Conocimiento de matemáticas especializado de los estudiantes para maestro de primaria en relación al razonamiento proporcional

Referencias

BALL, D. L.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching: What makes it special?Journal of Teacher Education, Washington, US, v. 59, n. 5, p. 389-407, 2008. BEHR, M.; HAREL, G.; POST, T.; LESH, R. Rational number, ratio, and proportion. In: GROUWS,D. (Ed.). Handbook of research on mathematics teaching and learning. New York: Macmillan, 1992. p. 296-333. BEHR, M.; KHOURY, H.; HAREL, G.; POST, T.; LESH, R. Conceptual units analysis of preservice elementary school teachers’ strategies on a rational-number-as-operator task. Journal of Mathematics Education, Berlin, v. 28, n. 1, p. 48-69, 1997. FERNÁNDEZ, C.; LLINARES, S. Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria. Enseñanza de las Ciencias, Barcelona, v. 30, n. 1, p. 129-142, 2012a. FERNÁNDEZ, C.; LLINARES, S. Relaciones implicativas entre las estrategias empleadas en la resolución de situaciones lineales y no lineales. Revista Latinoamericana de Investigación en matemática Educativa- RELIME, Rioja, México, v. 15, n. 1, p. 277-310, 2012b. FERNÁNDEZ, C.; LLINARES, S.; VALLS, J. Learning to notice students’ mathemathical thinking through on-line discussions. ZDM. The Journal of Mathematics Education, Berlin, v. 44, n. 6, p. 747-759, May 2012. FERNÁNDEZ, C.; LLINARES, S.; VAN DOOREN, W.; DE BOCK, D.; VERSCHAFFEL, L. Effectof number structure and nature of quantities on secondary school students’ proportional reasoning. Studia psycologica, Bratislava, v. 53, n. 1, p. 69-81, 2011. HART, K. Ratio: Children’s strategies and errors. Windsor, UK: NFER Nelson, 1984. HAREL, G.; BEHR, M. Teachers’ solutions for multiplicative problems. Hiroshima Journal of Mathematics Education, Hiroshima, v. 3, p. 31-51, 1995. HILL, H.; BALL, D.L.; SCHILLING, S. Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, Reston, VA, v. 39, n. 4, p. 372-400, July 2008. KAPUT, J.; MAXWELL, M. Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In: HAREL, G.; CONFREY, J. (Ed.). The development of Multiplicative Reasoning in the Learning of Mathematics. New York: SUNNY Press, 1994. p. 237-292. KARPLUS, R.; PULOS, S.; STAGE, E. K. Early adolescents’ proportional reasoning on ‘‘rate’’ problems. Educational Studies in Mathematics, Dordrecht, v. 14, n. 3, p. 219-234, 1983. LAMON, S. J. Teaching fractions and ratios for understanding. New Jersey: Lawrence Erlbaum Associates, 1999. LAMON, S. J. Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers. 2. ed. Mahwah, New Jersey: Lawrence Erlbaum Associates, 2005. LAMON, S. J. Rational numbers and proportional reasoning. In: LESTER, F. K. (Ed.). Second handbook of research on mathematics teaching and learning. A project of the National Council of Teachers of Mathematics. Reston, VA: NCTM, 2007. p. 629-667. LIVY, S.; VALE, C. First year pre-service teachers’ mathematical content knowledge: Methods of solution for a ratio question. Mathematics Teacher Education and Development, Melbourne, v. 1, n. 2, p. 22-43, 2011. MODESTOU, M.; GAGATSIS, A. Cognitive and metacognitive aspects of proportional reasoning.Mathematical Thinking and Learning, London, v. 12, n. 1, p. 36-53, 2010. PITTA-PANTAZI, D.; CHRISTOU, C. The structure of prospective kindergarten teachers’ proportional reasoning. Journal of Mathematics Teacher Education, Dordrecht, v. 14, n. 2, p. 149- 169, 2011. RIVAS, M. A.; GODINO, J. D; CASTRO, W. F. Desarrollo del conocimiento para la Enseñanza de la Proporcionalidad en Futuros profesores de Primaria. Bolema, Rio Claro (SP), v. 26, n. 42B, p. 559- 588, abr. 2012. SHERIN, M. G.; JACOBS, V. R.; PHILIPP, A. (Ed.). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge, 2010. SHULMAN, L. S. Those who understand: Knowledge growth in teaching. Educational Researcher. Washington, v. 15, n. 2, p. 2-14, Feb. 1986. VALVERDE, A. G.; CASTRO, E. Actuaciones de maestros en formación en la resolución de problemas de proporcionalidad directa. In: SOCIEDAD ESPAÑOLA DE INVESTIGACIÓN EN EDUCACIÓN MATEMÁTICA, 13rd, 2009, Santander, España. Actas… Santander: SEIEM, 2009, p. 523-532. ZAZKIS, R. Relearning Mathematics: A challenge for Prospective elementary School Teachers. Charlotte, NC: information Age Publishing, INC, 2011.