COLLEGE ALGEBRA REDESIGN: IMPROVE STUDENT LEARNING AND SUCCESS
USING A HYBRID EMPORIUM MODEL
by
Andrew Geddes, Johannes Hattingh, and April Church
A Senior Honors Project Presented to the
Honors College
East Carolina University
In Partial Fulfillment of the
Requirements for
Graduation with Honors
by
Andrew Geddes
Greenville, NC
May 2015
Approved by:
Dr. Johannes Hattingh and Ms. April Church
Thomas Harriot College of Arts and Sciences: Department of Mathematics
Introduction: Why Redesign College Algebra?
College Algebra, Math 1065, is the highest enrolled course in ECU’s Department of
Mathematics. Approximately 1400 students enroll in Math 1065 each semester. Prior to the
redesign, College Algebra was taught using traditional class lectures that met for three hours a
week, with class sizes up to 48 students. This set-up required a large number of classrooms, as
well as, large numbers of teaching faculty to cover the various sections of this course.
The External Review Final Report of the Department of Mathematics of 2010 made the
following recommendation regarding the role and teaching of College Algebra (Math 1065) and
of lower courses:
“There are two points here.
In essence, these courses are intended more to enhance a collection of mathematical
skills than to convey information. As has been noted in a number of studies nationwide,
the typical lecture format, while it is an efficient way to convey information, is not wellsuited for this different purpose, particularly if the classes are large. With class sizes in
these courses approaching 50 students, these classes are likely to be less effective than
desirable. The option is to try to hold the class sizes down or to adopt an alternate
instructional approach. We saw a very nice self-paced class being conducted at East
Carolina by a faculty member from Pitt Community College. Perhaps more classes of this
kind, perhaps supplemented by undergraduate assistants, can be used. Also, Virginia
Tech has, in recent years, used a self-paced drop-in computer driven model that seems
promising.
While it is certainly true that East Carolina must address the educational needs of its
students as they actually are, and while it is quite common to see College Algebra used to
fulfill a mathematical foundations requirement, it should be noted that the material up to
and including College Algebra is actually an admission requirement at most universities.
The East Carolina faculty, not just the Department of Mathematics, might do well to
reconsider what the mathematical component of its foundations curriculum should be.
Perhaps in the not so distant future, East Carolina will find a way to refocus the resources
it now devotes to these courses on mathematical courses more proper to the university
level. At that time, students seeking a higher education but lacking the mathematical
foundation for it will be better served by institutions like Pitt Community College [1].”
Addressing the external reviewers’ suggestions, the Department embarked on a redesign of Math
1065, investigating models that other institutions across the country have implemented in their
College Algebra courses.
Design Process
Approval for Redesign
In February of 2011 a small committee of Math Faculty submitted the proposal, “Support for
Students in High Enrollment Courses”, as a possible topic for East Carolina University’s Quality
Enhancement Plan (QEP). “A ‘QEP’ is a plan to implement and assess a focused set of initiatives
designed to improve student learning across the university [5].” The proposal called for a
redesign of the high-enrollment gatekeeper course Math 1065, College Algebra, to both improve
learning and reduce instructional cost. An overview of the proposal was presented at a university
convocation on March 17, 2011 by the Chair of the Department of Mathematics, Dr. Johannes
Hattingh. Although the proposal was not selected as ECU’s QEP topic, this presentation lead to
the approval and funding of the redesign of Math 1065.
Course and Facility Preparation
Before beginning the redesign process, the Math Faculty needed to learn more about best
practices for course redesign. In Spring 2011, a small group of Math Faculty visited Louisiana
State University (LSU) to learn about their successful redesign of College Algebra. Also in
Spring 2011, a few Math Faculty visited the University of Central Florida which had similar
success in its redesign of an introductory math course. In addition to visiting these universities,
the Math 1065 Coordinator, Cathy Wilkerson, attended a workshop on course redesign hosted by
Pearson, the company which developed and owns the online interactive education software
system MyMathLab (MML). Lastly, the Math 1065 Coordinator read various redesign articles on
the NCAT website. “NCAT is an independent non-profit organization dedicated to the effective
use of information technology to improve student learning outcomes and reduce the cost of
higher education [6].” After learning about the various models of course redesign, as well as best
practices, the Math Department decided on a hybrid emporium model similar to the model used
at LSU.
