Dual Representation and the Linking of Concrete and Symbolic Representations

As the articles in this special issue suggest, link- ing concrete and abstract representations remains a fun- damentally important challenge of cognition development and education research. This issue is considered from the perspective of the dual-representation hypothesis—all symbols are simultaneously objects in their own right and representations of something else—which can shed light on the challenges of linking concrete and symbolic repre- sentations. Manipulations that lead children to focus on the object properties may actually make it harder for them to focus on what the symbols represent. Conversely, decreasing children's attention to the object's properties can make it easier for them to establish a link between concrete and symbolic. The educational implications of the dual-representation hypothesis are considered. KEYWORDS—symbols; transfer; mathematics; representa- tion; manipulatives

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