New Perspectives in Mathematics Education: A Celebration in Honor of the Contributions of Joseph G. Rosenstein on the Occasion of His 60th Birthday
March 16, 2002
Busch Campus Center, Rutgers University, Piscataway, NJ
Co-sponsored by DIMACS and CMSCE (Center for Mathematics, Science and Computer Education).
- Valerie DeBellis, East Carolina University, firstname.lastname@example.org
- Yakov Epstein, Rutgers University, email@example.com
- Fred S. Roberts, Rutgers University, firstname.lastname@example.org
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.
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.
Valerie A. DeBellis, East Carolina University
Mathematical Problem Solving: A Dance Between Affect and
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.
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.
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.
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.
Joan Ferrini-Mundy, Michigan State University
Doing Mathematics Education Reform, Discreetly: Lessons
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.
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.
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
Contacting the Center
Document last modified on February 15, 2002.