VIGRE: The University of Chicago's Vertical Integration Program

摘要：芝加哥大学的VIGRE项目将教学和研究垂直整合是芝加哥数学系几十年来的传统，而“垂直整合”一词已经使用了25年以上。我们的项目是建立在正式和非正式制度化的基础上的，在不同层次的人们之间进行互动。垂直整合的逻辑是基于这样一个原则，即在我们的教育和研究项目中，人们应该向更先进的人学习，向更落后的人教授。VIGRE计划将使我们能够在几个层面上更充分地实施这一原则。该项目完全由博士后、研究生和本科生的直接支持组成。平均每年资助博士后6人、研究生12人、本科生18人。这笔资金将用于进一步培训这些年轻人，加强数学系现有核心研究和教育项目的垂直整合，并更好地将这些项目与数学系的外展项目相结合。我们将从上到下简要介绍该部门的项目以及VIGRE对这些项目的影响。在最高水平上，高级研讨会和研究水平的研究生课程是终身教职员工、非终身教职员工和研究生的共同练习，这是院系的传统。这种形式在今年得到了极大的加强，举办了为期数年的专题研讨会，参加者范围广泛。该系提供了一个环境，博士后和研究生可以最大限度地发挥他们的潜力，成为富有成效的研究数学家。我们的大多数研究生都在主要的研究型大学找到了第一份工作，在过去的几年里，大多数主要的研究部门都雇佣了新的芝加哥博士。VIGRE资助将为博士后和研究生提供从教学中解放出来的时间，使他们能够更充分地专注于研究，从而大大有助于实现这一目标。VIGRE博士后的教学负担将减轻，VIGRE研究生将有一段时间免于教学职责。我们期望这将使更多的人能够更及时地完成博士学位。我们的研究生课程从第一年密集的基础课程开始，第一年的学生没有教学职责。研究生在第一年之后没有课程作业或考试。一个相对薄弱的环节是在我们第二年的研究生课程中，在第一年的课程和研究前沿或接近前沿的高级课程之间，课程设置不足。我们打算为一些VIGRE支持的博士后提供在研究生二年级举办他们领域的研讨会的机会，以代替常规教学。博士后和学生将在非正式会谈中介绍重要的基础材料。这将产生有益的影响，使这些年轻人有机会在比本科教学更高的水平上发表演讲，并将促进博士后和研究生之间的互动。芝加哥大学的本科教学非常明确地建立在一个垂直整合系统的基础上。数学可能令人生畏，这是不言自明的。人们需要在提问时感到自在。他们需要耐心的帮助才能理解。他们不应该害怕暴露自己的无知。我们使用垂直整合，在一个友好和无压力的环境中提供最大的学习机会。通常情况下，人们发现那些只比自己年长几岁的老师比那些年长很多的老师更不令人生畏。当然，情况并非总是如此，这也不能成为高级教师在各级教学中缺乏参与的理由。更确切地说，这是一个关于合作教学的争论，一个年长的和年轻的老师一起工作。我们的教学是小班授课，由教师和研究生助理授课，或者由研究生在本科生的帮助下授课。这种教学方法在教师和研究生以及研究生和本科生之间建立了牢固的联系。上述由博士后举办的第二年研究生研讨会的想法是这一想法的延伸。本科班级通常不超过25名学生，每年教授200多个季度课程。高级本科课程由初级和高级教师独家授课。他们的助手是“学院研究员”，他们是研究生二年级的学徒教师。学院研究员会旁听课程，主持问题和复习会议，有办公时间，并偶尔授课。他们向教师提供反馈，使他们能够立即审查和扩大尚未被很好地吸收的材料。较低水平的课程，低于荣誉微积分，主要由研究生讲授，但并非全部由研究生讲授。他们由作为导师和评分员的本科生协助。在我们三个轨道中最低的微积分课程和其他一些较低水平的课程中，每堂课都有几个导师。辅导老师以学生为小组，通常是8-10名学生为一组，帮助他们在一个开放和无威胁的环境中获得自信和掌握。这种教学方法可以在保持我们传统的数学严谨水平的同时，教授数学背景相对薄弱的学生。导师们发现，辅导的过程提高了他们对数学的理解。同样，当学生对材料的任何方面有困难时，导师会向老师报告，允许即时反馈和课程修改。指导这些导师的研究生获得了指导他人的经验。本科生在我们最具特色的外展项目之一中也扮演着重要的教学角色，该项目每年7月将大约100名有天赋的芝加哥地区高中和初中学生带到系里。该项目是美国国家科学基金会青年学者项目的一个分支，为这些学生提供数学、计算机科学和物理方面的各种材料。它在几个轨道上运行，轮流使用主题材料，这样学生就可以在六个夏天的时间里参与并接触到新的材料。本科辅导员是这个项目成功的核心。担任辅导员的本科生也参加由讲座、学习小组和研究项目组成的reu型数学项目。在较低水平的本科课程和教学天赋的小学生的经验吸引了许多芝加哥大学数学专业的学生进入教学生涯。VIGRE计划将使我们能够为更多的本科生提供经过验证的reu型活动与外展服务的结合，而这在过去是可能的。我们的学生渴望得到这个机会。近年来，许多人都对芝加哥大学的季度时间表感到沮丧，因为他们无法参加其他地方的REU项目。REU的活动将由资深教师组织和管理，他们将进行系列讲座并提供监督。研究小组和研究项目将由四到五名本科生组成的小组进行，由VIGRE支持的迪克森导师和研究生指导。这种指导将大大加强REU项目，并大大加强迪克森教师和研究生作为大学教师的培训。在自愿的基础上，VIGRE支持的博士后和研究生将有机会参加RE

Proposal: DMS-9977134Principal Investigator: J. Peter MayAbstract: The University of Chicago's VIGRE ProgramVertical integration of teaching and research has been a tradition of the Department of Mathematics at Chicago for decades, and the very term "vertical integration" has been in use for over twenty-five years. Our program is based on both formal and informal institutionalization of interactions among people at different levels. The logic of vertical integration is based on the principle that people in our educational and research programs should learn from those more advanced and teach those less advanced. The VIGRE program will allow us to implement the principle more fully at several levels. The program consists entirely of direct support of postdocs, graduate students, and undergraduates. On average, 6 postdocs, 12 graduate students, and 18 undergraduates will be supported each year. This support will be used to further the training of these young people, to enhance vertical integration of the existing core research and educational programs of the Department of Mathematics, and to better integrate these programs with the outreach programs of the Department. We will briefly describe the Department's programs and VIGRE's impact on them, working from the top level down.At the highest level, it is departmental tradition that the advanced seminars and research level graduate courses are a communal exercise of tenured faculty, nontenured faculty, and graduate students. The form this has taken has intensified dramatically this year, with several year long topical seminars with a broad mixture of participants. The Department provides an environment in which postdocs and graduate students can maximize their potential to become productive research mathematicians. Most of our graduate students obtain first jobs at major research universities, and most major research departments have hired new Chicago PhD's in the last few years. The VIGRE grant will greatly aid in this by providing postdocs and graduate students with release time from teaching that enables them to focus more fully on research. VIGRE postdocs will have a decreased teaching load, and VIGRE graduate students will have periods free of teaching duties. We expect that this will allow greater numbers of them to complete their Ph.D.s in a more timely fashion.Our graduate program begins with an intensive first year of basic courses, and first year students have no teaching duties. There are no course assignments or examinations for graduate students beyond their first year. One relatively weak link has been in our second year graduate program, where there have been insufficient course offerings intermediate between the first year courses and the advanced courses at or near the frontier of research. We intend to offer some VIGRE supported postdocs the opportunity