Connecting Classrooms with Online Interclass Tournaments: A Strategy to Imitate, Recombine and Innovate Teaching Practices

Abstract

UNESCO’s Sustainable Development Goal 4 and new curricula around the world call for a better quality of education. Among the main challenges of improving quality is increasing the integration between disciplines and improving the preparation of students for the personal and work requirements of a smarter and rapidly changing society. For that purpose, we need to design new and effective didactic strategies. However, current classrooms are isolated. They practically never connect. This hinders the exchange of ideas. It inhibits imitation and recombination, the basic blocks of cultural evolution and innovation. In this paper, we analyze four online interclass tournaments that we have implemented in the last decade. This long-term view is crucial for estimating the sustainability of new teaching strategies. These tournaments are very uncommon lessons, where entire elementary or middle school classes interconnect synchronously and play an educational game. This increased interconnectedness is only possible thanks to digital communication technology. We found that these interclass tournaments are feasible to implement in schools; that they are a promising mechanism for teaching with an increased integration of disciplines; and that they facilitate imitation, recombination, and innovation of teaching strategies. Thus, interclass tournaments could be a feasible strategy to help innovate and improve the quality of education.

1. Introduction

Quality education is one pillar of the United Nations 2030 Agenda for Sustainable Development. To improve quality, there are several challenges. One challenges is greater integration across disciplines in K12 [1]. Another challenge is better preparation of students for global citizenship. We have to prepare them for the personal and job challenges of a fast-changing and smarter society [2,3]. This is because, on the one hand, teaching in a more connected way, and more related to real-life problems, can make education more relevant, more meaningful, increase motivation to learn, and improve student achievement [4,5]. On the other hand, students need a deeper understanding of the core ideas of each discipline. Integration across disciplines helps to achieve a profound understanding of each discipline. Thus, the call is to link concepts and skills learned from two or more disciplines, in order to gain more far-reaching knowledge and understanding. This, in turn, prepares students for a world of constant and enormously disruptive changes. In that world, a deeper understanding of the central ideas is critical.

Therefore, for a quality education, teachers need to learn to teach connected disciplines. They should help students learn core STEM concepts and develop STEM skills that promote connections, such as rigorous argumentation, problem solving, and modeling abilities [6]. They should help students understand core science concepts [7], such as patterns, information, conservation laws, data and modeling, the particulate nature of nature, energy and metabolism, and natural and sexual selection. Moreover, integration also means that STEM teachers should help students deal with key current national and global challenges, such as climate change, social inequalities, emotion and cognition, pandemics, and impersonal trust [3,5]. They should also help students develop oral and written communication and argumentation skills. Teachers should also help to develop and cultivate students’ values, beliefs, attitudes, responsible citizenship, cooperation, and teamwork. In addition, teachers should make students’ learning more meaningful and improve their preparation for the personal and job challenges of a fast changing and smarter society. They should do all this without hindering their teaching of each discipline.

One key integration strategy is teaching real world applications. According to [8] (p. 146), “Interdisciplinarity has gained the most ground in applied fields, where the assumptions and common methods of different fields can be brought to bear on the same substantive questions and outcomes”. In the case of mathematics, an example is statistics. All disciplines are generating more and more data and at an increasing speed. This translates into an increased use of statistics in a growing number of disciplines [9]. Other examples are mathematical modeling [4,10,11] and computational modeling [12,13,14,15]. There are also contents and practices in computational thinking that are gaining increasing importance in industrial and consumer-oriented applications. Nevertheless, they do not yet have a place in the K12 curriculum. For example, agent-based modeling [13], machine learning [5], or natural language and image processing do not yet appear in the national curricula. These recent computational developments directly connect mathematics and computation with the social sciences, psychology, biology, and language. Here, there is huge potential for across discipline integration.

However, integration has several barriers. First, a significant proportion of students have poor understanding of the core ideas in the individual disciplines. Thus, for them, connecting ideas across disciplines is not straightforward at all [1,16]. This means that teachers are primarily concerned with teaching the core concepts of their discipline, and do not have time to spend exploring ways to integrate with other disciplines.

