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«University Of North Dakota Math Emporium Proposal Executive Summary The University of North Dakota Mathematics Department seeks support to redesign ...»

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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 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

Definitions

Introduction

Current challenges

What is a Math Emporium?

The UND Math Emporium

Benefits of a Mathematics Emporium

Launch and Operation Costs

Potential Locations

Timeline

Conclusion

References

Appendix A: Disciplines that require Mathematics service courses

Appendix B: Suggested Emporium Layout

Appendix C: Instructional Costs

Appendix D: Multiple Mini Emporiums

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.

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.

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.



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