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The Emporium Model

How to Structure a Math Emporium
Advice from NCAT's Redesign Scholars

In redesigning introductory mathematics courses, NCAT’s partner institutions have found that the Emporium Model has consistently produced spectacular gains in student learning and impressive reductions in instructional costs.

Two different versions of the Emporium Model have been successful. In both versions, mandatory attendance (e.g., a minimum of 3 hours weekly in the emporium) ensures that students spend sufficient time on task and receive on-demand assistance. In both versions, mandatory weekly group meetings enable instructors to follow up where testing has identified weaknesses or emphasize particular applications. Group activities help build community among students and with instructors.

Flexible Attendance: Mandatory lab hours may be completed at the student’s convenience. Examples:

Fixed Attendance: Mandatory lab hours are scheduled by the institution for student cohorts. Examples:

NCAT Redesign Scholars Phoebe Rouse and Kirk Trigsted originally created this FAQ to answer commonly asked questions about how to structure math courses using the Emporium Model. The FAQ has been modified to differentiate between the two versions described above, which reflect new implementations of the original model that adapt to particular institutional constraints. For some questions, the same answer applies to both the Flexible Attendance and Fixed Attendance versions. For other questions, the answers are different.

Course Structure

Q: Should lab hours be required?

A: Don’t even bother to redesign if you are not going to require lab hours. There are mixed opinions about whether or not students’ required hours should be reduced throughout the semester if they earn a certain grade on each test. Some institutions, for example, lessen the required time in the lab if a student earns a B or better; others do not lessen the required time.

Q: How many lab hours should be required each week?

Flexible Attendance A: In most institutions, for a three-credit-hour course, three hours are required in the lab (along with one hour required in the classroom). For a five-credit-hour course, five hours are required in the lab (along with two one-hour meetings required in the classroom).

Fixed Attendance A: In most institutions, students are divided into course sections and meet at fixed (scheduled) times in the lab with an instructor equivalent to meeting times in the traditional format--i.e., two or three times a week. In addition, students may also meet with the instructor in a classroom for one hour per week.

NOTE: At some institutions, students only meet in the lab—i.e., there is no weekly class meeting.

Q: If we only meet in a classroom once a week, how can we possibly teach a week’s worth of material in 50 minutes?

A: Don’t try to “teach a week’s worth of material.” The goal of the weekly class meeting is to focus students’ attention on the week’s upcoming tasks. Here are some tips for what instructors should do in a weekly class meeting:

  • Start out with a short recap of the previous weeks’ material, especially if it leads into new material.
  • Give an overview of the week’s new material.
  • Cover important concepts and work especially difficult examples, pointing out common errors.
  • Focus on examples that combine multiple skills and concepts.
  • Review the schedule of work due for the week.
  • Discuss study strategies.
  • Be sure to take attendance.
  • Above all, do not try to cram in a traditional lecture and do not go over homework.

Q: How can students possibly learn the material if we don’t teach it to them?

A: About 75% of the student learning takes place in the lab setting. The instructor role in the classroom is to guide students, pull concepts together and help them avoid common pitfalls. Your role as sage-on-the-stage is diminished. You trade that role for tutor-in-the-trenches while students are doing their work independently. This is a huge adjustment for many experienced instructors and inexperienced instructors as well.

Q: How many students should be in the weekly class meeting?

A: Careful consideration should be given to the size of a section. Most institutions' sections contain between 25 and 45 students, which works well. Some institutions have much smaller sections, and others have much larger sections (some have 80 and a few have as many as 300.) Regardless of the size, the key point is to structure the activities of the weekly class meeting as described above.

Q: Doesn’t the Emporium Model reduce the interaction between students and instructors?

A: On the contrary, there is more interaction between students and instructors than ever before, and that interaction is more meaningful, more individualized and more focused. The main reason why students learn better in this model is that they are less passive and more actively involved doing math, and they receive help based on their individual needs.

