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Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization
Abstract
To improve our understanding of novice students' production of symbolic algebraic expressions, this article contrasts students' presymbolic and symbolic procedures in generalizing activities. Although a significant amount of previous research on the learning of algebra has dealt with students' errors in the mastering of the algebraic syntax, the semiotic cultural theoretical approach presented here focuses on the role that body, discourse, and signs play when students' refer to mathematical objects. Three types of generalizations are identified: factual, contextual, and symbolic. The results suggest that the passage from presymbolic to symbolic generalizations requires a specific kind of rupture with the ostensive gestures and contextually based key linguistic terms underpinning presymbolic generalizations. This rupture means a disembodiment of the students' previous spatial temporal embodied mathematical experience.
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Citations
Cited by
Embodied cognition and its significance for education
Shapiro, L., & Stolz, S. A. (2019) · Theory and Research in Education · doi:10.1177/1477878518822149 · Cited by 274
Recursive and explicit rules: How can we build student algebraic understanding?
Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2006.11.004 · Cited by 76
Generalizations of third and fifth graders within a functional approach to early algebra
Pinto, E., & Cañadas, M. C. (2021) · Mathematics Education Research Journal · doi:10.1007/s13394-019-00300-2 · Cited by 61
“Although definitions of generalization vary in the field of mathematics education (e.g., Dienes 1961; Dubinsky and Harel 1992; Kaput 2008; Mason 1996; Radford 2003; Sfard 1991), a growing research effort seeks to demonstrate the importance of elementary students’ generalization.”
BackgroundYeşildere İmre, S., & Akkoç, H. (2012) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-012-9203-6 · Cited by 33
Investigating a learning progression of functional thinking for elementary students
Deng, X., Ding, R., & Huang, R. (2025) · Educational Studies in Mathematics · doi:10.1007/s10649-024-10376-8 · Cited by 4
Metadata
- Authors
- Radford, L.
- Venue
- Mathematical Thinking and Learning
- Publisher
- Informa UK Limited
- Published
- 2003-01
- Volume
- 5
- Issue
- 1
- Pages
- 37-70
- ISSN
- 1098-6065 (ISSN-L)
- 1532-7833
- OpenAlex
- W1970580174
- Cited by
- 444
- References
- 0
- FWCI
- 69.61
- Type
- journal article
- Language
- en
- Open access
- closed
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- Radford, L. (2003). Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization. Mathematical Thinking and Learning. https://doi.org/10.1207/s15327833mtl0501_02
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