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«TEACHING LARGE MATH CLASSES: THREE INSTRUCTORS, ONE EXPERIENCE Veselin Jungic, Deborah Kent and Petra Menz ABSTRACT. This article identifies ...»

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International Electronic Journal of

Mathematics Education


Volume 1, Number 1, October 2006


Veselin Jungic, Deborah Kent and Petra Menz

ABSTRACT. This article identifies challenges involved in teaching a mathematics class with 350 or more

students. It discusses issues of preparation, organization, course administration, instruction, use of

technology, and student management, while offering constructive help and useful techniques for teaching large mathematics classes. General reflections from three instructors on their large class teaching.

experiences are followed by a model of how large freshmen Calculus courses are conducted at Simon Fraser University in Burnaby, BC.

KEYWORDS. Large Classes, Mathematics, Teaching, Calculus, Online Assignments, Learning Management System.


In the current university environment, instructors are often called on to teach large classes, especially to incoming students. There have been some recent studies aimed at improving teaching and learning in a large class environment, but we have found no resources specific to teaching a large mathematics course (AUTC, 2001; Carbone, 1998; Gedalof, 2002;

Gibbs, 1992; MacGregor, 2000; Stanley, 2002). This article thus aims to identify challenges, offer constructive help, and share useful techniques for teaching large classes, which we define to be classes with 350 or more students managed by a single instructor. The included suggestions are drawn from the experiences of three instructors who taught large entry-level mathematics courses at Simon Fraser University for more than two semesters. General reflections on our shared large-class teaching experiences are followed by a case study about how we conduct a freshmen Calculus course. While there are concerns specific to large mathematics classes, the issues of preparation, organization, course administration, instruction, use of technology, student management, and grading are common to large classes of other subject areas.

The magnitude of undertaking large class teaching presents many obstacles. How does an instructor maintain a level of human interaction with so many students? How might one address challenges of scheduling office hours, dealing with e-mail, assigning homework, and recording grades on a large scale? Under these conditions, how does an instructor effectively communicate the subject material? Not only must the instructor organize the course and communicate the material as in a smaller class, but it is also especially important in a large class

–  –  –

to overcome difficulties of presentation and crowd control, while addressing freshman anxiety, providing feedback to students, and creating an atmosphere conducive to learning. Below, we describe challenges of administration, management, instruction, and interaction and outline techniques that we have used to meet those challenges in our collective experience teaching large mathematics classes.

A lecture hall filled with 350 or more entry-level undergraduates can be intimidating for both the students and the instructor. It becomes easy to ignore the importance of human interaction in this course format. These entry-level courses are content-heavy, fast-paced, and seem impersonal, which is often overwhelming for beginning university students (Erickson, 1991, pp. 29-45). Unfortunately, students who feel anonymous may not be motivated to attend class, much less seek help, ask questions in class, or communicate with other students and the instructor. Other types of students view the anonymity as an invitation to chat noisily even during lectures thereby showing disrespect for the instructor, fellow students and the course. On the other hand, the instructor looking out on a sea of dimly lit student faces can simply fail to see a timidly raised hand or to hear a cautiously ventured question. Sometimes, plunging onward with zeal to pass on knowledge can ruin opportunities for teaching and learning. Creating an atmosphere of learning where both the instructor and students take risks requires a certain level of comfort and experience in any course, but it is especially important in a large class to work towards an environment of individual learners rather than a mass of people. Person-to-person dialogue with students needs to be encouraged before, during, and after lectures to facilitate connections between the instructor and students, thus providing a platform for asking questions.

We have found that electronic communication such as e-mail and discussion boards increases interaction with students. Soliciting student feedback mid-semester not only gives students an opportunity to comment on the course, but also gives the instructor an opportunity to value student input and suggestions.

An instructor teaching a first-year university course has seemingly contradictory tasks to balance. On the one hand, the instructor has a responsibility to teach foundational material and – in an aim to prepare students for future courses – to establish a level of rigor appropriate for university courses that is new to most freshmen. Such introductory courses often serve a gatekeeping function and issue early warnings to those students with inadequate academic abilities or working habits. On the other hand, the instructor plays an important role in welcoming, encouraging, and supporting students during one of the major transitions in their lives. Clearly communicating expectations for student work in the course, such as how much time they should plan to spend outside of class or how to study and prepare for class, can help smooth the adjustment to university life, (Davis, 1993). Often, it can be beneficial for both the instructor and the students of introductory courses to acquaint students with information about resources that offer guidance for the first year (Erickson, 1991).

International Electronic Journal of Mathematics Education / Vol.1 No.1, October 2006 3 There is no unique solution to the problem of managing a large class, since individual instructors vary and different institutions uphold different requirements and maintain a variety of expectations. It is our opinion, however, that managing a large group of students requires advanced organization and detailed planning. Students in a well set up course are better able to focus on their learning rather than dealing with logistical issues of where to hand in or pick up assignments, where to turn for help, and so on. Before the course begins, the instructor should distribute the course material over the given time period, set midterm and final exam dates, select questions for homework assignments and assign their due dates, select old exams for students to study from, choose office hours – typically three per week, settle on a grading scheme, and define course and lecture policies.