Q: How do we get students to go to the weekly class meeting and to the lab?

A: You will never get all students to attend the weekly class meeting or put in the required hours, but you can get most students to attend regularly by making class and lab participation at least 10% of the final grade. (Some advocate giving a higher percentage for participation.) This is extremely important. Without giving course points for participation, success rates will be very low.

Q: Can students do homework and quizzes outside of the lab?

A: Absolutely. Encourage students to work as much as possible on math anywhere and anytime, but only give participation credit for time spent in the lab with tutors available and with certainty as to who is doing the work.

Course Personnel

Q: Who should be responsible for the course?

Flexible Attendance A: Some one needs to take overall responsibility for ensuring that the course works well, that all students have the same learning experiences and assessments, and that all course policies and procedures are implemented consistently. Make sure that you have a course coordinator who can offer the necessary leadership. At the same time, it is important to emphasize teamwork and to involve others in the decision-making process.

Fixed Attendance A: Instructors are responsible for their individual sections as in the traditional format. In smaller institutions, the department chair usually has overall responsibility for ensuring that the course works well, that all students have the same learning experiences and assessments, and that all course policies and procedures are implemented consistently. In larger institutions, a course coordinator may assume that responsibility.

Q: How much training is needed for instructors?

A: Instructors working in a redesigned setting for the first time need enough training to understand the new philosophy of teaching that is required because a change in the basic mindset must take place. Some people embrace this change immediately, while others may have to be dragged along. Here are some tips:

  • Plan to get instructors involved as early as possible.
  • Involve instructors in curricular decision-making.
  • Offer workshops with discussions and presentations.
  • Bring in guests from other schools that have successfully implemented an emporium.
  • Hold a workshop for instructors new to redesign at the beginning of each semester.
  • Then hold a meeting with all instructors for the semester to review old policies and point out any new ones.
  • As the semester progresses, meet frequently with all instructors to offer ongoing training. Some institutions meet weekly, others meet on a less regular basis.

Q: How does the instructor’s role change?

A: Faculty members no longer spend time preparing lectures, grading homework or preparing and grading tests. Therefore, they can dedicate more time to helping students. The faculty role becomes one of facilitator of student learning and guide of each student’s study in math. Instructors meet with classes, in or out of lab, tutor students, counsel students, monitor each student’s progress and provide support and intervention as needed. Instructors may also lead small-group discussions on topics particularly difficult for groups of students.

Q: What redesigned teaching load is equivalent to a traditional three-credit-hour course?

A: There is no simple answer to this question since every institution and every department has a different set of "rules" (policies and procedures) in regard to faculty load. Redesign will require you to revisit some of those rules because of the way that redesigned courses are structured. A teaching assignment that used to be a three-day-a-week hour-long lecture with paper assessments is now very different since the software both provides most of the "lecture" and automates most of the assessments.

A common assumption in higher education is that instructors spend two hours outside of class (preparing and grading) for every one spent in class. That means that a three-credit course typically requires the instructor to spend nine hours per week on the course. Since both the in-class time and the preparation and grading time are reduced in the Emporium Model, you need to reallocate instructor time accordingly. This might translate to something like two one-hour weekly class meetings, two hours for preparation and five hours in the lab tutoring students each week. You will need to make decisions based on your own institutional "rules" and the changes you have made in the redesigned course structure.

In addition, many institutions ask instructors to schedule some of their office hours in the lab, which adds to the number of hours they spend in the lab, so that they can provide assistance to all students in the lab when they do not have scheduled appointments with their own students.

Q: How many tutors will we need in the lab?

Flexible Attendance A: For the first three to four weeks, you will need one tutor for every 15 students. As the semester progresses and students become familiar with the lab and the software, that ratio drops down to 1:25 and often is as low as 1:40 by the end of the semester. If testing is done in the lab, be sure to have an appropriate test proctor (rather than student tutors.)

