David Múñez

The Effect of External Representations on Compare Word Problems: Supporting Mental Model Construction

This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps and language consistency). Data from errors and response times indicated that adding a graph to compare word problems helped accuracy (d =.60) and response time (d =.44). This effect was larger for difficult and cognitively demanding problems. Findings suggest that external representations might help problem-solvers build a mental model of the described problem situation. In addition, working memory was not found to moderate the effectiveness of external representations.

Arithmetic Word Problem Solving: Evidence for a Magnitude-Based Mental Representation

Previous findings have suggested that number processing involves a mental representation of numerical magnitude. Other research has shown that sensory experiences are part and parcel of the mental representation (or “simulation”) that individuals construct during reading. We aimed at exploring whether arithmetic word-problem solving entails the construction of a mental simulation based on a representation of numerical magnitude. Participants were required to solve word problems and to perform an intermediate figure discrimination task that matched or mismatched, in terms of magnitude comparison, the mental representations that individuals constructed during problem solving. Our results showed that participants were faster in the discrimination task and performed better in the solving task when the figures matched the mental representations. These findings provide evidence that an analog magnitude-based mental representation is routinely activated during word-problem solving, and they add to a growing body of literature that emphasizes the experiential view of language comprehension.

Análisis de la práctica educativa en clases de matemáticas españolas de Educación Primaria: una posible explicación para el nivel de competencia de los alumnus

Resumen Para explorar si la práctica educativa podría influir en el bajo nivel de competencia matemática que muestran los alumnos españoles en evaluaciones internacionales, se analizó el modo en el que cinco profesores desarrollaron una unidad didáctica de matemáticas y cómo se integraron los diferentes tipos de actividades en ellas. Como medidas se tomaron la proporción de cada clase dedicada a planificar, demandar, resolver y revisar tareas; el grado de novedad de los contenidos tratados; el tipo de agrupamiento de las clases; la procedencia de las actividades; y el nivel cognitivo al que se dirigieron esas actividades. Los resultados reflejaron cómo, al igual que otros países cuyos alumnos también mostraron baja competencia matemática, en las clases analizadas apenas se formulaba un objetivo, se presentaron pocos contenidos nuevos, predominó el agrupamiento en grupo-clase e individual, la mayoría de las actividades procedió de los libros de texto y estaban dirigidas a trabajar procesos de bajo nivel cognitivo.

Marcadores nucleares de la competencia aritmética en preescolares

espanolLas habilidades numericas y aritmeticas son predictores criticos del exito academico. En trabajos recientes, se ha cuestionado que habilidades numericas basicas se relacionan con la ejecucion en aritmetica, si el procesamiento de magnitudes numericas no simbolicas o el procesamiento de magnitudes simbolicas. En el presente estudio se tomo una muestra de 104 escolares del segundo curso de Educacion Infantil (EI), que completaron una tarea de comparacion de magnitudes numericas no simbolicas, una de comparacion de magnitudes numericas simbolicas y una tarea de enumeracion, asi como un test estandarizado de rendimiento en matematicas (TEMA-3). Ademas, se controlaron habilidades cognitivas generales como inteligencia, velocidad de procesamiento, amplitud de memoria, control inhibitorio y memoria visuo-espacial. Para comprobar si las variables de procesamiento numerico predicen mas alla de las variables de control, se realizo un analisis de regresion jerarquica, utilizando como variable dependiente el TEMA-3, e introduciendo las variables de control y las tareas de procesamiento numerico en sucesivos pasos. El modelo explico el 65.5% de la varianza. Pero solo la comparacion de magnitudes simbolicas y la enumeracion contribuyeron a la varianza en ejecucion aritmetica mas alla de las variables de control, mientras que la comparacion de magnitudes no simbolicas no contribuyo significativamente. Estos resultados sugieren que un buen conocimiento de los numeros simbolicos es importante para el desarrollo matematico de los ninos, y que particularmente el acceso a la magnitud desde los numeros simbolicos mas que la representacion de la magnitud per se es crucial para este desarrollo de la aritmetica. EnglishThe numerical and arithmetic skills are critical predictors of academic success. In current studies, it has been questioned what numerical skills relate with arithmetic achievement, whether the non-symbolic numerical magnitudes processing or the symbolic magnitudes processing. In the current study a sample of 104 preschool children was taken. They completed a non-symbolic numerical comparison task, a symbolic numerical comparison task and a dot enumeration task, as well as a standardized arithmetic performance test (TEMA-3). Moreover, general cognitive skills such a intelligence, processing speed, inhibitory control, memory span and visuo-spatial memory, were controlled. To test whether the variables of number processing predict in the absence of the above predictors, it was conducted a hierarchical regression analysis, taking the TEMA-3 as a dependent variable and introducing the other predictors and the numerical processing tasks in next steps. The model explained 65.5% of the variance. But only the symbolic magnitudes comparison and the enumeration contributed to the arithmetic achievement variance in absence of the control variables, while the non-symbolic magnitudes comparison did not contribute significantly. These results suggest that a good knowledge of symbolic numbers is important to the children’s mathematical development, being particularly crucial the access to the magnitude from symbolic numbers more than the magnitude representation per se.