University Of North Dakota

North Dakota
Math Emporium
Executive Summary
The University of North Dakota Mathematics Department seeks support to redesign the
curriculum for our calculus preparation courses through the Math Emporium model. The courses
included in this redesign serve approximately 2,800 UND students each academic year from over 25
departments across campus. This endeavor would be a campus-wide initiative, similar to the UND
Writing Center. We assert that a UND Math Emporium will 1) support increased student learning,
success, retention and degree completion; 2) expand access to instructional opportunities through nontraditional delivery methods; and 3) enhance scholarly activity among mathematics faculty. Thus, making
a considerable contribution toward the goals outlined in the NDUS Strategic Plan (2014).
The creation of the UND Math Emporium will require a centrally located physical space and
infrastructure to support student access to instructional software and the “just in time” assistance that
are integral pieces of an emporium. Additional space is needed for students to gather for weekly focus
group meetings, which incorporate the use of instructional technologies and collaborative problem
solving to engage students in learning mathematics.
The UND Math Emporium proposal begins with a description of the challenges faced by the UND
Mathematics Department as we strive to provide students with a deep procedural and conceptual
understanding of mathematics. This includes strengthening mathematical connections, the ability to
apply mathematical concepts, and to communicate these ideas within and beyond mathematics class.
Next, we outline the essential elements of a successful emporium and a description of the UND Math
Emporium. Finally, we present the academic and financial benefits of implementing the Emporium.
University of North Dakota Math Emporium
Table of Contents
Executive Summary ....................................................................................................................................... 2
Definitions ..................................................................................................................................................... 4
Introduction .................................................................................................................................................. 5
Current challenges ........................................................................................................................................ 5
What is a Math Emporium? ........................................................................................................................ 11
The UND Math Emporium........................................................................................................................... 12
Benefits of a Mathematics Emporium ........................................................................................................ 16
Launch and Operation Costs ....................................................................................................................... 20
Potential Locations ...................................................................................................................................... 22
Timeline....................................................................................................................................................... 23
Conclusion ................................................................................................................................................... 24
References................................................................................................................................................... 25
Appendix A: Disciplines that require Mathematics service courses ........................................................... 26
Appendix B: Suggested Emporium Layout .................................................................................................. 27
Appendix C: Instructional Costs .................................................................................................................. 28
Appendix D: Multiple Mini Emporiums....................................................................................................... 31
To clarify terms used throughout this document, we provide the following definitions:
Calculus Preparation Courses – Mathematics courses a student needs to take in order to be prepared for
either Applied Calculus or Calculus I. These include Math 92/93 Algebra Prep II and III (formerly Math
102 Intermediate Algebra), Math 103 College Algebra, Math 105 Trigonometry, Math 107 Precalculus,
and Math 112 Transition to Calculus.
Developmental Mathematics Courses – Math 92/93 Algebra Prep II and III (formerly Math 102
Intermediate Algebra) and Math 107 Precalculus. Math 92 and Math 93 are pre-college level
mathematics. They do not count toward graduation. Math 107 is taken by students majoring in math
intensive programs which expect students to be prepared to enter Calculus their first semester. Thus
Math 107 does not count toward program completion.
Introductory Level Courses – All 100-level mathematics courses: Math 92/93 Algebra Prep II and III
(formerly Math 102 Intermediate Algebra), Math 103, Math 105 Trigonometry, Math 107 Precalculus,
Math 112 Transition to Calculus, Math 115 Introduction to Mathematical Thought, Math 146 Applied
Calculus, Math 165 Calculus I, and Math 166 Calculus II.
Large Enrollment Courses – multi-section courses serving more than 150 students in a semester. In the
math department, this is generally Math 92/93 Algebra Prep II and III (formerly Math 102 Intermediate
Algebra), Math 103 College Algebra, Math 146 Applied Calculus, Math 165 Calculus I, Math 166 Calculus
II, and the fall semester of Math 107 Precalculus.
Service Courses – Mathematics courses in which less than 50% of the enrolled students are math majors.
These are: all Introductory courses, Math 207 Linear Algebra, Math 208 Discrete Math, Math 265
Calculus III, Math 266 Elementary Differential Equations, Math 277 Elementary School Mathematics,
Math 321 Applied Statistical Methods, Math 352 Introduction to Partial Differential Equations, Math 377
Geometry for Elementary Teachers, Math 400 Methods and Materials of Teaching Middle and Secondary
Schools, and Math 477 Topics in Mathematics for Elementary Teachers. See Appendix A for information
on required math course for UND programs of study.
Major courses – Mathematics courses in which at least 50% of the enrolled students are math majors. A
partial listing of these courses includes Math 308 History of Math, Math 330 Set Theory and Logic, Math
409 Geometry, Math 412 Differential Equations, Math 421, 422 Statistical Methods I and II, Math 431,
432 Introduction to Analysis I and II, Math 435 Number Theory, Math 441 Abstract Algebra, Math 461
Numerical Analysis, and Math 488 Senior Capstone.
Meeting the need for a trained and educated workforce is just one of many
essential functions of the North Dakota University System’s 11 institutions. Research
and service to community remain vitally important. A vibrant and growing campus
community, serving its host community and the state as a whole, typically has needs
that range from classroom space to updated infrastructure and bandwidth. But at the
heart of a campus is its ability to attract highly qualified staff and faculty who serve
and inspire students. Growth is a great problem to have, but it offers challenges
nonetheless. (NDUS, 2014)
In alignment with the NDUS Strategic Plan (2014), the UND Mathematics Department has long
been concerned about the success of students in all of our courses. Our goal is to provide a curriculum
that meets the needs of UND students in accordance with 1) best practices for learning mathematics; 2)
the goals of the UND Essential Studies program; and 3) the content needed to be successful in
subsequent courses that build on these mathematical concepts. We propose that a significant redesign
of our curriculum and method of delivery using the “Math Emporium” model will accomplish these
goals, address many of our current challenges, and result in increased success for all UND students
served by the Mathematics Department.
In this proposal, we first delineate the challenges encountered as a result of our current
curriculum and method of delivery for Math 102* Intermediate Algebra, Math 103 College Algebra, Math
105 Trigonometry, Math 107 Precalculus, and Math 112 Transition to Calculus. Second, we describe the
Emporium model, which we propose for transforming our curriculum and method of delivery for the
aforementioned courses. Our discussion will include the essential components of a successful
mathematics Emporium, related research on the learning of mathematics, and the impact of the
Emporium model when adopted by universities and community colleges. Third, we discuss the
anticipated benefits for UND students, Mathematics Department and the university as a whole through
the implementation of a modified Emporium model. Finally, we address the financial aspect of launching
and operating a Math Emporium.
Current challenges
The NDUS Framework for Transformational Change (2014) acknowledges that growth is a great
problem to have, but it does offer challenges. Like many large-enrollment, introductory courses, our
* Math 102 is a 3 credit remedial course, so that the SBHE requires it to be numbered below 100.
Following BSC, we will split it into Math 92 and 93, which are 2 credits each. In this proposal, we will
refer to Math 102 when talking about the past and Math 92 and 93 when talking about the future.
calculus preparation courses face a number of challenges. The first area of concern is learning outcomes.