In Summer 2011, a committee of instructors was assembled to develop the course materials to be
used in all face-to-face sections of Math 1065 in order to avoid course drift. The committee
developed a course syllabus, online instructional materials (homework assignments, quizzes,
practice tests, and tests), and a course pack. During Fall 2011, the Math Department required all
instructors teaching the face-to-face sections of Math 1065 to use the materials that were
developed by the committee. Also during Fall 2011, the Math Department ran a pilot hybrid
emporium Math 1065 section. As the Math Department did not have a lab designated for Math
1065, the pilot study had to be conducted in a slightly different format than the planned redesign.
In the pilot course, students met with their instructor, in a computer lab, for fifty minutes on
Mondays, Wednesdays, and Fridays. On Mondays, the instructor provided a 50 minute lecture
using the course pack. On Wednesdays and Fridays, the students worked on their MML
assignments. If a student needed help while working on his/her assignments, the instructor was
available to answer any questions. Results from the pilot class are displayed below:
ABC Rate
A’s
B’s
C’s
DWF’s
90%
5
3
10
2
In anticipation of the implementation of the redesign, the Math Department submitted a request
to change the course description in the course catalog. This change was approved by the
University Curriculum Committee in February 2012.
In Spring 2012, Mrs. Wilkerson and Dr. Hattingh worked with ECU facilities, ITCS, Pearson,
Academic Affairs, and the Registrar’s Office to plan the construction of the tutorial lab, known
as the College Algebra Virtual Environment (CAVE). The CAVE was constructed during
Summer 2012, and opened its doors at the beginning of Fall 2012 semester.
Course Set-Up
Course Design
Math 1065 follows a hybrid emporium model featuring a combination of teacher directed
lectures and student centered learning lab hours. Students are required to attend a one hour
lecture at a fixed time each week in a classroom and then spend a minimum of three flexible
hours in the CAVE. In class, the instructor covers difficult concepts, connects topics and
concepts, work examples pointing out common student errors and misconceptions, guides
students through their semester responsibilities, and discusses study strategies. In the CAVE,
students complete course assignments. There are typically three to five employees working in
the CAVE to provide students with immediate personalized help with course work. CAVE
employees include Math 1065 instructors, math graduate assistants, and undergraduate tutors.
All graduate assistants and undergraduate tutors complete required training on the math concepts
covered in Math 1065 as well as educational strategies to better help struggling students. The
hybrid emporium model promotes active learning that addresses a variety of learning styles. “It
emphasizes ‘doing’ mathematics not just ‘watching’ someone else do mathematics [2].”
CAVE
The CAVE is restricted only to College Algebra students and is open Monday through Thursday
from 9am to 9pm and on Friday from 9am to 5pm. Typically, each week, students are required
to spend a minimum of three flexible hours in the CAVE. Some adjustments are made to CAVE
hour requirements during the weeks where there are holidays and testing (the CAVE is closed
during test days). A student’s CAVE week begins at 9am on the day his/her Math 1065 class
meets and ends at 9pm on the night before the next class meeting. For example, if a student’s
class meets on Wednesday, then his/her week starts at 9am on Wednesday and ends the
following Tuesday at 9pm. The database AccuSQL is used to track student hours in the CAVE.
Every time that a student enters/leaves the CAVE he/she is required to swipe in/out at the front
desk using their university ID (One Card). The time for each visit is recorded by AccuSQL. It is
the student’s responsibility to keep track of his/her CAVE hours. The tutor at the front desk can
only tell students their time completed for that particular visit, not the total hours for the specific
lab week. At the end of each week, each instructor receives a summary report of total CAVE
hours per student spent in the lab.
Testing
Testing takes place over the course of three scheduled test days. The proctored, password
protected tests (and final exam) are taken using MML in the CAVE. Prior to taking a test,
students are required to register for the test on MML using the program TestCal. After
registering for the test, TestCal sends a confirmation email to the student. The confirmation
email contains the details of the student’s test reservation (day and time of test). The day before
the student’s test, TestCal sends a reminder email about his/her scheduled test time on the
following day. Starting in the Spring 2013 semester, students were also required to earn a 60%
or higher on the appropriate practice test on MML prior to their scheduled test day/time. All
practice tests are copies of the actual tests.
On the day of the test, students arrive to the CAVE 15 minutes prior to their scheduled test time
in order to be checked in. The check-in process includes: checking student IDs, reading a testing
rules/policies sheet, turning in a big blue book, and having their calculators checked. Upon
entering the CAVE, students are randomly assigned a computer using poker chips and are given
the opportunity to check out a calculator if they did not bring one. Once all students are seated
and logged onto MML, blue books are passed out to the students and given a password to access
the test. The password is different for each test day/time to prevent any students from accessing
tests outside the CAVE. Students with special accommodations, such as extended test time,
register and take tests with the Department for Disability Support Services.
