EXPLORING ALGEBRAIC THINKING IN FIFTH GRADE STUDENTS
Carol W. Bellisio
Rutgers University
Davis (1985) recommended that students in elementary
grades be given activities that promote algebraic thinking to serve as a
foundation for the later, more formal study of algebra. This researcher examines early algebraic
thinking and use of algebraic notation by eight fifth grade students who were
brought together for a group interview after their class had been videotaped
six times over a two-month period, working on tasks involving fractions. These students were accustomed to sharing
ideas and justifying their solutions.
The inquiry was motivated by a study of data collected during a three
and a half year longitudinal research project conducted by mathematics
educators from Rutgers University. Data came from videotapes of the classroom
activities and the group interview, student work and researcher notes.
The problem discussed in this talk, required the
students to divide a 12 meter length of ribbon into bows that were fractional
parts of a meter long. The students
discovered that dividing the ribbon into lengths of 1/D resulted in “the
denominator times twelve” number of bows.
They first expressed this rule verbally using a specific example and
then tried to write their rule using words and letters. Finally they refined this rule to a general
case with a numerator other than one, using letters to represent words. This research gives evidence that children’s
generalizations are originally expressed in ordinary language and, given
sufficient time and opportunity, students can develop symbolic notation to
express their ideas.
Bellisio, C.W.
(1999). A study of elementary students’ ability to work with algebraic notation
and variables. Unpublished doctoral
dissertation. Rutgers University.
Davis, R.B. (1985). ICME-5 Report: Algebraic thinking in the early grades. The Journal of Mathematical Behavior, 4, 195-208.