Due largely to inadequate academic preparation and lack of engagement in learning, a significant portion
of students in these courses either drop the course early in the semester, or remain registered but stop
attending. Second, we are not as effective or as efficient in addressing student needs as we could be.
Inconsistencies among sections of the same course make it difficult to ascertain the extent to which
students master the necessary content and meet Essential Studies goals. Finally, we are struggling to
meet the needs of the students enrolled in our own programs. The demand on instructional staff to
teach ever increasing student credit hours in introductory and service courses has substantially reduced
the number of courses we can offer for our undergraduate and graduate students. This in turn impacts
our production of scholarly activity and our ability to recruit high quality faculty and graduate students
(i.e. GTAs). It is evident that our concerns are in alignment with the NDUS Strategic Plan (2014) which
calls for all ND universities to be student centered, for faculty to equip students for success, and
enhancement of research reputations.
Range of Students’ Academic Preparation
Our current model for teaching calculus preparation courses does not allow us to accommodate
the spectrum of students’ differing mathematical ability and content needs. Within the range of students
who place into a given course there is still a significant difference in mathematical abilities and
deficiencies. This is particularly true of students placed into Math 107 Precalculus. Often these students
have fairly strong algebra skills but lack the trigonometry knowledge needed to place into Calculus I.
These students are in the same class with students who have weaker algebra skills. The instructor must
set the pace of the course to meet the needs of the majority of the students in the course and to cover
the necessary content by the end of the semester. Students with the strong algebra skills are forced to
move at the same pace as the students with weaker skills. By the time the course reaches the more
difficult trigonometry content, the stronger students have often disengaged from the course and are
accustomed to relative success with little effort. When they realize that effort is needed to learn this new
material they are behind. Depending on the degree of difficulty the students have with trigonometry,
this can significantly impact their grade and they may still leave the course with an insufficient
understanding of trigonometry. Similar situations occur in most introductory level mathematics courses.
Student Engagement in Learning Mathematics
How to engage students in learning mathematics is a topic of discussion nationally and within
our department. It is widely noted that students in mathematics courses are frequently passive
recipients of knowledge through lectures (National Center for Academic Transformation (NCAT), n.d.).
The lack of student engagement in learning mathematics is a significant factor in retention of content
knowledge and the ability to apply mathematical ideas outside of mathematics class (NCAT, n.d.). This is
a significant concern for degree programs which require mathematics as prerequisites to courses for
their majors.
When a student has learned a procedure or concept, we expect that this knowledge will be
readily available, from memory, to make sense of and apply to future problems and situations.
Knowledge about the physiological changes that occur in the brain when this degree of learning takes
place and methods for triggering processes that lead to those changes has increased dramatically in the
last decade. Physiologically, learning occurs when neural connections in the brain are formed and
strengthened. This is referred to as durable encoding (Brown, Roediger & McDaniel, 2014).
Lecturing is indispensable for some content and in large classes. Lecture can effect learning if
instructors incorporate methods for triggering the types of processes that result in durable encoding of
the course content. If this does not occur regularly during class meetings, learning is left to the student
to do outside of class (deWinstanley and Bjork, 2002). The typical student in calculus preparation courses
often struggles to do this due to an insufficient knowledge base, and lack of effective study skills and
engagement during lecture. Time in class which facilitates learning, as defined above, is needed to
support student engagement.
The majority of calculus preparation courses in the Mathematics Department are taught through
lecture. Our Intermediate Algebra is generally taught by lecturers in sections of 80-120 students, College
Algebra is predominantly taught by GTAs, and Trigonometry, Pre-Calculus, and Transition to Calculus are
taught by GTAs, lecturers and tenure-track faculty as needed. For many reasons, the extent to which our
instructors incorporate methods to engage students in learning during lecture varies considerably.
Current Success Rates
Students’ academic preparation and the extent to which they engage in learning the course
content are significant factors in successfully completing a mathematics course. In this section we define
successful completion of a course to be earning a grade of C or better.
The success rates for courses included in the curriculum redesign and Applied Calculus, from Fall
2012 to Spring 2015 are presented in Table 1. Overall only 54% of Math 102 students and 52% of Math
107 students successfully complete these courses. These courses are prerequisites for subsequent
required mathematics and science courses for many of these students. Not completing these courses
causes significant delays in timely program completion for their degrees. Math 103 also serves as a preor co-requisite for other mathematics and science courses as well, but just as often it is a terminal
mathematics course for students. In either case a 30% DFW rate warrants concern, particularly for a
course that serves students pursuing degrees from a substantial number of programs across campus.
While Math 146 Applied Calculus will not be included in the Emporium, we anticipate that implementing
the Emporium model will better prepare students in Math 103 (pre-requisite for Math 146) and free-up
resources. This will allow us to address the abysmal DFW rate (54%) in this course.
Course Enrollment
Table 1. ABC Rates for all UND Calculus Preparation Courses and Applied Calculus
Clearly these success rates and the consequences students experience as a result of failing to complete
these courses play a role in UND’s overall retention and completion rates. The following statements show
how remedial courses correlate to decreased graduation rates nationally:
20% of entering freshmen at 4-year colleges require remedial course work in mathematics
(Complete College America, 8).
Of those who enroll in remedial math, 75% complete remediation, 37% complete the remedial
course work and associated college level courses within two years, and 35% graduate within six
years (ibid, 12).
In contrast, 56% of students who do not require remediation graduate within six years (ibid, 12).
At UND the statistics are similar,
25% of entering freshmen require remedial course work in mathematics.
Of those who enroll in Math 102, approximately 71% eventually complete Math 102, 51%
complete Math 102 and Math 103 within two years, and 49% graduate within six years.
In contrast, 57% of students who do not require remediation graduate within six years.
Inconsistent Student Experiences in Multi-Section Courses
A contributing factor to the DFW rate, with our current model for teaching calculus preparation
courses, is that the amount of content and depth to which it is addressed differs among the sections of
each course. Through Department curriculum committees, expectations for the content of each course
have been outlined and are updated when new textbooks are adopted. The inconsistencies among
sections are mostly due to the emphasis an instructor places on the required topics, the number of
optional topics addressed, and in assessment. These differences make it challenging to correlate grade
outcomes with mastery of learning across different sections. This concern is not unique to UND and is
often referred to as “course drift” (NCAT, n.d).
Essential Studies
These inconsistencies may impact our ability to fully incorporate the Essential Studies Goals in
Math 103 College Algebra. In addition to serving as a prerequisite for a range of degree programs across
campus, Math 103 College Algebra is also approved to fulfill three-credits of Essential Studies for the
Math/Science/Technology requirement, the Special Emphasis in Quantitative Reasoning and the Critical
Thinking Goal. Departmental Assessment Reports show that overall, Math 103 students are able to
demonstrate quantitative reasoning and critical thinking in algebra. Critical Thinking in relationship to
the concept of percent was noted as an area of concern in the Fall 2014 Assessment of Essential Studies
Goals for Math 103 (Mathematics Department Assessment Committee, 2015). This was the topic of one
of the two Essential Studies assessment questions embedded on the final exam. Of the random sample
of student solutions submitted, only 44% of the students demonstrated a “generally correct” or
“completely correct” solution when evaluated with the Critical Thinking Rubric. This concept is
applicable to quantitative reasoning and critical thinking needed in daily life. It is usually first introduced
to students in middle school and it is possible that GTAs assume that students know this content.