The online tests are comprised of both short answer and multiple choice questions that have been
pooled with different iterations and randomized to prevent cheating. Three tests and a final exam
are given in this course. Each test is cumulative and the final exam is comprehensive. The final
exam follows identical procedures except testing takes place over a five day period and there is
no minimum practice test score is required to take the final exam.
Grade Breakdown
In Math 1065, overall grades are determined by participation, homework, quizzes, tests,
and the final exam. Participation counts as ten percent of a student’s overall grade: five percent
for class attendance and five percent for CAVE attendance. Ten percent came from a suggestion
made by LSU’s College Algebra Coordinator, Phoebe Rouse. LSU tried various weightings for
participation and found that ten percent is an ideal amount to convince students to attend class
and complete their required lab hours. Quizzes and homework are both worth ten percent of the
overall grade. Students have unlimited attempts on homework problems, with the exception of
reading assessment questions where they have two attempts. Reading assessment questions are
fixed multiple choice questions that come from the textbook and test the students’ conceptual
knowledge of a topic/concept. Students receive ten attempts per quiz and MML uses the highest
attempt in the grade calculation. Quiz questions are pooled with different iterations and
randomized. The three tests count for a total of forty five percent of the overall course grade with
the option of the lowest test grade being replaced by the exam grade if it is higher. The final
exam grade is then worth twenty five percent of the overall course grade. The course uses the
below plus/minus grading scale:
A 93 and above
C 73-76
A- 90-92
C- 70-72
B+ 87-89
D+ 67-69
B 83-86
D 63-66
B- 80-82
D- 60-62
C+ 77-79
F 59 and below
Benefits for Redesign
Increase Student Success
Other colleges and universities across the country redesigned their introductory math courses in
hopes to improve student success, increase ABC rates, and reduce instructional costs. Below are
some of their results:
College
Course
Traditional
ABC rate
Redesign
ABC rate
Virginia Tech
Linear Algebra
81%
87%
U of Alabama
Intermediate
Algebra
40%
78%
U of Idaho
College Algebra
59%
74%
UNC-Greensboro
College Algebra
38%
51%
LSU
College Algebra
64%
75%
East Carolina University hoped to see similar success with the redesign of its College Algebra
course. Prior to redesign, College Algebra had one of the lowest ABC rates, approximately sixty
percent, at East Carolina University. After the redesign of College Algebra, we have seen an
increase in the annual ABC rate with the biggest improvement during the spring semesters.
Annual Data Summary
Academic Year
Format
Total
ABC rate
Face to Face total ABC
rate
Online total
ABC rate
2008-2009
Traditional
57%
58%
31%
2009-2010
Traditional
59%
59%
42%
2010-2011
Traditional
62%
62%
54%
2011-2012
Hybrid
68%
69%
39%
2012-2013
Redesign
66%
67%
41%
2013-2014
Redesign
60%
60%
51%
Fall Data Summary
Term
Format
Total
ABC rate
Face to Face total
ABC rate
Online total
ABC rate
2008
Traditional
62%
63%
32%
2009
Traditional
63%
64%
42%
2010
Traditional
67%
67%
45%
2011
Hybrid
73%
73%
36%
2012
Redesign
66%
67%
46%
*2013
Redesign
62%
63%
56%
2014
Redesign
70%
70%
NA
*Enrollment in 1065 over the capacity of the CAVE
Spring Data Summary
Term
Format
Total
ABC rate
Face to Face total
ABC rate
Online total
ABC rate
2009
Traditional
49%
50%
30%
2010
Traditional
49%
50%
42%
2011
Traditional
53%
53%
70%
2012
Hybrid
58%
59%
41%
2013
Redesign
65%
67%
37%
*2014
Redesign
56%
57%
47%
*Several snow days canceling classes, students had to complete work without class component
Decrease Course Drift
Prior to the redesign, there was course drift in College Algebra. “The phrase ‘course drift’ refers
what happens when individual instructors teach the course to suit their individual interests rather
than to meet agreed-upon learning goals for students, resulting in inconsistent learning
experiences for students and inconsistent learning outcomes [3].” Thus, course drift leads to
uneven preparedness for subsequent courses. Part of the redesign of College Algebra included
standardizing the course material to ensure consistent coverage of content, and thus minimizing
course drift.
Reduce Instructional Cost
In addition to improving student learning, a course redesign was necessary due to budget cuts.
