Abstracts for talks
AMS-MAA-MER Special Sessions on Mathematics and Education Reform
Joint Annual Meeting, Baltimore, January, 2003
Title: Seeing the Connections: Promoting Profound Understanding of Secondary Mathematics
Presenter: Steve Benson, Education Development Center and Al Cuoco, Education Development Center
Abstract: The connections between higher level mathematics and school mathematics are deep, but are so rarely made explicit in the education of teachers that their potential contribution to the teaching of school mathematics is lost. Recent reports acknowledge the disjuncture between what teachers study as undergraduates and what they teach, and they describe what has come to be known as a knowledge of mathematics for teaching.
We will speak about promoting a profound understanding of secondary mathematics that keeps precollege mathematics at the center of undergraduate coursework for teachers. This does not mean that college students are taking precollege courses or that secondary topics are being treated from an "advanced perspective." Rather, we see potential in the undergraduate curriculum for helping secondary teachers develop the mathematical knowledge required in their careers in education.
We believe that designing such programs and courses requires a clear philosophy of mathematics teaching and learning, so we will discuss our basic assumptions and provide examples of courses and topics designed with this underlying philosophy.
Title: The Role of Mathematical Content in Professional Development
Presenters: Carolyn R. Mahoney, Elizabeth City State University and Dick Stanley, University of California, Berkeley
Abstract: Consider professional development of mathematics teachers at a particular grade level. We claim that there is a legitimate, but largely neglected field of mathematical content that treats, as an integrated whole:
A. the mathematical content of this grade level.
B. mathematical content that is closely connected to the content of the grade level, but that goes beyond what is appropriate for students at this grade level.
We use the term "teachers' mathematics" to refer to this sort of field of mathematical content. Our claim is based on two kinds of recent work in professional development at a high school level:
• An in-service program for high school teachers developed in Texas, "In-Depth Secondary Mathematics"
• An upper division mathematics text for pre-service high school teachers, "Mathematics For High School Teachers: An Advanced Perspective"
We will discuss some of the reasons that treating content of types A and B as an integrated whole is not common, and will argue that, as a profession, we need to do a better job of developing the content of this field.
Title: Learning Mathematics on a New Playing Field-- Discrete Mathematics
Presenters: Valerie A. DeBellis, East Carolina University, and Joseph G. Rosenstein, Rutgers University
Abstract: Professional development programs for K-8 teachers of mathematics that focus on teaching traditional topics of arithmetic, geometry, and algebra often evoke negative experiences and attitudes about mathematics. Teachers also tend to resist learning new information and strategies about topics that they believe they already understand. However, when K-8 teachers learn new content (e.g., from discrete mathematics), they do so eagerly because they are able to see applications, recognize the benefits for their students, and find the problems interesting and challenging. These topics don't evoke their negative experiences with mathematics. In a sense, it offers them a new start with mathematics. This presentation will discuss the experiences of the Leadership Program in Discrete Mathematics, an NSF-funded program at Rutgers University that over the past eleven years has involved nearly 1000 practicing K-8 teachers. It will also discuss an NSF-funded project to develop text materials for an undergraduate discrete mathematics course for K-8 teachers. Such a course has been offered at East Carolina University for the past four years. We will focus particularly on what and how participants learn about mathematics, problem solving, and effective teaching strategies.
Title: Integrating Mathematics and science with Preservice K-8 Teachers
Presenter: Philip Wagreich, University of Illinois at Chicago
Abstract: In this talk we will outline a course developed for preservice teachers at the University of Illinois at Chicago who are completing a "study in one discipline" in mathematics. The course is organized around the concept of variable. We focus on six variables fundamental to mathematics and science: number, length, area, volume, mass, and time. Students carry out experiments during which they collect data, organize the data, represent the data visually (generally on a graph), and then determine whether the data suggest a relation between the variables. If there is a relation between the variables they attempt to describe or model the relationship in words, graphically, or in symbols. Students use their models to make predictions and verify whether their predictions are "close." Among the issues that students have to grapple with are:
a) accuracy and precision of measurements
b) experimental and measurement error vs. systematic error
c) design of experiments, particularly the importance of controlling variables
d) when is a prediction "close'?
e) what is a good theory? What is the relation between theory and data?
f) finding the "best " model: best fit lines and best fit curves.