However, students may not have this prerequisite knowledge which could warrant additional time
devoted to this topic and/or a different approach to teaching it. Thus, we are not meeting Essential
Studies goals as fully as we could.
Current Math Learning Center
One resource currently available to students in introductory level courses is the Math Learning
Center (MLC). The MLC, located on the 3rd floor of Witmer Hall, is inadequate to meet the needs of
students. The MLC is regularly overcrowded with students seeking tutoring, as well as a place to study
individually or with peers. While tutoring is only provided for students in introductory level courses, the
MLC is used by students in all levels of mathematics. Over the last year, tutors have had to ask upper
level math students to leave the MLC because there were no seats available for those seeking a tutor.
Research has shown several limitations attributed to the disparate levels of mathematics studied in the
MLC and its location in Witmer with respect to course instruction. Lower-level mathematics students
often feel inadequate or inferior to their more mathematically adept peers, which makes the act of
entering the MLC a negative idea. When these students finally go to the MLC and hear others discussing
higher-level mathematics they are further intimidated and anxious about admitting they need help.
Additionally, the lower-level mathematics courses are typically taught on the first floor of Witmer. Even
when instructors encourage students to use the MLC and signs are posted for the MLC on the first floor
of Witmer, students do not readily think to use it and it is inconvenient to go out of their way to get
there (Halcrow and Iiams, 2011).
We are often asked to provide tutoring for statistics courses offered in departments on campus
(Psychology, Sociology, Biology, and Economics). Due to the limitations of our current location we have
not been able to provide this service to students.
Faculty and Graduate Students
There is substantial imbalance between faculty effort going to service courses and effort going to
major courses, particularly graduate courses. According to the 2013-2014 Annual Report our
instructional staff generated 467 faculty credit hours. Of these, 398 (85%) credit hours were for service
courses. The remaining faculty credit hours included 23 courses for our major with 6 at the 500-level.
Moreover, from the 2009-10 AY to the 2013-14 AY, our total student credit hour (SCH) production has
increased by almost 50% (see Table 2), with no corresponding growth of resources for the department.
Academic Year
Total SCH production
Percent Increase since 2009-10 AY
Table 2. Mathematics Department Student Credit Hours Generated.
Due to increased service course demands and fewer faculty, we are only able to offer each
graduate student sequence once every three semesters. Instead of teaching the full sequence every year,
we must take a semester off between offerings. Consequently, we often have graduate students whose
prerequisite needs are out of step with our graduate course offerings. They either cannot take the
courses, or must attempt them without proper preparation. Additionally, we have only offered one
graduate-level special topics course since Fall 2010. At one time we offered one such course every 2 -3
semesters, including Summer. Lastly, our GTAs are overworked in comparison to other universities. With
a few exceptions, each GTA is 100% responsible each semester for two 35 student sections of Math 103
College Algebra.
These issues have a significant impact on our graduate program and faculty time dedicated to
scholarly activity. Improving GTA work load is not possible without more graduate students – which
won’t happen if we don’t have more courses to offer them. For example, offering a special topics course
each summer would keep graduate students active and allow us to offer some financial support over the
summer. Moreover, the special topics courses were often related to faculty research. Teaching these
courses exposed graduate students to new areas of research and regularly resulted in a graduate student
choosing to complete an independent study in that area. In turn, this facilitated additional scholarly
activity by the faculty member. The heavy commitment to teaching service courses, with a bare
minimum of graduate level courses makes it difficult to recruit graduate students and high quality,
research producing faculty.
Other Concerns
As noted above, Math 146 Applied Calculus, which also serves a variety of programs across
campus, has a 54% DFW rate. The diverse programs served by this course (e.g. Aviation, Biology,
Business, and Pre-Health) make it difficult to provide content that meets the needs of the students
enrolled in this course. In addition, Math 146 is typically taught in sections of 100 - 120 students with no
recitation and no TA support. The size of the sections of this course exacerbate the concerns delineated
In addition to recognizing the extensive Departmental commitment to teaching service courses it
is important to take into account faculty teaching preferences. Every two years the Department Chair
distributes a “teaching preference questionnaire” to all of our instructors. This is a list of all courses
offered by the Department. Instructors are asked to rate each course according to their interest in
teaching it. There are five possible responses, ranging from “I really want to teach this course” to “I really
do NOT want to teach this course.” The responses from the 2014 questionnaire for the 16 tenure-track
faculty for courses up through Calculus II are presented in Table 3. While some faculty are willing to
teach the calculus preparation courses if needed, most do not want to do so. Responses change
significantly for Math 165 Calculus I and Math 166 Calculus II, which indicates that faculty are not averse
to teaching freshmen-level courses.
I (really) do NOT
I (really) want to
I don’t mind
want to teach this
teach this course
teaching this course
Table 3. Tenure-track Faculty Responses to “Teaching Preference Questionnaire.”
The challenges outlined above are not recent developments. The effects of these issues have
compounded over time as the Mathematics Department has been asked to meet an increasing number
of needs from programs across UND with fewer resources. In the next section of this proposal we offer a
vision for redesigning our pre-calculus curriculum based on the Emporium model.
What is a Math Emporium?
The basic premise of the Emporium model is: “Students learn math by doing math, not by
listening to someone talk about doing math” (Twigg, 2011). The physical elements of a Math Emporium
include 1) designated space and computers for students to actively engage in learning mathematics
through the use of interactive instructional software; 2) designated space and computers for students to
complete on-line assessments; 3) tutors to provide “just in time” assistance and guidance to support
student engagement in learning; 4) faculty to facilitate weekly class meetings (focus groups) to support
student learning and administer written assessments; and 5) staff to manage the daily operation (e.g.,
training and supervision of tutors and focus group faculty; maintaining database; communication with
students, faculty, and administration). The “Emporium” model is named after what Virginia Tech
University, the model’s originator, called its initial course redesign because of its location in a former
department store. As Carol Twigg states, a math emporium “is as close to a silver bullet as one can get in
the complex world of teaching and learning.”
The original Math Emporium design eliminated all class meetings and replaced them with Webbased resources, such as interactive tutorials, computational exercises, an electronic hypertextbook,
practice exercises with video solutions to frequently asked questions, applications, and online quizzes.
The course material was organized into units that students cover at the rate of one or two per week,
each one ending with a short, electronically graded quiz. The role of the faculty was to point students
toward appropriate resources and strategies. The redesigned course allowed students to choose when to
access course materials, what types of learning materials to use depending on their needs, and how
quickly to work through them. As the model was adopted by other universities, modifications such as
weekly focus group meetings with course faculty, required lab time, and required completion of reading
guides were incorporated to support student learning.
The majority of a student’s time in the Math Emporium generally includes reading the etextbook and watching tutorials, working examples in the reading guide or in web-based assignments.
