Connecting Mathematics Education Research and Teaching Practice

Moderator: Jerry L Bona, University of Texas at Austin

Panelists: Chris Rasmussen and Rina Zazkis (SIGMAA on RUME)
           Deborah Ball and Phil Daro (RAND Study Group)


Abstract: This panel discussion will focus on connecting mathematics
education research with teaching practice. There is a growing body of
investigation into the process of knowing and learning mathematics.
However, many (possibly most) curricular development projects and classroom
practices remain uninformed about this research. The usual outlets for
reporting mathematics education research are journals that are primarily
read by other researchers in the field. It is to the issue of making the
connection between research and practice in this area that the panel will be
devoted. The panelists will each present a short overview of what they
perceive to be the major issues and the current limitations to bridging the
gap between research and practice. This will be followed by the moderator
posing prepared questions and accepting audience questions and both panelist
and audience discussion.

8:00            973-S1-671   
A comparative investigation in college algebra of  student appeals to
authority in written mathematical justification.                               
      
                        Shandy Hauk*
                        Matthew Isom

8:20            973-S1-709   
The Evolution of Preservice Elementary Teachers's Beliefs in a
Reform-Oriented Instructional Environment.                                     
               
                        Jeff D. Farmer*
                        Janet Stapleton

8:40            973-S1-618   
Cognitive structures and their role in success in algebra courses.             
                                   
                        Lillie F Crowley*

9:00            973-S1-386   
Preservice Teachers' Understanding of Mathematical Logic: A Preliminary
Report.                                    
                        Harel Barzilai*
                        Homer W Austin

9:20            973-S1-472   
The Role of Culture in International Teaching Assistants' Beliefs about
Mathematics and the Teaching and Learning of Mathematics: A Preliminary 
Report.                                             
                        Thomas C DeFranco*
                        Jean M McGivney-Burelle 

9:40            973-S1-426   
An examination of the knowledge base for teaching among university
mathematics faculty.                           
                        Kimberly B Santucci*
                        Thomas C DeFranco
                        Jean McGivney-Burelle

10:00           973-S1-561   
The Student Take on the Epsilon-Delta Definition of a Limit.                   
                                  
                        Eileen Fernandez*

10:20           973-S1-627   
Calculus students' views about justification in mathematics: preliminary 
report.                                
                        Margaret L Morrow*
                        Manya Raman

10:40           973-S1-558   
Actual infinity: mental constructions and metaphors.                           
                           
                        Anne Brown*
                        Michael McDonald
                        Kirk Weller

How can mathematical concepts by learned?  
Synthesizing APOS theory and mathematical formalism to get one possible answer.
     

How can a student, on hearing, reading or working with a mathematical
concept, come to understand it?   There seems to be general agreement
that whatever the answer, it involves some kind of idea or mental
structure, an image that was not previously present but must develop
in the student's mind.  There is considerably less agreement about the     
nature of such images and how they get into one's mind.

In this talk I will consider some answers to this question that have been
proposed, such as metaphors, natural language, representations and
contrast them with APOS Theory. Then I will describe how APOS Theory
can  be combined with mathematical formalism to not only describe how
difficult mathematical concepts, such as uniform vs. pointwise
convergence of a sequence of functions, can be learned, but also to help
students learn such concepts.    

8:00            973-S1-37    
Assessing Understanding in Calculus.
                        Melvin A Nyman*
                        John Berry

8:20            973-S1-303   
Small-class Teaching of Calculus in Classes of 2000
                        Eleftherios C Zachmanoglou*

8:40            973-S1-38    
Resolving Conflicts Between Teachers' and Students' Beliefs About
Mathematics.                            
                        Gideon L Weinstein*
                        Kathi G Snook

9:00            973-S1-378   
The Role of Metaphor in Student Acquisition of New Concepts.                   
                                    
                        Carol E Seaman*


9:20            973-S1-496   
Effects of Use of MATHEMATICA in Learning of Basic Linear Algebra
Concepts.                                        
                        Hamide Dogan*

9:40            973-S1-614   
Integrating Mathematics and Pedagogy: A large scale research study of an
intervention designed  to change prospective teachers' beliefs about
mathematics in order to maximize their mathematics learning                    
                                    
                        Rebecca CA Ambrose*
                        Jennifer Chauvot
                        Lisa Clement
                        Randy Philipp

10:00            973-S1-565
A Visual Analysis of Knowledge Networks: Students Discuss Calculus.
 
			 Eric S Hsu*

10:20           973-S1-622   
Adaptation and extension of the framework of reducing abstraction to
explain students' construction of solution to differential equations.          
    
                        Debasree Raychaudhuri*

10:40           973-S1-700   
The Development of Mathematical Norms in an Undergraduate Number Theory
Course.                             
                        Jennifer C Smith*

1:00            973-S1-403   
Exploring Changes in Elementary Education Students' Mathematical Beliefs.      
                           
                        Stephen D Szydlik*
                        Jennifer E Szydlik

1:20            973-S1-556   
How Much Logic is Used in Transition Course Proofs and How Do Students
Know It?                                    
                        Annie Selden*
                        John Selden
                        Scott Baker

1:40            973-S1-162   
Instructional Implications of Attending to Students' Spontaneous Reasoning.    
                            
                        Michael C Furnish Oehrtman*

2:00            973-S1-608   
Transformational Reasoning as a Tool for Defining, Conjecture and Proof.       
                                    
                        Michelle J Zandieh*
                        Mark Burtch
                        Denise Nunley