Investigar las fracciones: experiencias inspiradas en la metodología de los experimentos de diseño

Referencias

Backhoff, E., E. Andrade, A. Sánchez, M. Peon y A. Bouzas (2006), El aprendizaje del español y las matemáticas en la educación básica en México: Sexto de primaria y tercero de secundaria. México, Instituto Nacional para la Evaluación de la Educación. Ball, D. L. (1993), “Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions”, en T. P. Carpenter, E. Fennema y T. A. Romberg (eds.), Rational Numbers: An Integration of Research, Hillsdale, Lawrence Erlbaum. Behr, M., R. Lesh, T. Post y E. Silver (1983), “Rational number concepts”, en R. Lesh y M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, Nueva York, Academic Press, pp. 91-125. Brousseau, G., N. Brousseau y V. Warfield (2004), “Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurement”, Journal of Mathematical Behavior, vol. 23, pp. 1-20. Charles, K. y R. Nason (2000), “Young children’s partitioning strategies”, Educational Studies in Mathematics, vol. 43, pp. 191-221. Cobb, P. (1999), “Individual and collective mathematical learning: The case of statistical data analysis”, Mathematical Thinking and Learning, vol. 1, núm. 1, pp. 5-44. ————— (2007), “Putting philosophy to work: Coping with multiple theoretical perspectives”, en F. Lester (ed.), Second Handbook of Research on Mathematics Teaching and Learning, Greenwich, Information Age Publishing-NCTM. Cobb, P. y J. Bowers (1999), “Cognitive and situated learning perspectives in theory and practice”, Educational Researcher, vol. 28, núm. 2, pp. 4-15. Cobb, P., J. Confrey, A. A. diSessa, R. Lehrer y L. Schauble (2003a), “Design experiments in education research”, Educational Researcher, vol. 32, núm. 1, pp. 9-13. Cobb, P., K. Gravemeijer, E. Yackel, K. McClain y J. Whitenack (1997), “Mathematizing and symbolizing: The emergence of chains of signification in one first-grade classroom”, en D. Kirshner y J. A. Whitson (eds.), Situated Cognition: Social, Semiotic, and Psychological Perspectives, Mahwah, Lawrence Erlbaum, pp. 151-232. Cobb, P., K. McClain y K. Gravemeijer (2003b), “Learning about statistical covariation”, Cognition and Instruction, vol. 21, pp. 1-78. Cobb, P., Q. Zhao y J. Visnovska (2008), “Learning from and adapting the theory of realistic mathematics education”, Education et Didactique, vol. 2, núm. 1, pp. 55-73. Confrey, J. y A. Lachance (2000), “Transformative teaching experiments through conjecture-driven research design”, en A. Kelly y A. Lesh (eds.), Handbook of Research Design in Mathematics and Science Education, Mahwah, Lawrence Erlbaum Associates, pp. 231-266. Cortina, J. L., E. R. Cardoso y C. Zúñiga (2012a), “El significado cuantitativo que tienen las fracciones para estudiantes mexicanos de 6º de primaria”, Revista Electrónica de Investigación Educativa, vol. 14, núm. 1, pp. 71-85. Cortina, J. L., J. Visnovska y C. Zúñiga (2012b), “Alternative starting point for teaching fractions”, en J. Dindyal, L. P. Cheng y S. F. Ng (eds.), Mathematics Education: Expanding Horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia, eBook, Singapore, MERGA, pp. 210-217. Cortina, J. L., J. Visnovska y C. Zúñiga (en prensa), “Unit fractions in the context of proportionality: Supporting students’ reasoning about the inverse order relationship”, Mathematics Education Research Journal. Cortina, J. L. y C. Zúñiga (2008), “La comparación relativa de tamaños: Un punto de partida alternativo y viable para la enseñanza de las fracciones”, Educación Matemática, vol. 20, núm. 2, pp. 5-23. Cortina, J. L., C. Zúñiga y J. Visnovska (2013), “La equipartición como obstáculo didáctico en la enseñanza de las fracciones”, Educación Matemática, vol. 25, núm. 2, pp. 7-29. Davydov, V. V. (1969/1991), “On the objective origin of the concept of fractions”, Focus on Learning Problems in Mathematics, vol. 13, núm. 1, pp. 13-64. Freudenthal, H. (1983), Didactical Phenomenology of Mathematical Structures, Dordrecht, Kluwer. Gould, P. (2005), “Year 6 students’ methods of comparing the size