The use of contemporary technology greatly simplifies the huge task of managing a large class. We have found course web pages invaluable for administrating and communicating with large classes. A standard way of maintaining a course web page is through one of many existing learning management systems (LMS). A typical LMS contains a grade book, chat rooms, and a discussion board. A course web page thus allows for communication between the instructor and the students, as well among the students themselves. With e-mail and an LMS, each student in the class is easily reachable by the instructor. From the discussion board the instructor can take the pulse of the class. What confused students? Were certain examples helpful or unclear? What additional examples might help? Often, common concerns arise in a chat room and these can then be addressed by the instructor in the lecture setting. A typical LMS also has a bulletin board where the instructor can post various course materials – such as the course outline, lecture notes, assignment solutions, and old exams – for the students. Other examples of possible use of technology in teaching a course are online quizzes and online surveys. Online quizzes and assignments could be used both as tutorial and assessment tools, while surveys allow the instructor to receive timely feedback on the course.

One specific benefit of a web page is the ability to communicate a lecture policy early and so set the tone for the course. In this policy the instructor outlines rules of conduct expected during a lecture: no talking when the instructor speaks, raising a hand and calling the instructor’s name when a question arises, turning off of all electronic communication devices owned by students, and so on. This policy not only helps set the tone of the lectures, but it also and helps with classroom management in a large class.

Although structure is necessary for a smooth semester of large class teaching, it is important to build in some flexibility as well. Common student problems like illness, procrastination, cheating, and family deaths will naturally arise more frequently than in a smaller class. The instructor should anticipate exceptions and have a policy at hand to deal with these matters in a manner fair to all students. For example, the grading scheme is a policy that applies for all students, but this does not mean that an instructor cannot make an exception when a situation warrants it.

Jungic at al.

Managing a class of several hundred students is certainly a demanding job, but it cannot consume all of the instructor’s attention. In fact, the infrastructure for course administration should be running smoothly so that the instructor can primarily focus on delivering the subject material. Likewise, the instructor cannot focus too much on being a disciplinarian because the presentation and delivery of the subject material requires preparation and organization. Careful time management is thus another essential component of large class instruction. Often this requires adjustments from smaller class teaching. For example, reducing the material presented in the classroom from two applications to one allows more time for questions from a large body of students. Skipping steps in proofs or calculations is another option to create more time;

however, the instructor should only opt for this method of teaching when just a rough proof outline is sufficient or the instructor has established that the students are able to follow the sketchy proof. Sometimes, explaining a single example twice, slowly and in detail, is more effective than covering a handful of different applications.

These are helpful methods for maximizing time, but we have found that the most effective way to use time efficiently in a large class is simply to prepare typed lecture notes for students in advance. These notes list motivations, definitions and theorems that will be presented in the lecture. They also include unsolved examples and applications that will be worked out in class. Providing these notes in electronic format a few days ahead of time allows students to print them out and to come to the lecture prepared. Students who are not hunched over, frantically working to copy down detailed mathematics can better concentrate on the presentation. The details are in the notes, so more class time can be spent communicating the bigger picture, clearing up confusion, and motivating students to work outside of class. Instead of talking to a room full of bent heads, the instructor can explain definitions and theorems to students that have been given the opportunity to pay attention. Furthermore, the instructor can demonstrate how to read examples and applications effectively and allow time for more questions.

It is very likely, that an instructor new to a content-heavy course will not get through as many examples and applications as were planned. It is therefore especially important to motivate students to learn more on the subject matter outside of the lecture hall. Online quizzes on present lecture material that are due before the next lecture are an effective method in keeping students on the task of learning the material outside the lecture. If the quizzes are also designed around definitions and theorems, then it encourages students to engage in reading the textbook on a deeper level as well. Furthermore, this method provides opportunities for students to see more examples and applications when an instructor is unable to give that many in a content-heavy course.

The delivery of a lesson deserves a few more remarks. In our experience, a large class is far less tolerant of small, common human errors such as making a calculation mistake, getting stuck in an explanation, loosing a train of thought, or forgetting a formula. We believe that an International Electronic Journal of Mathematics Education / Vol.1 No.1, October 2006 5 instructor of a large class is much like an actor on a stage and in that role must also rehearse. It is important to proofread one’s slides and to go through the lecture mentally, noting where time can get created and where it cannot. New terms and concepts must be clearly and slowly introduced, not just orally but also visually. Just like an actor, an instructor needs to have a vast repertoire of effective lecture methods on hand. Students can benefit from being kept on their toes and surprised every once in a while. “[Students] would welcome being able to make use of the many different perspectives, knowledge-bases, interests and approaches present in their community of learners, when they are learning mathematics” (Burton, 2004, p. 179). For example, slicing fruit to demonstrate the disk and shell method is an unexpected approach.

Getting students involved in demonstrations can be effective, too. Another idea is to bring in graphics or animation projections that further aid visual understanding of a concept.

Furthermore, maintaining high energy and communicating your enthusiasm for the subject throughout the lecture helps to retain student attention. You should use the vast space of the large lecture hall to maximum advantage. Moving around the auditorium not only helps to hold students’ attention, but it also helps to reduce chatter, which saves precious class time otherwise spent to get the lecture hall in order.

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