This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in the third year of secondary education from a privately-owned but state-funded school in Madrid. Thirty-five students who have been taught traditionally formed the control group, and 43 formed the experimental group in which the methodology was implemented. To evaluate its goodness, we have used the Student’s t-test to assess the existence of significant differences between both groups. The results reported by the test show that there is a difference of 3.9 points between the scores of both groups which is significant at the level of 0.05. In addition, the user experience in the experimental group has also been evaluated to assess the students’ opinions of the hologram in the learning process. The overall results have assisted us in corroborating the efficacy of the hologram as a teaching medium.

The management of a car-rental service becomes more complex as long as one-way bookings between different depots are accepted. These bookings can increase the operational costs due to the necessity of moving vehicles from one depot to another by the company staff in order to attend previously accepted bookings. We present an iterative model based on flows on networks for the acceptance of bookings by a car-rental service that permits one-way reservations. Our model lets us also recover the movement of the fleet of vehicles between the depots over the time. In addition, it also permits including restrictions on the amount of cars managed at every single depot. These results can be of interest for an electric car-rental service that operates at different depots within a city or region.

The changes in our society in recent years and the consequent idiosyncrasy of young people demand new teaching methodologies. The methodology known as flip teaching, in which pupils study the subject before the class experience, using the material given by the teacher, makes it possible to turn the classroom into a place to solve different problems, to introduce new advanced concepts and to participate throughout collaborative learning in the classroom. Parallel to the social transformation, Information and Communication Technologies, also known as ICT, have undergone an important development accompanied by a clear reduction in costs and ease of use of different devices to create and edit quality videos, as well as the possibility of disseminating them on the network. In this way, the didactic material provided to the student can be in video format, which let us to be closer to students and also allow them to revise the class everywhere and all the times they need. In this work, we present and discuss the results of an experience carried out over several years with students of first and fourth grade of the subjects Discrete Mathematics and graphs, models and applications, respectively, at the Universitat Politècnica de València, in relation to the acceptance, advantages and drawbacks of flip teaching.