The web-based assignments provide immediate feedback to students. Tutors and faculty are available to
assist students as needed. Tutors guide students to watch the appropriate video lessons and complete
the appropriate part of the reading guide before answering students’ content questions. This supports
student engagement in learning the content. At regular intervals, students also complete low stakes
quizzes for feedback and to minimize math anxiety. After each quiz, students receive immediate
feedback, which helps them assess their level of understanding and pinpoints areas of weakness for the
student to address. Optional live lectures that cover the material are also provided to serve students
who prefer to have more frequent interactions with the instructor.
The UND Math Emporium
Physical Space Requirements
We have identified key spaces required in the Emporium: focus group classrooms, lab space,
small group rooms, a live lecture room, office space, informal entry space, check-in counter, and
bathrooms (see Appendix B for a possible floor plan). The four focus group classrooms will contain 28
workstations. Ideally the classrooms would be accessible from both inside and outside the lab space. The
classrooms and lab would be separated by sliding glass walls so the lab space is easily expanded into the
classrooms when there is high demand. The entrance outside of the lab would allow minimal disruption
to students working in the lab when a focus group is dismissed and would also allow other departments
use of the room when demand for lab space is low. The lab space will contain 50 workstations, with the
glass walls into the focus group rooms allowing the lab space to expand to 162 workstations during peak
usage. Tutors would be available for “just in time” help in the lab space. There would be 3 small group
study rooms off of the lab space for student collaboration and study. Office space will be needed for staff
and tutors. Students will be required to check in and out of the lab so a check-in space is needed. This
area will also serve as a greeting and informational desk for students. We would like an informal lounge
area directly outside of the Emporium for students to meet or wait for focus group meetings or lab
space. Ideally, there would be bathrooms located inside of the Emporium so students do not have to
check in and out if needed.
Instructional Software
After considering several instructional software programs we consider ALEKS to be the best product for
meeting the goals of the Emporium and the needs of UND students.
ALEKS (Assessment and LEarning in Knowledge Spaces) is an adaptive online learning system.
When the students begin using ALEKS they complete a 25-30 question assessment to determine which
topics they have mastered and which topics they have mastered the prerequisites for and are ready to
learn. Each question in the assessment is based on the answers they give to previous questions. After
the initial assessment is completed, students are ready to enter Learning Mode. A student is presented
with a pie chart with topics that they are “ready to learn.” In Learning Mode, explanations, videos, links
to the e-book, and sample questions are presented to the student. After the student has successfully and
consistently answered questions about a particular topic, that topic is considered to be learned.
Instructors may create homework assignments, quizzes, and exams within ALEKS. An ALEKS course may
be set up with specific deadlines for students to complete topics or set up as a completion based course.
Throughout the course, periodic assessments are given to ensure that students have achieved long-term
retention of topics. ALEKS questions are rarely multiple choice, so students must mimic how they would
write an answer with paper and pencil.
Essential Elements for Success
NCAT has identified eight elements that are essential to the success of the Emporium Model. In
this section we describe our vision for the UND Emporium in the context of these essential elements.
1. Redesigning the entire course and/or program to create consistency.
We propose to fully redesign each of our calculus preparation courses, Math 92, Math 93, Math
103, Math 105, Math 107 and Math 112. Every student in a particular class will have access to
the same instructional materials and complete comparable assignments, quizzes and exams
through the chosen instructional software. During focus groups, students will engage in
comparable activities designed to develop conceptual understanding and elicit student thinking
through spoken and written explanations. Since most grading occurs within the instructional
software, and the common activities developed by the instructors will be used consistently in
focus groups, grades across sections will more accurately reflect student activity and learning
outcomes. Frequent training and collaboration of staff will help to maintain consistency among
focus group sections.
2. Require students to “do” math.
Students will be required to work in the lab a minimum of 3 or 4 hours per week, determined by
number of course credits. Students will actively choose methods and resources to direct their
own learning. This will include reading the e-textbook and watching tutorials, working examples
in the reading guide and in web-based assignments, and completing low-stakes web-based
quizzes and assessments. The Math Emporium will house 162 work stations. Fifty-four stations
will have computers while the remaining stations will accommodate student-owned devices.
Tutors and faculty will also be an available resource for students. Their role is to support the
student in “doing” the work by guiding them toward video lessons, the text, and the appropriate
part of the reading guide, before answering the students’ content questions.
A pacing guide and deadlines will be established for each course to keep students on track for
completion of the course in a semester. Most students will need to spend additional time using
the instructional software to work on the assignments and quizzes for the course. This time may
be spent inside or outside of the lab.
In addition to the required lab time students will also be required to attend a weekly focus group
of 25-30 students. During this time, students will engage in problem solving designed to facilitate
quantitative reasoning, conceptual understanding, and making connections among the course
topics, as well as procedures. Students’ mathematical thinking will be communicated both orally
and in writing during the focus groups.
3. Hold class in a lab space utilizing instructional software.
Required lab time will be spent using the ALEKS instructional software programs discussed
above. Student progress and activity will be monitored to ensure that students are staying on
task while utilizing the software. Lab time would be in lieu of the traditional time spent in
4. Have frequent assessment and immediate feedback.
Students will be assessed with weekly online homework assignments and quizzes and receive
immediate feedback about their answers. Completing the homework assignments to a specified
standard will be required before attempting the quizzes. Two or three online exams will be given
throughout each course. The first attempt on each exam will occur during a focus group time. If
a student wishes to re-take the exam he/she will be able to do so in the lab within a specified
time frame.
Paper-pencil assessments will take on several forms. Students will receive feedback on their
mathematical knowledge and communication skills through computer generated worksheets to
be completed outside of class and through the problem solving activities in the focus groups.
One paper-pencil midterm will also be given during a focus group. The final exam will be a
combination of an online assessment and traditional written exam.
5. Provide students with one-on-one just in time assistance from trained tutors.
In addition to the tutor responsibilities described under element 2, it should be noted that tutors
will be available during all open hours of the Emporium. The tutors will receive frequent training
to support their efforts to guide students in problem solving rather than just providing the
6. Ensure students are spending sufficient time “doing” math.
As described under element 2, students will have required lab time. A pacing guide will be
established and deadlines communicated regularly to students. Students will need to check-in
and out of the lab to ensure credit for time spent in the lab. Additionally, ALEKS allows the
instructor to track student time, activity, and progress in the course.
7. Monitor students’ progress and provide intervention when necessary.
With access to this information described under element 6, students’ progress can be easily
monitored and intervention provided in a timely manner. Computer-based testing also provides
comprehensive, continuous data collection for faculty, so they can adjust instruction and give
individualized help as the course proceeds. In this way, the system offers a personalized
dimension that cannot be maintained in our current format.
A recent innovation at the University of Idaho is the implementation of “Try Scores”, which
report a student's effort in the course, and are notably unrelated to their mathematical ability.
We intend to implement “Try Scores” at UND. This “Try Score” would be available to students'
advisors to inform advising conversations and provide additional support for students. The
University of Idaho reports that 95% of students who receive a “Try Score” of 5 out of 5
complete the course with a C or better.
