MAA Minicourses are open only to persons who register for the Joint Meetings and pay the Joint Meetings registration fee in addition to the appropriate minicourse fee. The MAA reserves the right to cancel any minicourse that is undersubscribed. Participants in minicourses 4, 5, and 9 are required to bring their own laptop computer equipped with appropriate software. Instructions on how to download any data files needed for those courses will be provided by the organizers. The enrollment in each minicourse is limited to 50; the cost of a minicourse is US$80.
Minicourse #1: Humanistic mathematics, presented by Gizem Karaali, Pomona College, and Eric Marland, Appalachian State University; Part A, Wednesday, 9:00 a.m.–11:00 a.m.; Part B, Friday, 9:00 a.m.–11:00 a.m. As a scholarly stance, humanistic mathematics describes an approach to mathematics that views it as a human endeavor and focuses on its aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects. As a pedagogical framework, humanistic mathematics explores and builds on the relationship of mathematics with its nontraditional partners in the humanities, the fine arts, and social sciences, providing additional perspective for the role of mathematics in a liberal arts education. This minicourse exposes participants to both facets of humanistic mathematics.
In the first session, participants will learn about the implications of a humanistic approach to teaching and explore how it can contribute to a more sophisticated understanding of mathematics for all students. Also included will be a discussion of common implementation issues and an overview of a spectrum of materials available to use in the classroom. In the second session, participants will engage with the scholarship of humanistic mathematics, a body of literature that eschews disciplinary jargon in favor of reaching a more diverse audience. After a thorough introduction, participants will, through guided group work, initiate their own scholarly projects. Possible venues of communication, collaboration, and dissemination of work in humanistic mathematics will be discussed.
Minicourse #2: CATALST: Introductory statistics using randomization and bootstrap methods, presented by Andrew Zieffler, Robert delMas, and Nicola Parker, University of Minnesota; Part A, Thursday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 1:00 p.m.–3:00 p.m. This workshop introduces and provides hands-on experience with curriculum materials, lesson plans, and student assessments developed as part of the CATALST (Change Agents for Teaching and Learning Statistics) project (NSF DUE-0814433). Focused on the introductory, noncalculus-based statistics course, CATALST’s goals were to radically change the content and pedagogy in such a course.
CATALST makes exclusive use of simulation to carry out inferential analyses. The course also builds on best practices and materials developed in statistics education, research and theory from cognitive science, as well as materials and methods that are successfully achieving parallel goals in other disciplines (e.g., mathematics and engineering education).
Minicourse participants will be introduced to the TinkerPlots™ software. They will learn how this software can be used in the classroom to introduce students to randomization and bootstrap methods through empirical simulation. In addition, participants will leave the workshop with lesson plans, in-class student activities, and data to help them teach a one-semester introductory statistics course using randomization and bootstrap methods.
Minicourse #3. Improvisation for the mathematics classroom, presented by Andrea Young, Ripon College; Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.–5:30 p.m. Improvisational comedy, or just simply improv, is theater that is made up on the spot. Besides being funny, improv comedians take risks, solve problems, and support fellow actors. In this interactive minicourse, participants will explore how some of the fundamental tenets of improv can be applied to creating an open and engaging mathematics classroom. Participants will learn theater exercises that have been modified for use in undergraduate math courses, both as tools to demonstrate or review course content and as methods to boost participation, collaboration, and creativity of students. Participants will gain experience doing and leading these exercises, which will range from introductory name games to verbal concept-connection exercises to physical exam-review activities. We will also explore the concept of “teacher as performer”, and we will see how classroom management skills can be enhanced by the study of improv. Comfortable clothes and shoes are encouraged.
Minicourse #4. Teaching introductory statistics (for instructors new to teaching intro stats), presented by Michael Posner, Villanova University, and Carolyn Cuff, Westminster College; Part A, Wednesday, 9:00 a.m.–11:00 a.m. ; Part B, Friday, 9:00 a.m.–11:00 a.m. This minicourse, intended for instructors new to teaching statistics, exposes participants to the big ideas of statistics and the ASA-endorsed Guidelines for Assessment and Instruction in Statistics Education (GAISE) report. It considers ways to engage students in statistical literacy and thinking, and contrast conceptual and procedural understanding in the first statistics course. Participants will engage in many of the classic activities that all statistics instructors should know. Internet sources of real data, activities, and best practices articles will be examined. Participants will find out how they can continue to learn about the best practices for the first course in statistics by becoming involved in statistics education related conferences, newsletters, and groups. Participants are required to bring their laptops.
