Modelling Learning to Count in Humanoid Robots
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This thesis concerns the formulation of novel developmental robotics models of embodied phenomena in number learning. Learning to count is believed to be of paramount importance for the acquisition of the remarkable fluency with which humans are able to manipulate numbers and other abstract concepts derived from them later in life. The ever-increasing amount of evidence for the embodied nature of human mathematical thinking suggests that the investigation of numerical cognition with the use of robotic cognitive models has a high potential of contributing toward the better understanding of the involved mechanisms. This thesis focuses on two particular groups of embodied effects tightly linked with learning to count. The first considered phenomenon is the contribution of the counting gestures to the counting accuracy of young children during the period of their acquisition of the skill. The second phenomenon, which arises over a longer time scale, is the human tendency to internally associate numbers with space that results, among others, in the widely-studied SNARC effect. The PhD research contributes to the knowledge in the subject by formulating novel neuro-robotic cognitive models of these phenomena, and by employing these in two series of simulation experiments. In the context of the counting gestures the simulations provide evidence for the importance of learning the number words prior to learning to count, for the usefulness of the proprioceptive information connected with gestures to improving counting accuracy, and for the significance of the spatial correspondence between the indicative acts and the objects being enumerated. In the context of the model of spatial-numerical associations the simulations demonstrate for the first time that these may arise as a consequence of the consistent spatial biases present when children are learning to count. Finally, based on the experience gathered throughout both modelling experiments, specific guidelines concerning future efforts in the application of robotic modelling in mathematical cognition are formulated.
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