This paper takes an embodied and extended cognition perspective to ER integration – a cognitive process through which a learner integrates external representations in a domain, with her internal model, as she interacts with, uses, understands and transforms between those ERs. In the paper, I argue for a theoretical as well as empirical shift in future investigations of ER integration, by proposing a model of cognitive mechanisms underlying the process, based on recent advances in extended and embodied cognition. I present (...) this new model in contrast to the still dominant classical cognitivist approaches to ER integration, and the educational technology intervention designs such approaches inspire. I then exemplify this distinction between the information processing model and the new model through a case of arithmetic problem solving. Corroborative neuroscience evidence presented in relation to this case provides empirical support for the new model by showing how bodily actions are critical to ER integration and learning. Finally, as educational implications of the new model, I demonstrate the need for: re-viewing the development of ER integration and expertise as fine-tuning of the learner's action or sensorimotor system, and a shift of focus in new-media intervention design principles based on this newer understanding of ER integration in science, technology, engineering and mathematics. (shrink)

We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers have to be used precisely once to create a target number with basic arithmetic operations. We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number (...) Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. (shrink)

The very expertise with which psychologists wield their tools for achieving laboratory control may have had the unwelcome effect of blinding psychologists to the possibilities of discovering principles of behavior without conducting experiments. When creatively interrogated, a diverse range of large, real-world data sets provides powerful diagnostic tools for revealing principles of human judgment, perception, categorization, decision-making, language use, inference, problem solving, and representation. Examples of these data sets include patterns of website links, dictionaries, logs of group interactions, collections of (...) images and image tags, text corpora, history of financial transactions, trends in twitter tag usage and propagation, patents, consumer product sales, performance in high-stakes sporting events, dialect maps, and scientific citations. The goal of this issue is to present some exemplary case studies of mining naturally existing data sets to reveal important principles and phenomena in cognitive science, and to discuss some of the underlying issues involved with conducting traditional experiments, analyses of naturally occurring data, computational modeling, and the synthesis of all three methods. (shrink)