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Teaching and Managing Large Undergraduate Mathematics Courses
A Few Definitions and a Goal
This column is about teaching and managing large undergraduate mathematics courses. But what do we mean by that? And what role do we (or you) have in teaching and managing such courses? Let’s start off by laying out some of the possible contexts to which we could be referring. At our institution, “large” means total enrollments of between 500 and 2,000 students—we are at a large, public, R1 type of institution. But large enrollments do not imply large class sizes: we teach most of these courses in many small sections (of around 24 students), for which a mix of graduate students, postdocs, non-tenure-track faculty, and tenure-line faculty are the instructors of record. At other institutions, and in other courses at ours, this number of students may be taught in lectures of 100 or more students, possibly with recitations or labs. Clearly, the course structure that is possible in these different contexts varies widely, and changes both teaching and coordination: teaching 24 students is very different from teaching 300, and coordinating a team of 6 to 20 instructors is very different from coordinating a team of 70 or more.
While managing courses with large enrollments depends on how they are divided into sections, there are some common tasks or goals. For us, the course manager (“coordinator,” in our parlance) sets the daily schedule for the course, determines the content of all course-wide assessment instruments (exams, written homework, web homework, mastery assessments), sets dates for web homework and mastery assessments, and is the communicator-in-chief who works with all the instructors teaching the course. The first part of this (up to the “communicator-in-chief” bit) is pretty common whether we’re coordinating 75 sections of 24 students each, or 10 sections of 100 students. The number of sections matters, however, to the role of the coordinator: both because of the number of sections they need to oversee and be engaged with, and the number of instructors they are helping to teach the course.
With those definitions out of the way, maybe you are teaching in a large, coordinated course; or maybe you are going to be coordinating such a thing; or maybe this type of teaching or coordination is something you’re interested in as a possible career; or maybe you want some perspective on how this plays out. In the following, we’ll discuss these different areas in the context of research on student learning and equity-focused instruction.
Teaching in a Managed Course
We should start a discussion of teaching in a large, coordinated course with all of the recommendations that are applicable to mathematics teaching more generally: we know that active learning results in better student performance and retention than more traditional, passive forms of instruction
What is different when teaching in a managed course is that we do all of this in a framework in which we may have limited control of course structure and material. In coordinated courses at our institution, the daily schedule and the majority of formal course assessment is determined by the course coordinator. Thus, as an instructor in this system our goal is to embrace active learning and inclusive teaching in a manner that best promotes our students’ learning; and to ensure that the structure, assessment, and goals of the course are transparent to our students (which is itself essential to equity-focused instruction). When we are developing a course that we are teaching alone, we start with the goals we have for our students and create a pedagogical and assessment structure that will facilitate their accomplishment of these goals. When we are teaching a managed course, we start by developing an understanding of what the course structure and goals are, and then structure our instruction and classroom in that context.
It’s worth noting that because we know that active, equity-focused classrooms are the best way to promote student learning and success, their use in a managed course serves the course goals of having students succeed in the course and learn a specific canon of material! We just need to think about what students should get from the course and how to engage students to achieve that.
In some respects, a takeaway here may seem negative: we want to do what we would normally be trying to do in a classroom, but with less control and with a population of students that largely doesn’t want to be in the course and expects it to be designed to push them out of mathematics. But there’s an ace that we’re given as instructors of these courses: because we aren’t the coordinators, we are able to more convincingly position ourselves as being on the side of our students. In fact, in the coordinated courses at our institution we tell our instructors to take full advantage of the fact that they can say both “there is a reason why we are doing things this way” (that is, there are pedagogical arguments for our structure and course goals) and “unfortunately, that’s the way the coordinator requires it to be done, but I want to help you succeed and beat the system.” Many of our most successful instructors are those who are able to parlay this into their students’ (correct!) understanding that their instructors are on the students’ side; they truly want their students to succeed in the course, and believe they can.
Managing a Coordinated Course
Let us now turn the discussion around: if we are in charge of a course, what do we need to think about and do? Of course, a lot of this starts from the same point as our discussion of teaching: we need to think about how the course can be centered around active, equity-focused instructional techniques. And we need to do this in the context of having many different instructors teaching many students in many sections. We stress that this is completely nontrivial, and is worthy of an entire article itself. We do not attempt, therefore, to address the course design question of how to create this type of curriculum or pedagogical structure for a coordinated course. We focus instead on the mechanics of coordination, given the existence of the course structure: communication with instructors and students, and understanding what the course is and needs to do. This includes communication about, and work to encourage and support, the use of equitable and effective teaching strategies, but we will leave the question of what is possible and how to design it into a course for another piece.
