Speakers: Marilyn Carlson, Arizona State University
Title: A Survey of the Function Literature: What Have we Learned?
Abstract: An overview of the major results of the function research performed on university level students will be presented. Central aspects of developing a mature function understanding will be examined with student voices revealing the mental constructions and common obstacles possessed by high-performing undergraduate students. In recent years our understanding of ways in which college students use functions to interpret and represent dynamic situations has been informed by considerable research. A close look at the major aspects of reasoning about dynamic events will be examined, as will the importance of acquiring a view of a function as an entity that accepts input and produces output. Collectively, the function research suggests that acquiring an understanding of central aspects of the function concept is complex and students' notions about important aspects of the function concept are impoverished in many ways. The rapid pace of many calculus courses does not appear to promote the development of a well-connected function understanding. Experiences that promote sense making and assist students in confronting the complexities of knowing functions appear necessary for students to understand and orchestrate individual function components to work in concert.
Speaker: Barbara Edwards, Oregon State University
Title:Undergraduate Mathematics Students' Understanding of the Role of Definitions and the Consequences of These Understandings on Students' Ability to Use Definitions in a Mathematically Acceptable Way
Abstract: The purpose of this talk is to discuss undergraduate mathematics students' understandings of the role of formal mathematical definitions and the implications of those understandings on students' ability to understand the concepts defined and to use the definitions in a mathematically meaningful way in post-calculus mathematics courses. The research discussed here relied upon qualitative methods which included in-depth task-based interviews and teaching experiments in which the understanding or learning of the students in a course was continually monitored by the instructor and at least one observer in the classroom, and the goals of the instructor evolved in response to information gained from this monitoring. Results of the research indicate that many students do not fully understand or appreciate the role of formal definitions in mathematics and that these misunderstandings lead to both misunderstandings of the definitions themselves and of the concepts defined, as well as misuse of formal definitions. Several factors, including viewing a concept primarily as a procedure, an inability or unwillingness to think in terms of the infinite, and inexperience, make it difficult for students to accept the role of mathematical definitions even when this was emphasized in a course.
Speaker: Ed Dubinsky, Georgia State University
Title: Effects on students learning
topics in collegiate mathematics of pedagogy based on APOS Theory, using
cooperative learning, students writing computer programs and in-class
problem solving.
Abstract: The nature of APOS Theory, and how this theory drives the design of our pedagogy, indicating the roles of writing computer programs, cooperative learning and problem solving. Summary of data in 14 research papers (either published or in review) comparing what appears to be the knowledge of students who took courses based on our approach with similar students who took traditional courses. Many of the differences pass tests of statistical significance and almost all of the results, whether statistically significant or not, favor the experimental group in which our pedagogy is used.
There is also comparative data indicating student attitudes towards abstract algebra some time after the course, and the long term effects on finishing a sequence and then taking additional math courses. Here, the results are even more strongly in favor of the experimental courses.
In addition, there is a large amount of non-comparative data about student performance in the experimental courses. The results are consistent with high expectations for collegiate math courses.
Topics treated include mathematical induction, functions, differentiation, integration, sequences and series, quantification, binary operations, groups, subgroups, cosets, Lagrange's Theorem, normality and quotient groups.
Speaker: William Yslas Velez, University of Arizona
Title: Minorities are invisible in mathematics
Abstract: Chicano mathematicians are almost invisible. The number of Chicanos that receive PhDs in mathematics each year probably can be counted on one hand, with fingers left over. There are certainly economic factors at work that exclude us from participating in the educational endeavors in this country. However, in the almost thirty years that I have participated in the mathematical enterprise of this country, I have witnessed behaviors of mathematicians and mathematics departments that have contributed to our under-representation in mathematical careers. One of the more egregious is the lack of Chicano faculty at our research universities in the Southwest. In the late 70's, there were seven Chicano research mathematicians at our PhD granting universities in the Southwest. Today, I can count only five! We have gone backwards. If this trend continues, in ten years, there may be no Chicano Full Professors of mathematics at these institutions. The contributions of these few Chicano mathematicians to the education of the minority students is exemplary. The fact there are so few minority mathematicians at these institutions has negatively impacted the education of the minority population. In this talk I will address some of the behaviors and attitudes that I think have contributed to our under- representation.