8. Measure learning, completion and cost.
The first semester we offer courses in the Emporium, we will also run traditional sections of the
same courses. At this time, we will gather data on student learning through a common final,
compare the success rate and grade distribution and the instructional cost per student.
Student success in subsequent mathematics courses would also be tracked to inform
adjustments to the Emporium.
In addition to Virginia Tech, an emporium model of education has been successfully
implemented at over 30 colleges and universities. The percentage of students with final grades of C or
better in a traditional course versus an emporium course as reported by the NCAT for ten of these
universities (Squires 2012, Twigg, 2011) are presented in Table 4. Of the courses included in Table 1, with
Mississippi Valley State
Santa Fe College
University of Alabama
University of Central
University of Idaho
Intermediate Algebra
Cleveland State Community
Louisiana State University
Success Rate
Success Rate
Increase in
Success Rate
Intermediate Algebra
Intermediate Algebra
Intermediate Algebra
Intermediate Algebra
College Algebra
College Algebra
College Algebra
College Algebra
College Algebra
SUNY at Oswego
University of Central Florida
University of Missouri-St.
Table 4. Percentage of Students with Final Grades of C or Better in a Traditional Versus Emporium Course.
the Emporium model the increase in the success rate ranged from 7% to 38% with an average of 17%.
Additionally, some places report increased success in subsequent mathematics courses.
Changes to current Math Learning Center
The implementation of the Emporium model for calculus preparation courses will substantially alter the
population of students served by our current Math Learning Center. As stated previously, the current
MLC is not fully meeting the needs of UND students. The MLC is currently located on the 3rd floor of
Witmer in a space that used to be two classrooms. We propose to divide the current space into two
separate spaces: a study and collaboration space for math majors and students taking upper level math
classes and a seminar room to hold graduate classes. With the creation of the Emporium, the load on
classrooms on the 1st floor of Witmer will be significantly lowered. We propose to take 3 former
classrooms and create a Calculus and Statistics Help Center. This center would provide tutoring services
for students enrolled in all Calculus courses (Math 165, Math 166, Math 265) and any statistics courses
(Math 321, Psyc 241, Soc 326, Econ 210). Having a centralized statistics help center would encourage
collaboration of students across different disciplines. Moving to the 1st floor would allow us to create a
better and more accessible learning environment for students. The 3rd floor space does not contain any
windows and research has shown that visual access to green spaces and natural daylight contributes to
learning. According to Ehrig and Davis, classrooms with larger windows and daylight demonstrate 1526% higher achievement in math and reading (2014).
Benefits of a Mathematics Emporium
We have identified the challenges encountered by students and our department in meeting the
needs of the University, described our vision of the Emporium at UND, and the implications of this model
for our current MLC. The potential benefits of the Emporium extend beyond the students and the
courses offered within the Emporium to the University as a whole. We anticipate the primary benefit of
a Math Emporium to be increased student learning and success rates. The UND Emporium will support
an effective curriculum through a more responsive and efficient method of delivery for students in
calculus preparation courses. In return, this will allow us to better meet the needs of students in Math
146 Applied Calculus, statistics courses offered outside of the Mathematics Department, distance
students, and in our own undergraduate and graduate programs. Decreased demands on instructional
staff will give faculty the opportunity to dedicate more time to scholarly activity and reduce instructional
costs. Finally, we discuss other potential advantages of the Emporium model.
Student Learning and Success in Calculus Preparation Courses
If we are faithful to the elements for successful implementation outlined above, the data
indicates that our student success rates in the calculus preparation and subsequent mathematics courses
will increase significantly. In this section we present our plan to support the NDUS Strategic Plan goal “to
increase students’ overall attainment rates through increased participation, retention, and completion”
(NDUS, 2014, p. 5).
Required time in lab, active engagement in doing mathematics using the instructional software
and just-in-time assistance available in place of time in lectures will serve as the foundation for increased
learning and success. Unlike the lecture format, student engagement in various forms is built into the
Emporium model. Students will be engaged in activities that result in learning when reading the e-book,
taking notes from reading or short lectures that can be replayed, working practice problems, reviewing
the immediate feedback on practice problems, taking low-stakes quizzes and exams, and working with
tutors, faculty and peers in the lab and during focus groups. Students can also choose to attend live
The variety of ways students will be expected to engage in learning the mathematics will facilitate an
effective curriculum. An effective curriculum will meet the needs of students in accordance with
research-based practices for learning (Ambrose, et. al., 2010; Brown, Roediger III & McDaniel, 2014),
support the goals of the Essential Studies program, and increase students’ ability to learn mathematics
and to retain and apply mathematical concepts. The instructional software will support students in the
development of procedural fluency and flexibility. The development of students’ conceptual
understanding of mathematics, quantitative reasoning, and communication skills will be the primary
mission of focus group meetings. Connections among mathematical topics will be developed in both
The curriculum will be efficient in the sense that students will be able to move quickly through
content they have mastered and spend additional time on more challenging concepts. Most feedback
will be immediate, so that students will not spend time repeating a misconception and can receive
assistance targeted to their individual need. Using this feedback, students will be able to evaluate their
level of confidence to determine whether to review a topic or to move forward.
Additionally, course expectations will be consistent across sections of multi-section courses
making it possible to ascertain the extent to which students have met course objectives and Essential
Studies Goals. Access to this information will allow us to alter the curriculum or delivery method to
address identified deficiencies.
Two tutoring centers to better serve student needs
With the students enrolled in calculus preparation courses receiving tutor support in the
Emporium we have the opportunity to address the inadequacies of our current MLC and to expand
services to meet the needs of additional UND students. Moreover, with the requirement for calculus
preparation students to work in the Emporium, going to a tutoring center will be a common activity for
students. Since students studying calculus and higher mathematics will not be in the Emporium,
students’ concerns about the perceptions of peers studying more advanced mathematics will be
significantly reduced.
Furthermore, the proposed re-creation of the current MLC will allow us to provide improved
services for Calculus I and II students and to expand services to include students enrolled in Calculus III
and statistics courses across campus, approximately 1,900 students each year.
Outreach and Distance
The UND Emporium will provide a means for us to better serve high school students across the
state of North Dakota. Presently, Math 103 College Algebra is the only dual credit mathematics course
offered to North Dakota high school students. The opportunity to earn this college credit is beneficial to
students who do not intend to pursue a math-intensive major. However, students who intend to pursue a
STEM major often need Math 107 Precalculus before enrolling in Math 165 Calculus I. Starting in Math
107 the first semester at UND can delay students’ on-time completion of their chosen program. Through
the UND Emporium, Math 107 could be offered as a dual credit course, with the high school teacher
serving as the tutor and focus group facilitator. This partnership with statewide high schools will expand
access to instructional opportunities, addressing remediation and supporting K-12 initiatives such as the
“Leveraging the Senior Year” initiative (NDUS, 2014).
The UND Math Emporium will also provide a means to offer calculus preparation courses online.
At this time, we do not offer any synchronous calculus preparation courses for distance students. This is
due, in part, to the 37% to 81% DFW rates of our previous online offerings of Math 103 College Algebra.
