University

Of

North Dakota

Math Emporium

Proposal

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 non-

traditional 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.

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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

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Definitions

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.

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Introduction

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.

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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

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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 pre-

or 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 % ABC

102 1,601 54

103 3,312 70

105 95 76

107 1,080 52

112 74 69

146 2,243 46

Table 1. ABC Rates for all UND Calculus Preparation Courses and Applied Calculus

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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.

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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

2009-10 14,197

2010-11 15,095 6.3%

2011-12 16,291 14.7%

2012-13 17,946 26.4%

2013-14 21,053 48.3%

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

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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

previously.

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.

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Math

Course

I (really) want to

teach this course

I don’t mind

teaching this course

I (really) do NOT

want to teach this

course

102 1 6 9

103 1 9 6

105 3 10 3

107 5 9 2

112 1 8 7

115 2 5 9

146 4 6 6

165 11 5 0

166 14 1 1

Table 3. Tenure-track Faculty Responses to “Teaching Preference Questionnaire.”

Conclusion

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 Web-

based 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

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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 e-

textbook 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

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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.

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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

lectures.

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

answer.

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

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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

Institution Course Traditional

Success Rate

Emporium

Success Rate

Increase in

Success Rate

Mississippi Valley State

University

Intermediate Algebra 36% 49% 13%

Santa Fe College Intermediate Algebra 59% 78% 19%

University of Alabama Intermediate Algebra 40% 78% 38%

University of Central

Missouri

Intermediate Algebra 68% 85% 17%

University of Idaho Intermediate Algebra 59% 75% 16%

Algebra 59% 74% 15%

Pre-Calculus 68% 75% 7%

Cleveland State Community

College

College Algebra 65% 79% 14%

Louisiana State University College Algebra 64% 75% 11%

Trigonometry 59% 79% 20%

SUNY at Oswego College Algebra 42% 52% 10%

University of Central Florida College Algebra 65% 78% 13%

University of Missouri-St.

Louis

College Algebra 50% 78% 28%

Table 4. Percentage of Students with Final Grades of C or Better in a Traditional Versus Emporium Course.

16

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 15-

26% 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).

17

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

lectures.

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

settings.

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.

18

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.

19

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

students.

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 lower-

division 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).

20

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

(http://csgrid.org/csg/), 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.

Item # needed Unit price Total Cost

Chairs-Focus group rooms 112 $500 $56,000

Tables-Focus group rooms 56 $504 $28,224

Chairs-Lab area 40 $500 $20,000

Tables-lab area 4 $1500 $6,000

Stools for standing height tables-lab area 10 $700 $7,000

Standing height tables-lab area 5 $630 $3,150

Chairs-study rooms 12 $215 $2,580

Tables-study rooms 3 $1000 $3,000

4 office suite 1 $16,000 $16,000

Club chair-entry area 2 $450 $900

Sofa-entry area 1 $1,500 $1,500

Café Table-entry area 1 $308 $308

Café chairs-entry area 4 $215 $860

Check-in desk 1 $1000 $1,000

Kitchenette 1 $1,380 $1,380

Break Room – Table & Chairs 1 $523 $523

Tutor Lockers 8 $121 $968

Total Estimate $149,393

Table 5. Estimated Cost of Furnishing for the UND Math Emporium.

21

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

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

𝑦𝑒𝑎𝑟×

1 ℎ𝑜𝑢𝑟

𝑐ℎ 𝑤𝑒𝑒𝑘× 17 𝑤𝑒𝑒𝑘𝑠 ×

1 𝑡𝑢𝑡𝑜𝑟

20 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠×

$10.25

1 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟=

$54,889

𝑦𝑒𝑎𝑟

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

𝑤𝑒𝑒𝑘×

34 𝑤𝑒𝑒𝑘𝑠

𝑦𝑒𝑎𝑟×

$10.25

𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟] + [

32 𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟𝑠

𝑤𝑒𝑒𝑘×

11 𝑤𝑒𝑒𝑘𝑠

𝑠𝑢𝑚𝑚𝑒𝑟×

$10.25

𝑡𝑢𝑡𝑜𝑟 ℎ𝑜𝑢𝑟]

=$55,883

𝑎𝑐𝑎𝑑𝑒𝑚𝑖𝑐 𝑦𝑒𝑎𝑟

The tutor budget would be approximately $55,000 per academic year.

22

(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, Non-

touch, 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

approximately:

Item Cost

Furnishings $149,393

Computers $40,716

Total $190,109

Table 6. Estimated Cost of Furnishings and Computers for UND Math Emporium.

