The Modification of Attributes, Affordances, Abilities, and Distance for Learning Framework and Its Applications to Interactions with Mathematics Virtual Manipulatives

Abstract

While extensive research has examined the outcomes of interacting with virtual manipulatives, less research has focused on constructs and relationships among constructs involved in user-tool interactions. This chapter presents the Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning framework, which conceptualizes the relationships among these con- structs to describe user-tool interactions, including those involving virtual manip- ulatives. The framework is primarily grounded in theories of representation and embodied cognition, as user-tool interactions in mathematics involve internalizing and externalizing representations through physically embodied mathematical practices. In the framework, attributes, affordance-ability relationships, and distance are interrelated, and modification of one construct contributes to modification of the other constructs. Each attribute can contribute to many affordance-ability rela- tionships and to distance. Attribute modification can change the approach or degree of affordance access and alter the degree of distance present, which can, in turn, lead to attribute modification. This chapter illustrates the constructs and relation- ships among constructs that form the framework in the context of user-tool inter- actions in mathematics. The chapter then applies the framework to examples of children’s interactions with mathematics virtual manipulative touchscreen tablet apps. The MAAAD for Learning framework has implications and applications relevant to theory, development, implementation, and research concerning tech- nology tools, including virtual manipulatives. Keywords