Minicourse #5. Using randomization methods to build conceptual understanding of statistical inference, presented by Robin H. Lock and Patti Frazer Lock, St. Lawrence University; Kari Lock Morgan and Eric Frazer Lock, Duke University; and Dennis Frazer Lock, Iowa State University; Part A, Thursday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 1:00 p.m.–3:00 p.m. The goal of this minicourse is to demonstrate how computer simulation techniques, such as bootstrap confidence intervals and randomization tests, can be used to introduce students to fundamental concepts of statistical inference in an introductory statistics course. Simulation methods are becoming increasingly important in statistics, and can be effective tools for building student understanding of inference. Through easy to use free online tools and class activities, participants will see how to engage students and make these methods readily accessible. We illustrate how to use these methods to build conceptual understanding and also how to integrate them into an existing introductory statistics course without requiring a major overhaul. Participants are required to bring their laptops.
**CANCELLED**Minicourse #6. Historical role-playing in the mathematics classroom, presented by John P. Curran, Eastern Michigan University; Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00 a.m.–11:00 a.m. Participants in this session will learn how to use role-playing games in the mathematics classroom according to the “Reacting to the Past” pedagogy. This method lends itself to project-based and group-work-oriented courses, and encourages intensive student participation.
The presenter will discuss two games that he uses, including one he has cowritten. The “Ways & Means 1935” game can be used in a quantitative literacy course. Players, representing congressmen, debate the form of the Social Security bill, which contained a broad range of social welfare provisions in addition to old-age pensions. The game “Math Wars 1870: Educating for Empire”, designed by David Cohen et al, is appropriate for a history of mathematics or a mathematical education course. Students act as members of or witnesses testifying at the Royal Commission on Scientific Instruction and the Advancement of Science, intended to reform education at Cambridge University.
In order to learn how to teach with this method, and to gain confidence in it, it is important to play such a game oneself. We will spend part of the session playing a shortened version of one of the games mentioned above.
The session will include a discussion of how to develop games for your own courses.
Minicourse #7. Mathematics and dance, presented by Karl Schaffer, De Anza College; Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.–5:30 p.m. We will present several activities which combine dance and mathematics content in nontrivial ways. The activities connect to a variety of dance forms, as well as to several areas of mathematics, including symmetry, number theory, combinatorics, dynamical systems, and topology. Participants will take away activities useful in a wide range of undergraduate math classes or math clubs. The activities are collaborative and physically comfortable, and easily performed by those with little or no dance experience. These include folk dances, improvisations, and choreographic exercises with specific mathematical content, as well as kinesthetic tasks involving explorations of mathematical principles. In all cases, mathematics will illuminate the dance, and the dance will realize, in kinesthetic form, the mathematical concepts.
Minicourse #8. Directing undergraduate research, presented by Aparna Higgins, University of Dayton; Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00 a.m.–11:00 a.m. This minicourse will cover many aspects of facilitating research by undergraduates, such as getting students involved in research, finding appropriate problems, deciding how much help to provide, and presenting and publishing the results. Similarities and differences between research conducted during summer programs and research that can be conducted during the academic year will be discussed. The minicourse is designed for faculty who are new to directing undergraduate research. Although the examples used will be primarily in the area of discrete mathematics, the strategies discussed can be applied to any area of mathematics.
Minicourse #9. WeBWorK: An open source alternative for generating and delivering online homework problems, presented by John Travis, Mississippi College; Jason Aubrey, University of Missouri; and Paul Pearson, Hope College; Part A, Wednesday, 2:15 p.m.–4:15 p.m., Part B, Friday, 1:00–3:00 p.m. We will introduce participants to the WeBWorK online homework system. Supported by grants from the NSF, WeBWorK has been adopted by well over 500 colleges, universities, and secondary schools and is a popular open source alternative to commercial products. WeBWorK can handle problems in college algebra, calculus, linear algebra, ODEs, and more and comes with an extensive library of nearly 30,000 problems across the mathematics curriculum. WeBWorK recognizes a multitude of mathematical objects and allows for elegant solution checking. This minicourse will introduce participants to WeBWorK and equip participants with the knowledge and skills to use WeBWorK in the classroom. Participants are required to bring their own laptops/tablet computers with wireless Internet capabilities.
