The Mathematics Education Student Association
invites you to the colloquium:

Kernels of Algebraic Reasoning:

A Study of Sixth Grade StudentsŐ Mathematical Learning

in the Context of Mathematical Caring Relations



Amy Hackenberg

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

3:00 Đ 4:00 pm

Rm 116 Aderhold Hall


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


Visit MESA online at: