División de fracciones como comparación multiplicativa a partir de los métodos de los alumnos

Referencias

Ball, D. L. (1990), “Prospective elementary and secondary teachers’ understanding of division”, Journal for Research in Mathematics Education, vol. 21, núm. 2, pp. 132-144. Barlow, A. T. y J. M. Drake (2008), “Assessing understanding through problem writing: Division by a fraction”, Mathematics Teaching in the Middle School, vol. 13, núm. 6, pp. 326-332. Behr, M., G. Harel, T. Post y R. Lesh (1993), “Rational numbers: Towards a semantic analysis - emphasis on the operator construct”, en T. P. Carpenter, E. Fennema y T. A. Romberg (eds.), Rational Numbers: An Integration of Research, Hillsdale, Lawrence Erlbaum Associates, pp. 13-47. 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. 91-126. Boaler, J. y C. Humphreys (2005), Connecting Mathematical Ideas: Middle School Video Cases to Support Teaching and Learning, Portsmouth, Heinemann. Clarke, D. M., A. Roche y A. Mitchell (2008), “10 practical tips for making fractions come alive and make sense”, Mathematics Teaching in the Middle School, vol. 13, núm. 7, pp. 373-380. Day, M. M. (2010), Middle school mathematics students’ justification schemes for dividing fractions, tesis de doctorado, Tempe, Arizona State University. Duckworth, E. R. (2006),“The Having of Wonderful Ideas” and Other Essays on Teaching and Learning”, 3a edición, Nueva York, Teachers College Press. Empson, S. B. y L. Levi (2011), Extending Children’s Mathematics: Fractions and Decimals, Portsmouth, Heinemann. Flores, A. (2002), “Profound understanding of division of fractions”, en B. Litwiller y G. Bright (eds.), Making Sense of Fractions, Ratios, and Proportions, 2002 NCTM Yearbook, Reston, National Council of Teachers of Mathematics, pp. 237-246. Flores, A. y M. D. Priewe (2013), “Orange you glad I did say ‘fraction division’?”, Mathematics Teaching in the Middle School, vol. 19, núm. 5, pp. 288-293. Flores, A., E. E. Turner y R. C. Bachman (2005), “Posing problems to develop understanding: Two teachers make sense of division of fractions”, Teaching Children Mathematics, vol. 12, pp. 117-121. Harel, G. y J. Confrey (eds.) (1994), The Development of Multiplicative Reasoning in the Learning of Mathematics, Albany, State University of New York Press. Kieran, C. y L. Chalouh (1993), “Prealgebra: The transition from arithmetic to algebra”, en D. T. Owens (ed.), Research Ideas for the Classroom: Middle Grades Mathematics, Reston, National Council of Teachers of Mathematics, pp. 179-198. Kieren, T. E. (1976), “On the mathematical, cognitive, and instructional foundations of rational numbers”, en R. Lesh (ed.), Number and Measurement: Papers from a Research Workshop, Columbus, ERIC/SMEAC (Science, Mathematics, and Environmental Education Information Analysis Center), pp. 101-144. ————— (1988), “Personal knowledge of rational numbers: Its intuitive and formal development”, en J. Hiebert y M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Reston, National Council of Teachers of Mathematics, pp. 162-181. ————— (1992), “Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction”, en G. Leinhardt, R. Putnam y R. A. Hattrup (eds.), Analysis of Arithmetic for Mathematics Teaching, Hillsdale, Lawrence Erlbaum Associates, pp. 323-371. Kribs-Zaleta, C. (2008), “Oranges, posters, ribbons, & lemonade: Concrete computational strategies for dividing fractions”, Mathematics Teaching in the Middle School, vol. 13, núm. 8, pp. 453-457. Lamon, S. J. (1999), Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers, Mahwah, Lawrence Erlbaum Associates. Lesh, R., T. Post y M. Behr (1988), “Proportional reasoning”, en J. Hiebert y M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Reston, National Council of Teachers of Mathematics, pp. 93-118. Lobato, J. y A. B. Ellis (2010), Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning, Reston, National Council of Teachers of Mathematics. Ma, L. (1999), Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States, Mahwah, Lawrence Erlbaum Associates. Pirie, S. E. B. (1988), “Understanding: Instrumental, relational, intuitive, constructed, formalised...? How can we know?”, For the Learning of Mathematics, vol. 8, núm. 3, pp. 2-6. Polya, G. (1962), Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, vol. 1, Nueva York, John Wiley & Sons. ————— (1990), Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics, vol. 1, Princeton, Princeton University Press. Simon, M. A. (1993), “Prospective elementary teachers’ knowledge of division”, Journal for Research in Mathematics Education, vol. 24, núm. 3, pp. 233-254. Sinicrope, R., H. W. Mick y J. R. Kolb (2002), “Interpretations of fraction division”, en B. Litwiller y G. Bright (eds.), Making Sense of Fractions, Ratios, and Proportions, 2002 NCTM Yearbook, Reston, National Council of Teachers of Mathematics, pp. 153-161. Smith, J. P. (1995), “Competent reasoning with rational numbers”, Cognition and Instruction, vol. 13, núm. 1, pp. 3-50. Streefland, L. (1991), Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research, Dordrecht, Kluwer Academic Publishers. Thompson, P. W. (1994), “The development of the concept of speed and its relationship to concepts of rate”, en G. Harel y J. Confrey (eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics, Albany, State University of New York Press, pp. 179-234. Thompson, P. W. y L. A. Saldanha (2003), “Fractions and multiplicative reasoning”, en J. Kilpatrick, W. G. Martin y D. Schifter (eds.), A Research Companion to Principles and Standards for School Mathematics, Reston, National Council of Teachers of Mathematics, pp. 95-113. Toluk, Z. (1999), Children’s Conceptualizations of the Quotient Subconstruct of Rational Numbers, tesis de doctorado, Tempe, Arizona State University. Warrington, M. A. (1997), “How children think about division with fractions”, Mathematics Teaching in the Middle School, vol. 2, núm. 6, pp. 390-394.