Comparación de resoluciones algebraicas con y sin tablas de problemas de edades

Autores/as

Resumen

En el contexto de la resolución algebraica de problemas de edades, este trabajo estudia las similitudes y diferencias en la construcción del modelo de problema, los errores en las ecuaciones y los procesos subyacentes a estos, dependiendo de si se usan o no tablas. Mediante técnicas de interpretación cualitativa se analizó el discurso, los gestos y las producciones escritas de ocho pares de estudiantes de secundaria. Se obtuvo que cuando usaron tablas construyeron siempre un modelo de problema, mientras que cuando no en ocasiones usaron una estrategia sintáctica. Los errores en las ecuaciones fueron análogos en ambas formas de resolución –con y sin tablas– y la traducción fragmentada del lenguaje natural al algebraico fue un proceso subyacente a ellos en ambas formas.

Palabras clave

Educación secundaria, Lenguaje algebraico, Resolución algebraica, Tabla

Citas

Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183-198. https://doi.org/10.1016/j.learninstruc.2006.03.001

Arnau, D. y Puig, L. (2013). Actuaciones de alumnos instruidos en la resolución algebraica de problemas en la hoja de cálculo y su relación con la competencia en el método cartesiano. Enseñanza de las Ciencias, 31(3), 49-66. https://doi.org/10.5565/rev/ec/v31n3.967

Arzarello, F., Paola, D., Robutti, O. y Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70, 97-109. https://doi.org/10.1007/s10649-008-9163-z

Bednarz, N., Kieran, C. y Lee, L. (Eds.) (1996). Approaches to algebra: Perspectives for research and teaching. Kluwer Academic Publishers.

Bieda, K. N. y Nathan, M. J. (2009). Representational disfluency in algebra: evidence from student gestures and speech. ZDM Mathematics Education, 41, 637-650. https://doi.org/10.1007/s11858-009-0198-0

Bloedy-Vinner, H. (1996). The analgebraic mode of thinking and other errors in word problem solving. En L. Puig y A. Gutiérrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (pp. 105-112). International Group for the Psychology of Mathematics Education.

Cerdán, F. (2010). Las igualdades incorrectas producidas en el proceso de traducción algebraico: un catálogo de errores. PNA, 4(3), 99-110. https://doi.org/10.30827/pna.v4i3.6164

Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16-30. https://doi.org/10.2307/748434

Ding, M., Chen, W. y Hassler, R. S. (2019). Linear quantity models in US and Chinese elementary mathematics classrooms. Mathematical Thinking and Learning, 21(2), 105-130. https://doi.org/10.1080/10986065.2019.1570834

Ding, M. y Li, X. (2014). Transition from concrete to abstract representations: The distributive property in a Chinese textbook series. Educational Studies in Mathematics, 87, 103-121. https://doi.org/10.1007/s10649-014-9558-y

Duval, R. (2017). Understanding the mathematical way of thinking - The Registers of semiotic representations. Springer International Publishing.

Ernest, P. (2006). A semiotic perspective of mathematical activity: the case of number. Educational Studies in Mathematics, 61, 67-101. https://doi.org/10.1007/s10649-006-6423-7

Filloy, E., Puig, L. y Rojano, T. (2008). El estudio teórico local del desarrollo de competencias algebraicas. Enseñanza de las Ciencias, 25(3), 327-342. https://doi.org/10.5565/rev/ensciencias.3746

Filloy, E., Rojano, T. y Puig, L. (2008). Educational algebra. A theoretical and empirical approach. Springer.

Filloy, E., Rojano, T. y Solares, A. (2010). Problems Dealing with Unknown Quantities and Two Different Levels of Representing Unknowns. Journal for Research in Mathematics Education, 41(1), 52-80. https://doi.org/10.5951/jresematheduc.41.1.0052

Kaput, J. J. (1989). Toward a theory of symbol use in Mathematics. En C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 159-196). Lawrence Erlbaum Associates, Inc.

Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. En F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Information Age Publishing.

Kintsch, W. (1998). Comprehension. A paradigm for cognition. Cambridge University Press.