Second, the amount of knowledge in each discipline is increasing rapidly. There is a true explosion of ideas, methods, and results. Thus, there are strong pressures on the curriculum, to introduce new content in each discipline. This content is also new for teachers. For example, we now have proposals of new curricula with concepts of computational thinking and the introduction of machine learning concepts to statistics [2,17].

Third, the new concepts of each discipline are not always intuitive. Sometimes they seem to contradict our intuition or our previous knowledge. Teachers then have to invest time planning how to teach these new ideas. For example, in Bayesian reasoning, use of adequate representations is critical for true understanding [18,19].

Fourth, there is a clear division of labor at schools. This is the norm in the elementary schools in some OECD countries and is an increasing trend in the United States [20]. Teachers teach the discipline in which they have been educated. Even in traditionally closely related disciplines, such as mathematics and physics, teachers teach only one discipline. The only exception is in the first levels of elementary education. However, even there, the teacher does not make an integration across disciplines. Teachers teach each discipline as a world apart from the others. Teachers teach the two critical disciplines, language and mathematics, as if they had nothing in common. Today, with the development of computer science in the area of natural language processing, both disciplines are increasingly close; for example, in large language models (LLM) such as ChatGPT [21], which is having a great impact on society, and in particular on research and education. However, mathematics and language remain completely separate in the curricula and at schools.

Fifth, teachers need to learn how to teach disciplines with a much deeper integration between them. This is something new for most teachers. They were not educated in the teaching of several different disciplines, let alone how to integrate them. There are still very few instances of teacher education in integrating disciplines [22]. According to the National Survey of Science and Mathematics Education [23], only 26% of schools offered courses for teachers on how to integrate science, engineering, mathematics, and/or computer science. In a list of 16 types of course, integration courses were one of the least common.

Sixth, teaching is a very conservative profession; “pedagogical change offers the teacher little apparent benefit and a great apparent risk” [24] (p. 55). In addition, integration poses a high risk. Activities that integrate disciplines could be very motivational, but can hinder high-quality instruction that helps understand the practices and principles of each discipline [25].

Seventh, there is a lack of textbooks and materials with integrated disciplines [26]. For example, there are no math–biology or math–social sciences school textbooks. Moreover, in each discipline, the textbooks do not have much integration with other disciplines. Therefore, this lack of materials requires teachers to invest a great deal of time and energy in studying other disciplines, meeting and exchanging ideas with other teachers, and beginning to try out new classroom alternatives [26].

Eight, it is still not completely clear how mathematics taught according to the curriculum helps to gain a better understanding of other disciplines, nor do we understand how other disciplines help students in learning math [16].

Ninth, there is a “structural isolation” in the teaching profession. Teachers teach behind closed doors [27] (pp. 51–52). This structural isolation between teachers and the impenetrable walls between classrooms makes it very difficult to compare, imitate, and exchange educational strategies.

Finally, teachers do not receive feedback about cross-discipline integration from monitoring or evaluation systems. Typical teacher class observation protocols and teacher evaluation reports do not include information about integration. For example, IMPACT, one of the most used teacher assessments system in the U.S., is 50% based on the student score and 35% on classroom observations by the principal and subject-based expert teachers [28]. Additionally, each national or state test measures students’ learning in just one discipline. They do not include knowledge that measures integration across disciplines.

Thus, discipline integration has several formidable barriers to overcome. It is a completely new challenge. In addition, we need to learn to implement it at large scale. This is a huge professional development challenge for teaching.

2. Literature Review

2.1. Cultural Evolution: Imitation, Recombination, and Innovation

A review of classroom practices shows that almost no change has taken place over the last century [28,29]. Teachers mainly teach teacher-centered strategies. Some teachers are very effective when using such strategies. For example, in the Programme for International Student Assessment (PISA), the top-performing Organization for Economic Co-operation and Development (OECD) countries use more teacher-centered teaching practices in mathematics than other countries [30].

To improve teaching that integrates disciplines, we need to research and understand how to design and manage communities of teachers that work together. These communities should focus on devising innovative classroom practices that promote interdisciplinary learning. This type of research is new to the field of education. The results of this research will be crucial to the success of classroom practices that promote integration across disciplines and strategies that integrate educational research with classroom practice [31].

