Razonamientos de estudiantes en tareas de comparación, ordenación y representación de fracciones y números decimales

Referencias bibliográficas

• Barraza, P., Avaria, R. y Leiva, I. (2017). The role of attentional networks in the access to the numerical magnitude of fractions in adults/El rol de las redes atencionales en el acceso a la magnitud numérica de fracciones en adultos. Estudios de Psicología, 38(2), 495-522. https://doi.org/10.1080/02109395.2017.1295575
• Behr, M. J., Lesh, R., Post, T. y Silver E. (1983). Rational number concepts. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics concepts and processes, (pp. 91-125). Academic Press.
• Behr, M., Wachsmuth, I., Post T. y Lesh R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341. https://doi.org/10.2307/748423
• Braithwaite, D. W. y Siegler, R. S. (2018). Developmental changes in the whole number bias. Developmental Science, 21(2). https://doi.org/10.1111/desc.12541
• Carpenter, T. P., Fennema, E. y Romberg, T. A. (Eds.) (1993). Studies in mathematical thinking and learning. Rational numbers: An integration of research. Erlbaum.
• Clarke, D. M. y Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138. https://doi.org/10.1007/s10649-009-9198-9
• Cramer, K., Post, T. y delMas, R. (2002). Initial fraction learning by fourth-and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144. https://doi.org/10.2307/749646
• DeWolf, M. y Vosniadou, S. (2011). The whole number bias in fraction magnitude comparisons with adults. En L. Carlson, C. Hoelscher y T. F. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 1751-1756). Cognitive Science Society.
• DeWolf, M. y Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39-49. https://doi.org/10.1016/j.learninstruc.2014.07.002
• Durkin, K. y Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29. https://doi.org/10.1016/j.learninstruc.2014.08.003
• Fazio, L. K., DeWolf, M. y Siegler, R. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42(1), 1-16. https://doi.org/10.1037/xlm0000153
• Fischbein, E., Deri, M., Nello, M. S. y Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3-17. https://doi.org/10.2307/748969
• Gómez, D. M. y Dartnell, P. (2015). Is there a natural number bias when comparing fractions without common components? A meta-analysis. En K. Beswick, T. Muir y J. Wells (Eds.), Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 1-8). PME.
• Gómez, D. M. y Dartnell, P. (2019). Middle schoolers’ biases and strategies in a fraction comparison task. International Journal of Science and Mathematics Education, 17(6), 1233-1250. https://doi.org/10.1007/s10763-018-9913-z
• Gómez, D. M., Silva, E. y Dartnell, P. (2017). Mind the gap: congruency and gap effects in engineering students’ fraction comparison. En B. Kaur, W. K. Ho, T. L. Toh y B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 353-360). PME.
• González-Forte, J. M., Fernández, C. y Llinares, S. (2019). El fenómeno natural number bias: un estudio sobre los razonamientos de los estudiantes en la multiplicación de números racionales. Quadrante, 28(2), 32-52.
• González-Forte, J. M., Fernández, C., Van Hoof, J. y Van Dooren, W. (2020). Various ways to determine rational number size: an exploration across primary and secondary education. European Journal of Psychology of Education, 35(3), 549-565. https://doi:10.1007/s10212-019-00440-w
• González-Forte, J. M., Fernández, C., Van Hoof, J. y Van Dooren, W. (2022). Profiles in understanding the density of rational numbers among primary and secondary school students. AIEM Avances de investigación en educación matemática, 22, 47-70. https://doi.org/10.35763/aiem22.4034
• González-Forte, J. M., Fernández, C., Van Hoof, J. y Van Dooren, W. (2023). Incorrect ways of thinking about the size of fractions. International Journal of Science and Mathematics Education, 21, 2005-2025. https://doi.org/10.1007/s10763-022-10338-7
• Hiebert, J. y Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. En J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 199-223). Lawrence Erlbaum Associates, Inc.
• Khoury, H. A. y Zazkis, R. (1994). On fractions and non-standard representations: Preservice teachers’ concepts. Educational Studies in Mathematics, 27(2), 191–204. https://doi.org/10.1007/BF01278921
• Kieren, T. E. (1992). Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction. En G. Leinhardt, R. Putnam y R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 323–372). Lawrence Erlbaum.
• McMullen, J. y Van Hoof, J. (2020). The role of rational number density knowledge in mathematical development. Learning and Instruction, 65. https://doi.org/10.1016/j.learninstruc.2019.101228
• Merenluoto, K. y Lehtinen, E. (2002). Conceptual change in mathematics: Understanding the real numbers. En M. Limon y L. Mason (Eds.), Reconsidering conceptual change: Issues in theory and practice (pp. 233-258). Kluwer Academic Publishers.
