In the current times, the quality of education is significantly impacted by coexistence (Dobarro et al., 2013; Montero and Cervelló, 2019). Not in vain, in the well-known “Learning: the treasure within” report of the International Commission on Education for the 21st century to UNESCO (Delors, 1996), “Learning to live together or with others” is established as one of the four fundamental pillars of 21st century education. Similarly, Sustainable Development Goal 4 (Quality of Education) calls for a culture of peace and non-violence and for building and upgrading education facilities that provide safe, non-violent, inclusive, and effective learning environments for all by 2030 (United Nations, 2015).

If we pay attention to the literalness of SDG 4 established by the UN for sustainable development, the creation of safe, non-violent, and inclusive learning environments for all is marked as a priority for implementation in 21st-century schools. This reality, which should be guaranteed for all students in schools, is breached more often than desired. News and testimonies from students or alumni tell us about the bullying situations experienced at school. Bullying refers to a situation in which someone is exposed, repeatedly and over time, to negative actions on the part of one or more persons (Olweus, 2006), which instills in the victim what Seligman coined in the late 60s a feeling of “learned helplessness.” As defined by Olweus (2006), bullying has several characteristics. It is harassment with a clear intent to harm, hurt, or belittle by the victim (physically, morally, verbally, or psychologically); it must also be repeated harassment over time and not sporadic aggression; and finally, there must be an imbalance of real power or, at least, an imbalance felt by the victim.

This leads us to consider the best way to combat possible cases of bullying in schools. We understand that the most effective and appropriate way is to implement measures and actions within the teaching-learning process that can prevent bullying behaviors. Therefore, favoring measures and mechanisms for adequate coexistence in schools and classrooms can be a good solution.

One of the key measures within school coexistence that can contribute to preventing violence or bullying is the management of classroom climate, which can be defined as the social environment and emotional and physical aspects of the classroom (Sieberer-Nagler, 2016; Riekie et al., 2017; Aldridge et al., 2018; Montero and Cervelló, 2019). This is an important factor in learning development (Hattie, 2017). Hattie (2017) conducted a macro-study that collected over than 800 meta-analyses from 52,637 studies involving a sample of 240 million students. The present study aimed to determine the impact and effectiveness of various programs, educational policies, and teacher innovations designed to improve academic achievement. The study covered not only early childhood and primary education but also university education. Some of the factors related to classroom climate are among the 50 measures that, according to Hattie (2017), have the greatest influence on educational achievement. For example, teacher-student relationships (impact 0.72, position 12 of 150, high influence), classroom behavior (impact 0.68, position 16, high influence), and class management (impact 0.52, position 42, high influence) significantly affect learning. The quality of the interpersonal, social, and pedagogical relationships established in the classroom determines not only intellectual learning but also the emotional, moral, and social development of students (Dobarro et al., 2013; Codina, 2015).

Since positive classroom climate acts as a protective factor against problems related to school violence (Aldridge et al., 2016; Wang and Degol, 2016; Seray and Zúniga, 2021) and, conversely, poor classroom climate management acts as a risk factor, teachers need the pedagogical ability or technical resources (Remache-Bunci et al., 2022) to identify and act quickly in the face of potential problems [and] be aware of what is happening in the class (Hattie, 2017). Consequently, it would be possible to prevent and intervene in the problems of school violence that occur or can occur, analyze the possible responses and their effectiveness, and enhance the learning of all students. The results of the TALIS program in 2009, 2013 and 2018 Teaching and Learning International Surveys (OECD, 2010, 2013, 2019, respectively) clearly show that teachers' concern regarding things that can affect classroom climate is increasing (Table 1). When teachers were asked if the students' wellbeing was important for learning and personal, social, and moral development, the majority of surveyed teachers said yes. Similarly, the teachers affirmed that they were interested in what the students shared in this context. Specifically, Spanish teachers confirmed that they really helped their students when they needed something.