To do this, one of the main difficulties is that current classrooms are isolated. Reference [24] compares a school to a nuclear power station. Since each component of a nuclear facility is causally interrelated with the others, it is much easier to trace the chain of events and thus pinpoint the source of any deficiency and correct it. Schools, on the other hand, have completely independent units (classrooms). What happens in one unit does not affect the others. They practically never connect or exchange information. There are very few opportunities for interaction with other classrooms. This situation hinders sharing ideas and strategies, as well as copying and recombining them.

One tends to think that the problem is how to implement strategies carefully designed by authorities and experts. However, cultural evolution processes need the active participation of a large community. Moreover, innovation and change emerge from thousands of people coming up with and interchanging ideas [32]. No one is really in charge. For example, in the history of the critical cultural evolutions of humankind, such as the jump from tribal to larger societies, they did it without anyone having a global understanding of how it all fit together [33] (p. 102). It is an incremental, bottom-up, and rather random process. It occurs as a direct result of exchange, imitation, and recombination, and not as an orderly top-down process developed according to a plan.

Additionally, the collective brain perspective suggests an optimal amount of interconnectivity. Too much interconnectivity is not always better. The diffusion of complex behavior requires a mechanism that goes beyond simple interconnection. Complex behaviors follow a different adoption mechanism than that required for simple ones. Two key components are reiteration and homophily. Reiteration means a high frequency of interactions between teachers and between classrooms. Homophily means that the interactions should be with similar teachers and similar classrooms. Thus, teachers should interact frequently, and those interactions should be between similar types of teacher [34,35].

In summary, to achieve high-quality education under Sustainable Development Goal 4 of United Nations Educational, Scientific and Cultural Organization (UNESCO), we need to facilitate and speed up mechanisms for developing new teaching practices that include cross-discipline integration. This is a deep cultural evolution process. It requires devising powerful mechanisms of intergroup connection, with the appropriate diffusion mechanisms. These should foster innovation and the dissemination of new strategies. We have to devise appropriate network topologies, closer to a fishing net than a fireworks display [36], which connects teachers and their classroom with other similar teachers and their classrooms. We need to design collective learning strategies that promote social comparisons, such as intergroup competition and intragroup collaboration [37].

We have to understand the mechanics of knowledge creation and mobilization. We should design ways to accelerate how teachers and schools identify problems and develop interventions and strategies [31,38]. Finally, we depend on the fact that we are smart because we have culture, not the other way around [39]. In this paper, we use the framework of processes of cultural evolution to study the creation of innovations and their diffusion through tournaments.

2.2. Lesson Study and Open Lessons

Teachers need well-tested strategies. This means, teaching strategies developed in the classroom, and tested with students with similar grade levels, demographics, and socioeconomic profiles. This is not a top-down process. Bottom-up processes may be very effective, more sustainable, and scale better.

A popular bottom-up practice is lesson study. It is a teacher professional development strategy created in Japan in 1880. It is increasingly widespread in Asia and the rest of the world [40]. It is a collaborative teaching improvement process. Its goal is to build strong and productive communities of teachers, who share and learn from each other. According to [28] (p. 181), when teachers work together, they create pedagogical capital. This is a scarce resource, because isolation is endemic in schools. On the contrary, lesson study involves teamwork. Several teachers work together designing, testing, and improving a lesson. This process accelerates the production of effective lessons and lessons that aim to develop higher-order thinking skills [41]. It is a collective intelligence strategy to develop better lessons. It also helps innovation, in order to introduce new lessons adapted for new challenges. For example, lessons with integration across disciplines and that are also cross-border, integrating classes from different countries in a lesson [42,43,44].

After the team of teachers develop and test their lesson, a teacher delivers it in public. In a school theater or gym, tens or hundreds of teachers actively observe this open or public class. Then, in the same place, the teachers analyze it. It is a large community of teachers observing and analyzing together a class on a key topic they have to teach and with students similar to theirs. It is a true collective brain in action.