• Mitchell, A. y Horne, M. (2010). Gap thinking in fraction pair comparisons is not whole number thinking: Is this what early equivalence thinking sounds like? En L. Sparrow, B. Kissane y C. Hurst (Eds.), Shaping the future of mathematics education (Vol. 2, pp. 414–421). MERGA.
• Moss, J. (2005). Pipes, tubs, and beakers: New approaches to teaching the rationalnumber system. En Donovan, M. S. y Bransford, J. D. (Eds.), How students learn: History, Math, and Science in the classroom (pp. 309-349). National Academies Press.
• Ni, Y. y Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326985ep4001_3
• Nunes, T. y Bryant, P. (2008). Rational numbers and intensive quantities: challenges and insights to pupils’ implicit knowledge. Anales de Psicología/Annals of Psychology, 24(2), 262-270.
• Obersteiner, A., Alibali, M. W. y Marupudi, V. (2020). Complex fraction comparisons and the natural number bias: the role of benchmarks. Learning and Instruction, 67. https://doi.org/10.1016/j.learninstruc.2020.101307
• Pearn, C. y Stephens, M. (2004). Why you have to probe to discover what year 8 students really think about fractions. En I. Putt, R. Faragher y M. McLean (Eds.), Mathematics education for the third millenium: Towards 2010 (Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 430–437). MERGA.
• Resnick, I., Rinne, L., Barbieri, C. y Jordan, N. C. (2019). Children’s reasoning about decimals and its relation to fraction learning and mathematics achievement. Journal of Educational Psychology, 111(4), 604-618. https://doi.org/10.1037/edu0000309
• Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S. y Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20, 8-27. https://doi.org/10.2307/749095
• Rinne, L. F., Ye, A. y Jordan, N. C. (2017). Development of fraction comparison strategies: A latent transition analysis. Developmental Psychology, 53(4), 713- 730. https://doi.org/10.1037/dev0000275
• Sackur-Grisvard, C. y Léonard, F. (1985). Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2(2), 157-174. https://doi.org/10.1207/s1532690xci0202_3
• Siegler, R. S. y Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918. https://doi.org/10.1037/edu0000025
• Siegler, R. S., Thompson, C. A. y Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273- 296. https://doi.org/10.1016/j.cogpsych.2011.03.001
• Smith, C. L., Solomon, G. E. y Carey, S. (2005). Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter. Cognitive Psychology, 51(2), 101-140. https://doi.org/10.1016/j.cogpsych.2005.03.001
• Smith, J. P. (1995). Competent reasoning with rational numbers. Cognition and Instruction, 13(1), 3-50. https://doi.org/10.1207/s1532690xci1301_1
• Stafylidou, S. y Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
• Steinle, V. y Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in Grades 5 to 10. En C. Kanes, M. Goos y E. Warren (Eds.), Teaching mathematics in new times (pp. 548–555). Mathematics Education Research Group of Australasia.
• Torbeyns, J., Schneider, M., Xin, Z. y Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13. https://doi.org/10.1016/j.learninstruc.2014.03.002
• Vamvakoussi, X., Christou, K. P., Mertens, L. y Van Dooren, W. (2011). What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density. Learning and Instruction, 21(5), 676-685. https://doi.org/10.1016/j.learninstruc.2011.03.005
• Vamvakoussi, X., Christou, K. P. y Vosniadou, S. (2018). Bridging psychological and educational research on rational number knowledge. Journal of Numerical Cognition, 4(1), 84-106. https://doi.org/10.5964/jnc.v4i1.82
• Vamvakoussi, X., Van Dooren, W. y Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344-355. https://doi.org/10.1016/j.jmathb.2012.02.001
• Vamvakoussi, X. y Vosniadou, S. (2007). How many numbers are there in a rational numbers interval? Constraints, synthetic models and the effect of the number line. En S. Vosniadou, A. Baltas y X. Vamvakoussi (Eds.), Reframing the Conceptual Change Approach in Learning and Instruction (pp. 265-282). Elsevier.
• Van Dooren, W., Lehtinen, E. y Verschaffel, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction, 37, 1-4. https://doi.org/10.1016/j.learninstruc.2015.01.001
• Van Hoof, J., Degrande, T., Ceulemans, E., Verschaffel, L. y Van Dooren, W. (2018). Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners. Learning and Individual Differences, 61, 99-108. https://doi.org/10.1016/j.lindif.2017.11.010
• Van Hoof, J., Verschaffel, L. y Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56. https://doi.org/10.1007/s10649-015-9613-3