Beyond the Early Adopters: Escape Rooms in Science Education

Case studies report enthusiastically on the implementation of escape rooms in science education. This mixed-method study explores beyond the early adopting teacher, as the perceptions of 50 teachers and 270 students were investigated. Escape rooms are time restricted games where participants work together and accomplish a specific goal. The escape rooms’ usability for education in terms of goals, experiences during gameplay, outcomes, and boundary conditions are studied, using multiple data sources: online questionnaires, interviews, classroom observations and movie clips made by students about their experiences. The use of mixed methods and large samples on this topic is a novelty. Results show that teachers of different ages, gender and teaching experience were appealed in particular to the diversity of activities offered that call for multiple skills and teamwork. Students experienced the need to think hard using multiple thinking skills and enjoyed the feeling of autonomy and mastery during gameplay. This is interesting, as an escape room setup is very strict, with few degrees of freedom. According to teachers and students, escape rooms are suitable for processing, rehearsing and formative assessment of science knowledge and skills. However, the time restriction during gameplay appears to be an ambiguous factor in student learning.

Complexity of inheritance of ℱ-convexity for restricted games induced by minimum partitions

Let G = (N, E, w) be a weighted communication graph. For any subset A ⊆ N, we delete all minimum-weight edges in the subgraph induced by A. The connected components of the resultant subgraph constitute the partition 𝒫min(A) of A. Then, for every cooperative game (N, v), the 𝒫min-restricted game (N, v̅) is defined by v̅(A)=∑F∈𝒫min(A)v(F) for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of ℱ-convexity, i.e., if for every ℱ-convex game the 𝒫min-restricted game is ℱ-convex, where ℱ-convexity is obtained by restricting convexity to connected subsets. This implies that we can also decide in polynomial time for any unweighted graph if there is inheritance of convexity for Myerson’s graph-restricted game.

Convexity of graph-restricted games induced by minimum partitions

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition 𝒫min is i nduced by the deletion of the minimum weight edges. We provide five necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with 𝒫min. Then, we establish that these conditions are also sufficient for a weaker condition, called ℱ-convexity, obtained by restriction of convexity to connected subsets. Moreover, we prove that inheritance of convexity for Myerson restricted game associated with a given graph G is equivalent to inheritance of ℱ-convexity for the 𝒫min-restricted game associated with a particular weighted graph G′ built from G by adding a dominating vertex, and with only two different edge-weights. Then, we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G′.

ON THE COMPLEXITY OF COMPUTING VALUES OF RESTRICTED GAMES

The aim of this paper is to compute Shapley's and Banzhaf's values of cooperative games restricted by a combinatorial structure. There have been previous models developed to study the problem of games with partial cooperation. Games restricted by a communication graph were introduced by Myerson and Owen. Another type of combinatorial structure introduced by Gilles, Owen and van den Brink is equivalent to a subclass of antimatroids. Cooperative games in which the set of players is a partially ordered set, that is, games on distributive lattices was investigated by Faigle and Kern. We introduce a new combinatorial structure called augmenting system which is a generaligation of the antimatroid structure and the system of connected subgraphs of graph. We present new algorithmic procedures for computing values of games under augmenting systems restrictions and we show that there exist problems with polynomial algorithm complexity.