Exploring Young Students’ Functional Thinking
Tipo de documento
Autores
Lista de autores
Warren, Elizabeth, Miller, Jodie y Cooper, Thomas J.
Resumen
The Early Years Generalising Project (EYGP) involves Australian Years 1-4 (age 5-9) students and investigates how they grasp and express generalisations. This paper focuses on data collected from six Year 1 students in an exploratory study within a clinical interview setting that required students to identify function rules. Preliminary findings suggest that the use of gestures (both by students and interviewers), self-talk (by students), and concrete acting out, assisted students to reach generalisations and to begin to express these generalities. It also appears that as students become aware of the structure, their use of gestures and self- talk tended to decrease.
Fecha
2013
Tipo de fecha
Estado publicación
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Nivel educativo
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Revisado por pares
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Referencias
Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that pro- motes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446. Cooper, T. J., & Warren, E. (2008). Generalizing mathematical structure in years 3-4: a case study of equivalence of expression. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd Confer- ence of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 369-376). Morelia, Mexico: PME. Harel, G. (2002). The development of mathematical induction as a proof scheme: a model for DNR-based instruction. In S. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: research in cognition and instruction (pp. 185-212). New Jersey, NJ: Ablex Publishing Corporation. Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Lawrence Erlbaum Associates. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the em- bodied mind brings mathematics into being. New York, NY: Basic Books. Lannin, J. (2005). Generalization and justification: the challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258. Mason, J. (1996). Expressing generality and roots of algebra. Dordrecht, The Netherlands: Kluwer Academic Publishers. McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chica- go, IL: University of Chicago Press. Radford, L. (2006). Algebraic thinking and the generalization of patterns: a se- miotic perspective. In S. Alatorre, J. Cortina, M. Sáiz, & A. Mendez (Eds.), Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 2-21). Mérida, Mexico: PME-NA. Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37-62. Radford, L. (2012). On the development of early algebraic thinking. PNA, 6(4), 117-133. Sabena, C. (2008). On the semiotics of gestures. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: epistemology, history, classroom and culture (pp. 19-38). Rotterdam, The Netherlands: Sense pub- lishers.