Abstract:

The Laboratory activities described in this paper have been developed in the activities of the “Mathematical High School” Research Project of the University of Salerno (Italy) and aimed to provide an overview of the use of classroom experiments as an empirical method for testing hypotheses and theses of Mathematical models applied to Economics and the Social Sciences. The focus is methodological and it is illustrated by examples and applications from the literature. Laboratory experiments had strong influence on the development of Game Theory. It is well known that Reinhard Selten and John Nash used laboratory experiments at the beginning of their work.

In the literature of the teaching of Decision Theory, there is an increasing use of classroom laboratories that put students directly into the economic environments being to be analyzed. Students participate directly in market negotiations as buyers and sellers; in the choice of an option, a strategy; in the possibility of making binding agreements with other students, etc.

Students then test the results obtained with those expected from Economic theory, based on the Axiom of Rationality.

Very often students are surprised when standard theories fail, or when the result seems counterintuitive.

Students are introduced to the structural parameters of standard theories determined by individual incentives and specific rules, so the theoretical predictions can be calculated and used as a reference point for comparison.

In designing the class workshops, we used the methodology of Experimental economics.

We used small incentives for reducing noise in decision-making.
Classroom experiments are conducted in a lab-based format using technological artifacts that enable control of information flows and rapid communication.
Classroom experiments are less effective in large classes because it is well known that personal involvement stimulates students' interest. For this reason, in the laboratory, which due to the COVID-19 emergency took place at a distance using a platform, the classes were divided into smaller virtual classes (Breakout rooms) to improve student participation. The activities were developed with a constructivist approach and the students built their knowledge in the interaction and sharing between peers and with teachers. In the discussion of the results, we thought of follow-up questions, thus we took the wrong answers seriously and let the students criticize and question them in order to bring out the expected theoretical result in the mathematical models.

With the use of technology, when sometimes the result of the experiment does not perfectly match the prediction of the standard theory, students were able to immediately compare the results obtained. This provided an interesting way of exploration and analysis. In the discussions conducted at the end of the experiment, the aim was to provide students with a way to think more deeply about economic theory. Students often found it difficult to think critically about whether theories were correct or not. With the use of the technological artifacts, we provided students with a framework to help them see that one of the model's assumptions is not quite correct and to think about whether it is possible to create a better model.

At the end of the experiments in the classroom, students show a better attitude to the critical analysis of the economic phenomena and a widespread interest in issues they had never encountered.

Keywords:

Transdisciplinarity, Laboratory experiments, Decision Theory, Mathematics.