We conducted an empirical study to analyse the association between students' perception of surface and structural analogies among problems, and their algebraic success. Algebraic success was measured by the equations selected to solve each problem. Different surface and structural relationships between one source problem and four target problems were considered. We also considered high (daily life) and low (scientific) familiarity contexts for the problems. Similarities and differences between the source and each target problem were explicitly asked to students. Results showed a significant correlation between detecting the correct structural relation between these problems and selecting the correct equations to solve the target ones. Low familiarity (science) problems obtained lower success independently of other factors. Usual teaching procedures, based on isomorphism, could increase the probability that students consider isomorphism the only possible relationship between problems.Keywords: Problem-solving, analogies, surface and structure, familiarity, transfer. ResumenSe desarrolla un estudio empírico con estudiantes de Secundaria para analizar la asociación entre detectar las analogías superficiales y estructurales entre problemas, y el éxito algebraico medido a través de las ecuaciones seleccionadas para resolverlos. Se consideraron distintas relaciones superficiales y estructurales entre un problema fuente y cuatro problemas diana. Se consideraron problemas con temáti-cas de alta (vida diaria) o baja familiaridad (ciencia). Se pidió a los estudiantes comparar el problema fuente con cada problema diana para establecer las similitudes y diferencias entre ellos. Los resultados mostraron una correlación significativa entre detectar correctamente la relación estructural entre problemas y elegir las ecuaciones correctas para resolverlos. El éxito fue menor en los problemas de baja familiaridad (ciencias) independientemente de otros factores. La enseñanza habitual basada en la isomorfía podría incrementar la probabilidad de que los estudiantes considerasen este tipo de relación como la única posible entre problemas.Palabras clave: Resolución de problemas, analogías, superficie y estructura, familiaridad, transferencia.
We conducted a qualitative research of case studies based on think-aloud protocols. The aim was to carry out in-depth analyse secondary students' cognitive difficulties appearing in early stages of transfer processes in problem-solving. The task was to relate several source problems to a target problem, in order to solve it effectively. Source and target problems had different Surface and/or Structural similarities. In this paper, the solvers' high or low Familiarity with the problem stories on transfer processes was also focused on. Two emergent instructional phenomena are described, both associated to specific students' cognitive obstacles to achieve success in solving the target problem: the 'Screen effect' and the 'Sisyphus effect'. The obstacles were harder for low Familiarity problems.
ResumenEn resolución de problemas verbales por transferencia, la activación de problemas ya conocidos que sirvan de guía, depende de las analogías percibidas entre éstos y el problema a resolver. Se desarrollan dos estudios relacionados para analizar en qué características se basan los estudiantes para codificar problemas y detectar sus analogías, en tareas de categorización (sorting). Se utilizaron técnicas cuantitativas y cualitativas combinadas. Primero se analizó cómo los estudiantes de secundaria son influidos por diferentes variables características de problemas de ciencias. Una gran proporción de sujetos no fue capaz de percibir las analogías y diferencias adecuadas entre problemas. El segundo estudio trató de avanzar una explicación de estos resultados. El nivel académico y la familiaridad con las temáticas fueron factores significativos, pero los futuros profesores participantes mostraron demasiadas dificultades, alertando sobre la conveniencia de revisar algunos supuestos instruccionales habituales.Palabras clave: Resolución de Problemas Verbales Algebraicos. Superficie y Estructura de problemas. Familiaridad con la temática. Analogías entre Problemas. Categorización de problemas. AbstractSolving verbal problems by transfer implies the activation of other, previously solved problems by means of the analogies perceived between these and the 'target problems'. Two related studies are conducted to analyse what features students focus on to codify problems and to build analogies among them when sorting tasks are proposed. Quantitative and qualitative techniques were used in the analysis. First, we analysed how different science problem characteristics influence secondary students' task performance. A high proportion of participants were not able to perceive suitable analogies and differences among problems. The second study tried
Testing a model for the monitoring of worked-out algebra-problem examples: From behaviours to outcomes on a math task. Psicología Educativa. Ahead of print.
Resumen: Se presenta un estudio cualitativo, basado en entrevistas semi-estructuradas, de 2 casos que muestran dos fenómenos didácticos de interés en la resolución de problemas por transferencia analógica. El primero muestra un 'efecto pantalla', en el cual el sujeto no puede acceder a la estructura de los problemas a partir de los enunciados. En el segundo caso, el sujeto no logra alcanzar un estado estable de comprensión, a pesar de su avance, y por tanto acaba por retroceder a un estado de ausencia de conflicto cognitivo, pero indeseado desde el punto de vista didáctico ('efecto Sísifo'). Se discuten las posibles implicaciones didácticas de estos casos.Palabras clave: Resolución de problemas; Transferencia analógica; Superficie y Estructura de problemas; Entrevista semiestructurada; Educación secundaria.Abstract: A qualitative study, based on semi-structured interviews to two students, is presented. These two cases represent interesting learning phenomena related to problemsolving by analogical transfer. The first one shows a 'Screen effect' in which the student cannot access to the problems structure from their statements. The second case shows the 'Sisifo effect': the subject is progressing up on the 'learning slope', but is not able to arrive to a steady, new cognitive state. As a consequence, he/she returns to a 'lower' cognitive state, free from cognitive conflict but undesirable from the educational point of view. The possible educational consequences of these cases are discussed.
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