Modeling Students' Units Coordinating Activity

Primarily via constructivist teaching experiment methodology, units coordination (Steffe, 1992) has emerged as a useful construct for modeling students' psychological constructions pertaining to several mathematical domains, including counting sequences, whole number multiplicative conceptions, and fractions schemes. I describe how consideration of units coordination as a Piagetian (1970b) structure is useful for modeling units coordination across contexts. In this study, I extend teaching experiment methodology (Steffe and Thompson, 2000) to model the dynamics of students' units coordinating activity across contexts within a teaching experiment, using the construct of propensity to coordinate units. Two video-recorded teaching experiments involving pairs of sixth-grade students were analyzed to form a model of the dynamics of students' units coordinating activity. The modeling involved separation of transcriptions into chunks that were coded dichotomously for the units coordinating activity of a single student in each dyad. The two teaching experiments were used to form 5 conjectures about the output of the model that were then tested with a third teaching experiment. The results suggest that modeling units coordination activity via the construct of propensity to coordinate units was useful for describing patterns in the students' perturbations during the teaching sessions. The model was moderately useful for identifying sequences of interactions that support growth in units coordination. Extensions, modifications, and implications of the modeling approach are discussed.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2014

Author dc:creator

• Boyce, Steven James

Chair dc:contributor.committeechair

• Norton, Anderson H. III

Committee members dc:contributor.committeemember

• Wilkins, Jesse L. M.
• Wawro, Megan
• Zietsman, Lizette
• Ulrich, Catherine L.

• Units coordination
• Teaching experiment methodology
• Fractions
• Multiplicative reasoning

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:3622

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/50430