Busch Campus Center, Rutgers University, Piscataway, NJ

**Organizers:****Valerie DeBellis**, East Carolina University, debellis@dimacs.rutgers.edu**Yakov Epstein**, Rutgers University, yepstein@rci.rutgers.edu**Fred S. Roberts**, Rutgers University, froberts@dimacs.rutgers.edu

1. Gerald A. Goldin, Rutgers University Systems of Representation for Mathematical Learning and Problem Solving A framework for characterizing learning and problem solving in mathematics must be sufficiently complex to account for diverse empirical observations, yet simple enough to be accessible and useful in educational practice. I shall describe and explain such a framework based on five kinds of internal, developing representational systems, interacting with each other and with external, conventional systems of mathematics and of culture. Attention is focused on constructs related to imagistic thinking, to heuristics and strategic thinking, and to affect.

2. Susan Picker, New York Public Schools An International Study of Student Images of Mathematicians This talk will describe a research project that used a variation of the 'Draw-A-Scientist-Test' to investigate and compare the images of mathematicians held by 7th grade students (ages 12-13) in five countries (n = 476). With small cultural differences, certain stereotypical images of mathematicians, and some surprising and disturbing images, were common to students in all of these countries. Further, it appears that for students of this age, mathematicians and the work they do, are for all practical purposes, invisible. The images students therefore adopt to fill this void arise either from the media, or, in some cases, from negative experiences in mathematics classes. A later intervention with a group of students (n = 174) in New York City, in which they were able to meet with and question a panel of mathematicians was successful in showing that such stereotypical images can begin to be changed.

3. Valerie A. DeBellis, East Carolina University Mathematical Problem Solving: A Dance Between Affect and Cognition Mathematical problem solving is more than a cognitive endeavor. From novice to expert, emotions appear to be an essential component in the development of mathematical understanding and problem solving ability. In this presentation, I will describe the complex interplay (i.e., the dance) between the affective domain and mathematical thinking. Aspects of this complexity include: that the most powerful affect is positive; that a problem solver can discern and regulate negative affect to useful purpose; that affect frequently changes; that affect can be under the control of the solver; and that affect involves the construction of mathematical knowledge. Characteristics such as mathematical intimacy, mathematical bluffing, and mathematical integrity will be highlighted.

4. Henry Pollak, Teachers College, Columbia A Recent History of the Teaching of Mathematical Modeling. Mathematical Modeling has always been at the center of applications of mathematics, but it is only recently that (some) mathematics teachers have considered it as part of their job to teach mathematical modeling. We shall take a look at the history of this, and begin to consider the pedagogic problems involved.

5. Margaret (Midge) Cozzens, University of Colorado, Denver, and Colorado Institute of Technology Teaching, Learning, and the Role of Assessment No matter what one teaches in high school mathematics courses, assessment drives what students learn and are able to do with that knowledge. The debate about basic skills vs problem solving vs real contexts etc. is played out in the curriculum discussions but not usually in the assessment tools used by teachers, schools, states, and nationally or internationally. Thus there is often a disconnect between what is taught, what is learned, and what is labeled as being taught by NAEP and TIMSS, further fuelling the debate. This talk will address the role of assessment in teaching and learning and the media hype about mathematics.

6. Claudia Pagliaro, University of Pittsburgh Problem Solving in Education of Deaf and Hard-of-Hearing Students and the Impact of a Visual Language Problem solving has been advocated as a central component in the development and understanding of mathematical concepts. Deaf and hard-of-hearing students, however, consistently perform significantly below grade level in this area, well behind their hearing peers. This presentation will feature research on problem solving in the deaf education classroom and the impact of a visual language (American Sign Language) on mathematics instruction and learning.

7. Joan Ferrini-Mundy, Michigan State University Doing Mathematics Education Reform, Discreetly: Lessons and Challenges Making change and improvement in the K-12 mathematics education system requires steady work and patience, as well as commitment and energy. Some reflections on collective efforts over the past decade to improve the quality of the mathematics we teach, and that students learn, in our schools.

8. Joseph G. Rosenstein, Rutgers University Mathematical Problem Solving: A Personal Perspective Any mathematician who wants to get involved in education needs to understand that improving mathematics education is a real challenge, one that will draw on all of the problem-solving skills at his or her disposal. In this presentation, I will discuss some of the events that have shaped my perspectives about mathematics education, and the lessons that I have learned from them.

9. THE DEBATE: Carol Lacampagne and Roger Howe We look forward to an interesting and stimulating discussion which addresses the following questions: "What is -- or what should be -- the responsibility of college mathematics departments with respect to mathematics education? What impediments exist within colleges that make it difficult for mathematics departments to play this role and how can they be overcome? Should they be overcome?"

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Document last modified on February 15, 2002.