Lesson study and open lessons are powerful strategies that promote collaborative work among teachers, who imitate and then improve these strategies. However, they have some constraints [45]. They require a lot of time from teachers. They have to coordinate, find a common time to meet and observe a classroom, visit other schools and review recorded lessons together. Another constraint is the lack of a constant comparison between classes, since there is no competition between classes. Intergroup competition is a core mechanism of cultural evolution [33]. It constantly forces teams to compare each other, and search for what works best; “It pushes against the within-group forces of cultural evolution, which often favor self-interest, zero-sum thinking, collusion, and nepotism” [33] (p. 360).

Contrary to other human endeavors, the lack of interclass competition in education is due, in part, to a noncompetitive culture. This is very curious, because there is competition in some popular school events. For example, in athletic and team sport olympiads, musical contests, and math and science olympiads. These are very popular in schools [46]. Moreover, intergroup competition increases intragroup cooperation [47]. Nevertheless, in schools there are practically no competitions or tournaments between entire classes for academic subjects. On the contrary, in all schools, there is a much stronger competition but of different nature. It is competition between students in the same class. It is the competition generated by the usual student assessments, grade point averages (GPAs), and intraclass rankings. This intraclass competition inhibits collaboration.

3. Materials and Methods

There are two great challenges for the dissemination of educational practices generated by activities such as interclass tournaments. On the one hand, the creation, dissemination, and sustainable adoption of educational practices is a slow process that takes several years. Therefore, this requires detailed observation of the evolution of the tournaments and their effects for at least a couple of years. On the other hand, interclass tournaments are not a common activity in schools. It is a very innovative type of event. Moreover, they are not simple to implement. Each one requires the synchronous participation of several schools. This is a major logistic problem. It requires the coordination of tens of schools. For this reason, we take advantage of the implementation of several of interclass tournaments, and the observations and studies that have already been carried out on some of them. This long-term view is crucial for estimating the sustainability of new teaching strategies.

Thus, the methodology consists of the reviewing of four different interclass tournaments that we have implemented over several years in the last decade. They are four independent tournaments, implemented in different schools and districts in Chile. In addition, they are tournaments with very different contents. One tournament is on machine learning and statistical modeling, another is on physics, the third is on word problems in mathematics, and the fourth is on natural selection in biology. These are interclass tournaments carried out in several grade levels of elementary and middle school. They share one key feature: they are online interclass tournaments. In all of them, different schools participated. In each one, we studied the emergence of the diffusion of interclass and cross-schools learning and teaching strategies and practices.

First, we describe the conceptual framework of intergroup play as an educational tool. Then, we will define the research questions, the methodological approach, and the materials.

3.1. Intergroup Play

Play is a natural educational strategy. Mammals and even birds play to learn [48]. For this reason, playing to learn has great potential for teaching and learning [49,50]. This explains the interest in educational games [51]. Play is the natural pedagogy. Thus, the proposed theoretical framework in this paper is play. However, a uniquely human type of play is competitive play between groups. This is coalitional play fighting between two or more groups. Intergroup play is very popular and is the basis of team sports. Ethnographic evidence from hunter-gatherers suggests that intergroup games are universal and have been a basic learning strategy in the evolution of human culture. Dyadic play fighting occurs in many species, but only humans engage in coalitional play fighting [52].

Additionally, the scale and popularity of some team sports, and the size of the entertainment industry based on team sports, indicate that we have psychological components that make them attractive and engaging to us. “Participation in team sports such as ice hockey and soccer provides many children and adolescents with their first experience of intergroup competition, which may have lasting psychological effects” [33] (p. 350). Moreover, “This shared experience seemed to create a collective sense of meaning and greater solidarity among the student body” [33] (p. 351). According to [33], team sports and sports leagues “placed nonviolent intergroup competition at the center of people’s leisure time, where it often became part of their personal identity. Participation in team sports became central to raising children (well, at least boys)” [33] (p. 360).