Fixed Attendance A: In this version of the Emporium Model, instructors meet with their individual sections in the lab at fixed times. Additional tutors may be needed during those times and are definitely needed at times when the lab is open but there are no scheduled classes. The ratios described above for later in the semester then apply. If testing is done in the lab when classes are not scheduled, be sure to have an appropriate test proctor (rather than student tutors.)

Q: Who are the lab tutors?

A: You will need your instructors to tutor in the lab; their presence is essential. In addition, undergraduate math majors and other interested undergraduate students make excellent tutors. Volunteers from the community such as retired high school teachers can be used to tutor. Adjunct faculty may be paid extra to work additional hours in the lab. Math graduate students can also be used if they are available. All tutors must be trained to guide and lead students along rather than just giving students the answers.

The Lab

Q: How should we track lab participation?

Flexible Attendance A: You will need a system to track students using a commercial product or a homegrown program. Most institutions use a card swipe with student IDs and have some mechanism to move this information to specific instructors on a weekly basis by email or by direct download to grading software.

Fixed Attendance A: Instructors take attendance via a sign-in sheet when their sections meet in the lab. For institutions that also require students to spend additional hours in the lab, you will need a system as described above.

Q: How can we smooth out demand for the lab throughout the week?

Flexible Attendance A: While there are typically peak usage times in the lab, it is important to stagger your due dates and your weekly class meeting times to spread out demand on the lab since most students tend to do their work at the last minute--i.e., don’t have all weekly class meetings on the same day of the week and don't have all assignments due on the same date of the week.

Fixed Attendance A: In this version of the Emporium Model, demand is smoothed out by scheduling weekly class meetings appropriately.

Q: What are the peak times in the lab?

Flexible Attendance A: Of course, this varies among institutions, but many institutions have peaks around 10:30 AM, 1:30 PM, and again around 6 PM. For some unknown reason, it appears that Tuesday afternoon is the busiest time at many institutions. Keep track of lab attendance every quarter hour, put this in a table and study it to determine staffing decisions for future semesters.

Fixed Attendance A: In this version of the Emporium Model, peaks are managed by scheduling section meetings appropriately.

Q: How do we determine how many computers we need in the lab for students?

Flexible Attendance A: This is a difficult question to answer without knowing specific facts about your particular situation. Here are some things to consider:

  • There is obviously a relationship between the number of hours that the lab is open and the number of computers needed. (The more hours you are open, the fewer computers you need and vice versa regardless of the number of students enrolled in the course.)
  • You should carefully stagger your due dates and your weekly class meetings to even out the times students go to the lab.
  • Even with careful scheduling, all open labs experience peak attendance periods (for some it’s late afternoon and early evening; for others it’s early afternoon and early evening.) Planning must take this into account—i.e., you do not want students arriving at the lab to find that all computers are taken.
  • You should determine when the lab will be open based on your institution’s demographics, especially when students tend to be on campus.
  • If possible, create a space within the lab for students to use their own laptops to supplement the number of pcs you need.

Many of the redesigns that use the Emporium Model have large number of students and keep their labs open 60 or more hours per week. In addition, their campuses are primarily residential, which means that student participation is relatively evenly distributed throughout the day. Their experience, based on requiring three hours of lab participation per week per student and keeping the lab open 60+ hours per week, translates into the following rule of thumb:

The number of computers required = the number of students/15 if you do not test in your lab or the number of students/11 if you do test in your lab.

Examples without testing
1000 students/15 = 67 computers
800 students/15 = 53 computers
500 students/15 = 33 computers

Examples with testing
1000 students/11 = 91 computers
800 students/11 = 73 computers
500 students/11 = 46 computers

While the numbers shown above translate roughly to 4 computer hours per student if you do not test and 5.5 hours per student if you do test, the large number of open hours and the relatively even distribution of student participation are necessary components of making those ratios work. Once your lab is open fewer hours, which may be necessary because of staffing constraints, lab availability or student attendance patterns, these ratios do not hold. Smaller numbers of students and smaller numbers of open hours create additional constraints that require special attention in order to make an open lab work.

