Minicourses

All MAA MathFest 2015 Minicourses will take place at the Omni Shoreham Hotel
2500 Calvert St NW
Washington, DC 20008
Map.

MAA Minicourses are partially supported by the William F. Lucas Fund. Read more about Prof. Lucas here.

1. The Hitchhiker’s Guide to Mathematics

Part A: Thursday, August 6, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Hampton Room
Part B: Saturday, August 8, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Hampton Room

A guided tour of some little known attractions of elementary mathematics, all closely related to and easily accessible from freshman-sophomore college mathematics. In the midst of these seemingly mundane surroundings lurk wonders to surprise, delight, and intrigue the mathematical eye. Some may make great enrichment topics for the participants’ students, but the course’s primary motivations are the edification and enjoyment of the participants themselves. 

The Hitchhiker’s Guide to Mathematics answers questions like these: What simple method reveals the sum of the reciprocals of a polynomial’s roots? What does the quadratic formula have to do with the functions max(x,y) and min(x,y)? What is the point of reversing a polynomial and its derivative, and then dividing one into the other? What are palindromic polynomials, and how can they be solved up to degree 9?

Participants are encouraged to bring a calculator (or mobile device/laptop with basic computing functionality).

Dan Kalman, American University
Bruce Torrence, Randolph-Macon College

2. The Mathematics of Games and Gambling

Part A: Wednesday, August 5, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Hampton Room
Part B: Friday, August 7, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Hampton Room

In this course, you will learn about the mathematics that underlies many of the great games that people enjoy today. Learn the optimal basic strategy for playing blackjack, along with some simple card counting techniques. Learn the mathematics needed to play great poker and other games. Since you’re a mathematician, most people assume that you’re already good at these things. This course will teach you those skills and you’ll learn some fun mathematics along the way.

The Game Plan:

• Great Expectations and Winning Wagers Optimal Blackjack and Simple Card Counting
• Scams and Hustles 
Zero Sum Games and Practical Poker Probabilities

All material in the course will be accessible to undergraduates. The instructor takes no responsibility for any get-rich-quick schemes that students learn from this class. 

Arthur Benjamin, Harvey Mudd College

3. Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Part A: Wednesday, August 5, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Hampton Room
Part B: Friday, August 7, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Hampton Room

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.

Glen Van Brummelen, Quest University
Joel Silverberg, Roger Williams University

4. Recruiting Students to Take More Mathematics Courses and to Be Mathematics Majors

Part A: Wednesday, August 5, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Calvert Room 
Part B: Friday, August 7, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Calvert Room

We will discuss some principles and specific activities we have used to increase the number of students taking mathematics courses and becoming math majors. Principles include creating a culture of “Math is cool!”, exposing students to careers and opportunities available to those who study mathematics, and being proactive in your efforts. Specific activities include a “Careers in Mathematics” seminar, a freshman/sophomore class titled “Intro to being a math major,” the creation of a student advisory council, a big screen HDTV display with a PowerPoint presentation about mathematics, a set of math t-shirts, and the “We Use Math” website.

Michael Dorff, Brigham Young University

5. Using Videos of Students Developing Proofs to Guide Teaching and Learning

Part A: Thursday, August 6, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Calvert Room
Part B: Saturday, August 8, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Calvert Room

This minicourse will be of interest to anyone engaged in the teaching of proof- writing. Participants will develop a deeper understanding of students’ struggles as they view and discuss short videos of students constructing proofs for problems used in introduction-to-proof courses. The emphasis of the minicourse will be on identifying and implementing teaching strategies that help students overcome their difficulties and help them develop more effective proof-writing skills. Participants will be provided ongoing access to a library of edited student videos, developed by the organizers, which can be used as a classroom tool.

James Sandefur, Georgetown University
Connie Campbell, Millsaps College
Kay Somers, Moravian College


6. Creating Flipped Learning Experiences in the College Mathematics Classroom

Part A: Thursday, August 6, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Calvert Room
Part B: Saturday, August 8, 1:00 PM - 3:00 PM, Omni Shoreham Hotel, Calvert Room

In the “flipped learning” approach to teaching, sometimes called the flipped classroom, direct instruction is moved outside the class meeting space, and the resulting freed­up time in class is used for group explorations of the most challenging ideas. In this minicourse, participants will work together to learn about the core ideas of the flipped classroom and create materials for flipped learning in college mathematics. We will also discuss related issues such as formative and summative assessment, getting student buy­in, technical questions about content creation, and making the flipped classroom a sustainable professional practice.

Robert Talbert, Grand Valley State University

7. Teaching Mathematics with Bead Crochet

Part A: Wednesday, August 5, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Calvert Room
Part B: Friday, August 7, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Calvert Room

We are all on the lookout for ways to entice people into mathematical discovery, especially those who might otherwise be intimidated by math. Bead crochet offers an entrée into many fields of mathematics, including geometry, topology, and abstract algebra. In this course, participants will learn ways to motivate deep ideas in math for their students through bead crochet models and the design and practice of bead crochet. In the first session, everyone will learn the basics of bead crochet needed to make their own mathematical models. In the second session, we will discuss how to use bead crochet models and puzzles in the classroom.

Susan Goldstine, St. Mary's College of Maryland
Ellie Baker, Freelance

8. Getting Started in the Scholarship of Teaching and Learning

Part A: Thursday, August 6, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Hampton Room
Part B: Saturday, August 8, 3:30 PM - 5:30 PM, Omni Shoreham Hotel, Hampton Room

This course will introduce participants to the scholarship of teaching and learning (SoTL) in mathematics and help them begin projects of their own. We describe a taxonomy of SoTL questions, provide examples of SoTL projects in mathematics, and discuss methods for investigation. Participants will learn about collecting and analyzing different types of evidence, dealing with human subjects requirements, and selecting venues for presenting or publishing their work. With the presenters’ guidance, participants interactively select and transform a teaching problem of their own into a question for scholarly investigation and identify several types of evidence to gather.

Jackie Dewar, Loyola Marymount University
Pam Crawford, Jacksonville University