There is a long history of using team-game tournaments (TGT) in classrooms for academic subjects [53,54]. For example, [55] proposed a TGT, in which each week students from one class compete against members of other teams from the same class. In one of the earliest TGT in mathematics, [54] measured the effect of a noncomputer based math game played within the classroom by teams. During the game, students received immediate feedback, while each individual’s score was public. Low ability students achieved a significant improvement.

However, at school, the natural team is the class. Being in the same classroom for months and years creates a powerful sense of belonging and identity. Nevertheless, despite these facts, schools and teachers do not use interclass games for teaching.

Regarding tournaments, we can differentiate several types. There are the tournaments in which a selected member of the class participates. This is what happens in the typical math and science olympiads. These are excellent events for finding and training talented students. Another type is team tournaments. Here, each class selects a team, which represent the class, for example for a group discussion contest. This option recruits more students than the previous one, but sometimes it can create conflicts inside the class. There are conflicts about the number of teams, who makes up those teams, and who is left out. The third option is when everyone in the classroom actively participates together in one team. If this type of tournament is frequent, week after week, then there is a greater chance of learning for all the students of the class. This last type of tournaments is the one we study in this paper.

A benefit automatically provided by interclass tournaments is an efficient social dissemination mechanism. The frequently reiterated interactions between different schools enhance the probability of the diffusion of strategies. Moreover, the tournament designers can include a fishing net network topology between schools [36]. This type of networking facilitates the interaction between similar schools, and therefore facilitates imitation. This mechanism of social interaction can be more efficient than other community learning strategies. It can also accelerate improvement and innovation. Interclass tournaments simultaneously put a larger number of classes to work on a common activity. That is, a large number of students, teachers, and coordinators connect with each other. They then imitate more successful ideas and strategies. This is a great learning opportunity, since population size correlates positively with the number and complexity of innovations [32,56]. These tournaments also allow coordinating various groups that modify the activities. They test variants and adaptations of activities, in order to improve the teaching of core concepts and crosscutting concepts. Thus, interclass tournaments could also facilitate cultural evolution mechanisms for the innovation of new didactic activities that improve interdisciplinary integration. Moreover, interclass tournaments where all students participate create an environment that forces students of differing abilities to interact.

3.2. Research Questions

ICT makes it possible to implement online interclass synchronous tournaments, where students participate without leaving their schools. Teachers can also interconnect frequently with other teachers through the Internet. These experiences of frequent interconnection through the Internet between teachers facilitate the evolution of teaching strategies. For example, during the COVID-19 pandemic, in an Internet-interconnected community of teachers, we found evidence of imitation and improvement in didactic strategies [57]. This leads to the conjecture that for interclass tournaments there may be a similar process between teachers. In this paper, we consider two research questions:

Research question 1: To what extent is it feasible to hold interclass tournaments with topics from various disciplines, where all students learn the central ideas of each discipline and crosscutting concepts?

Research question 2: To what extent do interclass tournaments help to innovate and disseminate educational strategies?

3.3. Methodological Approach

In this paper, we analyze the evolution of four online interclass tournaments over a period of approximately a decade. For each of the tournaments, we previously carried out and published impact studies on student learning. In addition, we performed several studies on the effect of gamification on learning, which used the word problems game of one of the interclass tournaments. These were carried out in two randomized controlled trials [58,59], each one in different years and conditions. We have also carried out qualitative studies with semi-structured interviews with teachers, principals, and students.

The objective of this work is different from the abovementioned studies. Here, we do not study the effect on student learning. Instead, we focus attention on the evolution of tournaments and on the teaching practices for these tournaments. That is, the objective is to understand the cultural processes of dissemination of ideas and strategies, and the generation of innovations. For this purpose, we study the changes experienced over the years in teaching practices during the preparation for and participation in the tournaments, and regarding changes to the tournaments and the games that comprise them. These are changes documented in the interactions with teachers and students, and thereafter documented in specifications to software upgrades.

Changing practices is a very slow process. From the last century and the beginning of this one, teaching practices have changed very little, despite major transformations in educational policies [28]. According to Cuban, the appropriate educational metaphor is that educational policy changes are huge hurricanes, but that the classrooms are at the bottom of the ocean. Therefore, they have remained unchanged.