Currently, our calculus preparation courses are only offered asynchronously through UND
Correspondence. These courses regularly have DFW rates in the neighborhood of 70%. Offering calculus
preparation courses online could be possible using the UND Math Emporium instructional software and
the Smarthinking online tutoring service. The UND Math Emporium faculty would need to explore
options for providing tutoring and focus groups for online (non-outreach) students since Virginia Tech
faculty, Quinn and Williams (2003) assert that an online emporium model will not enjoy the same levels
of success. The results of their research suggest that student success in the emporium model is strongly
dependent on human help. They also found that online help was less effective and more expensive. In
2016 it is possible that the needed technology to overcome the identified obstacles will be available at a
reasonable cost.
Instructional Costs
The department will also benefit from the UND Math Emporium. Switching to an emporium
model will save the mathematics department instructional costs in the currency of faculty credit hours.
For the 2014-15 academic year the department generated 467 faculty credit hours. The projection for
the 2016-17 academic year is 464 faculty credit hours. Of these, 161 faculty credit hours are projected
for the calculus preparation courses, i.e. courses to be moved to the Emporium.
Based on the emporium at the University of Idaho, we approximate that administrating the
emporium will require at most 1 ½ FTE (Full-time Equivalent) of faculty time. This converts to 36 faculty
credit hours since the math discipline group identifies a 24 credit hour teaching load as full time.
At current enrollment levels the UND math emporium would require 58 focus groups of size 25
(best practices size) for the fall, and 33 focus groups of size 25 in the spring. This means a total of 91
focus group hours. Since there would only be one focus group preparation per week we convert this to
61 faculty credit hours based on the conversion factor of 3 focus group hours being equivalent to 2
faculty credit hours.
Best practices would require every live lecture to be scheduled three times per week. Since the
live lectures only require preparation and no assessment, we convert 2 live lectures to 1 faculty credit
hour of teaching load. So a total of 30 live lectures per week would equate to 15 faculty credit hours per
semester, which amounts to 30 faculty credit hours per academic year.
Since CILT may be able to cover some of the administrative load, and experience in other
emporiums indicate that students do not attend the live lectures, the department can expect to save at
least 37 faculty credit hours per year, and perhaps as much as 70 faculty credit hours per year (see
Appendix C).
As described in the “Current Challenges” section of this document, the issues needing attention
in the Mathematics Department extend beyond providing more responsive instruction for students in
our calculus preparation courses. Consequently, the identified savings in instructional costs need to be
re-invested in our department. Options for investment include a reduction in tenure-track faculty load to
allow for more time for scholarly activity, and reducing section sizes for Math 165 – Calculus I to allow
instructors to incorporate active learning instructional strategies. An option with the potential for return
is to offer every graduate sequence every year, and offer a topics course each semester. This would aid in
graduate student recruitment and retention, which in turn could help generate more faculty credit hours
in terms of graduate assistantships and further resources to be re-invested in the department. See
Appendix C for additional discussion of instructional costs.
Mathematics Students and Faculty
Undergraduate math majors would benefit from the UND Math Emporium if instructional
resources were re-invested to offer regular topics courses at the advanced undergraduate/beginning
graduate level. We currently offer these topics courses with such infrequency that students are wary of
registering for them since they don’t know what to expect. Thus, the courses are often in danger of
being closed due to low enrollment.
As explained in the section on instructional costs, graduate students in mathematics would
benefit from the UND Math Emporium in increased offerings. There is also the potential that the
teaching load of graduate students would be reduced, which could aid in recruitment of quality graduate
The tenure-track faculty of the department would benefit from the UND Math Emporium. On
average, 50% of tenure-track faculty effort is dedicated to teaching service courses, mostly at the lowerdivision level. For these courses it is rarely the case that the professor’s scholarly activity informs their
teaching, and even rarer that their teaching informs their scholarly activity. In contrast, each tenure-track
faculty is assigned to teach, on average, one course per year which is primarily for mathematics majors.
In this situation, it is much more likely that the professor’s scholarly activity will inform their teaching.
More regular offerings of special topics and graduate courses would allow more tenure-track faculty an
opportunity to teach a course which also informs their scholarly activity. This synergy between teaching
and scholarly activity is valuable as a faculty recruiting tool, and promotes faculty intellectual well-being
and scholarly activity production. This is clearly stated as a goal of the NDUS Strategic Plan (2014).
Curriculum responsive to needs of other departments
Math 146 Applied Calculus, Math 165 Calculus I, and Math 166 Calculus II each serve a variety of
majors. With the establishment of the UND Emporium, opportunities for the Mathematics Department
to be more responsive to the needs of these students will be created. Several options are presented in
the Instructional Costs Appendix C.
Other benefits
The UND Emporium facility will be ideal for administering placement exams during the summer
orientation program for incoming freshmen. Finally, as a benefit to UND as a whole, the UND
Emporium’s computers could contribute to UND's distributed computing project, the Citizen Science Grid
(, taking its computational power from approximately 1.6 teraflops to
approximately 5.2 teraflops.
Launch and Operation Costs
The largest cost for creating the emporium will be renovating the space. We are uncertain where
the emporium will be located. Several possible locations are discussed in a subsequent section of this
proposal. This approach also makes it impossible for us to reliably estimate the renovation cost. The next
largest cost for creating the emporium will be the furnishings.
# needed
Unit price
Total Cost
Chairs-Focus group rooms
Tables-Focus group rooms
Chairs-Lab area
Tables-lab area
Stools for standing height tables-lab area
Standing height tables-lab area
Chairs-study rooms
Tables-study rooms
4 office suite
Club chair-entry area
Sofa-entry area
Café Table-entry area
Café chairs-entry area
Check-in desk
Break Room – Table & Chairs
Tutor Lockers
Total Estimate
Table 5. Estimated Cost of Furnishing for the UND Math Emporium.
We recommend the Emporium contain 4 focus group rooms, a main lab area, 3 smaller study
rooms, office space, a small space for tutors, a check-in desk, and an informal entry area. In Table 5 we
provide an estimate of most of the major furnishing expenses. This estimate does not include the glass
relocatable walls that would separate all spaces in the Emporium. We would also need a tutor
notification system. CILT is currently investigating possible approaches and their costs.
The largest annual cost for the emporium would be the staff. While instructional costs would be
born by the university, we anticipate the following staffing needs:
Emporium director
This person would manage the overall Emporium, its software, and its hardware. The director
should be tenured or tenure track, and have the rank of at least Associate Professor.
Administrative assistant
This could be a partial appointment of the department secretary.
Tutor Coordinator
This person would manage the personnel of the Emporium and Calculus and Statistics Help
Center by scheduling, training, and interacting with the tutors. The coordinator would also be
responsible for leading focus groups, providing tutoring in the lab, and giving live lectures. The
tutor coordinator should have the rank of at least Senior Lecturer.
Tutors would be present during all operational hours of the Emporium to provide “just in time”
assistance for students. They would have regular training sessions to prepare them to effectively
help students. Tutors will be graduate teaching assistants or undergraduate students with a
strong proficiency in math. The tutor to student ratio would be approximately 1:20. As we
anticipate 6,300 student credit hours each year, and will require 1 hour each week in the
computer lab for each credit hour, this will require
6300 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑐ℎ 1 ℎ𝑜𝑢𝑟
1 𝑡𝑢𝑡𝑜𝑟
× 17 𝑤𝑒𝑒𝑘𝑠 ×
𝑐ℎ 𝑤𝑒𝑒𝑘
20 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 1 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟
We also calculated the annual cost for tutors by considering the number of tutor hours per week
we anticipate. Each week in the fall and spring semester, we anticipate an average of 150 tutor
hours per week and in the summer we anticipate an average of 32 tutor hours per week.
