Connections between Advanced and Secondary Mathematics: Exploring the Impact of Abstract Algebra on the Teaching and Learning of Secondary Mathematics

这个会议项目将汇集一群不同的学者和从业者，他们有兴趣研究抽象代数在大学水平上的研究和教师在K-12数学中使用的抽象代数之间的联系。最近的政策文件提倡将抽象代数等高级主题作为中学教师准备的基本部分，绝大多数学校要求学生学习抽象代数。理解这一要求的含义对于改进中学数学教育是必要的。本次会议将通过提供一个跨越社区的共同空间（例如，教育机构、研究机构、教师教育工作者），这是既定会议通常不提供的机会。通过会议的专门工作组，所有与会者将在研究和专业发展方面取得进展，这将直接有助于推进围绕高等数学和中学数学（特别是抽象代数）之间的联系在教师准备中的作用的知识。会议将实现三个目标。第一个目标将是分享目前的研究高等数学和中等数学之间的数学联系，特别侧重于抽象代数。第二个目标是制定研究和/或专业发展计划，以扩大高等数学和学校数学之间联系的现有知识，以便与会者能够采取具体措施推动研究向前发展。第三个目标是为数学家、数学教育工作者和其他利益相关者提供一个空间，讨论他们的工作，并为未来的发展方向制定一个共同的愿景。特别是，将提供机会审视研究和实践，命名共同目标，并制定研究和支持中学教师在教学中理解和使用抽象代数需求的轨迹。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 conference project will bring together a diverse group of scholars and practitioners interested in studying the connections between abstract algebra as studied at the university level and the abstract algebra used by teachers in K-12 mathematics. Recent policy documents advocate for including advanced topics such as abstract algebra as a fundamental part of secondary teacher preparation, and a large majority of schools require students to take abstract algebra. Understanding the implications of such a requirement is imperative to improving secondary mathematics education. This conference will gather together people interested in this topic by providing a common space that cuts across communities (e.g., teaching institutions, research institutions, teacher educators), an opportunity not typically offered by established conferences and meetings. Through the dedicated working groups at the conference, all attendees will make progress on research and professional development that will directly contribute to advancing knowledge around the role of connections between advanced and secondary mathematics (particularly abstract algebra) in the preparation of teachers.The conference will meet three objectives. The first objective will be to share current research on mathematical connections between advanced and secondary mathematics, focusing specifically on abstract algebra. The second objective will be to develop plans for research and/or professional development to expand current knowledge on connections between advanced and school mathematics, so that attendees can take concrete steps to move research forward. The third objective will be to provide a space for mathematicians, mathematics educators, and other stakeholders to discuss their work and develop a common vision for future directions. In particular, opportunities will be provided to look across research and practice, name common goals, and elaborate a trajectory for researching and supporting the needs of secondary school teachers to understand and use abstract algebra in their teaching.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.