Cultural evolution does not occur easily, because it requires a population size and a minimum degree of social interconnectedness [60]. This is difficult to achieve in schools with isolated classes. Furthermore, the diffusion and generation of technical ideas such as innovations in algorithms are difficult to pass on [61]. Using well-designed experiments with several generations of imitation of artificial objects (images and knots), these processes can be detected [60]. For natural phenomena, such as educational practices, the emergence of innovations is more complex.

However, the controlled nature of tournaments, the number of schools involved in these activities, and the interconnectedness generated by online interclass tournaments facilitate innovation and the detection of certain changes, even when their evolution is a slow process. This detection is facilitated because these changes translate into very well-defined changes in the games. In the tournaments studied in this paper, the changes translated into software changes. These are changes in the software of the games and in software for the management of the tournaments. The tournament development team has documented these changes, as required by software management practices. The team had to describe the upgrades in precise specifications and discussed and revised them with software engineers. Furthermore, after each new software version, the tournament development team had to test the changes and make sure they agreed with the specifications.

Thus, the methodology followed in this paper considers monitoring the requests and implementation of software changes and the interactions with teachers that led to those changes. We concentrate on the major changes in the software releases. For each tournament, we summarize three type of change. First, we list the main misconceptions that teachers had detected. This is because the tournaments included important innovations in areas of knowledge that are not normally taught. Thus, these are concepts not well mastered by teachers. Being new concepts, in the tournaments, there was a learning process on the part of the teachers. They were discovering misconceptions that they were unaware of. These discoveries generated changes to teaching strategies and adjustments required to the games. Second, we summarize the main changes in teaching practices. Teachers discovered new strategies. Some of these strategies were more efficient than others. We list the ones that seemed more efficient. Third, we summarize the main requests for software changes or changes to physical devices. Not all the requests were implemented. Only the ones that seemed most promising. These included innovations in the games used in the tournaments, as well as some innovations in the management of the tournaments.

3.4. Materials

We used the data obtained from previous research on the effect on students’ learning of four interclass games and tournaments for teaching integrated STEM [62,63,64,65,66,67]. These are four interclass tournament activities for elementary and middle school students.

One interclass tournament is for teaching machine learning and statistical modeling. A second activity is to teach the conservation of momentum in physics and its practical application in an engineering optimization challenge. The third is for teaching word problems, integrated with financial literacy. The fourth is for teaching natural selection and sexual selection in evolutionary biology, along with developing statistical and population thinking. In all these online interclass tournaments, there is some degree of integration between the science and mathematics curriculum. They additionally integrate meaningful engineering and technology challenges.

We review all four tournaments, looking for information on how teachers imitated and recombined strategies, and how the nature of the games used in the tournaments evolved with teacher feedback. Online interclass tournaments are a new type of academic activity unprecedented before the ICT age.

3.4.1. Machine Learning Interclass Tournament

This is a synchronous interclass tournament [62,63]. Our team designed this game in 1995 [62], and the first online interschool tournaments started in 2008 [64]. Players have to detect patterns. For each round, the platform shows a box of a certain size and color. The box is closed but inside it contains 12 cells (Figure 1). The box displayed in each round is the same for all classes. However, for each cell, the platform assigns black or white using hidden rules. For example, if the height of the box is larger than 6 cm and its color is yellow, then cell number 5 is white, otherwise it is black.

After watching the new box and studying patterns between boxes and cells in previous rounds, each player must bet on the color, white or black, of his corresponding cell. After 2 min, the time is over, and the box opens to display its contents. If the student’s prediction is correct, he receives 2 points, if it is not, then he loses a point. Alternatively, each player can bet “gray”, meaning “I do not know”, and earn one point. Another option is betting by writing a model. This is a classification rule, typical of machine learning. If the rule predicts the right color for his cell, then the player earns 4 points. If the rule predicts the wrong color for the slot, then he loses 4 points. Thus, betting by writing a rule is appealing but also more risky because the loss is higher.

