Grounding fingers, words and numbers in a cognitive developmental robot

Abstract

The young math learner must make the transition from a concrete number situation, such as that of counting objects (fingers often being the most readily available), to that of using a written symbolic form that stands for the quantities the sets of objects come to represent. This challenging process is often coupled to that of learning a verbal number system that is not always transparent to children. A number of theoretical approaches have been advanced to explain aspects of how this transition takes place in cognitive development. The results obtained with the model presented here, show that a symbol grounding approach can be used to implement aspects of this transition in a cognitive robot. In the current extended version, the model develops finger and word representations, through the use of finger counting and verbal counting strategies, together with the visual representations of learned number symbols, which it uses to perform basic arithmetic operations. In the final training phases, the model is able to do this using only the number symbols as addends. We consider this an example of symbolic grounding, in that through the direct sensory experience with the body (finger counting), a category of linguistic symbol is learned (number words), and both types of representations subsequently serve to ground higher level (numerical) symbols, which are later used exclusively to perform the arithmetic operations.