We observed when discussing teaching in a coordinated course that we don’t have to set the course structure. As a coordinator, of course, we do! In many cases we will be picking up the reins of an existing course, with an existing structure and set of expectations. If that is the case there is a good argument for changing things incrementally: in many of these courses most of the structure is there for a reason, and it’s always better to understand why something is as it is before changing it and discovering that there was a lot that it was supporting. Changing course content requires awareness of the needs of a large student population from many programs; changing the assessment requires understanding of what students can do and instructors can grade; and so on. With this in mind, let’s think first about the actual instruction in the course, and then build out from there.
How we are able to shape the actual teaching in these courses is a function of the course structure (large lecture, small class, etc.), course instructors (tenure-line faculty, non-tenure-line faculty, postdoctoral faculty, graduate students, etc.), and precedent. If the course is taught in many small sections by graduate students, it is much easier to say that they must use active learning in the classroom (and expect that we have the authority to impose that requirement)—but it may be much harder for them to do it, and for us to know what is actually happening in a multitude of classrooms. If the course is taught in a handful of lectures of 100 or more by tenure-line faculty, it may be much harder to impose a teaching style—but much easier to know what is actually going on. But in either case, we need to think about what it is possible for the instructor to do in the space in which they are teaching (both to engage students and to create a supportive and equitable classroom community), and how best to support our instructors to do that. In particular, we want our classrooms to include significant active learning. To promote active learning in a course taught in many small sections (e.g., a pedagogy centered around mini-lectures plus group work), we might provide training, lesson plans, and other instructional materials such as example worksheets or suggested group problems, as well as ongoing workshops, seminars, or course meetings to help them implement such an active learning classroom. Ideally, we also might provide instructors with an experience in which they can see and learn now to implement this type of teaching without having to be solely responsible for it before they are put into the classroom as the instructor of record. For example, in our training program we have instructors practice running interactive group work in much the same way as we have them practice lecturing, so that they are able to get (more) used to the demands of that instructional mode. To promote active learning in a course that is taught in large sections, we might include the use of an audience response system (“clickers”), or think-pair-share type activities. To support this type of instruction, we may need or want to provide course materials, such as lesson outlines and clicker questions, or group-worthy problems, along with information about how they might be used in class. We may need to have a presemester meeting to ensure that instructors are comfortable with the technology being used, and follow-up meetings to ensure that they are able to resolve any issues that they experience in using the techniques being emphasized for use in class. As noted above, for graduate students or postdoctoral faculty we might also provide training and practice opportunities.
In all cases, the effective use of whatever active-learning and inclusive pedagogy we are putting in our course requires instructor buy-in. An engaged, inspired instructor will do a much better job using these techniques than an unengaged, uninspired one. To cultivate instructor buy-in we may need evidence-based arguments for the use of these techniques, and significant departmental support to provide the authority to implement (or require) its use. It is also tremendously valuable to have some instructors who are willing to advocate to other instructors for the course model we are using.
Once we have an instructional model for the course there is the challenge of ensuring that instructors know what is expected of them, and that they know what they need as they are teaching through the academic term. In our experience, the challenges in doing this are significant. Communication of everything that an instructor needs to know about the course at the start of the semester requires that they absorb a very large amount of information at once, while a “just-in-time” communication model can result in the instructor not having the information that they need to respond to student questions early in the semester. Some instructors will be good at managing email communication about course topics; others may be better served by a channel on a networking site or a discussion board. In all cases, there is a need for communication of resources and structural information, and for more interactive communication centered on questions and answers to them. For many of our courses we have multiple modes of communication with instructors: a site where much of the needed information is available (e.g., a site in our content management system that is strictly for instructors of the course), a forum for questions and answers (e.g., a threaded discussion site for instructors), and direct communication between the coordinator and instructors (e.g., weekly meetings and email from the coordinator). These can all be effective, but all do depend on instructors taking the time to read and process the information. At the end of the day, this comes back to our observation that buy-in is a fundamental issue of instruction in a large course environment: if our instructors are concerned with their effectiveness and with their students’ learning, the work they do and the coordinator’s efforts to communicate with them are both likely to prove successful.