Speaker: Etta Z. Falconer, Spelman College
Title: Attracting Undergraduate Minorities To Mathematics.
Abstract: Minorities are severely underrepresented in mathematics. In the past this was true at Spelman College, but now five percent of Spelman students are mathematics majors. A comprehensive approach to attracting African American women to the mathematics major and preparing them for graduate study in mathematics has been successful at Spelman. The Model Institutions for Excellence Program (MIE) supports curricular reform, retention activities, infrastructure development, and student research in science, engineering and mathematics. The Mathematics Department has utilized collaborative programs with science departments as well as programs designed specifically for mathematics to develop strategies for the recruitment, retention and preparation of students for graduate study and careers in mathematics and mathematics-related areas.
Speaker: David Manderscheid, University of Iowa
Title: Increasing the Number of Minority PhDs in Mathematics
Abstract: This academic year 20% of the 90 graduate students in the Mathematics Department at the University of Iowa are US minorities from groups underrepresented in mathematics. In the August 28, 1998 issue of Science the University of Iowa is listed as tied for fourth in the granting of PhDs in Mathematics to minorities from underrepresented groups for the period 1992-1996. This listing is based on the NSF/NIH/NEH/USED/USDA Survey of Earned Doctorates for the period. In this talk I will discuss our experiences in the recruitment and development of minority graduate students. I will emphasize the ideas that work and that might be transportable to other institutions.
Speakers: Christine Stevens, St. Louis University, Joseph Gallian, University of Minnesota-Duluth, Aparna Higgins, University of Dayton
- Abstract: At colleges and universities of all kinds, mathematics departments are re-thinking their missions and seeking to integrate teaching, research and scholarship, and service. Project NExT (New Experiences in Teaching) is a professional development program that assists new and recent Ph.D.s in the mathematical sciences as they assume the diverse professional roles that they are expected to play, focusing on issues in undergraduate mathematics education. During the last six years, over 400 new faculty have participated in this program, which is sponsored by the Mathematical Association of America and funded, in part, by the Exxon Education Foundation. We reflect upon our experiences with Project NExT and their implications for new Ph.D.s entering the profession, for the mathematics departments that prepare and hire them, and for the mathematical community at large. We also sketch the future plans of Project NExT.
Speaker: Michele Intermont, Kalamazoo College
Title: From One Community to the NExT
Abstract: Project NExT is more than simply a workshop or a year-long program. It is a community that serves to ease the transition from graduate school to the professional mathematical community. This talk will present reflections on the ways in which Project NExT functions as a community and on its success from the perspective of the NExT fellows.
Speaker: Douglas Ensley, Shippensburg University of Pennsylvania
Title:New Experiences with Tenure
Abstract: Many Project NExT discussions are centered on professional issues and how they relate to the tenure process. Now that many Fellows are receiving tenure, the familiar question resounds, "What's Next?" This paper will draw upon the combined experiences and opinions of several recenty tenured NExT Fellows to discuss the shift of professional focus that they encounter as they relinquish the familiar role of Junior Faculty.
Speaker: Jim Lewis, University of Nebraska, Lincoln
Title: Project NExT - A Chair's View
Abstract: One of a department chair's most important duties is hiring outstanding faculty. Once new faculty arrive at your university, it is equally important to provide an environment in which the new faculty member will thrive professionally. This is particularly important when the new faculty member is also new to the profession, i.e. a new Ph.D. The speaker will discuss his experiences in supporting Project NExT Fellows and his view as to the role Project NExT plays in assisting new faculty in making the transition from graduate student to successful faculty member with strengths in both research and teaching.
Speakers: Alfred Manaster, University of California, San Diego
- Abstract: While mathematicians have long been members of the National Council of Teachers of Mathematics (NCTM), in the period since the 1989 publication of the NCTM Standards there has been a significant increase in the interest in the organization and its work. Their impact upon mathematics education has been substantial and it has been controversial. More recently, several mathematicians have become involved in the development of their revision to appear this spring, the Standards 2000 Project. This panel will discuss why they, as mathematicians, became involved in K-12 mathematics education and in this project. Indeed, John Thorpe will discuss what role the NCTM Standards played in his decision to become executive director at NCTM while others will discuss their participation as writers in the Standards 2000 Project. In conclusion, members of the panel will discuss how mathematicians can continue to work to strengthen K-12 mathematics education in the future.
