title: Cognitive Analysis of Educational Games: The Number Game.
abstract: 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 (for instance, 2, 5, 9) have to be used precisely once to create a target number (for instance, 27) with basic arithmetic operations (solution: [5-2] × 9). 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.
authors.affiliation: Department of Psychology, University of Amsterdam.
authors.forename: Han L J
authors.initials: HLJ
authors.lastname: van der Maas
authors.affiliation: Welten Institute, Open University.
authors.forename: Enkhbold
authors.initials: E
authors.lastname: Nyamsuren
mesh_terms: D003071:Cognition; D003405:Creativity; D006801:Humans; D007858:Learning; D008433:Mathematics
keywords: Arithmetic; Education; Games; NP Complete; Number game; Reasoning