MAA Minicourses are partially supported by the William F. Lucas Fund. Read more about Prof. Lucas here.
1. Creating A Purposeful Student Learning Experience
Part A: Friday, August 5, 3:30 p.m. - 5:30 p.m., Taft B
Part B: Saturday, August 6, 3:30 p.m. - 5:30 p.m., Taft B
Do your requirements for your departmental majors constitute an integrated framework designed to build skills necessary for students to succeed in the workplace or in graduate school, or are they just a set of individual classes covering a standard array of content? Do your faculty work together effectively to develop and implement plans to achieve those desired outcomes and to assess your progress? Do you strategically incorporate experiences outside the classroom in student learning? This minicourse, taught in a hands-on workshop format, will assist and guide you in identifying practical steps toward achieving those goals and creating a learning-focused departmental culture. Departmental teams of 2 – 4 are encouraged to enroll, but are not required.
G. Daniel Callon, John Boardman, Justin Gash, Stacy Hoehn, Paul Fonstad, and Angie Walls, Franklin College
2. Visualizing Projective Geometry through Photographs and Perspective Drawings
Part A: Thursday, August 4, 1:00 p.m. - 3:00 p.m., Taft B
Part B: Friday, August 5, 1:00 p.m. - 3:00 p.m., Taft B
This Minicourse will introduce hands-on, practical art puzzles that motivate the mathematics of projective geometry---the study of properties invariant under projective transformations, often taught as an upper-level course. This Minicourse seeks to strengthen the link between projective geometry and art. On the art side, we explore activities in perspective drawing or photography. These activities provide a foundation for the mathematical side, where we introduce activities in problem solving and proof suitable for a sophomore-level proofs class. In particular, we use a geometrical analysis of Renaissance art and of photographs taken by students to motivate several important concept in projective geometry, including Desargues' Theorem, Casey's Theorem and its applications, and Eves' Theorem. No artistic experience is required.
Annalisa Crannell, Franklin & Marshall College
Fumiko Futamura, Southwestern University
Marc Frantz, Indiana University
3. Teaching Linear Algebra: Learning Concepts Often Difficult to Understand
Part A: Thursday, August 4, 3:30 p.m. - 5:30 p.m., Taft B
Part B: Saturday, August 6, 1:00 p.m. - 3:00 p.m., Taft B
Participants will work with GeoGebra interactive applets/worksheets supporting instruction in Linear Algebra. The workshop will consist of a) an overview of the topics that are often difficult for students to understand; b) participants will work with selected worksheets with activities illustrating the connection between the visual, algebraic, and numeric perspectives of concepts. (A short introduction to GeoGebra will occur first); c) discussion of possible pedagogical approaches for understanding difficult concepts; d) a look at some related application problems; e) summary of preliminary evaluation results; f) wrap-up, including remarks and suggestions by participants and the link to other freely available resources.
James D. Factor and Susan Pustejovsky, Alverno College
4. Teaching the Lebesgue Integral to Undergraduates
Part A: Thursday, August 4, 1:00 p.m. - 3:00 p.m., Taft D
Part B: Friday, August 5, 1:00 p.m. - 3:00 p.m., Taft D
This minicourse shows how to teach a course on the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Students who mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to success is the use of a “Daniell-Riesz approach.” The treatment is self-contained; the course, often currently offered as Real Analysis 2, no longer needs Real Analysis I as a prerequisite. Along with Complex and Real Analysis I, the course provides a comprehensive undergraduate study of functions. Completion of any one course enhances the other two. Students can enroll after Calculus II or after a course in proofs. The minicourse thus shows how to give undergraduates the background for collaborative research and improved access to journal articles in analysis, creating a course with SLO topics that can include: the definition and properties of the Lebesgue integral; Banach and Hilbert spaces; integration with respect to Borel measures with associated L^2(µ) spaces; and bounded linear operators. Traditionally thought of as advanced and out of reach, the minicourse shows how these topics are accessible for undergraduates and able to be taught by anyone who might also, e.g., teach Real or Complex Analysis.
William W. Johnston, Butler University
Derek Thompson, Taylor University
5. Teaching Modeling First Differential Equations - Building Community in SIMIODE
Part A: Thursday, August 4, 3:30 p.m. - 5:30 p.m., Taft D
Part B: Saturday, August 6, 1:00 p.m. - 3:00 p.m., Taft D
This minicourse permits participants to experience SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations, an online (www.simiode.org) community of teachers and learners of differential equations who use modeling and technology throughout the learning process. Participants do modeling scenarios from the student perspective, discuss pedagogical and content issues that might arise in such teaching, and initiate the development of their own modeling scenario contributions to SIMIODE through partnering with other participants during and after the minicourse. The minicourse is appropriate for all interested in teaching differential equations in a modeling first approach.
Therese Shelton, Southwestern University
Brian Winkel, United States Military Academy
6. Teaching Introductory Statistics with Simulation-Based Inference
Part A: Friday, August 5, 3:30 p.m. - 5:30 p.m., Taft D
Part B: Saturday, August 6, 3:30 p.m. - 5:30 p.m., Taft D
The goal of this minicourse is to help participants to revise their introductory statistics course to focus on the logic and scope of statistical inference by using simulation-based methods, as opposed to methods based on the normal probability distribution, to introduce students to concepts of statistical inference. The minicourse will provide direct experience with hands-on activities designed to introduce students to concepts of statistical inference. These activities make use of freely available applets to explore concepts and analyze real data from genuine research studies. Presenters will also offer advice and lead discussion about effective implementation and assessment of student learning.
Allan Rossman, Beth Chance, and Soma Roy, Cal Poly San Luis Obispo