**CANCELLED**Minicourse #10. Heavenly mathematics: The forgotten art of spherical trigonometry, presented by Glen Van Brummelen, Quest University, and Joel Silverberg, Roger Williams University; Part A, Friday, 1:00 p.m.–3:00 p.m.; Part B, Saturday, 1:00 p.m.–3:00 p.m. Trigonometry came into being at the birth of science itself, merging Greek geometric models of the motions of celestial bodies with the desire to predict where the planets will go. With the sky as the arena, spherical trigonometry was the “big brother” to the ordinary plane trigonometry our children learn in school. We shall explore the surprisingly elegant theory that emerges, as well as its appropriation into mathematical geography motivated by the needs of Muslim religious ritual. The beautiful modern theory of spherical trigonometry (including the pentagramma mirificum), developed by John Napier along with his logarithms, leads eventually to an astonishing alternate path to the subject using stereographic projection discovered only in the early 20th century. We conclude with a consideration of some of the ingenious techniques developed by navigators in the 19th century to find their locations, using as data only a couple of observations of stellar altitudes.
Minicourse #11. Public- and private-key cryptography, presented by Chris Christensen, Northern Kentucky University, and Jeffrey Ehme, Spelman College; Part A, Wednesday, 4:45 p.m.–6:45 p.m.; Part B, Friday, 3:30 p.m.–5:30 p.m. The interesting mathematical aspects of public-key ciphers have sparked interest by mathematics faculty in these ciphers as applications of mathematics that can be presented in undergraduate courses. Often ignored, however, are the modern private-key ciphers— “the workhorses of cryptography”. Modern private-key ciphers are equally mathematically interesting. In this minicourse, we will explore both modern public-key and private-key ciphers and their mathematical foundations. We will also briefly explore the historical evolution of both types of ciphers. No previous experience with these topics is assumed.
Minicourse #12. A Game Theory path to quantitative literacy, presented by David Housman, Goshen College; Part A, Wednesday, 9:00 a.m.–11:00 a.m.; Part B, Friday, 9:00 a.m.–11:00 a.m. Game Theory, defined in the broadest sense, can be used to model many real world scenarios of decision making in situations involving conflict and cooperation. Further, mastering the basic concepts and tools of game theory requires only an understanding of basic algebra, probability, and formal reasoning. These two features of Game Theory make it an ideal path to developing habits of quantitative literacy among our students. This audience participation minicourse develops some of the material used by the presenter in general education and math major courses on Game Theory and encourages participants to develop their own, similar, courses.
Minicourse #13. Teaching an applied topology course, presented by Colin Adams, Williams College, and Robert Franzosa, University of Maine; Part A, Thursday, 9:00 a.m.–11:00 a.m.; Part B, Saturday, 9:00 a.m.–11:00 a.m. Applications of topology have proliferated in recent years. It is now possible to teach a course in topology, still covering much of the same material that would appear in a traditional topology course, but motivated entirely by applications. Typically, offering an “applied” topology course immediately doubles the enrollments. Applications include areas such as geographic information systems, robotics, chaos, fixed point theory in economics, knots in DNA and synthetic chemistry, and the topology of the spatial universe. Through the applications students become engaged with the material. In this minicourse we will introduce the various applications, and provide participants with the background necessary to design and teach their own applied topology course.
Minicourse #14. Visualizing projective geometry through photographs and perspective drawings, presented by Annalisa Crannell, Franklin & Marshall College; Marc Frantz, Indiana University Bloomington; and Fumiko Futamura, Southwestern University; Part A, Wednesday, 2:15 p.m.– 4:15 p.m.; Thursday, 1:00 p.m.–3:00 p.m. Projective geometry is the study of properties invariant under projective transformations, often taught as an upper level course. Although projective geometry was born out of the ideas of Renaissance artists, it is often taught without any reference to perspective drawing or photography. This minicourse seeks to re-establish the link between mathematics and art, motivating several important concepts in projective geometry, including Desargues’ Theorem, Casey’s Theorem and its applications, and Eves’ Theorem. This minicourse will consist of hands-on activities, but no artistic experience is required.
Minicourse #15. Developing strong mentoring relationships, presented by Donna Joyce Dean, Association for Women in Science; Part A, Wednesday, 2:15 p.m.– 4:15 p.m.; Part B, Friday, 1:00 p.m.–3:00 p.m. This minicourse will provide individuals with an appreciation for the importance of mentoring, from the mentor’s perspective as well as from the mentee’s perspective. Pragmatic tools and techniques will be presented that participants can deploy in their roles as mentor or mentee. The intent of the minicourse is to help individuals to 1) understand the differences among mentoring, advising, coaching, and sponsoring roles; 2) recognize how to identify mentoring needs from both perspectives; 3) learn how to identify and approach potential mentors; 4) understand how mentors can help participants achieve their professional goals; 5) identify the do’s and don’ts involved in being a good mentee or mentor; and 6) appreciate how mentoring can have an impact on understanding one's work-life satisfaction.