The platform displays the team’s accumulated points and the national ranking. Students in the team have a different pattern detection problem than the rest of their team. However, all teams have the same set of pattern detection problems. This creates individualized accountability for each student. Since the time is short, the probability of having a team member solving the problem instead of the assigned student is very low.

Based on the grade level of the classes and the learning objectives of the math curriculum, the tournament coordinator selects the hidden rules. These rules define the complexity of the patterns. For example, in the fourth grade, the coordinator can use simple fractions for the hidden rules. For the seventh grade, he can use linear inequalities for the hidden rules. This game has achieved a high degree of integration between numbers, statistics, probability, and supervised machine-learning concepts. Additionally, in the preparation sessions before the actual tournaments, the teacher explains some real world applications. A typical example was diagnostics. The teachers suggested students imagine that the box represents a car motor. That the characteristics of the box—length, width, height, and color—represent characteristics or symptoms of the engine, such as hours of use, viscosity, temperature at which it boils, and color of the oil. The act of opening the box corresponds to opening the motor, and the white or black color of the cell corresponds to whether or not the motor is faulty. There are several other diagnostic examples.

3.4.2. The Conservation of Momentum Interclass Tournament

This is an interclass tournament of predictions and explanations related to conservation of momentum [65]. It was first implemented offline in 2013, and online in 2016. It consists of a first session in which students answer a pretest on basic knowledge of the physics of movement. Students then participate in a 90 min session with four experiments. Later, in a third session, students participate in a synchronous tournament.

The experiments are as follows (Figure 2): The first experiment is about predictions when jumping off a skateboard in various conditions, and then verifying by jumping in those same conditions. For example, the students have to predict whether the skateboard moves and to where, if the student jumps forward from the skateboard. In addition, the students have to predict what happens to the skateboard if the student jumps harder forward. Moreover, students have to predict what happens to the skateboard if the student jumps carrying a heavy backpack.

The second experiment is with a golf ball mounted on a toy truck and released by a slip. Again, students have to predict, and then verify their predictions. For example, the students have to predict what happens to the toy truck when the ball slides and falls to the ground. They also have to predict what happens to the toy truck if the angle of the slip is greater and the ball falls faster.

The third experiment is with a golf ball mounted on a toy truck that has a plastic tube mounted with an internal spring. When the spring is released, it launches the golf ball. As before, the students have to predict, and then verify their predictions. For example, the students have to predict the motion of the toy truck for different retractions of the spring.

The fourth experiment is with rockets made from disposable plastic bottles. Students fill a fraction of the bottle with water and then they pump air up to a specified pressure using a bicycle pump. They have to first predict and then measure the optimal fraction of water for the rocket to rise the highest. To carry out the measurements, they must make several launches with different proportions of water, ensuring that the pressure is always the same. An interesting problem is to devise some way to measure height or reach. Here, they can use knowledge of geometry. The students tabulate the data on paper or in a spreadsheet. In this way, the students can compare their measurements and find out how to synthesize the information using averages. Besides core science concepts, the activity promotes several math concepts that students must use. Among the main ones are fractions, measurement, statistics, and geometry.

In [65], we found that students who participated in the tournament learned significantly more than those who did not. Students with weak academic performance who participated in the tournament improved the most, reducing the gap with the academically stronger students.

The interclass tournament ends in a synchronized online activity. It is an online synchronous test. It contains questions that ask for a deeper understanding of the experiments. For example, it asks for an explanation of how the rocket rises, what is the optimal fraction of water, and their predictions with analogous reasoning using the skateboard and the toy trucks with slips and springs throwing golf balls. An interesting challenge is to explain why the optimal fraction of water is close to a third, and not the extremes.

