2010 Annual Meeting

Abstract: Analysis is what happened to calculus in the 19th century as mathematicians discovered that their intuition of how to apply calculus was failing them, especially as their repertoire of infinite series expanded. The conceptual difficulties that they encountered are precisely where we should expect our own students to have trouble. Understanding how these controversies were resolved illuminates many of the definitions, axioms, and theorems that baffle our students. This talk will focus on how our modern understanding of the Fundamental Theorem of Calculus arose and what it really says.

Banquet talk, around 8:00pm, Friday, April 9, 2010.

Title: Math is Music--Stats is Literature

Prof. Richard D. De Veaux, Williams College

(He gave a short course in the AMS-MAA annual joint meeting in 2009)

Abstract: Gauss could add up hundreds of numbers in his head by the age of 3 and Mozart was playing the pieces he'd heard in church at home by about the same age. But who ever heard of a literary prodigy? Why not? Because literature is about the world and the wisdom one gains with experience, not about abstract rules and symbols. The same is true of Statistics. Rather than highlight the formulas that underlie Statistics, we need to emphasize the learning that Statistics gives us about the world. That makes our jobs harder, but ultimately more rewarding. The most common mistakes students and practitioners make in Statistics have nothing to do with calculation but everything to do with interpretation and context. How can we help students to use statistical thinking effectively in the chaotic maze of the real world? We think this is best done by outlining the steps in statistical thinking. We'll outline our strategy for informing and exciting students about Statistics and how we use these steps in an introductory course.

Opening talk, 8:30-9:30am, Saturday, April 10, 2010.

Title: My Teaching Philosophy and the Development of the Keystone Method

Prof. Vali Siadat, Daley College

(He was the MAA's Haimo Award winner in 2009)

Abstract:

(a) My Teaching Philosophy

Teaching mathematics is the fusion of two beautiful subjects: mathematics and people. Teaching may begin in the college, but it is really a community experience, radiating outward. The mathematical knowledge and thinking skills students carry with them affect their families, friends, co-workers, and communities. Any success I have had as a teacher of mathematics is, I think, attributable to feeling these connections. That sense of connectedness, of concepts, of ideas, of skills, and of people, and seeing it continue outward – this is what makes teaching so rewarding, so deeply rewarding. A teacher, especially in an abstract a discipline such as mathematics, needs to know, deep in the heart, that its elements can be taught to every one – that there are no barriers to entering this fascinating world of numbers and concepts except those perceived by the learner, whether from personal experience or society’s stereotypes. We must be flexible and use common sense, calling on a range of approaches from lecturers to cooperative learning and individual discovery. That is at the heart of my teaching, which combines and varies these classroom experiences for each group of students. To my great pleasure (and my initial surprise) this often improves their performance in other classes as well. I love pointing out that this confirms an observation by Plato that skill in mathematics sharpens the mind for other subjects.

As deeply as we may wish to motivate student learning, we often fail when seeking to do so as individual teachers. My role is to cultivate each group of students, making their educational experience as engaging and productive as possible. At best, we create and nurture gardens – burgeoning academic networks of students and teachers. What feeds my love of teaching is those occasions when I begin to see such a garden taking root. Best of all are those amazing times when I see that the garden has far outgrown my classes and the college.

(b) Keystone Method:

A Synergistic Model for Teaching and Learning

Have you noticed……how people with a talent for calculation are naturally quick at learning almost any other subject; and how a training in it makes a slow mind quicker…? Plato, The Republic.

The Keystone method is a synergistic approach to teaching and learning of mathematics at the college. Drawing upon the research literature on learning, educational psychology, and causes of student failure in mathematics, this method focuses on the links between students’ difficulties in mathematics and specific behaviors, attitudes, and habits that inhibit learning. These include short attention spans, limited time horizons, poor attendance patterns, passivity, failure to learn from errors, inattention to homework assignments, inattention to teacher’s statements, and -- underlying all -- a lack of confidence and self-esteem.

How does the Keystone method address these difficulties? The key element is the continuous monitoring of the students’ progress, paralleled with a set of teaching/learning strategies targeted to identified weaknesses. Carefully designed daily quizzes become an invaluable tool of communication between students and teacher. The instructor's preparation for each class session is informed by quiz results. That quizzes are administered at each class meeting improves class attendance and punctuality. That the quizzes are based on homework encourages the students to do their homework assignments for each class. This regimen eliminates the disconnected study spurts and cramming for the tests, encouraging regular study from the very beginning of the term -- which soon becomes a "study habit." Timed restricted quizzes focus students’ attention and improve their concentration skills. Finally, the fact that quizzes are cumulative consolidates students’ learning and enables them to integrate their knowledge of the topics covered in the course at all times. Computer scoring of quizzes provides statistical data such as the mean and standard deviation for the entire quiz, as well as the item analysis of each question. The teacher not only receives a global view of the class performance overall, but also obtains the valuable information on students’ performance on each question. The teacher provides immediate feedback, reviews the troublesome questions, and repeats them on the next quiz to encourage attainment of the mastery and learning from mistakes. By achieving a higher level of success each time, the student gets motivated to do better and becomes more self-reliant. Success of students improves their self-esteem.

The Keystone method is a student-centered and versatile teaching approach. When the standard deviation of the quiz scores is high - indicating a serious split in skill levels - the teacher moves from lecture to cooperative learning and peer tutoring. In such circumstances, weaker students are tutored by stronger students. The stronger students benefit in turn by reinforcing their own knowledge. Such peer learning experiences are especially effective at addressing student passivity.

