Prospective Elementary School Teachers´ Proportional Reasoning

• Autores: Gabriela Valverde, Encarnación Castro Martínez
• Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 7, Nº. 1, 2012, págs. 1-19
• Idioma: inglés
• DOI: 10.30827/pna.v7i1.6134
• Enlaces
  • Texto completo (pdf)
• Dialnet Métricas: 3 Citas
• Resumen

  • We present the findings of a study on prospective elementary teachers� proportional reasoning. After describing some of the teachers� performance in solving multiplicative structure problems that involve ratios and relations of direct proportionality between quantities, we were able to establish classifications of their answers according to various categories of proportional reasoning.

• Referencias bibliográficas
  • Allain, A. (2000). Development of an instrument to measure proportional reasoning among fast-track middle school students. (Unpublished master’s...
  • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education,...
  • Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grows (Ed.), Handbook of research...
  • Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different...
  • Ben-Chaim, D., Keret, J., & Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: the impact...
  • Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407.
  • Durmus, S. (2005). Identifying pre-service elementary school teachers’ conceptualization levels of rational numbers. Kuram ve Uygulamada Eğitim...
  • Fernández, A. (2009). Razón y proporción. Un estudio en la escuela primaria. Valencia: Universidad de Valencia.
  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Reidel.
  • Graeber, A., Tirosh, D., & Glover, R. (1989). Pre-service teachers’ misconceptions in solving verbal problems in multiplication and division....
  • Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children’s anticipatory scheme for constancy of taste....
  • Hart, K. (1984). Ratio: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. London,...
  • Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescents’ proportional reasoning on “rate” problems. Educational Studies in Mathematics,...
  • Lamon, S. (1993). Ratio and proportion: Connecting and children’s thinking. Journal for Research in Mathematics Education, 24(1), 41-61.
  • Lamon, S. (2007). Rational numbers and proportional reasoning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching...
  • Lobato, J., Orrill, C., Druken, B., & Jacobson, E. (2011, April). Middle school teachers’ knowledge of proportional reasoning for teaching....
  • Ministerio de Educación y Ciencia (2006). Real Decreto 1513/2006 de 7 de diciembre, por el que se establecen las enseñanzas mínimas de la...
  • Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”....
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part 1. Differentiation of stages. Educational Studies...
  • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept. Part 2. Problem-structure at successive stages. Problem-solving...
  • Norton, S. (2005). The construction of proportional reasoning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference...
  • Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254.
  • Simon, M. A., & Blume, G. W. (1994). Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary...
  • Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: a review of the literature. Educational Studies in Mathematics, 16(2), 181-204.
  • Valverde, G. (2008). Razonamiento proporcional: un análisis de las actuaciones de maestros en formación. (Unpublished master’s thesis). Universidad...
  • Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: effects of age and problem...
  • Van Dooren, W., De Bock, D., & Verschaffel, L. (2006). La búsqueda de las raíces de la ilusión de linealidad. Indivisa, Boletín de Estudios...
  • Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (Vol....
  • Wheeler, M. (1983). Much ado about nothing: Pre-service elementary school teachers’ concept of zero. Journal for Research in Mathematics Education,...