Example
200 students
Lab is open 20 hours per week
Requires 40 computers
Ratio = 5:1

Example
240 students
Lab is open 12 hours per week
Requires 120 computers
Ratio = 2:1

Fixed Attendance A: If you do not have a large lab and/or your numbers are small, we strongly recommend that you schedule lab hours for students rather than rely on an open lab in order to be sure that the number of computers available match student demand. What is most important in the Emporium Model is that students are working in the lab the requisite number of hours, not the flexibility of those hours. Block scheduling can be equally effective as open scheduling in this model.

While the lab should include sufficient numbers of computers for each student to have one during scheduled times, some additional computers should be available for those students who would like to work additional hours in the lab beyond the scheduled meeting times.

Q: Should students get partial credit for spending part of the required time in the lab?

A: There is some disagreement on this, but most institutions do not give partial credit. The reason for not doing it is that if you do, students will decide what grade they want and spend only that percentage of the required time in the lab. Unfortunately, they often misjudge.

Q: How can we stop students from doing things other than math in the lab?

A: You need strict rules and you need to enforce them. Students caught violating the policy must have a severe penalty such as loosing participation credit for the week. Be sure to put this in the course syllabus. Lab computers can be set to allow access to only certain IP sites, and tutors walking around the lab can observe what students are doing.

Assignments

Q: When should quizzes and tests be due?

A: This varies a bit based on the specific model, but in general homework should be due either the night before or two nights before the weekly class meeting. Often quizzes are due the night before the weekly class meeting.

Q: What assignment setting is best for homework, quizzes and tests?

A: Homework: should be open from the beginning of the semester with unlimited attempts prior to the due dates. Feedback should be immediate with the opportunity to rework an exercise until mastery. Mastery levels can be set before students are allowed to move on to the next homework assignment. Students should use all tutorial resources available to them for homework.

Quizzes: should be set so that no tutorials and no feedback are allowed until submission. Remember that quizzes are preparation for tests. Students should be given many attempts to retake quizzes. A common number used with success is 10 attempts. Questions on quizzes should be pooled so that additional attempts allow students to see a range of exercises within one objective. Students should not be able to go back and rework individual exercises on a quiz to improve their grade on it. Often quizzes are timed to give students a more realistic sense of the upcoming test situation. The best score should be kept to encourage students to continue to take a quiz to improve their grade or just to get additional practice with no penalty.

Tests: can be attempted just once or multiple times depending on whether or not some plan is in place to require time to pass for students to re-prepare for a retake. This often depends on the resources of the institution and the level of the course. Multiple testing opportunities are a must if mastery is required.

Q: How should we handle testing?

Flexible Attendance A: This is a difficult question to answer without knowing specific facts about your particular situation. Here are some tips that apply to most situations.

  • Stagger the testing schedule to reduce overloading the lab.
  • Allow students to schedule their tests online if the testing schedule can be flexible. If you do this, give a deadline for students to schedule. Beyond that deadline, students have in effect missed the test and get a grade of zero. This may sound harsh, but if you don’t do this, you will have a huge mess that is unfair to students who followed the policies.
  • Allow students to take their test before the deadline as long as there is a test proctor present so that they can proceed through the course at a faster rate.

Fixed Attendance A: In this version of the Emporium Model, testing is managed within the weekly class meeting. At some institutions, students are permitted to test anytime the lab is open and an approved test proctor is present.

Additional tips:

  • Provide scratch paper for students using varying colored paper, pick up the paper as students leave, and shred the paper after the testing window closes. Some institutions return this paper to students. If you choose to do this, be sure to have a system in place.
  • Watch calculators carefully. Many new scientific calculators have symbolic manipulation capabilities, so do not allow those unless you specifically choose to do so.
  • Insist that cell phones and other like devices are not allowed.
  • Create a plan in advance to handle technology issues and makeup tests. These will inevitably arise.