Cognitive Analysis of Educational Games: The Number Game. (20th November 2016)

• Record Type: Journal Article
• Authors: van der Maas, Han L. J.; Nyamsuren, Enkhbold
• Is Part Of: Topics in cognitive science. Volume 9:Number 2(2017:Apr.)
• Page Start: 395
• Page End: 412
• Publication Date: 2016-11-20
• Subjects: Education -- Games -- Arithmetic -- Reasoning -- NP Complete -- Number game; Cognitive science -- Periodicals; Cognitive Science -- Periodicals; 153.05
• DOI: 10.1111/tops.12231
• Languages: English
• ISSNs: 1756-8757

Abstract

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. Abstract : The subtitle of this paper could have been, "Big Data meets Education to advance Cognitive Science." In it, the authors analyze 20 million answers to 1700 simple arithmetic problems in an educational number game to determine "what makes some problems harder than others." The results contribute to the cognitive science of arithmetic skill acquisition and have the potential to change how math is taught.