One of the first classroom climate questionnaires to analyze the classroom environment was developed by Walberg in 1966 (Anderson and Walberg, 1967). In 1973, Trickett and Moos (1973) developed a scale to measure classroom climate (CES Classroom Environment Scale). Since then, this scale, along with many different surveys and other methods of gathering information as direct observation, has been widely used. Many previous studies have focused on issues related to school life (Cava and Musitu, 2009; Peiró, 2012; Luengo, 2018) and classroom climate (Cohen, 2013; Murillo, 2015) or analyzed the problems arising from inadequate management of coexistence or classroom climate, such as school violence (Fernández, 2001; Ortega, 2015; Luengo, 2017), bullying (Bisquerra, 2014; Hinduja and Patchin, 2017; Navarro et al., 2018), or, more recently, cyberbullying (Ortega et al., 2016; Machimbarrena and Garaigordobil, 2018; Rey et al., 2018).

The theoretical model developed in this study allows for the simulation of the classroom climate throughout an academic year. It consists of state variables that indicate the stage of the system at all times and are represented graphically by rectangles. These variables typically represent the accumulation or reserves of physical elements or emotional states.

The situation in which the state variables are found may change over time. This change is represented graphically by arrows and the so-called information flows that represent activities or actions, physical or emotional, and whose speed can be modified by convertors, which are represented graphically by circles. A graphical representation of the model is shown in Figure 3.

Accordingly, the developed model has a psychological and a physical part. In total, it consists of four state variables or accumulators of material, individuals, or emotions. Two of them would be in the psychological module and two in the physical. The present study aimed to present a different study tool that would allow the optimization of the factors that influence classroom climate, establish mechanisms to detect and predict how the modification of these factors can positively or negatively affect it, and determine the most appropriate way to intervene before it occurs.

Table 2 presents the results where a classroom of 100 students was simulated for 40 weeks. The scenarios ranged from one to three humiliation activities each week. How emotional and physical situations evolved at 20 and 40 weeks of class were evaluated.

For example, when there was one act of humiliation per week, the percentage of isolation at the end of the course was ~21%, and the level of rage was 3%. In this situation, one aggressive student can assault two classmates. This situation is controllable, although the model does not include correction measures. However, if nothing is done, humiliation activities per week increase. In the case of three humiliation activities per week, at the end of the course, the percentage of estimated isolation was more than double that in the first case (70%), and the Rabies Level also increased exponentially from 3 to 28%. Consequently, if there was one aggressive student, there would have been 10 students in the classroom who may have attacked 31 classmates by the end of the course (see Table 2).

Dynamic mathematical models can be very useful when working on the problem of school violence, although they have possible limitations. Predicting the future behavior of humans remains a highly complex mission. However, despite this, these predictions can help guide future actions with a degree of certainty regarding expected outcomes. As Ruiz Coronel and Padilla (2012, p. 122) state, the mathematical model “does not ensure the prophetic forecast of events, but it certainly allows for a better-informed decision making and the contemplation of at least a good number of affected variables.”

Regarding the most significant benefits that this tool can bring us, some stand out. On the one hand, we can adapt the instrument to the specific characteristics of the class group by introducing or eliminating variables depending on their relevance to the problem at hand. In this way, it is a customizable tool that responds to our reality such that the results and intervention proposals derived from it will respond to our real problem. On the other hand, this versatile tool not only adapts to the reality of the classroom but also to the specific moment in which the students are. One of the advantages of the dynamic system is that it is open, and all the information we consider relevant can be incorporated at any time and the more information we have, the more customized the model can be. However, gathering the type of information needed to develop the model is complicated.

Although a theoretical model based on classroom experience has been constructed, its evaluation using real data is yet to be conducted. However, it has been observed that, in the absence of measures to control harassment, aggression increases exponentially (see Figure 4) due to the feedback nature of the situation.

Moreover, the model allows the incorporation of new factors related to violence in classrooms as well as measures and activities to reduce aggressiveness and abuse. This tool could be efficient not only for detecting classroom climate but also for the prediction and prevention of school violence.

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

IH: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Supervision, Writing—original draft, Writing—review and editing. RS: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Supervision, Writing—original draft, Writing—review and editing. EM-L: Conceptualization, Data curation, Methodology, Writing—original draft. All authors contributed to the article and approved the submitted version.