Emerging Trends in
The Math Emporium
• Ever had to take an introductory math class with
499 other students?
• Ever find that you had no idea what was going
on in the class?
• Ever realize you didn’t quite get the material
even though you did ALL the homework
• Welcome to the new idea gaining ground
at large universities-
• The Math Emporium
What exactly is the Math
• In an old abandoned store in a mall near to the
Virginia Tech campus, the math department has
installed tons of computers.
• They have created a space for students to go at
their own convenience to do homework
problems online, take practice quizzes and take
• The space is open 24 hours a day, 7 days a
How are they “taught?”
• Students are to attend a lecture once a week.
• The homework is then available at the emporium
• Homework and graded exams are proctored and
there is a a time window for completion.
• Weekly quizzes are required.
– The quizzes are offered on an honor code bases.
– Students can take practice quizzes as many times as
they want but must take the quiz one time for credit
before the week is over.
• The emporium itself is able to provide
human resources on a one-to-one basis to
students at the computer in a financially
• Course material and course testing is
entirely under control of individual faculty
members, and can be readily tailored to
meet special demands.
• The university
stresses that this is
NOT to be considered
• The key to this style of education is the “test
engine” provided by the emporium. Each time a
student calls up a quiz on the material under
study, he will receive a different set of problems.
• In fact, the test engine can create, practically
speaking, an almost unlimited number of
different quizzes on the same material.
• In this fashion the practice quiz functions as a
recitation, with the test engine providing
instantaneous grading of the material, as well as
comments and suggestions on problems the
student does incorrectly
• Initially designed as a resource for women’s
groups in Africa, this type of emporium set up is
being expanded to other courses besides math.
• We are already seeing courses of this type
offered in our middle school – Read 180.
• This is designed for low achieving students who
need the kind of repetition and reinforcement
offered in this kind of instruction.
Connection to Middle School
• The key to the effectiveness of most technical
courses is repetition.
• The conventional college course in the United
States uses homework in order for the student to
master material covered in the lecture.
• The drawback in the conventional method is that
the student typically tries each homework
problem once, and at a much later time is
advised as to which problems he completed
• With the testing machinery in an
emporium course, and the encouragement
for the student to practice each quiz and
test problem as often as he might wish
before actually taking the quiz or test for
credit, and with instantaneous feedback as
to which problems are incorrect, we
believe this pedagogical model is not just
cost efficient, but actually far more
effective than conventional lecture
• Active learning, as opposed to the
traditional lecture model, improves
• Faculty and other coaches provide just-in-
time assistance using techniques
designed to allow the students to discover
• Practice quizzes and the quiz-for-credit can be
accessed from any Internet site anywhere in the
world using virtually any browser by students
enrolled in the course. However, there is a
distinct advantage to taking quizzes at the
emporium itself, since on-site resources there
include tutoring labs and on-line videos, as well
as an emporium support staff which responds to
individual student requests for assistance, with a
response time on most days of under one
Comments from another evaluator
• The Math Emporium supports a variety of
• Active, independent learning through locally
developed, self-paced online math courses
designed to let students learn on their own
schedules, while providing immediate feedback
and sufficient structure to ensure students
understand expectations and meet required
• One-on-one coaching by professors, graduate students, and advanced
• undergraduates who are available 15 hours a day to assist students having
• difficulty with material, in a comfortable, less-threatening environment than
• a faculty office.
• Proctored online exams, from which most of a student’s grade for target
• courses is derived.
• Group projects and help sessions, facilitated by comfortable, easily
• chairs and generous work space around each computer.
• Online video lectures for students who prefer that format.
• Independent study by anyone in the Virginia Tech community who wishes
• take advantage of the high-end computers or the quiet study environment.
• What Is Unique or Noteworthy?
• The Math Emporium has improved math education at Virginia Tech
• costs by using an innovative learning paradigm with new
expectations and motivations.
• The system is supported by locally developed software and made
• by the unique organization of space, complemented by high-end
• Important features include:
• Taking advantage of the bottom-line orientation of many students
• I need to know to pass the test?”)
• Replacing broadcast education with one-to-one coaching and
• allow students to succeed at their own pace
• Tracking performance and providing immediate feedback
• Converting students from passive spectators to active participants
Closer to Home
• High School:
– Plato: Being used at Alhambra High School
for credit recovery
– Students read and do activities.
– They get 5 tries to take mastery test
– Then they take a Unit Test
– If they fail the unit test they either move on at
teacher’s discretion or review it and retake
and then move on.
English – all levels but 12 and all levels of
Math - all levels
• Martinez Junior High
– Read 180
• Being used as a remediation tool for students who are below
the proficient level.
• Attempts to address gaps in students’ skills through the use
of a computer program, literature and direct instruction.
• The program directly addresses individual needs through
differentiated instruction, adaptive and instructional software,
high-interest literature, and direct instruction in reading,
writing, and vocabulary skills.
• The software component of the program aims to track and
adapt to each student’s progress. In addition to the computer
program, the READ 180 program includes workbooks
designed to address reading comprehension skills,
paperback books for independent reading, and audiobooks
with corresponding CDs for modeled reading.
