Some thoughts on teacher preparation in mathematics education
	(From various works in progress and in print)

Michael L. Connell, Ph.D.
307 MBH
University of Utah
Salt Lake City, Utah 84112

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** CONNELL@GSE.UTAH.EDU <-- THIS ADDRESS WILL WORK **
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	For a meaningful change to take place in the mathematics 
instruction of our young people, teachers must be in charge of a 
significantly different instructional sequence, evaluation scheme, and 
curriculum.  Merely stating the need for these items, however, is not 
enough to ensure they will take place.  Neither are simple "two-week" 
in-service, or additional coursework separate from actual classroom 
experience, sufficient if these goals are to be reached .  A major 
barrier to implementation is that elementary teachers are simply not in 
a position to implement such changes.  Teachers must first be able to 
expand their own thinking beyond purely procedural views of 
mathematics to grasp and utilize essential conceptual constructs 
themselves.  Teacher preservice, in-service, and support must bring 
about conceptual understandings on the part of the teachers and 
parallel actual classroom implementation via extensive co-teaching 
and modeling by master teachers throughout the course of the 
intervention.  Furthermore, sufficient time and support must be spent 
that the new and desired understandings are thoroughly integrated into 
the teachers' normal routines.   
	Mathematics education is certainly a case in point.  
Practicing teachers are often plagued by various conceptions 
regarding mathematics which are at odds with those held by 
practicing mathematicans.  A dichotomy has evolved in which there is 
"school mathematics" and "real mathematics" (For a more detailed 
discussion, see Connell, M. L., Peck, D. M., Buxton, W., Kilburn, D.  
(In press).  True collaboration: An analysis of a conceptual change 
program in elementary mathematics.  In S. Odell & M. O'Hair (Eds.),  
Teacher Education Yearbook: Partnerships in Education II  (pp. 255-
274).  New York:Harcourt Brace and Javonovich).  
	If our young people are to enter into the world of "real 
mathematics", it is essential that practicing teachers become aware of, 
and members in, the "real world" mathematics culture.  This cannot 
occur without the active and willing participation of the teachers 
themselves. 
	In examing the features of "real world" mathematics it 
becomes clear that even with the full participation of teachers this 
induction will be a difficult process.  Practice in allowing students to 
make their own determinations of "right" or "wrong", for example, 
requires much practice and modeling for the teachers.  Nor is this the 
only area which needs time to develop.  Consider some of the other 
crucial areas which must be addressed for this transition to take place. 
What constitutes a good problem for use in problem solving?  How can 
children demonstrate their understandings when a correct answer 
alone is not sufficient?  What curriculum should be used?  How should 
instruction procede?  How might technology be effectively used in this 
process?
	This discussion strand will focus on how teacher education 
might address these and related issues in mathematics education. 

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