150 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟𝑠 34 𝑤𝑒𝑒𝑘𝑠
32 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟𝑠 11 𝑤𝑒𝑒𝑘𝑠
𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟
𝑠𝑢𝑚𝑚𝑒𝑟 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟
𝑎𝑐𝑎𝑑𝑒𝑚𝑖𝑐 𝑦𝑒𝑎𝑟
The tutor budget would be approximately $55,000 per academic year.
(Possibly) Database/Software engineer
This person would need to be proficient in or familiar with SQL, a scripting language, browser
extensions, JavaScript, HTML, CSS, and LaTeX. This position could be combined with the director.
A recurring cost for the emporium will be the computers. The lab will contain 162 workstations
with a workstation to computer ratio of 3:1, requiring 54 computers. We propose purchasing new
computers every three years. (Experience with the department's computer lab has shown, however, that
it is best to purchase them all at once, necessitating that we save for two years before purchasing in the
third year.) One possible computer that we have discussed with CILT is an OptiPlex 3030 All-in-One, Nontouch, which would cost $754. The leads to a hardware cost of $13,572 per year.
The budget to launch the emporium (excluding the renovation costs for the room) is
Table 6. Estimated Cost of Furnishings and Computers for UND Math Emporium.
The budget for yearly operations is approximately:
Staffing (director, admin. asst., tutor
coordinator, software engineer)
1.5 FTE
1.5 FTE + $68,572
Table 7. Estimated Budget for Annual Operation of UND Math Emporium
Potential Locations
The following are potential locations for the UND Math Emporium. They are presented in the
order we believe will best serve the students of UND.
1. First floor of Chester Fritz Library
Including the UND Math Emporium in this location will bring approximately 2,800 students
to the library each academic year. It would allow us to leverage the current library
renovations to offset the infrastructure costs. The first floor would also allow us to have a
separate entrance from outside. The downside is that this would take away from space in
the library for other things. The first floor is also slightly below ground level, which
contributes to undesirable stereotypes of a computer lab. It may also not be ready until the
2017-2018 AY (or later), which is longer than we would prefer to wait.
2. Second floor of Chester Fritz Library
In contrast to the first floor, this would have more natural lighting. The downside is it will be
completed after the first floor, and would not have outside access.
3. Southeast corner of Witmer
Witmer forms an “L” shape, and there is an approximately 50’ x 120’ area of land in the
angle of this L. We propose constructing an addition onto the south side of Witmer for the
emporium. This would also have the advantage of being adjacent to the math department.
Because this would be new construction, the new space could be created with maximum
daylight and visual access to the outdoors. The primary disadvantage is cost and time.
Construction would be expensive, approximating one million dollars.
The primary downside of this location is the timeframe. A capital project would require a
request from the state board, the chancellor, and possibly the state legislature. This would
mean that the allocation could not happen until the summer of 2017, so that the emporium
would not be completed until fall of 2019.
4. Former School of Medicine
This will be available late fall of 2016. The primary downside is that its location is not central
in the campus. A central, easy to access location has been shown to be extremely important
in the success of a math emporium.
5. First floor of Montgomery
With the availability of the former School of Medicine, several departments will be
relocating. Assuming CSD and the dean’s office move, we would be able to renovate the
building for the emporium. Preliminary investigations have shown that the building may be
difficult to renovate. Additionally, renovating the building starting in 2017 would mean that
the emporium would not be ready until fall of 2018 at the earliest.
Considering all these factors, our ideal choice would be for the emporium to be in the first floor
of the Chester Fritz Library until an addition is completed for Witmer. If an addition to Witmer happens
the walls on the classrooms could be moved into the Witmer location. The relocation of the emporium
during the summer of 2019 would also allow incorporating lessons learned from the first two years of
the emporium.
If the necessary physical space is completed by the Fall of 2016 we believe the following time-line is
Summer 2016
Trial run of select
courses In Math
Fall 2016
Full implementation
of Math Emporium
Spring 2017
Add Distance and
Outreach Courses
Fall 2017
The courses selected to run in the Fall of 2016 would also be offered in the traditional format in order to
compare success rates and learning outcomes between the two delivery methods. Since enrollment in
the calculus preparation courses is less in the spring than the fall, full implementation in the Spring 2017
allows us to continue to refine the system with a smaller set of students.
The UND Math Emporium is truly a campus-wide initiative with the potential to promote the
goals of the NDUS Strategic Plan (NDUS, 2014). In this document we presented a broad range of reasons
to support the creation of the UND Math Emporium. The faculty of the Mathematics Department are
dedicated to offering a high quality curriculum and to serving the UND community to the best of our
ability. The challenges we face in our efforts to do so are many and have been compounded over time.
The emporium model has helped other universities facing similar issues to increase student success in
mathematics while decreasing instructional costs. We have every reason to believe UND will experience
comparable results, the impact of which will resonate throughout the UND community and the state of
North Dakota.
Ambrose, S. A., Bridges, M. W., DiPietro, M., Lovett, M. C., Norman, M. K. (2010). How Learning Works: 7
Research-Based Principles for Smart Teaching. Jossey-Bass. San Francisco, CA.
Brown, P. C., Roediger III, H. L., and McDaniel, M. A. (2014). Make it Stick: The Science of Successful
Learning. Belknap Press. Cambridge, MA.
Complete College America. (2012). Remediation: Higher Education’s Bridge to Nowhere.
de Winstanley, P. A. & Bjork, R. A. (2002). Successful Lecturing: Presenting Information in Ways That
Engage Effective Processing. New Directions for Teaching and Learning, 89, pp. 19-31.
Ehrig, C., & Davis, J. (2014). Designing with Intelligence: Dynamic Facades for Dynamic
Learning [PowerPoint slides]
Halcrow, C. and Iiams, M. (2011), You Can Build It, but Will They Come?, PRiMUS, 21(4), pp. 323-337
Mathematics Department Assessment Committee. (2015). Fall 2014 Assessment of Essential Studies
Goals for Math 103. Grand Forks, ND: Author
The National Center for Academic Transformation. (2013). How to Redesign a College-Level or
Developmental Math Course Using the Emporium Model.
The National Center for Academic Transformation. (n.d.). Five Principle of Successful Course Redesign.
North Dakota University System. (2014). A Framework for Transformational Change: Report to the State
Board of Higher Education: NDUS Strategic Plan 2015-2020, Unleashing potential, inspiring our future. Accessed August 15 2015.
Quinn, F and Williams, M., “Lessons from the Emporium 1: Goals and economics,” Preprint November
Squires, John. Aug 29, 2012. “The Emporium Model: Fact and Fiction”, Getting Past Go. Accessed Jul 30,
Twigg, C. A. (2011) “The Math Emporium: Higher Education's Silver Bullet”, Change: The Magazine of
Higher Learning. 43(3).