to run seminars in their field on the second year graduate level in lieu of regular teaching. The postdocs and the students will present essential basic material in informal talks. This will have the salutary effect of giving these young people a good first opportunity to present lectures at a higher level than undergraduate teaching, and it will foster interaction between postdocs and graduate students.Undergraduate teaching at the University of Chicago is very explicitly based on a system of vertical integration. It is a truism that mathematics can be intimidating. People need to feel comfortable to ask questions. They need patient help to reach understanding. They must not be afraid to show their ignorance. We use vertical integration to provide maximal opportunities for learning to take place in a friendly and unstressful setting. It is usually the case that people find those just a few years older than themselves to be less intimidating teachers than people considerably senior. This is certainly not always the case, and it is not an argument for lack of involvement of senior faculty in teaching at all levels. Rather it is an argument for collaborative teaching, where an older and younger teacher work together. Our teaching is done in small classes taught by faculty with graduate student assistants or by graduate students with assistance from undergraduates. This method of teaching fosters strong ties between faculty and graduate students and between graduate students and undergraduate students.The idea of second year graduate seminars run by postdocs described above is an extension of this idea.Undergraduate classes usually have no more than 25 students, and over 200 quarter courses are taught each year. Upper level undergraduate courses are taught exclusively by junior and senior faculty. They are assisted by "College Fellows," who are second year graduate students serving as apprentice teachers. The College Fellows sit in on classes, hold problem and review sessions, have office hours, and teach occasional classes. They provide feedback to the faculty that allows immediate review and amplification of material that has not been well assimilated. Lower level courses, below honors calculus, are taught primarily, but not exclusively, by graduate students. They are assisted by undergraduates who serve as tutors and graders. In the lowest of our three tracks of calculus courses and in a few other lower level courses, there are several tutors per class. The tutors work with small groups of students, typically 8-10 students to a tutor, helping them gain confidence and mastery in an open and nonthreatening environment. This method of teaching makes it possible to teach students with relatively weak mathematical background while retaining our traditional level of mathematical rigor. The tutors find that the process of tutoring enhances their own mathematical understanding. Again, the tutors report back to the teachers when students are having trouble with any aspect of the material, allowing immediate feedback and course correction. The graduate students supervising these tutors obtain experience in supervising others.Undergraduates also play a major teaching role in one of our most distinctive outreach programs, one which brings around 100 gifted Chicago area high school and middle school students to the department each July. The program, which is an outgrowth of the NSF's Young Scholars Program, offers these students a diversity of material inmathematics, computer science, and physics. It is run on several tracks with rotating subject material, so that students canparticipate and encounter new material over six summers.Undergraduate counselors are central to the success of this program. Undergraduates serving as counselors also participate in REU-type mathematical programs that consist of mixes of lectures, study groups, and research projects. The experience of tutoring in lower level undergraduate courses and teaching gifted grade school students has enticed many mathematics majors at the University of Chicago into teaching careers. The VIGRE program will allow us to offer the proven combination of REU-type activities with outreach service to many more undergraduates than has been possible in the past. Our students are eager for the opportunity. In recent years, many have been frustrated by the fact thatthe quarter schedule of the University of Chicago has prevented themfrom participating in REU programs elsewhere. The REU activities will be organized and run by senior faculty members, who will give lecture series and provide supervision. The study groups and research projects will be carried out by groups of four or five undergraduates mentored by VIGRE supported Dickson Instructors and graduate students. This mentoring will both significantly enhance the REU programs and significantly enhance the training of Dickson Instructors and graduate students as college teachers. On a voluntary basis, VIGRE supported postdocs and graduate students will have the opportunity to participate in the RE