Exploring young students' functional thinking

Autores/as

  • Elizabeth Warren Australian Catholic University, Australia
  • Jodie Miller Australian Catholic University, Australia
  • Thomas J. Cooper Queensland University of Technology, Australia

DOI:

https://doi.org/10.30827/pna.v7i2.6131

Palabras clave:

Generalización, Matemáticas de primaria, Pensamiento funcional, Semiótica

Resumen

The Early Years Generalizing Project (EYGP) involves Australian years 1 to 4 (age 5 to 9) students and investigates how they grasp and express generalizations. This paper focuses on data collected from 6 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 generalizations and to begin to express these generalities. It also appears that as students became aware of the structure, their use of gestures and selftalk tended to decrease.

Exploración del pensamiento funcional de estudiantes jóvenes

El Early Years Generalizing Project (EYGP) implica a estudiantes de primer a cuarto curso de la educación primaria australiana (de 5 a 9 años) e investiga cómo comprenden y expresan las generalizaciones. Este artículo se centra en los datos recogidos de 6 estudiantes de primer curso en un estudio exploratorio con entrevista clínica que requería que los estudiantes identificaran patrones funcionales. Los resultados preliminares sugieren que el uso de los gestos (de estudiantes y entrevistadores), las conversaciones con ellos mismos (de estudiantes), y las actuaciones concretas, ayudaron a los estudiantes a buscar generalizaciones y a comenzar a expresar estas generalidades. También parece que cuando los estudiantes tomaron conciencia de la estructura, el uso de gestos y de las conversaciones con ellos mismos tendió a disminuir.

Handle: http://hdl.handle.net/10481/22369

Nº de citas en WOS (2017): 3 (Citas de 2º orden, 3)

Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 0)



Descargas

Los datos de descargas todavía no están disponibles.

Biografía del autor/a

Elizabeth Warren, Australian Catholic University, Australia

Jodie Miller, Australian Catholic University, Australia

Código ORCID

Thomas J. Cooper, Queensland University of Technology, Australia

Código ORCID ResearcherID

Citas

Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes 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 Conference 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 embodied 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. Chicago, IL: University of Chicago Press.

Radford, L. (2006). Algebraic thinking and the generalization of patterns: a semiotic 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 publishers.

Descargas

Publicado

2013-01-01

Número

Sección

Artículos