Last month, in MOOCs Revisited, I looked at one version of the use of online resources. This month I’d like to comment on another approach to using technology to improve student learning while cutting costs, the Math Emporium, first adopted on a large scale at Virginia Tech. It shifts math classes from large lecture halls to computer labs where students are required to put in a certain number of hours each week in which they work through computer supplied problems while wandering tutors help those in difficulty.

My column is inspired by a visit I made in February to a large public university that uses a Math Emporium for their pre-calculus courses: Intermediate Algebra, College Algebra, Trigonometry, and Pre-Calculus. Their operation is on a large scale. Just over 4,000 of their students took one of these four courses in fall 2014. This was my first opportunity to observe and probe the workings of a Math Emporium. This column, however, is not about what I found at that particular university. Rather, I am using that experience to reflect on what I see as the strengths, weaknesses, and possibilities of the emporium model.

As I observed the workings of the emporium, I noted four distinguishing characteristics:

**Self-pacing.**The fact that computers mediate almost all of the learning means that students have a great deal of flexibility in the pace at which they proceed through the course. This was particularly appreciated by returning adult students and those for whom their last mathematics class was in the distance past. For them, it was helpful to be able to work at assignments until they were correct and postpone quizzes until a level of mastery had been achieved.

**Compulsory laboratory attendance.**In the emporium that I observed, students were required to spend at least three hours per week in the laboratory, a tightly structured environment in which they had access to nothing except their computer, which was locked onto that week’s lessons, videos, homework problems, and quizzes. For three hours a week, there was nothing they could do except work on mathematics. Almost all of the students I talked with chafed at this. They would prefer to do this work in a more personal and relaxed environment. Yet, the fact is that many students, especially those at most risk, do not know how to structure their time effectively. The lab forced a structure on them.

One lesson I took away from the particular emporium I visited was the importance of a welcoming environment within the computer lab. The prospect of being forced to spend time in a sterile, unfriendly room can be a strong disincentive to enrolling in a math course run in the emporium model.

**Tutoring.**An essential feature of a Math Emporium is the presence of tutors circulating among the working students. Students can use the computer to signal a request for a tutor, but often the interaction happens more informally when a student catches a tutor who happens to be walking by. Moreover, tutors are trained in how to identify students who are struggling and how to offer assistance. Not all students are willing to signal for help.

Help in the laboratory comes from three categories of personnel. There are the instructors responsible for setting the syllabus, homework assignments, quizzes, and exams as well as meeting regularly with the tutors to prepare them for potential student difficulties with the upcoming materials. Spending time in the emporium is part of their responsibilities. There are graduate students, usually in their first year, for whom this is their work assignment. And there are undergraduate students, many of whom also experienced the emporium as students. Talking with students, it is clear that the dedication and abilities of the tutors, especially the graduate students, vary widely.

The particular university I visited continues to run one 50-minute lecture per week for each class of 300 to 400 students. It serves as an introduction to the material but offers little to no opportunity for student/faculty interaction. However, I found that most of the students identified strongly with their instructor and preferred to snag him (none of the instructors are women) when in the emporium. As a helpful feature, the screens are color-coded so that instructors can identify the students in their classes from a distance, and student names are prominently displayed on the screen so that instructors can pretend they know them by name.

This raises an interesting point that I touched on last month: For most students, it is important to have some sense of a personal connection with their instructor. One can question how much benefit students derive from their once-a-week 50-minute meeting with the instructor in the company of 350 other students, but the students with whom I talked did feel some connection to their instructor, strengthened when the instructor would stop to talk with them in the emporium. Many of them chose the time they came to the emporium by when they knew their instructor would be present.

**Assessments.**Students know that what counts is what is on the test. One of the major drawbacks of purely computer-mediated testing is that the problem format has usually been restricted to multiple choice and short answer questions, a format that enforces a view of mathematics as a collection of procedures to be mastered, with little opportunity for assessing the development of a structured understanding of the undergirding principles.

For the courses at the Math Emporium that I observed, high school courses that many if not most of the students are repeating, there may be a case for instruction focused on one-step procedural fluency. Nevertheless, one of the dominant complaints among the faculty in this Department of Mathematics was that the students enter calculus with little experience in multi-step problem solving or justification of what they have done. Technology is changing what can be assessed, but changing large-scale assessment to capture multi-step problem solving and conceptual understandings is still difficult.

The Math Emporium was created as a response to the reality of teaching large numbers of students with few instructors, combined with the recognition that large lecture classes were not working. Large lecture classes can work, as attested in Frank Morgan’s Huffington Post blog, “Are smaller college calculus classes really better?”. In fact he quotes my observation from the MAA National Study of College Calculus that revealed no correlation between class size and changes in student attitudes. But I think that lack of correlation has more to do with the fact that classes of any size can be taught poorly than that class size is really immaterial. Furthermore, I am unconvinced by Frank’s examples of large lecture classes that work. All of his examples are at institutions with very highly motivated students who know how to study on their own. I also believe that, while 100–120 students constitute a large class, there is a qualitative difference between large classes of this size and classes of 300–400 students where instructors cannot possibly monitor or encourage the performance of more than a small number of their students.

The Math Emporium is far from the ideal of what we would like undergraduate education to be. Unfortunately, that ideal is incredibly expensive. The emporium model does provide a relatively inexpensive means of structuring how students study, monitoring their progress, and providing some degree of individual attention. There is every reason to believe that it provides a framework that can work for many students. Moreover, there are and will continue to be opportunities to improve its effectiveness.