of fractions”, en P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce et ál. (eds.), Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia, Sydney, MERGA, pp. 393-400. Gravemeijer, K. y P. Cobb (2006), “Design research from a learning design perspective”, en J. van den Akker, K. Gravemeijer, S. McKenney y N. Nieveen (eds.), Educational Design Research: The Design, Development and Evaluation of Programs, Processes and Products, Nueva York, Routledge, pp. 45-85. Hannula, M. S. (2003), “Locating fraction on a number line”, en N. Pateman, B. Dougherty y J. Zilliox (eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, vol. 3, Honolulu, PME, pp. 17-24. Hart, K. (1989), “Fractions: Equivalence and addition”, en K. Hart, D. C. Johnson, M. Brown, L. Dickson y R. Clarkson (eds.), Childrens’ Mathematical Frameworks 8-13: A Study of Classroom Teaching, Windsor, NFER-Nelson, pp. 46-75. Kieren, T. E. (1980), “The rational number construct: Its elements and mechanisms”, en T. E. Kieren (ed.), Recent Research on Number Learning, Columbus, ERIC/SMEAC, pp. 125-149. Lamon, S. J. (2007), “Rational numbers and proportional reasoning: Toward a theoretical framework for research”, en F. K. Lester (ed.), Second Handbook of Research on Mathematics Teaching and Learning, Charlotte, Information Age Pub, pp. 629-667. Maya, F. (2011), El razonamiento multiplicativo en jóvenes universitarios del área económico administrativa, tesis doctoral, México, Universidad Pedagógica Nacional. McGatha, M., P. Cobb y K. McClain (2002), “An analysis of students’ initial statistical understandings: Developing a conjectured learning trajectory”, Journal of Mathematical Behavior, vol. 16, núm. 3, pp. 339-355. NCTM (2000), Principles and Standards for School Mathematics, Reston, National Council of Teachers of Mathematics. Norton, A. (2008), “Josh’s operational conjectures: Abductions of a splitting operation and the construction of new fractional schemes”, Journal for Research in Mathematics Education, vol. 39, pp. 401-430. OECD (2010), PISA 2009 Results: What Students Know and Can Do: Student Performance in Reading, Mathematics and Science, vol. 1, París, Organisation for Economic Co-operation and Development. Saenz-Ludlow, A. (1994), “Michael’s fraction schemes”, Journal for Research in Mathematics Education, vol. 25, pp. 50-85. Saxe, G. B., E. V. Taylor, C. McIntosh y M. Gearhart (2005), “Representing fractions with standard notations: A developmental analysis”, Journal for Research in Mathematics Education, vol. 36, pp. 137-157. Skovsmose, O. (2005), Critical Mathematics Education for the Future (Working Papers on Education), Denmark, Aalborg University. Steen, L. A. (2001), “The case for quantitative literacy”, en L. A. Steen (ed.), Mathematics and Democracy: The Case for Quantitative Literacy, Princeton, National Council on Education and the Disciplines. Steffe, L. P. y J. Olive (2010), Children’s fractional knowledge, Nueva York, Springer. Steffe, L. P. y P. W. Thompson (2000), “Teaching experiment methodology: Underlying principles and essential elements”, en A. Kelly y A. Lesh (eds.), Handbook of Research Design in Mathematics and Science Education, Mahwah, Lawrence Erlbaum Associates, pp. 267-307. Stephan, M., J. Bowers, P. Cobb y K. Gravemeijer (eds.) (2003), Supporting Students’ Development of Measuring Conceptions: Analyzing Students’ Learning in Social Context, Reston, National Council of Teachers of Mathematics. Streefland, L. (1991), Fractions in Realistic Mathematics Education. A Paradigm of Developmental Research, Dordrecht, Kluwer. Thompson, P. W. y L. A. Saldanha (2003), “Fractions and multiplicative reasoning”, en J. Kilpatrick, G. Martin y D. Schifter (eds.), Research Companion to the Principles and Standards for School Mathematics, Reston, National Council of Teachers of Mathematics, pp. 95-113. Tzur, R. (2007), “Fine grain assessment of students’ mathematical understanding: Participatory and anticipatory stages in learning a new mathematical conception”, Educational Studies in Mathematics, vol. 66, pp. 273-291.