- Abstract: "Girls on Track" is a three-year NSF supported project to increase middle grade girls interest in math-related careers by engaging them in computer-based mathematical explorations of urban and community problems. In July 1999 at team of Girls on Track personnel from North Carolina State University and Meredith College led a summer academy with 12 middle school math teachers, 3 pre-service teachers, 2 school counselors and 40 middle school girls ready for Algebra I. Teachers worked with teams of students to model local population growth, trash disposal, and traffic problems. Students used Excel to explore and display data and presented their results to various audiences using PowerPoint. Sports Algebra, Good Jill Hunting; and short talks by local women with math/computer-related careers were also regular events. This paper presents the results of this successful first summer academy and the in-progress school-year follow-up.
Speaker: Solomon Friedberg, Boston College
Title: Training Mathematics TAs Using Case Studies
Abstract: This talk reports on the development of new materials---case studies---for use in the TA-training component of a mathematics graduate program.
Case studies are fictional scenarios depicting life-like situations, to be analyzed and discussed. The use of case studies as a teaching tool is common in certain disciplines such as business and law; cases are also used in many subjects for faculty development at both the university and pre-collegiate levels. Our goal is to find ways to adopt this methodology for the TA-training of mathematics graduate students. This talk will describe what we have found and the case study materials we have created, and will look for feedback from the community.
Our project, the Boston College Mathematics Case Studies Project, is headed by the Solomon Friedberg; additional development team members include Avner Ash, Elizabeth Brown, Deborah Hughes Hallet, Margaret Kenney, William McCallum, Jeremy Teitelbaum, and Lee Zia. The project evaluator is Mary Sullivan. The project is funded by FIPSE.
Speakers: William Davis, The Ohio State University
- Astract: There has been much rhetoric and many projects and activities aimed at improving mathematics education in the United States. Some have been general in nature, some directed towards women and minorities. Many of these have been at the preK-12 level, with a focus on curricuoum, and assessment. What lessons are there that we can use to help us think about improving the teaching of mathematics at the university level? We know something about the current status; we know something about how people learn; we know something about some programs that work. We know that we are losing too many of those who should be succeeding in mathematics. We also know the importance of thinking about the problem in terms of a system. Does any of this make sense for the calculus or linear algebra classroom? Let's look at some of the evidence, think about the context, and begin to build a framework for making a difference.
Speaker: Virginia Warfield, University of Washington
Title: Can one person make a difference? Yes!
Abstract: Some opportunities to be helpful come about as a result of long and elaborate planning. Others result from one person's being present, alert and willing to invest some energy when an occasion presents itself. This talk will tell the tale of the consequences of one such occasion, presented two years ago to one of my colleagues at the University of Washington. She now leads a project involving several faculty members, a bunch of graduate students and dozens of elementary school teachers. Imitating parts of her project would be very worthwhile, and imitating her spirit of inspired opportunism even more so!
Speaker: Bernice Sandler, National Association for Women in Education
Title:Mentoring: Myths and Realities, Dangers and Responsibilities
Abstract: Mentoring is often overestmated as a panacea to help women (and others) professional advancement. This report describes some of the dangers of mentoring, the advantages of multiple mentoring and networks, as well as the commandments for those who do the mentoring.
Speaker: Shirley Malcom, American Association for the Advanceme
nt of Science (AAAS)
Title: Rethinking K-12 Mathematics Education
Abstract: Since the promulgation of the standards in mathematics, much has happened to support change in the way that school mathematics is perceived, such as a broadening of the topic beyond computation; and a change in the tools available for use in instruction. But much has yet to change: the way that teachers are educated; the form of professional education; the implementation of mathematics instruction as an inclusive activity; the weak links between school mathematics instruction and mathematics in the out-of-school setting. The presentation will explore opportunities presented by reform to re-think teaching and learning goals and the role of the university in supporting the new aspirations for K-12 mathematics education.