ABSTRACT
The study aimed to examine the developmental trajectories of non-symbolic and symbolic addition capacities in children and the mapping ability between these two. We assessed 106 4- to 7-year-old children and found that 4-year-olds were able to do non-symbolic addition but not symbolic addition. Five-year-olds and older were able to do symbolic addition and their performance in symbolic addition exceeded non-symbolic addition in grade 1 (approximate age 7). These results suggested non-symbolic addition ability emerges earlier and is less affected by formal mathematical education than symbolic addition. Meanwhile, we tested children's bi-directional mapping ability using a novel task and found that children were able to map between symbolic and non-symbolic representations of number at age 5. Their ability in mapping non-symbolic to symbolic number became more proficient in grade 1 (approximate age 7). This suggests children at age 7 have developed a relatively mature symbolic representation system.
ABSTRACT
How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.
Subject(s)
Comprehension/physiology , Mathematics , Memory, Short-Term/physiology , Problem Solving/physiology , Symbolism , Child , Child Development , Child, Preschool , Female , Humans , Male , Regression AnalysisABSTRACT
Introducción. Se requieren muchos años para que los niños aprendan aritmética simbólica. Sin embargo, al igual que los animales y los adultos sin educación formal, los infantes y niños pueden representar el número aproximado de conjuntos de objetos y secuencias de eventos, y utilizar esta capacidad para realizar adiciones y sustracciones aproximadas. Objetivo. Evaluar si niños preescolares que no hayan recibido educación formal son capaces de realizar adiciones no simbólicas a través de representaciones abstractas de la magnitud. Métodos. Los participantes fueron 17 niños preescolares de un jardín de infantes privado de una población de clase media de la Ciudad Autónoma de Buenos Aires. La tarea fue adicionar dos conjuntos de puntos azules presentados por separado y comparar su suma con un conjunto de puntos rojos, determinando si la suma de puntos azules o el conjunto de puntos rojos era más numeroso. Se midió el porcentaje de respuestas correctas de cada niño. Resultados. Los niños respondieron sobre la chance (67,89%, chance= 50%, t(16)= 6,89, p <0,001), observándose el característico efecto de la proporción [(F(1,16)= 8,45, p <0,01, ANOVA] y sin recurrir al uso de estrategias alternativas no aritméticas. Conclusiones. Este trabajo aporta más evidencia sobre las habilidades aritméticas no simbólicas presentes antes de la instrucción formal y genera junto con investigaciones recientes, importantes aportes en el ámbito educativo, que ayudan a entender cómo los niños aprenden matemáticas, un hecho útil para establecer nuevas formas de enseñanza.
Introduction. Children take years to learn symbolic arithmetic. Nevertheless, such as animals and human adults, infants and children can represent approximate number in arrays of objects and sequences of events, and use these capacities to perform approximate addition and subtraction. Objective. To evaluate whether preschool children without formal education could perform non-symbolic additions, through abstract representations. Methods. We evaluated 17 preschoolers from a private kindergarten recruited from the city of Buenos Aires. They had to add to groups of blue dots, and then compare their addition with a third group of red dots, determining if the blue or the red dots were more numerous. We measured accuracy of responses of each child. Results. Across all the problems, children performed well above chance (67.89%, chance= 50%, t(16)= 6.89, p <0.001), showing the characteristic ratio effect [F(1, 16)= 8.45, p <0.01, ANOVA], and without resort to non-arithmetic strategies. Conclusions. This study provides further evidence regarding the non-symbolic arithmetic skill present before formal education, and together with recent research, raises important contributions in education, trying to understand how children learn mathematics and to establish new methods of teaching.