Prospective elementary school teachers´ proportional reasoning
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Valverde, Gabriela y Castro, Encarnación
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.
Fecha
2012
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Referencias
Allain, A. (2000). Development of an instrument to measure proportional rea- soning among fast-track middle school students. (Unpublished master’s the- sis). North Carolina State University, United States. Ball, D. L. (1990). Prospective elementary and secondary teachers’ understand- ing of division. Journal for Research in Mathematics Education, 21(2), 132- 144. Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York, NY: Macmillan. Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C., & Miller, J. (1998). Pro- portional reasoning among 7th grade students with different curricular experi- ences. Educational Studies in Mathematics, 36(3), 247-273. Ben-Chaim, D., Keret, J., & Ilany, B. (2007). Designing and implementing au- thentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10(4-6), 333-340. Cramer, K., & Post, T. (1993). Connecting research to teaching proportional rea- soning. Mathematics Teacher, 86(5), 404-407. Durmus, S. (2005). Identifying pre-service elementary school teachers’ concep- tualization levels of rational numbers. Kuram ve Uygulamada Eğitim Bilimle- ri, 5(2), 659-666. 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’ misconcep- tions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102. Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children’s anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25(4), 324-345. Hart, K. (1984). Ratio: Children’s strategies and errors. A report of the strate- gies and errors in secondary mathematics project. London, United Kingdom: NFER-Nelson. Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescents’ proportional reasoning on “rate” problems. Educational Studies in Mathematics, 14(3), 219-233. 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 and learning (pp. 629-667). Charlotte, NC: Information Age Publishing. Lobato, J., Orrill, C., Druken, B., & Jacobson, E. (2011, April). Middle school teachers’ knowledge of proportional reasoning for teaching. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA. Abstract retrieved from http://www.kaputcenter. umassd.edu/downloads/products/workshops/AERA2011/Lobato_Orrill_Druk en_Erikson_AERA_2011.pdf Ministerio de Educación y Ciencia (2006). Real Decreto 1513/2006 de 7 de di- ciembre, por el que se establecen las enseñanzas mínimas de la educación primaria (Vol. BOE, no 293, pp. 43053-43102). Madrid: Author. Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reason- ing: A result of the epistemological obstacle of “linearity”. Educational Psy- chology, 27(1), 75-92. 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 in Mathemat- ics, 11(2), 217-253. Noelting, G. (1980b). The development of proportional reasoning and the ratio concept. Part 2. Problem-structure at successive stages. Problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(2), 331-363. Norton, S. (2005). The construction of proportional reasoning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 17-24). Melbourne, Australia: PME. 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 teach- ers. Journal of Mathematical Behavior, 13(2), 183-197. Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: a review of the litera- ture. 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 de Granada, Spain. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57-86. Van Dooren, W., De Bock, D., & Verschaffel, L. (2006). La búsqueda de las raí- ces de la ilusión de linealidad. Indivisa, Boletín de Estudios e Investigación. Monografía IV, 115-135. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (Vol. 2, pp. 141-161). Reston, VA: National Council of Teachers of Mathematics. Wheeler, M. (1983). Much ado about nothing: Pre-service elementary school teachers’ concept of zero. Journal for Research in Mathematics Education, 14(3), 147-155.