Algunos aspectos del desarrollo del pensamiento algebraico: el concepto de raíz y de variable en ecuaciones polinómicas de segundo grado. Un estudio de casos realizado con estudiantes uruguayos de enseñanza secundaria

Referencias

Arcavi, A. (1994), “Symbol sense: informal sense-making in formal mathematics”, For the Learning of Mathematics, vol. 14, núm. 3, pp. 24-35. Bardini, C., L. Radford y C. Sabena (2005), “Struggling with variables, parameters, and indeterminate objects or how to go insane in mathematics”, en H. L. Chick y J. L. Vincent (eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, University of Melbourne, Australia, vol. 2, pp. 129-136. Booth, L. (1984), Algebra: Children’s Strategies and Errors, Windsor, NFER-Nelson. Filloy, E. y T. Rojano (1984), “From an arithmetical to an algebraic thought: a clinical study with 12-13 years old”, Proceedings of the Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 51-56. Fischbein, E. (1987), Intuition in Science and Mathematics. An Educational Approach, Dortretch, D. Reidel. Fischbein, E. y D. Schnarch (1997), “The Evolution With Age of Probabilistic, Intuitively Based Misconceptions”, Journal for Research in Mathematics Education, vol. 28, núm. 1, pp. 96-105. Fujii, T. (2003), “Probing Students’ Understanding of Variables Through Cognitive Conflict Problems: Is the Concept of a Variable so Difficult for Students to Understand?”, Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, vol. 1, pp. 49-65. Kieran, C. (1981), “Concepts associated with the equality symbol”, Educational Studies in Mathematics, núm. 12, pp. 317-326. ————————– (1984), “Cognitive mechanisms underlying the equation-solving errors of algebra novices”, en Southwell y cols. (eds.), Proceedings of PME VIII, Sydney, Australia, pp. 70-77. ————————– (2006), “Research on the Learning and Teaching of Algebra”, en A. Gutiérrez y P. Boero (eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future, Rotterdam, Sense Publishers, pp. 11-49. Kieran, C. y E. Filloy (1989), “El aprendizaje del álgebra escolar desde una perspectiva psicológica”, Enseñanza de las Ciencias, vol. 7, núm. 3, pp. 229- 240. Knuth, E. J., A. C. Stephens, N. M. McNeil y M. W. Alibali (2006), “Does understanding the equal sign matter? Evidence from solving equations”, Journal for Research in Mathematics Education, vol. 37, núm. 4, pp. 297-312. Küchmann, D. (1981), “Algebra”, en K. M. Hart (ed.), Children’s understanding of mathematics: 11-16, Londres, John Murray, pp. 102-119. Lima, R. N. (2008), “Procedural embodiment and quadratic equations”, artículo presentado en ICMI 11, Monterrey, México. Linchevski, L. y N. Herscovics (1996), “Crossing the Cognitive Gap between Arithmetic and Algebra: Operating on the Unknown in the Context of Equations”, Educational Studies in Mathematics, vol. 30, núm. 1, pp. 39-65. McNeil, N. M., L. Grandau, E. J. Knuth, M. W. Alibali, A. C. Stephens, S. Y. Hattikudur y D. E. Krill (2006), “Middle school students’ understanding of the equal sign: the books they read can’t help”, Cognition and Instruction, vol. 24, núm. 3, pp. 367-385. Ochoviet, C. y A. Oktaç (2009), “If A * B = 0 then A = 0 or B = 0?”, The Montana Mathematics Enthusiast, vol. 6, núm. 1 y 2, pp.113-136. Papaieronymou, I. (2007), “Student difficulties in understanding the difference between the algebraic expressions and the concept of linear equation”, Proceedings of CERME 5, Working group 6, pp. 934-943. Radford, L. y L. Puig (2007), “Syntax and Meaning as Sensuous, Visual, Historical Forms of Algebraic Thinking”, Educational Studies in Mathematics, núm. 66, pp. 145-164. Schoenfeld, A. y A. Arcavi (1988), “On the meaning of variable”, Mathematics Teacher, vol. 81, núm. 6, pp. 420-427. Trigueros, M., S. Ursini y D. Lozano (2000), “La conceptualización de la variable en la enseñanza media”, Educación Matemática, vol. 12, núm. 2, pp. 27-48. Trigueros, M. y S. Ursini (2003), “First-year Undergraduates’ Difficulties in Working with Different Uses of Variable”, en Annie Selden, Ed Dubinsky, Guershon Harel y Fernando Hitt (eds.), CBMS Issues in Mathematics Education, vol. 12. Research in Collegiate Mathematics Education V, American Mathematical Society in cooperation with Mathematical Association of America, vol. V, pp. 1-29. Ursini, S. y M. Trigueros, (2006), “¿Mejora la comprensión del concepto de variable cuando los estudiantes cursan matemáticas avanzadas?”, Educación Matemática, vol. 18, núm. 3, pp. 5-38. Vaiyavutjamai, P. y M. A. Clements (2006), “Effects of classroom instruction on students’ understanding of quadratic equations”, Mathematics Education Research Journal, vol. 18, núm. 1, pp. 47-77. Vaiyavutjamai, P., N. F. Ellerton y M. A. Clements (2005), “Students’ attempts to solve two quadratic equations: a study in three nations”, en P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce y A. Roche (eds.), Building connections: Research, theory and practice (Proceedings of MERGA 28, vol. 2, pp. 735-742). Melbourne, Australia, MERGA Program Committee. Van Engen, H. (1961a), “A Note on ‘Variable’”, The Mathematics Teacher, marzo, pp. 172-173. Van Engen, H. (1961b), “On ‘Variable’_a rebuttal”, The Mathematics Teacher, marzo, pp. 175-177. Vinner, S. (1990), “Inconsistencies: their Causes and Function in Learning Mathematics”, Focus on Learning Problems in Mathematics, vol. 12, núm. 3 y 4, pp. 85-98. Wagner, S. (1983), “What are these things called variables?”, Mathematics Teacher, núm. 76, pp. 474-479.