Bridging students’ informal discourse and formal discourse on limits
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Jungeun Park [1]
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[1] University of Delaware
University of Delaware
Estados Unidos
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 12, 2025, págs. 2419-2439
- Idioma: inglés
- DOI: 10.1080/0020739X.2025.2563124
- Texto completo no disponible (Saber más ...)
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Resumen
Definitions of mathematical terms are often presented as part of formal mathematical discourse, which students are expected to accept even when these definitions conflict with their existing thinking. Considering defining as part of students' developing mathematical discourse, we examined students’ progression from initial discourse to formal discourse as they reinvented a definition of the limit of a convergent sequence with the instructor’s guidance. Initially, students faced a conflict when their definition failed to classify graphs of sequences that they created – intended as examples and nonexamples – into the examples and nonexamples as they had planned. This conflict was eventually resolved through activities in which students engaged with elements of their definitions using routines familiar to them, but in a manner deemed appropriate by the instructor. Our analysis focuses on interdiscursivity, the blending of students’ existing discourse and formal discourse. Our results show how students’ application of familiar routines led to new meanings and uses for these elements, ultimately introducing quantities and their relations to define sequence convergence – characteristics of formal discourse. This approach supports intrinsically motivated learning by allowing students to build mathematical discourse from their own discourse, and our study reports on how the interdiscursivity could promote such learning.
