学知识相关的课程的影响，他们如何参与数学实践共同核心标准，以及他们对数学教学和学习的信念，以及(3)与数学界接触，旨在支持其他人为未来的中学教师设计和修改高年级数学课程。这四个项目研究问题涉及未来教师：1)教学知识，2)对《数学实践标准》的投入，3)对数学教与学的信念，4)对教学实践的投入。这项工作既有实际贡献(创建新课程)，也有设计型研究的理论贡献(产生关于教师的中学数学知识、他们对数学教学和学习的信念以及他们的数学和专业实践的研究性知识)。该项目将包括在三个不同背景下的三个学期的课堂设计实验迭代，每个实验将包括三个阶段的回溯性数据分析。该项目将通过出版物、网站、讲习班、会议和工作组传播其成果，着眼于吸引早期课程采用者为课程开发提供信息。NSF IUSE：EDU计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。该项目的部分资金来自罗伯特·诺伊斯教师奖学金项目。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims to serve the national interest by creating and investigating the impact of an upper division elective course, Inquiry-Oriented Dynamical Systems and Modeling for prospective secondary mathematics teachers. In doing so, this NSF IUSE: EDU Engaged Student Learning Level II project aims to address the well-documented disconnect between upper division mathematics courses and the needs of prospective secondary school teachers. This project will include the development of an open-source semester-long curriculum, where modeling applications will include a variety of environmental, ecological, sustainability, and social issues of interest to students and which will be intimately connected to high school mathematics topics. The curriculum will include student tasks as well as teacher resources and strategies for teaching the course. The project will investigate the prospects and possibilities for deep and meaningful connections between secondary school mathematics content and teaching in an Inquiry-Oriented Dynamical Systems and Modeling course specifically for prospective secondary teachers. The project will be supported by a diverse team of researchers at multiple universities and consultants from math education, mathematics, and secondary education. A National Advisory Board of experts will advise the project team on its core work and will assess the success of the project. The project has potential to significantly impact undergraduate mathematics education and to indirectly impact secondary mathematics education through the curriculum and plans to disseminate work with the mathematics community.The three broad goals of the project are: (1) creation of the open-source curriculum including student tasks and instructor resources, (2) research on the impact of the curriculum related to prospective teachers content knowledge, how they engage in the Common Core Standards for Mathematical Practice, and their beliefs about teaching and learning mathematics, and (3) outreach to the mathematics community aimed at supporting others in designing and modifying upper division mathematics courses for prospective secondary teachers. The four project research questions concern prospective teachers': 1) content knowledge, 2) engagement in the Standards for Mathematical Practice, 3) beliefs on teaching and learning mathematics, and 4) engagement in approximations of teaching practice. This work has both practical contributions (creation of a new curriculum) and theoretical contributions from design-based research (producing research knowledge about teachers' knowledge of secondary mathematics, their beliefs about mathematics teaching and learning, and their mathematical and professional practices). The project will include three semester-long classroom design experiment iterations in three different contexts and each will include a three-phase retrospective data analysis. The project will disseminate its results through publications, a website, workshops, conferences, and working groups with an eye on engaging early curriculum adopters to inform the curriculum development. The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.Partial funding for the project is from the Robert Noyce Teacher Scholarship program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.