The **M****athematics ****E****ducation ****S****tudent ****A****ssociation**

invites you to the colloquium:

*Kernels of
Algebraic Reasoning: *

*A Study
of Sixth Grade StudentsŐ Mathematical Learning *

*in the
Context of Mathematical Caring Relations** *

* *

*Speaker:*

**Mathematics Education, University of
Georgia **

The purpose of
this study was
to understand how sixth graders reason quantitatively as a basis for beginning
to reason algebraically in interaction with a teacher who endeavors to enact
mathematical caring relations (MCR) with them. From a teacherŐs perspective,
MCR is an orientation to balance stimulation and depletion, or increases and
decreases in levels of energy and feelings of well-being, in student-teacher
interactions aimed toward mathematical learning. From a studentŐs perspective,
MCR involves willingly engaging with the teacher in mathematical activity and
pursuing questions of interest. To this end, the researcher taught two pairs of
sixth graders from a rural middle school in Georgia in a constructivist
teaching experiment from October 2003 to May 2004. Teaching practices included
posing situations that involved multiplicative reasoning in fractional contexts
to build toward solving problems that underlie basic linear equations (of the
form *ax*
= *b*),
adapting problem situations to harmonize with and challenge studentsŐ current
ways of operating, and tracking studentsŐ engagement with and affective
responses to this interactive activity. Retrospective analysis entailed
creating chronologies for each pair of students that mapped changes in their
ways of operating and in their engagement in mathematical activity with the
researcher. The results of the study highlighted the construction of
multiplicative structures as a significant factor in studentsŐ construction of
schemes for reversing multiplicative relationships among quantities, the
difficulty students had in constructing reciprocity and operating on unknowns,
and the influence of MCR on the construction of self as an able doer of
mathematics.

**Wednesday, February 16, 2005**

**Rm 116 Aderhold Hall**

** **

******Refreshments Will Be
Served******

* *

Visit MESA online at: www.coe.uga.edu/mesa

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