The Design of a Research Based Curriculum for Real Analysis

数学科学(21)：这个项目是在本科高级分析中研究学生的学习模式，这是一门对打算从事高级数学工作的学生来说至关重要的课程。该项目的最终目标是为亚利桑那州立大学(ASU)和美国各地的其他机构设计一个基于研究的课程，其中包括学习材料，用于亚利桑那州立大学(ASU)的实数分析本科数学课程。该项目将通过以下方式对STEM本科课程产生积极影响：1.创建学习材料和教学策略，包括课程模块和衡量学生准备程度的工具；2.通过全班教学实验和对个别学生的任务访谈来实施教育创新；3.开展研究，探索学生的理解、障碍和学习模式；以及有效的教学策略，以促进学习。智力优势：关于学生在高级本科分析等高层次抽象数学课程中的障碍及其学习模式的研究很少。虽然已经对教育理论的应用进行了大量的研究，并为K-12和一些较低级别的本科数学开发了材料，但没有证据表明这项工作适用于高级抽象课程。这个项目是填补这一研究文献空白的一步。更广泛的影响：分析课程，如亚利桑那州立大学正在学习的课程，也存在于美国大多数四年制学院和大学，通常是数学和中学数学教育本科学位的必修课。拟议中的项目将帮助全国大量的数学学生和未来的高中教师成功过渡到高年级数学课程。该项目还通过阐明在不同教育环境中适应创新的挑战和机会来发展教师的专业知识。

Mathematical Sciences (21): This project is studying student learning patterns in undergraduate advanced analysis, a critical course for students who intend to do advanced work in mathematics. The ultimate goal of the project is to design a research based curriculum with learning materials for the undergraduate mathematics course in Real Analysis at Arizona State University (ASU), as well as for other institutions throughout the U.S. This project will positively affect STEM undergraduate programs by:1. Creating learning materials and teaching strategies, including lesson modules and an instrument to gauge students' readiness,2. Implementing educational innovations through a whole-class teaching experiment and task-based interviews with individual students, and 3. Conducting research to explore students' understanding, obstacles and their learning patterns; and effective teaching strategies to enhance learning.Intellectual Merit: There is little research about students' obstacles and their learning patterns in upper level abstract mathematics courses, such as advanced undergraduate analysis. While much research on the application of educational theories has been done and materials have been developed for K-12 and some lower division undergraduate mathematics, there is no evidence that this work applies to advanced abstract courses. This project is a step toward filling this gap in the research literature.Broader Impact: Analysis courses, such as the one being studied at Arizona State are also present at most 4-year colleges and universities in the U. S. and are often required for undergraduate degrees in mathematics and secondary mathematics education. The proposed project will help a significant pool of mathematics students and future high school teachers across the nation to have a successful transition to upper division mathematics courses. This project is also developing faculty expertise by illuminating challenges to and opportunities for adapting innovations in diverse educational settings.