Program Schedule

Friday, June 8, 2012
11:30am Registration
12:00pm Section NeXT Lunch
1:00pm
Section NeXT Lecture
1:30pm
Executive Committee Meeting
3:00pm
Palindromes and other Good Questions

Christine von Renesse, Westfield State University

Abstract: What kind of questions or mathematical problems can we use to motivate students to engage in thinking deeply? Questions that can be investigated from elementary school through College and be rich on every level? Questions that can be solved in different ways and also connect to many areas of mathematics and life? Questions that allow the students to discover all the answers themselves?

In the project “Discovering the Art of Mathematics” we develop activities based on good questions. The topics range from Games, Music and Dance through Geometry, Calculus, Number Theory and Knot theory. While the target audience is liberal arts students the materials have been used successfully with mathematics majors and future teachers.

In this talk you will be engaged in exploring the example of musical palindromes. While palindromes are clearly defined in language it turns out to be not quite as simple for rhythms - and the arising conflict leads to many interesting mathematical questions and connections. Many of the questions were raised and then solved by students at Westfield State University in our Mathematics Exploration class. Of course, you will have a chance to answer some of the questions yourself during the talk. 

The series of books “Discovering the Art of Mathematics” is being developed under a CCLI NSF grant and supported by Harry Lukas. See http://artofmathematics.westfield.ma.edu.

4:00pm
A President, A. Partridge, and Practical Mathematics

Dick Jardine, Keene State College

Abstract: One of our founding fathers was also one of our young nation’s significant scientists, well-versed in mathematics. This presentation reviews a correspondence between Thomas Jefferson and a native New Englander about mathematical methods for calculating the elevation of mountains. The exchange between these two men actively engaged in “practical mathematics” during the Jeffersonian era includes application of geometry, trigonometry, and the calculus suitable for inclusion in undergraduate calculus, differential equations, and history of mathematics courses. Should time permit, there will also be a brief discussion of other American mathematicians of the Jeffersonian period.

5:00pm
Undergraduate Student Talks
6:00pm

Reception and Banquet
8:00pm

Battles Lecture: Factors Influencing College Success in Mathematics: Predicting Success in College Calculus

Phil Sadler, Harvard

Abstract: Succeeding in college calculus carries considerable importance in career decisions as poor performance can prematurely end the pursuit of potential science, technology, engineering, computer science, and health careers. We have studied 10,492 college calculus students' backgrounds in 352 instructors' classrooms at 135 randomly selected 2- and 4-year colleges and universities. We identify predictors of performance while controlling for demographic differences to reveal the relationship between the decisions made by high school mathematics teachers and later success in introductory college calculus. Our study reveals the most common student pathways to college calculus and gauges the specific impact of variety of potentially important factors in later success. These include: taking (AP or non-AP) calculus in high school, taking math for all four years of high school, the teaching practices of mathematics teachers, the role of technology, and the effectiveness of college pre-calculus coursework (and the associated math placement exams.

Saturday June 9th, 2012
9:00am

Registration
9:00am

12, 5, 6, n Angry Men: Mathematics and the Jury Problem

Jeff Suzuki

Abstract: The sixth amendment guarantees the accused in a criminal trial the right to a trial by jury. But the constitution specifies neither the size of the jury, nor the quota by which it must render a decision. What can mathematics tell us about the size and quota of a jury consistent with our notion of justice?

10:00am Break
10:30am A Changing Landscape for High School Mathematics

Marlene M. Lovanio and Timothy Craine

Abstract: With the adoption of the Common Core State Standards (CCSS) by 45 states across the US, including Connecticut, there is great potential for change for the future of high school mathematics.  The Content and Mathematical Practice Standards in the CCSS are the basis for major curricular overhaul and the development of two assessment systems driven by partner states.  In this session, we will explore the standards for high school, the design of a future college and career readiness assessment and the implications for the written and enacted curriculum in general and in a specific small urban district in Connecticut.

11:30am

Business Meeting
12:00pm

Lunch
1:00pm Render Unto Bernoulli: The Origins and Contents of de l’Hôpital’s Analyse

Rob Bradley, Adelphi University

Abstract: Guillaume François Antoine de l’Hôpital’s Analyse des infiniment petits (1696) was the first ever calculus textbook.  It was also something of an enigma.  For one thing, it was published anonymously, although de L’Hôpital’s authorship was no secret.  Also, it made no mention of the integral calculus: instead, its introduction to the differential calculus was followed by what can only be described as an advanced text on differential geometry, motivated by what were then cutting-edge problems in mechanics and optics.

However, the oddest aspect of this book is its genesis.  The introductory chapters were based on Johann Bernoulli’s Lectiones de calculo differentialium, lessons that only ever existed in manuscript form and were unknown to the scholarly community until 1921.  De l’Hôpital received his copy when he hired Bernoulli to tutor him in 1691-92.  Subsequently, he “purchased” the advanced material of the later chapters, in an arrangement under which he supported Bernoulli with a stipend in 1694-95.

In this talk, we will consider both the mathematics that was presented in the Analyse and the process by which in came into being.  We will compare de l’Hôpital’s exposition of the elements of the differential calculus with that of Bernoulli and examine some of the more advanced results presented in the Analyse.
2:00pm Contributed Paper/Graduate Student Talks
3:00pm - Session 1 iPad Apps for Math: Respond to your math students: quick, light, and mobile

Hendree Milward, Tunxis Community College

Abstract: Tablet computing gives instructors a unique blend of instructional tools. Skitch and Educreations are two free apps for the iPad that have worked well for my math classes. I will be doing a demonstration of both apps and taking questions.

3:00pm - Session 2

Using GAP in an Abstract Algebra course

Joseph E. Fields, Southern Connecticut State University

Abstract: GAP (Groups, Algorithms and Programming) is an extremely powerful CAS (Computer Algebra System) designed for and by researchers in group theory.  GAP is free software, it is available at no cost.  It is also free in the sense that all of the source code which goes to make up the system is available to users.    
While GAP is principally a tool for researchers in group theory (and related areas) it has also been shown to be a useful adjunct in the classroom.  Among others, Hulpke, Rainbolt and Gallian have developed GAP materials intended for use in undergraduate Abstract Algebra courses.  We will demonstrate a variety of activities that students can use to build their intuition about how groups work and also show how the system can easily be extended.

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