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Mini Courses

About the Courses

Course 1: Quantitative Reasoning in the News

Presenters: Stuart Boersma, Ph.D., Central Washington University and Caren Diefenderfer, Ph.D., Hollins University

Brief Description: Quantitative literacy is necessary for a well functioning democratic society. However, many educated adults remain functionally innumerate. Many mathematics departments at our colleges and universities have been asked to help address this problem by teaching quantitative reasoning courses. These courses vary greatly in content and pedagogy, are often considered "terminal" courses, and are frequently used to "teach" remedial algebra skills.

As dedicated and passionate teachers of mathematics, we should use these courses to give our students the tools they need to think for themselves, ask intelligent questions of experts, and to confront authority with confidence. Newspapers can provide a surprisingly wide variety of study materials for a quantitative reasoning course.

In this minicourse, the presenters will describe the mechanics of using newspapers for a quantitative reasoning course and the participants will work through a variety of case studies associated with media articles.

Course 2: Teaching Mathematical Modeling through Patterns in Nature

Presenter: John Adam, Ph.D., Department of Mathematics & Statistics, Old Dominion University, Norfolk, VA

Brief Description: This mini-course is intended for those who teach, or plan to teach a course in mathematical modeling. This presentation identifies some of the underlying mathematical and physical principles undergirding some of the common and not-so-common patterns in the natural world around us. The word pattern implies an underlying scientific and mathematical basis for describing and explaining what we see (to some degree, at least). Indeed, mathematics has been called the science of patterns. I am convinced that the beauty of nature can be further revealed by mathematics, and the beauty of mathematics is revealed in nature, if we are prepared to study it, and further, that this can be a source of fascination for students, at any academic level - nature is a resource for teaching mathematics, and it's free! Examples will be taken from a senior/first-year graduate level course taught by the presenter, possibly supplemented by some basic principles of "Guesstimation".

Since the ability to see is dependent on the light that reaches our eyes, it is perhaps not surprising that several of the examples considered in this mini-course come from the field of atmospheric optics. We will examine some ray-theoretic models of rainbows, ice-crystal halos (including circum-horizontal and circum-zenithal arcs) and "glories", and along the way discuss a model of some shadow-related phenomena, namely crepuscular and anti-crepuscular rays. Fermat's Principle of Least Time and the Euler-Lagrange equation enable us to discuss many of these and other phenomena in mathematical terms, and in particular, mirages and what I refer to as the "mirage theorem". By condensing the relevant fluid dynamical equations we will examine the idealized behavior of linear waves on the surface of puddles, ponds, rivers and oceans, and the delightful "ship-wave" patterns that are readily noticed from the air. Time permitting, we may also look at the importance of dimensional analysis in modeling, certain types of cloud pattern, a mathematical model of river meanders, the Fibonacci "Golden Angle", models of bird eggs, tree 'tumors', to name but a few possible topics.

 

About the Instructors

John Adam: Please see the Invited Speakers page.

Stuart Boersma: Stuart received his B.S. from The University of Puget Sound, Ph.D. from Oregon State University and is currently Professor of Mathematics at Central Washington University. He was Department Chair at CWU from 2004-2007 and chair of the Pacific Northwest section of the MAA from 2005-2006. Currently, he is the chair of SIGMAA-QL, the Mathematical Association of America's special interest group on Quantitative Literacy, and a Governor of the MAA.

Together with Bernie Madison, Shannon Dingman, and Caren Diefenderfer, he has been designing and teaching introductory college level quantitative reasoning courses based on the critical reading of newspaper articles. In addition to these QL courses, he enjoys teaching vector calculus, topology, and cryptology courses.

Stuart enjoys writing expository papers for undergraduates and received the 2005 Trevor Evans Award for one of his Math Horizons papers. His most recent publications have appeared in Math Horizons, SIURO, Primus, and Numeracy.

Caren Diefenderfer: Caren Diefenderfer received her A. B. (1973 - summa cum laude) in the first coed class at Dartmouth College, and her M.A. (1975) and PhD (1980) from University of California at Santa Barbara. Currently Dr. Diefenderfer is a professor of mathematics at Hollins University, where she joined the Hollins University mathematics faculty in 1977. Her two terms as chair of the mathematics and statistics department at Hollins were preceded by a term as chair of the division of natural and mathematical sciences.

Professor Diefenderfer has been involved with the AP Calculus program since 1969, when she took the AB exam as a high school senior. She served as Chief Reader for AP Calculus from 2004-2007. She also has a long-standing relationship with the Mathematical Association of America (MAA). She was the Secretary of the MD-DC-VA Section, was Chair of SIGMAA QL, the quantitative literacy special interest group of the MAA, is currently Chair of SIGMA TAHSM, the special interest group on teaching advanced high school mathematics, serves on several MAA committees, and has been a consultant and speaker at numerous institutions who are interested in learning about Quantitative Literacy/Reasoning.

Professor Diefenderfer sings with her church choir, is a member of the Bahama Mamas (a female steel drum band), loves to swim and enjoys reading fiction. She lives with three baseball enthusiasts; her husband, David, and her two sons, Mark and Joseph.

 
 

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