You are invited to Alayne Armstrong the Final Oral Examination:
PROGRAMME
The Final Oral Examination
For the Degree of
DOCTOR OF PHILOSOPHY
(Curriculum Studies)
ALAYNE CHERYL ARMSTRONG
B.A.H., Queen’s University, 1988
M.A., University of Manitoba, 1995
B.Ed., University of British Columbia, 1997
M.A., University of British Columbia, 2006
Wednesday, January 16, 2013, 9:00 am
Room 203, Graduate Student Centre
Latecomers will not be admitted
“Problem posing as storyline: Collective authoring of mathematics by small groups of middle school students”
EXAMINING COMMITTEE
Chair:
Dr. Pierre Walter (Educational Studies)
Supervisory Committee:
Dr. Ann Anderson, Research Supervisor (Curriculum and Pedagogy)
Dr. Anthony Clarke (Curriculum and Pedagogy)
Dr. Susan Gerofsky (Curriculum and Pedagogy)
University Examiners:
Dr. J. Scott Goble (Curriculum and Pedagogy)
Dr. Carl Leggo (Language and Literacy Education)
External Examiner:
Dr. Elizabeth de Freitas
Ruth S. Ammon School of Education
Adelphi University
Garden City, New York
United States
ABSTRACT
This dissertation investigates the problem posing patterns that emerge as small groups of students work collectively on a mathematics task, and describes the characteristics of problem posing that result.
This case study is a naturalistic inquiry about four small groups of Grade 8 students in the Lower Mainland of British Columbia who are working in a classroom setting, with the researcher acting as participant/observer and videographer.
The concept of author/ity is used to highlight human agency in mathematics. Small groups, as learning systems, are considered to be “authors” of their discourse, and the improvisational nature of authoring is discussed. A parallel is drawn between the storyline of a literary work and the storyline that emerges as a group poses problems in order to work its way through a mathematical task.
The metaphor of a tapestry is used as a way of describing how the threads of group discourse weave together. To address the challenge of documenting collective behavior at the group level, a method of data analysis is introduced that “blurs” the data in order to capture patterns that emerge over time – transcripts are color-coded and then shrunk to create tapestries that provide visual evidence of collective problem posing patterns.
This dissertation finds that collective problem posing is an emergent process. Each group poses its own set of problems, and the number of problems posed and their frequency also vary, resulting in individual tapestries for each group. The tapestry patterns are then used to compare characteristics of the groups’ discussions.
Problem posing appears to be an activity that these groups are able to do without receiving formal instruction or direction. The reposing of problems helps to structure each group’s discussion, with the role that each problem plays in the conversation evolving as it reemerges. The concept of groups working as bricoleurs is also explored, with bricolage in mathematics being characterized as a creative and generative process.
The dissertation concludes with a discussion of expertise in school mathematics and what implications an “aesthetic of imperfection” might have in the mathematics classroom.
EXAM DETAILS for ALAYNE CHERYL ARMSTRONG
1. Exam Time: 9:00 AM on Wednesday, January 16, 2013 (Please arrive 5 minutes early, so the exam can begin promptly).
2. Exam Location: Room 203 of the Graduate Student Centre (6371 Crescent Road).