The budget for yearly operations is approximately:

Item Cost

Computers $13,572

Tutors $55,000

Staffing (director, admin. asst., tutor

coordinator, software engineer)

1.5 FTE

Total 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.

23

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.

Timeline

If the necessary physical space is completed by the Fall of 2016 we believe the following time-line is

feasible:

Curriculum Development

Summer 2016

Trial run of select courses In Math

Emporium

Fall 2016

Full implementation of Math Emporium

Spring 2017

Add Distance and Outreach Courses

Fall 2017

24

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.

Conclusion

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.

25

References

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. http://www.thencat.org/Guides/Math/CLM-

PDF-TOC.html

The National Center for Academic Transformation. (n.d.). Five Principle of Successful Course Redesign.

http://www.thencat.org/PlanRes/R2R_PrinCR.htm.

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.

http://www.ndus.edu/uploads/reports/127/a-framework-for-transformational-changes-2015-2020-

strategic-plan.pdf. Accessed August 15 2015.

Quinn, F and Williams, M., “Lessons from the Emporium 1: Goals and economics,” Preprint November

2003. http://www.math.vt.edu/people/quinn/education.

Squires, John. Aug 29, 2012. “The Emporium Model: Fact and Fiction”, Getting Past Go.

http://gettingpastgo.org/blog/2012/08/29/the-emporium-model-fact-and-fiction/. Accessed Jul 30,

2015.

Twigg, C. A. (2011) “The Math Emporium: Higher Education's Silver Bullet”, Change: The Magazine of

Higher Learning. 43(3).

26

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.

27

Appendix B: Suggested Emporium Layout

Main Lab Area

28

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.

Course F12 S13 F13 S14 F14 S15 F15 8/12 Ave F Ave S proj F16 proj S17

102 285 213 426 159 363 163 na 358.00 178.33 na na

103 561 477 740 451 648 374 595 649.67 434.00 650 435

107 242 132 245 136 210 115 193 232.33 127.67 235 130

146 391 347 410 351 401 343 425 400.67 347.00 400 350

165 282 185 278 176 252 170 274 270.67 177.00 252 180

166 166 174 181 211 192 199 197 179.67 194.67 180 200

207 42 36 37 71 36 49 68 38.33 52.00 70 70

208 71 74 73 74 64 71 51 69.33 73.00 70 70

265 140 109 147 115 149 126 199 145.33 116.67 150 130

266 103 109 98 107 105 111 106 102.00 109.00 108 108

321 66 72 74 73 72 71 108 70.67 72.00 108 108

Table 8. Projected enrollment for the AY16-17.

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).

Course F16

sections

S17

sections

faculty cr

hr

92 1L1S 1L 1S 8

93 2L 1S 1L 1S 10

103 18 at 35 14 at 35 96

105 0 1 at 36 2

107 7 at 35 4 at 35 44

112 1 at 25 0 1

115 1 at 20 0 3

146 4 at 100 3 at 120 21

165 7 at 36 5 at 36 48

166 6 at 36 6 at 36 44

207 2 at 36 2 at 36 8

208 2 at 36 2 at 36 12

265 5 at 36 4 at 36 36

266 3 at 36 4 at 28 21

321 3 at 36 3 at 36 18

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

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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.

course F S

92 6 4

93 10 4

103 26 18

105 1 1

107 10 5

112 1 1

Total 54 33

Table 10. Number of size 25 emporium focus groups.

A proposed live lecture schedule offering every lecture 3 times per week is:

M T W H F

8

9

10 107.1 103.1 107.3 103.2 107.2

11 92.1 105 92.3

noon 93.1 93.3

1

2 107.2 103.2 107.1 103.1 107.3

3 105 92.2 92.1

4 93.2 93.1

5

6 107.3 103.1 107.2 103.2 107.1

7 92.3 92.2 105

8 93.3 93.2

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.

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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.

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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:

Item Single Emporium Cost Multiple Emporium Cost

Furnishings $149,393 $221,323

Computers $40,716 $60,320

Total $190,109 $281,642

Table 12. Budget to launch multiple mini emporiums.

The budget for yearly operations is approximately:

Item Single Emporium Cost Multiple Emporium Cost

Computers $13,572 $20,107

Tutors $55,000 $126,923

Staffing (director, admin. asst., tutor

coordinator, software engineer)

1.5 FTE 2.5 FTE

Total 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

viable.