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

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

Abstracts:

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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