• In this article we will illustrate the emporium model with an
engineering mathematics course. The model is being utilized for
courses in a number of departments, and the conclusions we draw
seem equally valid for introductory and mid-level courses throughout
science and engineering. This emporium model is suitable for the
implementation of a combined lecture-based computer-assisted
course. Such courses maintain the human connection which
traditional education has always provided, and the lack of which can
be a significant detriment in “on-line” university courses. It is
important to emphasize this is not “on-line” instruction. The
traditional faculty lecture role is retained, and the emporium itself,
because of its size, is able to provide human resources on a one-to-
one basis to students at the computer in a financially economical
setting. Moreover, course material and course testing is entirely
under control of individual faculty members, and can be readily
tailored to meet special demands.
• vector calculus, required of all mathematics, science and engineering
undergraduates. Previously, this course was taught each semester in 25
sections of about 40 students each, meeting twice weekly and requiring, of
course, 50 lectures per week. Moreover, the lecturers were responsible for
assigning and grading recitations and exams for each section. Currently, all
1000 students are taught in 6 sections, each involving one weekly lecture
and the emporium component to be described, that is to say, 6 lectures per
week. The reason that so many students can be handled in one lecture is
that the entire burden of recitations, quizzes and exams is carried by the
computer emporium. This course and those like it have no weekly
homework assignment or recitation. Instead, the course requires a weekly
cycle of practice quizzes and quizzes-for-credit, all offered at the computer
• Students report to the emporium at their own pleasure throughout the week
following each lecture, and can practice the quiz problems on the weekly
lecture topic as often as they wish. However, they must take the quiz for
credit one time only before the weekly deadline. Since the computer
emporium is open 7 days a week, 24 hours a day, students can access the
quizzes at the emporium at virtually any time of their choosing.
• The key to this style of education is the “test engine” provided by the
emporium. Each time a student calls up a quiz on the material under
study, he will receive a different set of problems. In fact, the test
engine can create, practically speaking, an almost unlimited number
of different quizzes on the same material. In this fashion the practice
quiz functions as a recitation, with the test engine providing
instantaneous grading of the material, as well as comments and
suggestions on problems the student does incorrectly. The test
engine also records and archives the scores attained on the quiz-
for-credit for each student. Periodically, the student takes a
proctored examination covering the previous three or four weeks of
material, and at the end of the semester a cumulative final
examination, with the examination and its grading also provided
entirely by the test engine.
• In just the course under discussion, for example, each of
the 1000 students per semester takes on average about
50 practice quizzes, 10 quizzes-for-credit and 4
examinations. The typical quiz has 8 problems, with tests
having from 15 to 30 problems. Since each problem
must be individually generated for each student each
time the problem is accessed, it is evident that the
volume is quite massive, in fact, more than a half million
quiz problems for just this one course. We believe our
emporium test engine is the largest such engine in
• Practice quizzes and the quiz-for-credit can be accessed
• A paramount consideration at all times is to ensure that the system is
scalable to large transaction volumes.
• III. Hardware requirements
• These simple design requirements imply that the server consist of a
standard web server (we use Apache) and a page delivery service capable
of very high volumes of transactions. Apache is public domain, which means
it is standards-compliant and free to use. Apache has proven to be
extremely robust. In order to retain sufficient programming control to attain
these transaction volumes, the most practical environment is java server-
pages (JSP). JSP permits a maximum of computational speed and
processing in a rich environment. With this architecture, a high-powered
machine as server is not necessary. We utilize a pair of aging Sun 3000
servers with 4G of memory and RAID storage. One of the machines does
the web serving, while the other accommodates the database. Except when
we do builds, we rarely see usage exceed 10% of capacity on any machine.
• We use Oracle as the database management
• For the types of courses we have
developed, the “practice quiz” plays the
most fundamental role in the learning
process. In the United States, in the
traditional lecture format this role is played
by the assigned homework problems.
• The conversion of traditional classroom course offerings
to models of the sort described in the preceding has
substantially reduced costs, as well as improving staff
working climate and morale, primarily by reducing the
demands on senior lecturers in so many classrooms.
Furthermore, when the performance in later courses of
students who have completed courses under the
emporium model are compared to those who learned the
material under the traditional model, we find that the
former significantly out-perform the latter. We believe
this is due to increased time-on-task during the course.
• An emporium configuration requires
• The hardware cost for construction of a computer emporium in
Africa with 250 computers and two workstations, assuming $100 for
battery-backed computers and two workstations with UPS’s at
$5,000 each, as well as $2,000 for cabling, would be $37,000. If
each student were allotted 6 hours computer time per week per
course, and the emporium were accessible 18 hours daily for 6
weekdays, the emporium could handle 4,500 student courses per
semester. At that rate, with a projected hardware lifetime of five
years, the cost per student semester course would be less than 1
dollar. Even at a current cost of $150 for a simple laptop, the cost
would be barely over one dollar per student semester course.
• A large and secure venue is required for the computer
• Although the computer emporium requires no outside
networking, the emporium at Virginia Tech has Internet
access available on every emporium machine. At the
present time, the cost of wide-spread internet access for
universities in many developing countries is prohibitive.
World Bank estimates that the cost of internet access for
sub-Saharan African universities is $13,000 per
Mbps/month, compared to $120 in the U.S.  It is likely
that eventually the rates in Africa will be greatly reduced
by communication cables operating with regulated return
on investment. In that event, Internet access on
emporium machines will open up many other educational