**2. Learning by playing**

One of the lacking aspects in most school curricula, at any level, is the development of problem-solving skills, whether in mathematics or arising from other contexts. Generally, schools instruct students on how to apply so-called "rules", whether mathematical or grammatical or how to solve exercises by applying formulas or predefined schemes. In this way, students have difficulty framing problems, extracting relevant information, developing critical thinking, and proposing solutions [13]. It is well known [14, 15] that this mode of learning has the effect of killing students' creativity and interest, and in most cases induces them to resort to learning by heart instead of reasoning.

The techniques that we adopted to awake the reasoning skills and the creativity of the students are mainly puzzle-based learning and creative writing. Both techniques are very playful and engaging since the beginning.

#### **2.1 Puzzle-based learning**

Puzzle-based learning [16] is a learning approach that is intended to develop reasoning skills, perseverance, and motivation in dealing with problems. That is, it intends to build the fundamental foundations of what problem-solving is. This is done not from real problems, but rather by taking cues from games that do not require any special contextual knowledge and that have the sole intent of being engaging and challenging [17].

In this context, the curricular teacher and the external expert become guides and facilitators of knowledge within a community of learners [18] which is the classroom. Each student becomes the main player of a learning process where she is an active builder of her own knowledge, acting in cooperation with peers, according to the theories of collaborative learning and guided discovery of Vygotskij [19, 20].

In practice, the role of the teacher is not to "teach" how to solve problems, but rather to propose stimulating games for all students, to follow their reasoning, to arrive together with them at the solution [21]. The teacher must be ready to accept methods of solving problems other than the one she has thought of, or tried to solve together with the student's problems posed by them. In short, the fundamental purpose is not the solution of problems, but the effort that is made to achieve it. The teacher must therefore be ready to get involved and not be uncomfortable in the face of possible setbacks. Adopting a sporting similarity, the teacher takes on, during puzzle-based learning, the role of the coach, whose motivational skills must be preponderant over the merely technical ones.

The assessment phase is also strikingly different from the usual context. After the first few games, the enthusiasm shown by the students in arriving at a solution on their own goes far beyond a good grade. Therefore, more than rewarding the result achieved, the effort to reach it is to be encouraged even if it was not successful [22].

#### **2.2 Creative writing**

Creative writing is a way to approach the world of literature and to acquire greater critical awareness. It is closely linked to the idea of "invention", so it does not have universally valid rules, but rather has "techniques". The invention is a very important moment that must be guided and trained. The literature on creative writing is particularly rich [23]. However, we took advantage of the presence of the local writer Luigi dal Cin, who has also a long record of collaborations with schools at all levels. According to Luigi dal Cin [24], many writers agree that invention springs from five mental attitudes:

*Inspiration*: the first mental attitude is the most important and is developed mainly through the "fantastic pair" (the juxtaposition of two concepts, characters, situations, very different from each other).

*Proliferation*: linking different situations and characters, even contradictory ones, to the first idea.

*Selection*: select characters and situations.

*Preservation*: do not forget anything that was initially discarded.

*Re-crossing*: resume the plot of the story and try to develop it even with what was initially discarded.

It is curious to note that, although with different terminology and in a context very distant from the creation of a story, we find similar techniques in the design of heuristic algorithms for solving mathematical problems: Genetic algorithms, Simulated Annealing, Neural Networks, Tabu Search, Evolutionary algorithms, etc. [25].

Creative writing techniques also go beyond those mentioned above, however, given the purpose of the experience, it was deemed appropriate to focus on some of the simplest and of immediate impact on the students.