Appendix A: Disciplines that require Mathematics service courses
A list of service courses offered by the UND Mathematics Department
Math 102 Intermediate Algebra
Math 103 College Algebra
Math 105 Trigonometry
Math 107 Pre-calculus
Math 112 Transition to Calculus
Math 115 Introduction to Mathematical Thought
Math 146 Applied Calculus I
Math 165 Calculus I
Math 166 Calculus II
Math 207 Introduction to Linear Algebra
Math 208 Discrete Mathematics
Math 265 Calculus III
Math 266 Elementary Differential Equations
Math 277 Math for Elementary Teachers
Math 321 Applied Statistical Methods
Math 352 Partial Differential Equations
Math 377 Geometry for Elementary School Teachers
Math 400 Math Methods for Secondary Education
Math 477 Topics in Elementary Mathematics Education (3 rotating topics)
Medical Laboratory Science, Nursing, Nutrition and Dietetics, Psychology, Public Administration,
and Elementary Education all require Math 103. Elementary Education also requires Math 277. Middle
level education requires Math 115, Math 277, Math 377, Math 400, and Math 477 plus one of Math 146,
Math 165, or Math 208.
Accountancy, Aviation, Entrepreneurship, Finance, Information Systems, Management,
Marketing, and Technology all require Math 103 and Math 146. Technology also requires Math 105.
Economics requires either Math 103 and Math 146, or Math 165, Math 166, Math 265, and
Math 266. Biology requires either Math 146 or Math 165.
Atmospheric Sciences, Chemical Engineering, Electrical Engineering, Geological Engineering,
Mathematics, Mechanical Engineering, Petroleum Engineering, and Physics all require the calculus
sequence: Math 165, Math 166, Math 265, and Math 266. Electrical Engineering may also require Math
207 and Math 208. Physics also requires Math 207 and Math 352. Many engineering programs highly
suggest Math 321.
Computer Science, Forensic Science, and the BS Ed Science programs all require Math 165 and
Math 166. Computer Science also requires Math 208, and may also require Math 207.
Occupational Safety and Environmental Health requires Math 146. Chemistry requires Math 165,
Math 166, and Math 265. Geology requires Math 165, Math 166, and Math 265 or Math 321 for the BS.
The BA in Geology requires Math 103 and Math 105.
Appendix B: Suggested Emporium Layout
Main Lab Area
Appendix C: Instructional Costs
In order to forecast instructional costs, we computed the average enrollment over the last three
years for multi-section courses offered by the department.
S14 F14 S15 F15 8/12
Ave F
Ave S
159 363 163
358.00 178.33
451 648 374
649.67 434.00
136 210 115
232.33 127.67
351 401 343
400.67 347.00
176 252 170
270.67 177.00
211 192 199
179.67 194.67
71 36 49
74 64 71
115 149 126
145.33 116.67
107 105 111
102.00 109.00
73 72 71
Table 8. Projected enrollment for the AY16-17.
proj F16
proj S17
We converted this to a credit hour load by assuming that certain courses would be covered in
large sections (on the order of 100 students), while the remaining would be in small sections (room
capacity 35 or 36).
faculty cr
1L 1S
2L 1S
1L 1S
18 at 35 14 at 35
1 at 36
7 at 35
4 at 35
1 at 25
1 at 20
4 at 100 3 at 120
7 at 36
5 at 36
6 at 36
6 at 36
2 at 36
2 at 36
2 at 36
2 at 36
5 at 36
4 at 36
3 at 36
4 at 28
3 at 36
3 at 36
Table 9. Credit hours required to teach multi-section courses.
For Math 92 Algebra Prep II, and Math 93 Algebra Prep III the total enrollment should equal the
forecast enrollment for Math 102 which is being discontinued. Each semester there will be one small
section (capacity 35) of Math 92 taught 4 days a week for the first 8 weeks, followed by a section of
Math 93 taught four days a week for the second 8 weeks. Large sections for Math 92 and Math 93 will be
capped at 100 students each.
Meanwhile, for the UND Math Emporium load the forecast was used to compute the number of
focus groups of size 25 required for each course and for each semester.
Table 10. Number of size 25 emporium focus groups.
A proposed live lecture schedule offering every lecture 3 times per week is:
Table 11. Example schedule giving 3 time slots per live lecture.
This assumes that there would be 2 lectures per week for Math103, 1 lecture per week for
Math105, and 3 lectures per week for Math107 (all based on one fewer lecture than the number of
credit hours). We would propose to keep 2 lectures per week for both Math92 and Math93 since the
student population is likely to need more support than the student populations for the other courses.
We assume that 2 live lectures per week are equivalent to 1 credit hour of teaching load, and
that 3 focus group sessions per week are equivalent to 2 credit hours of teaching load.
Costs of options:
We can also compute the cost in faculty credit hours required to carry out certain options.
For example, to offer every graduate sequence every year, and a special topics course every
regular semester would require 12 faculty credit hours.
Best practices in teaching calculus I include using more active learning facilitated by smaller
section sizes. The Mathematical Association of America recommends that sections of math classes be no
larger than 30 students, so smaller sections of calculus I would be 25 students per section. To achieve
this, we would need to schedule 3 more sections each semester. This would be 6 additional sections for
the year totaling 24 faculty credit hours.
To reduce the section capacities of Math146 to 60 students per section (much closer to the
national average of 45) would also require 3 additional sections per semester totaling 18 faculty credit
hours. To get the section capacities of Math146 to 35 students per section (much closer to MAA
recommendations) would require 45 faculty credit hours.
Currently Math146 Applied Calculus is not serving the needs of the students enrolled. In
particular, representatives from the Departments of Aviation and Biology have indicated support for a
quantitative reasoning course. This course would replace Math146 as a required course for the aviation
majors, and supplement the math requirements for biology majors. The development of such a course is
not possible given current resources available to the math department. The UND Math Emporium could
facilitate this project.
Appendix D: Multiple Mini Emporiums
A recurring suggestion is to avoid the difficulties of renovating by having several smaller
emporiums spread throughout campus. This approach would require more computers, more overall
space, more administration, and more tutors.
Each focus group room would require an adjacent emporium lab room. Assuming each room
has a capacity of 30 working students, we would need 10 computers in each room. The price for
furnishings would increase proportionally. Because we would need to staff tutors expecting that each
location would be fully utilized, and we cannot split tutors to cover multiple locations, the number of
tutors would increase at a rate greater than proportionally.
Therefore, the launch budget is approximately:
Single Emporium Cost
Multiple Emporium Cost
Table 12. Budget to launch multiple mini emporiums.
The budget for yearly operations is approximately:
Single Emporium Cost
Staffing (director, admin. asst., tutor
coordinator, software engineer)
1.5 FTE
Multiple Emporium Cost
2.5 FTE
1.5 FTE + $68,572
2.5 FTE + $147,030
Table 13. Annual budget to operate multiple mini emporiums.
This shows that it will cost an additional two full time salaries to operate multiple miniature emporiums,
as well as requiring more classroom space. For these reasons, we do not believe this approach will be