North Carolina made several large funding cuts since 2008. As a result, the East Carolina
University Math Department’s salary budget was reduced by approximately $450,000. If
College Algebra were taught in the traditional approach with 28 sections offered each semester,
the department would require 7 FTEs, assuming each fixed-term faculty member would be
teaching 4 sections. Fixed term faculty made approximately $39,000/academic year and the
Math Department spent about $10,000/year on the printing of common final exam utilizing the
traditional format. Thus the total cost to the department for College Algebra being offered in the
traditional setting was about $283,000/year. If College Algebra is offered in the hybrid
emporium model with 28 sections offered each semester, the department would require 3 FTEs
and a CAVE Director. Fixed term faculty make approximately $39,000/academic year, the
CAVE Director makes $48,000/year, and $24,000/year is spent on staffing the CAVE (money
provided to the department by Academic Affairs). Thus the total cost to the department and
university, for College Algebra, is about $189,000/year. By redesigning College Algebra, the
Math Department saves approximately $94,000 per academic year.
Future Course Redesign
Due to the academic and financial successes of the Math 1065 redesign, the Department of
Mathematics has decided to look into redesigning Pre-Calculus (Math 1083). Around the
country, there has already been several institutions that have redesigned their pre-calculus
programs using the emporium model. Some of these institutions include the University of North
Carolina at Chapel Hill, the University of North Carolina at Greensboro, Louisiana State
University, the University of Idaho, and Auburn University [4]. The emporium model requires
students to spend a fixed amount of time in a math computer lab. Within the lab, students watch
tutorial videos, learn from their online textbook, complete homework and quizzes, and take their
tests [4].
While the emporium model has been a success for other schools, with East Carolina University’s
current resources and previous redesign successes, the best option for a pre-calculus redesign at
ECU would be a hybrid emporium model. Results from the Spring 2014 semester, for Math
1065, show that when students do not receive a lecture, in conjunction with their required lab
hours, their academic success diminishes. During the Spring 2014 semester, East Carolina
University had several closings due to inclement weather. As a result, all of the college algebra
sections missed at least one class with several of the sections missing up to three classes. The
ABC rate for this semester was 10% lower than the Spring 2013 ABC rate and 2% lower than the
Spring 2012 ABC rate. Therefore, for ECU students, it is import to have a weekly lecture in
conjunction with fixed lab hours to maximize student success.
The Math Department’s plan is to redesign Math 1083 using a hybrid emporium model that is
similar to the one used in Math 1065. Under this format, students would attend a fixed 75
minute lecture once a week and would spend a minimum of two flexible hours in a virtual
learning environment. The lecture time was extended for Math 1083 because this course covers
more difficult concepts than those in Math 1065 and therefore instructors will need additional
time to cover the content. The intended location of the virtual learning environment is the Math
CAVE, which is currently used only for Math 1065. Since East Carolina University has a small
Pre-Calculus enrollment of approximately 230 students per academic year, it will be plausible for
both courses to share the CAVE. In order to accommodate for a new course, the CAVE will
need to make several modifications including: providing staff with additional training to cover
the more advanced concepts, increasing the number of staff on duty to handle a larger student
population, and sync the schedules of the two programs together to allow tests to be administered
on the same days to minimize CAVE closures. The same information technology (MyMathLab,
AccuSQL, and TestCal) will be used for Math 1083 to avoid overcomplicating check-in
procedures and student struggles with learning a new mathematics software.
As completed in the redesign of college algebra, Pre-Calculus faculty will need to meet and
standardize all material, approval will need to be obtained from the University Curriculum
Committee, and a pilot section must be assembled and completed prior to implementing the
redesign.
Resources
[1] Coburn, L., McNulty, G., Obrien, K., & Ye, Z. (2010). East Carolina University Department
of Mathematics External Review Final Report (p. 5).
[2] Course Redesign Using Technology. (2010). In LSU: College of Science Department of
Mathematics. Retrieved November 12, 2014, from
https://www.math.lsu.edu/courses/1021/Redesign.
[3] Five Principle of Successful Course Redesign. (n.d.). In The National Center for Academic
Transformation. Retrieved March 19, 2015, from www.thencat.org/PlanRes/R2R_PrinCR.htm.
[4] (n.d.). In The National Center for Academic Transformation. Retrieved from
http://thencat.org/PCR/Proj_Success_all.html.
[5] Quality Enhancement Plan. (n.d.). In East Carolina University Academic Affairs. Retrieved
November 12, 2014, from http://www.ecu.edu/cs-acad/qep/.
[6] Who We Are. (n.d.). In The National Center for Academic Transformation. Retrieved
November 12, 2014, from http://www.thencat.org/.