Kolmogorov complexity predicts the relative difficulty of abducing such programs – for easy rearrangements, such as reversing the order of the cars, to difficult ones, such as splitting a train in two and interleaving the two resulting halves (equivalent to a faro shuffle). They rely on such loops to compute recursive functions for rearranging the order of cars in trains on a track with a siding. Participants in our experiments spontaneously simulate loops of instructions in kinematic mental models. Our theory aims to explain how naive individuals devise informal programs in natural language, and is itself implemented in a computer program that creates programs. Some of these programs are semi-circular too, but they needn’t be, because repeated loops of instructions can compute any recursive function. Any function that is computable – and many are not – can be computed in an infinite number of distinct programs. In the logic of computability, a function maps one or more sets to another, and it can have a recursive definition that is semi-circular, i.e., referring in part to the function itself. This article presents a theory of recursion in thinking and language. Findings indicate that the Toolkit was considered an engaging approach to game creation, making it a valuable resource to support educators in game design activities. The toolkit was used by 53 upper-secondary and 114 undergraduate students along several game creation sessions, leading to the development of 66 digital games. When research also mentions obstacles in involving students to explore educational contents through game design, this paper presents the Gamers4Nature Toolkit, an artifact developed to support the creation of digital environmental-related games by younger students with no experience in game design. As regard to games, and in the field of environmental education, they emerge as an innovative approach to raise environmental awareness among youths, namely by challenging students to develop their own games for learning. In recent years, serious games and gamification strategies have been used in the education field and seen as highly motivating for educating and motivating younger people.
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