Title: Opportunities and Challenges in the School-Undergraduate Continuum, Part I
Presenter: Eric Robinson, Ithaca College
Abstract: New and potential directions in school and undergraduate mathematics provide more reason than ever to consider the bridge between K-12 and undergraduate mathematics. Part I of this joint presentation will discuss changes in K-12 mathematics that are underway. The intent is to identify commonalties and differences as well as opportunities and challenges for bridging the gap between these two educational levels.
Title: Opportunities and Challenges in the School-Undergraduate Continuum, Part II
New and potential directions in school and undergraduate mathematics provide more reason than ever to consider the bridge between K-12 and undergraduate mathematics. Part II of this joint presentation will discuss the directions in which undergraduate mathematics seems to be headed. The intent is to identify commonalties and differences as well as opportunities and challenges for bridging the gap between these two educational levels.
Presenter: Bill Haver, Virginia Commonwealth University
Abstract: New and potential directions in school and undergraduate mathematics provide more reason than ever to consider the bridge between K-12 and undergraduate mathematics. Part II of this joint presentation will discuss the directions in which undergraduate mathematics seems to be headed. The intent is to identify commonalties and differences as well as opportunities and challenges for bridging the gap between these two educational levels.
Title: Some Articulation Issues between High School and College Mathematics Education.
Presenter: John Maceli, Ithaca College
Abstract: Some commentators suggest that the current U.S. K-16 mathematics education has evolved more from tradition and convenience than careful coordination. What is the relationship between high school and college mathematics education and what should it be?
Title: What Graduates of Reform Mathematics Programs Bring to College Mathematics
Presenter: Dan Fendel, San Francisco State University
Abstract: The mathematics education reform of the past decade has produced new curriculum programs with new ideas about how students learn. Colleges are now beginning to see significant numbers of students who have graduated from these programs, including the high school programs sponsored by the National Science Foundation. These students bring more to their college mathematics classrooms than mechanical algebra skills or the ability to reproduce standardized geometry proofs. They bring the willingness and ability to tackle complex problems. They bring experience in discussing mathematical ideas. They bring knowledge of areas of mathematics beyond algebra and geometry. And they bring an enthusiasm about mathematics based on experiences in which they have developed their own ideas and shared ideas with their peers. This session will discuss how graduates of reform programs are different from students in the past, and will look at how college mathematics instructors might take advantage of these developments.
Title: Mathematical Content in Standards-Based Curricula
Presenter: Sol Garfunkel, COMAP
Abstract: This talk will focus on the presentation of new and traditional content in the standards-based secondary school mathematics curricula. We will describe the way in which these curricula integrate&Mac226; the development of this content and make use of both technology and applications material. Emphasis will be on the implications for and articulation with the undergraduate mathematics program for both majors and non-majors.
Title: Panel on the Mathematical Needs of Teachers.
Moderator: Eric E Robinson, Ithaca College
Panelists: Joan Ferrini-Mundy, Michigan State University, Ira Papick, University of Missouri, and Amy Cohen-Corwin, Rutgers University
Abstract: Much has been written lately about better meeting the mathematical needs of K-12 teachers. The panel will assist us in looking at some issues and strategies concerning this matter. Mathematicians, especially faculty teaching pre-service teachers in any of their courses, as well as teacher educators need to be involved.
Title: Introduction and Background for "Undergraduate Programs and Courses in the Mathematical Sciences: A CUPM Curriculum Guide"
Presenter: Harriet S. Pollatsek, Mt. Holyoke College
Abstract: This talk will provide the background for the new CUPM Curriculum Guide on the Undergraduate Program and Courses in the Mathematical Sciences. It will discuss the new Guide's relationship to previous CUPM reports and the activities of CUPM over the past two years preparing for the new Guide.
