ERIC Number: EJ1405348
Record Type: Journal
Publication Date: 2023
Pages: 34
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-2198-9745
EISSN: EISSN-2198-9753
The Interplay between Individual and Collective Activity: An Analysis of Classroom Discussions about the Sierpinski Triangle
Geoffrey B. Saxe; Amelia M. Farid
International Journal of Research in Undergraduate Mathematics Education, v9 n3 p632-665 2023
This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area and perimeter of the Sierpinski triangle, a unique mathematical object with zero area and infinite perimeter. As participants conceptualize and communicate about the Sierpinski problem, they unwittingly generate a linguistic register of action word forms (e.g., "fencing," "zooming") and object word forms (e.g., "area," "infinity") to serve Sierpinski-linked mathematical reasoning functions, a register that we document in the first analytic section of the article. In the second analytic section, we report a developmental analysis of microgenetic, ontogenetic, and sociogenetic shifts in the word forms constitutive of the register and their varied functions in participants' activities. In the third analytic section, we provide a cultural analysis of the classroom's collective practices, practices that enable and constrain participants' constructions of form-function relations constituting the register. We examine the ways in which participants work to establish a common ground of talk in their communicative exchanges, exchanges supported by classroom norms for public displays of reasoning and active listening to one another's ideas. We show that it is as participants work to establish a common ground that the register emerges and is reproduced and altered. We conclude by pointing to ways that the analytic framework can be extended to illuminate learning processes in other classroom settings.
Descriptors: Mathematics Instruction, Learning Activities, Thinking Skills, Language Usage, Discourse Analysis, Cooperative Learning, Individualism, Group Discussion, Geometry, Problem Solving, Language Variation, Classroom Techniques, Active Learning, Learning Processes
Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://bibliotheek.ehb.be:2123/
Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A