The second major communication hurdle for coordinators relates to students. In a small seminar one is teaching by oneself it is possible to have direct communication with every student in the class. In a coordinated course of hundreds or thousands of students, direct communication with every student is a recipe for unmitigated disaster. Ideally the coordinator has clear and effective channels of communication with their section instructors, and the instructors are effective in communicating with students. Our experience is that the reliability of this model decreases with the number of independent sections and instructors. As a result, we have multiple channels of communication with students as well, including a central site in our course management system (CMS)—or a template that allows us to prepopulate content in the CMS sites for individual sections, course-wide announcements that originate from the CMS, and email to specific students (e.g., exam accommodations) that originates from the staff in our department who support our large coordinated courses. In general, and especially if there are multiple people involved in the coordination of the course, it is helpful to have a coordinator email address or mailbox that can be monitored by multiple people and is a single commonly known contact point for the coordination team.
It is well worth adding that, in the same manner that instructor buy-in is critical to our success in these courses, student buy-in is similarly important. Engaged, motivated students learn. Our instructors are the best motivators for our students, but in our work as coordinators we can (and must!) also shape student opinion, even if we are only able to do this incrementally.
Conclusion
At the end of the day, or end of the semester, teaching in or managing a large coordinated course comes down to the same thing as teaching other courses—structuring our work to maximize the success of all of the students in the course. But in these large courses, accomplishing this requires that we communicate in a manner that teaching a smaller course does not, and that we stay on top of a large number of moving pieces and structural elements. As instructors, we are communicating with our coordinators to be sure that we know what our students need to succeed in the course, and are communicating that to our students as we teach. As coordinators, we are setting our instructors up to do this.
This type of communication also is a key aspect of equity-focused instruction, that allows us to support all of our students: transparency in expectations and clear communication of what our students need to do to succeed is central to inclusive, equitable instruction
This is not easy work, but it has a reward that can be tremendous: we have the potential to have a significant positive impact on very many students. As instructors we are part of a team that is building this impact across many sections. As coordinators, we are building this team so that all of our instructors engage with their students with active instruction that accomplishes this. We tell our instructors to pass the buck, saying that they are on their students’ side working to beat the system, and to use that to build a classroom community. But the reality is as coordinators and as instructors we are all—we must all—be on our students’ side in a positive learning community that enables all of them to succeed in our course.
References
[ 1] - CBMS Statement on Active Learning in Post-Secondary Mathematics Education.
[ 2] - S. Freeman, S. Eddy, M. McDonough, M. Smith, N. Okoroafor, H. Jordt, and M. Wenderoth, Active learning increases student performance in science, engineering, and mathematics, Proc. Natl. Acad. Sci. U.S.A. 111 (2014), no. 23, 8410–8415, https://www.pnas.org/content/111/23/8410.abstract.
[ 3] - Elaine Seymour and Nancy M. Hewitt, Talking about Leaving: Why Undergraduates Leave the Sciences, Westview Press, 1997.
[ 4] - D. B. Martin, Researching race in mathematics education, Teachers College Record 111 (2009), no. 2, 295–338.
[ 5] - M. Abell, L. Braddy, D. Ensley, L. Ludwig, and H. Soto, , MAA Press, 2017.
[ 6] - V. Sathy and K. A. Hogan, Want to Reach All of Your Students? Here's How to Make Your Teaching More Inclusive, Chronicle of Higher Education, July 22, 2019.
[ 7] - M. Winkelmes, M. Bernacki, J. Butler, M. Zochowski, J. Golanics, and K. Harriss Weavil, A teaching intervention that increases underserved college students’ success, Peer Review 18 (2016), no. 1/2, 31–36.
[ 8] - L. Hausmann, F. Ye, J. Ward Schofield, and R. Woods, Sense of Belonging and Persistence in White and African American First-Year Students, Research in Higher Education 50 (2009), no. 7, 649–669.
P. Gavin LaRose is a professor and Karen Rhea Collegiate Lecturer in mathematics at the University of Michigan. His email address is glarose@umich.edu.
Article DOI: 10.1090/noti3055
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Photo of P. Gavin LaRose is courtesy of P. Gavin LaRose.