Panel on Undergraduate Programs and Courses in the Mathematical Sciences: A CUPM Curriculum Guide
Organizers and Panelisits: Harriet S. Pollatsek, Mt. Holyoke College, Susanna Epp, DePaul University, Susan Ganter, Clemson University, and Bill Haver, Virginia Commonwealth University
Abstract:
A panel organized by Harriet Pollatsek, Mount Holyoke College and Susanna Epp, DePaul University. Panelists include Susan Ganter, Clemson University; William Haver, Virginia Commonwealth University; Harriet Pollatsek (moderator), and Susanna Epp. The MAA Committee on the Undergraduate Program in Mathematics (CUPM) periodically reviews its curricular recommendations for college and university departments and revises them as needed to fit new circumstances. A CUPM Curriculum Guide will appear late in 2003; it will be the first Guide explicitly to address the needs of non-majors as well as majors. Panelists will describe the latest draft of the Curriculum Guide, and there will be an opportunity for comments and questions from the audience. The Guide is informed by the CRAFTY Curriculum Foundations Project, as well as by the MAA report CUPM Discussion Papers about Mathematics and Mathematical Sciences in 2010: What should students know?, work that has been done on the first college course, quantitative literacy, and the mathematical preparation of teachers, and by three rounds of focus groups on earlier drafts of the Guide. Most recently, it has been revised based on discussion at Mathfest 2002.
Title: Mathematical Thinking and the CUPM Curriculum Guide
Presenter: Susanna S. Epp, DePaul University
Abstract: A striking finding from the CRAFTY Curriculum Foundation Workshops is that, contrary to the belief of many mathematicians, colleagues in our partner disciplines-- engineers, economists, and natural and computer scientists-- care more about having students develop conceptual understanding of basic mathematical facts than about having them learn specific computational techniques. They value the precise, logical thinking that they perceive to be an integral part of mathematics and would like to see more emphasis on it in early collegiate mathematics instruction. This talk will discuss the ways in which the draft of the new CUPM Curriculum Guide addresses both their concerns and the related concerns of mathematics departments about the preparation of their majors. It will focus on the specific recommendations and examples contained in the Guide that deal with analytical, critical reasoning, and problem-solving skills.
Title: Undergraduate Issues for Research Universities
Presenter: David Bressoud, Macalester College
Abstract: This presentation will address some of the issues in the CUPM Curriculum Guide that relate to research universities. These institutions face both particular opportunities and limitations that we have tried to address in the Curriculum Guide. There are also points at which the CUPM guide is informed by and can reinforce the recommendations of the AMS Task Force on Excellence.
Title: The CUPM Curriculum Foundations Project: Looking at the First Two Years
Presenter: Susan Ganter, Clemson University
Abstract: Given the impact of mathematics instruction on engineering, the sciences, and the quantitative social sciences--especially instruction during the first two years --significant input from partner disciplines is needed to inform the CUPM Curriculum Guide. The CUPM subcommittee on Curriculum Renewal Across the First Two Years (CRAFTY) gathered much of this necessary information between Fall 1999 and Spring 2001 through a series of invitational disciplinary workshops, funded and hosted by a wide variety of institutions. This presentation will focus on what was learned from those workshops, as well as the implications for the undergraduate program in mathematics.
Forum on Strategies for Increasing the Diversity of Students in Mathematics
Moderator: Naomi Fisher, University of Illinois at Chicago
Panelists: Dennis Davenport, Miami University, Raymond Johnson, University of Maryland, College Park, Roosevelt Johnson, National Science Foundation, Robert Megginson, Mathematical Sciences Research Institute, Teri Murphy, University of Oklahoma, and Ami Radunskaya, Pomona College
Abstract: The six invited speakers in the forum-- Dennis Davenport, Raymond Johnson, Roosevelt Johnson, Robert Megginson, Teri Murphy, and Ami Radunskaya-- bring to the discussion a range of experience in successfully supporting the participation in mathematics of students from groups underrepresented in mathematics. They will highlight salient points learned from their experiences, including: what strategies work, possible pitfalls, and the essentials for a successful program. The forum will also take up the question of the need to continue to promote efforts throughout the mathematics community to increase diversification of students in mathematics, and consider strategies for addressing this challenge. Comments from the audience will be welcome in the question and discussion period.
This forum is presented in coordination with the MAA contributed papers session on Strategies for Increasing the Diversity of Students in Mathematics on Friday morning's program. Projects exemplifying the strategies and issues related to this forum will be discussed in the MAA session.