In short, the Keystone approach creates a synergy among various pedagogical techniques parlaying these into a highly effective teaching program for improving student learning.

Closing talk, 12:05-1:05pm, Saturday, April 10, 2010.

Title: Rogue Waves, Tsunamis and Sand Bars

Prof. Jerry Lloyd Bona, University of Illinois at Chicago

Abstract: After a short review of the history of the water wave problem, some rudiments of the modern theory are sketched. It is then shown how the theory can be used to increase our understanding of interesting geophysical phenomena such as tsunami propagation in the deep ocean, rogue wave formation and the generation of sand bars in the near-shore zone of large bodies of water.

Conference Workshop, 8:45am-11:45am, Friday, April 9, 2010.Title: Data Mining and New Trends in Teaching Statistics

Prof. Richard D. De Veaux, Williams College

Abstract: Forty years ago, the emphasis in Introductory Statistics was on formulas and their calculation. For example, students were taught the formula for standard deviation and learned alternatives for avoiding rounding errors and short cuts for grouped data. Technology has made much of that subject matter irrelevant and obsolete. Today, we have been freed by technology to focus on the concepts of data analysis and inference. Where is this trend taking us? This workshop will discuss how the introductory course has changed and how the course differs from a mathematics course. It should be especially valuable to the mathematician who is faced with teaching an introductory statistics course for the first time.

The workshop will start with an overview of how the Introductory course is taught today and what the main concepts are. Examples of how technology enables us to get to the heart of the subject early will be given. Some elementary modeling concepts will be reviewed before we embark on an introduction to data mining. Then, we will use case studies and real data sets to illustrate many of the algorithms used in data mining. The applications will come from a wide variety of industries and include applications from my personal experiences as a consultant for companies that deal with such topics as financial services, chemical processing, e-commerce, pharmaceuticals, and insurance.

Student Math Contest

You have a deck of 10 cards and on each card there is a single digit between 0 and 9, inclusive. The digit on the top card equals the number of cards which have a zero on them, and so forth until the digit on the last card is the number of cards with a nine on them. What are the digits, in order from top to bottom, on the cards?

Is this the sort of problem that intrigues you? Then you should consider competing in our Thirteenth Annual Student Mathematics Contest which will be held on the afternoon of Friday April 9, 2010 during the Annual Meeting of the Illinois Section of the MAA at Augustana College in Rock Island, Illinois.

The Contest is likely to have a minimum of four problems for the teams to consider. A team from a particular college is to consist of up to 3 undergraduate students. A college or university may enter more than one team. Team members may work together in solving the problems and will submit one team solution for each. Electronic computational devices (and slide rules and log tables and abacii) are not allowed. Competitors will have their conference registration fee waived.

For more samples of the kinds of problems to expect, see the problems from past contests. (You might also look at the Challenge of the Week problems from the Department of Mathematics at Eastern Illinois University.)

Teams need not register until the day of the Contest, but if you intend to participate in the contest, it would be helpful if you would inform Pat Kiihne at pkiihne@ic.edu This will help us to adjust plans accommodate for the participants

The participating teams will receive the results of the contest as soon as they become available. The Contest results will also be posted on the ISMAA website.

For additional information on the contest, please contact Pat Kiihne at the above e-mail address or Zhuan Ye at ye@math.niu.edu.

ISMAA- OUR Awards Announcement

OUTSTANDING UNDERGRADUATE RESEARCH (OUR) AWARD

The Illinois Section of the Mathematical Association of America (ISMAA) invites submissions for the 2010 Award for Outstanding Undergraduate Research in Mathematics. The awards will be given to the best three research papers authored and presented by undergraduate students in any field of mathematics. For this award student participants are encouraged to produce complete research projects including, but not limited to focusing on interesting mathematical problems, the process of writing manuscripts, creating professional presentations and speaking at professional meetings. Faculty mentors will encourage their students to work on problems with more research emphasis. In addition to helping outstanding students fund their travels to ISMAA Meetings, we believe this award will help introduce selected students gain experience in conducting, writing, presenting and funding research projects.

Working in collaboration with a faculty advisor, undergraduate students who wish to apply for one of these awards should submit the following materials electronically (either as a PDF or MS Word document) to the Awards Committee.

The completed research article that will be presented at the upcoming meeting. Even if the presentation is going to include only a part of the article, the entire manuscript needs to be submitted.
A letter of support from the faculty advisor which also describes the student’s contribution to the paper.

Please include "OUR-Award-Submission" in the subject heading. Papers need not have been submitted for publication in a professional journal at the time of consideration for this award but they have to be complete scientific manuscripts.

The awards will be given to the projects that have the three highest combined scores for both the scientific paper and the presentation This year the awards for the top three ranked winners will be $250, $150 and $100. The deadline for OUR Award applications is March 29, 2010.

Questions? Email oakman@ilstu.edu .

Undergraduate Travel Awards

Student Travel Awards Available

Travel funds are available to support student attendance at the ISMAA meeting. Up to $50 per student is available for Illinois institutions to use in support of student travel, with a max of $250 per institution. Limited funds are available.

We ask that institutions which already provide full support not request these funds. Travel funds are not available to the hosting institution or to institutions within 30 miles of the meeting site. Travel awards are available for all students (secondary, undergraduate, or graduate); however, preference will be given to students presenting at the meeting.

The travel form is available as a Word document or a PDF. Please send completed forms electronically to Jon Johnson ((jonj@elmhurst.edu) by March 15, 2010.