McNeil, N. M. y Fyfe, E. R. (2012). «Concreteness fading» promotes transfer of mathematical knowledge. Leaning and Instruction, 22(6), 440-448. https://doi.org/10.1016/j.leaminstruc.2012.05.001

Ministerio de Educación, Cultura y Deporte (2014). Real Decreto 1105/2014, por el que se esta¬blece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato. Boletín Oficial del Estado, 3, 169-546.

Molina, M., Rodríguez-Domingo, S., Cañadas, M. C. y Castro, E. (2017). Secondary school students’ errors in the translation of algebraic statements. International Journal of Science and Mathematics Education, 15(6), 1137-1156. https://doi.org/10.1007/s10763-016-9739-5

Nathan, M. J., Kintsch, W. y Young, E. (1992). A theory of algebra-word-problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9(4), 329-389. https://doi.org/10.1207/s1532690xci0904_2

Neuman, Y. y Schwarz, B. (2000). Substituting one mystery for another: the role of self-explanations in solving algebra word-problems. Learning and Instruction, 10, 203-220. https://doi.org/10.1016/S0959-4752(99)00027-4

Ng, S. y Lee, K. (2009). The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems. Journal for Research in Mathematics Education, 40(3), 282-313. https://doi.org/10.5951/jresematheduc.40.3.0282

Peräkylä, A. (2005). Analysing talk and text. En N. K. Denzin y Y. S. Lincoln (Eds.), The SAGE handbook of qualitative research (pp. 869-886). SAGE Publications.

Phan, H. P., Ngu, B. H. y Yeung, A. S. (2017). Achieving optimal best: Instructional efficiency and the use of cognitive load theory in mathematical problem solving. Educational Psychology Review, 29(4), 667-692. https://doi.org/10.1007/s10648-016-9373-3

Radford, L. (2000). Signs and meanings in students’ emergent algebraic thinking: a semiotic analysis. Educational Studies in Mathematics, 42, 237-268. https://doi.org/10.1023/A:1017530828058

Radford, L. (2003). Gestures, speech, and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37-70. https://doi.org/10.1207/S15327833MTL0501_02

Radford, L., Bardini, C. y Sabena, C. (2007). Perceiving the general: The multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, 38(5), 507-530. https://doi.org/10.2307/30034963

Rellensmann, J., Schukajlov, S. y Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95, 53-78. https://doi.org/10.1007/s10649-016-9736-1

Sanjosé, V., Solaz-Portolés, J. J. y Valenzuela, T. (2009). Transferencia inter-dominios en resolución de problemas: una propuesta instruccional basada en el proceso de traducción algebraica. Enseñanza de las Ciencias, 27(2), 169-184. https://doi.org/10.5565/rev/ensciencias.3729

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

Soneira, C. (2022). The Use of Representations when Solving Algebra Word Problems and the Sources of Solution Errors. International Journal of Science and Mathematics Education, 20(5), 1037-1056. https://doi.org/10.1007/s10763-021-10181-2

Soneira, C., González-Calero, J. A. y Arnau, D. (2018). Indexical Expressions in Word Problems and their Influence on Multiple Referents of the Unknown. International Journal of Science and Mathematics Education, 16(6), 1147-1167. https://doi.org/10.1007/s10763-017-9824-4

Stacey, K. y MacGregor, M. (2000). Learning the Algebraic Method of Solving Problems. The Journal of Mathematical Behavior, 18(2), 149-16. https://doi.org/10.1016/S0732-3123(99)00026-7

Uesaka, Y. y Manalo, E. (2012). Task-Related Factors that Influence the Spontaneous Use of Diagrams in Math Word Problems. Applied Cognitive Psychology, 26(2), 251-260. https://doi.org/10.1002/acp.1816

Recepción: septiembre 2021 • Aceptación: enero 2023 • Publicación: marzo 2023

Soneira,C. (2023). Comparación de resoluciones algebraicas con y sin tablas de problemas de edades. Enseñanza de las Ciencias, 41(1), 43-61. https://doi.org/10.5565/rev/ensciencias.5546

Publicado

02-03-2023

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