3.4.3. Word Problem Interclass Tournament

In this tournament, students play a computer-based board game [66]. Its objective is to improve performance in word problems, which is a great challenge in mathematics education [68]. Our team designed the game in 2002 and started to use it for online interclass tournaments in 2014. Each player plays against a student from another school in a sequence of alternating rounds. The score of each student adds to the score of her class. The student has three beads to run through a spiral path of cells (Figure 3). The path ends at the center of the board, where the goal is located. On each turn, the student moves a lever that activates a raffle, from which a word problem randomly emerges. The solution to the word problem is the number of positions that the player has to move one of her three beads. The player chooses the most convenient bead. If she moves an incorrect number of positions, she loses points. If, after moving the bead, it ends up in a cell containing coins, then she wins the corresponding amount of points. If her bead arrives at a position with a springboard with a number, then she has to move the bead forwards or backwards the corresponding number of positions. If the bead ends up in a position with a trap then her bead goes to the start cell. If her bead ends up in position containing one of their rival’s beads, then that rival’s bead goes back to the start cell. Therefore, the player has to select which bead to move in order to maximize her gain. The player that reaches the goal cell first obtains extra points and the play is over.

All players play synchronously. The tournament coordinator announces the school ranking every 5 min. He sends this information in real time by video streaming. Each class projects the video streaming announcements in front of the classroom and using loudspeakers with a high volume level, to create a tournament atmosphere.

During the game, the student has to solve several word games selected according to the learning objectives of the curriculum. In each round, the student also has to make strategic decisions to maximize her gain and minimize her opponent’s gains. The platform keeps the number of times the student solved the word problems correctly. It also knows the decisions the student used to maximize her gain.

We found an important social facilitation effect: a significant improvement in the performance of male students weak in math, and therefore a reduction in the performance gap between mathematically weak and strong male students. Female students weak in math also had a significant gain, but this was lower than the one obtained by weak male students.

3.4.4. Natural and Sexual Selection Interclass Tournament

This is a synchronous interclass tournament [67]. We designed the first version of the game in 2009, and started to use it for online interclass tournaments in 2012. It involves organisms belonging to three species, each of which is a different color. The species of red color feeds on the green species, which in turn feeds on the blue species, and the blue species feeds on the red species (Figure 4). Thus, the three species form a nontransitive cycle. At the beginning of the game, the platform randomly assigns a species to each team. It also assigns to each student of the team a herd of four organisms belonging to the team’s species. Different teams can have organisms of the same species, but the game assigns organisms, so that initially all species have an approximately equal number of organisms. The game has several rounds. Each round corresponds to one generation. During the tournament, students play six rounds, which takes a total time of 60 to 90 min.

In each generation, the organisms live a maximum of 20 virtual days. They autonomously move, chasing prey and avoiding predators. They do this according to their six innate traits, inherited from their parents, and to the instructions given to the whole herd by the student that owns it. On the one hand, each student, just before starting a round, specifies four parameters for her herd. For this, she uses four continuous sliders. The parameters are aggressiveness, exploratory attitude, punishment of uncooperative behavior, and imitation of the more energetic organism of the same species. On the other hand, all the innate traits of the organisms are binary: vision (short, long), velocity (slow, fast), ability to feel fear if close to predator (on, off), ability to feel hunger (on, off), ability to detect the remaining energy of prey (on, off), and cooperativeness (on, off). The platform graphically displays all of these traits. Players can detect them by visual inspection. Furthermore, there are filters or digital inks with which the player can stain the organisms, and thus she can easily count traits in the populations.

At the beginning of each round, players must make two predictions about the distribution of two features in the two species. The platform randomly assigns to each student the traits and species to track for the entire game. They are different from those assigned to other team members. Both trait predictions are about the proportion of the trait in the assigned species at the end of the generation. In addition, each player must make a binary prediction about the growth (increase, decrease) of the size of the population in each species. These predictions are a critical part of the educational aim of the game.

At the end of each round, each player has to select a sexual partner for each one of her female organisms that survived the round. For each female organism, the platform displays a list with the five nearest male organisms. Once the student selects a male, the platform creates an even number of offspring: half goes to the owner of the female organism, and the other half goes to the owner of the male organism. The number of offspring is proportional to the energy accumulated by the female at the end of the 20 virtual days. The offspring inherit the traits from their parents, according to a matrix unknown to the players.

The score of the team is the average of the score of its members. The score of a player is a mix between the agreement of the predictions and the size of the player herd. Every five minutes, the tournament coordinator announces the class ranking, in order to create an exciting tournament atmosphere.

One objective of the game is to promote population thinking [69]. This is a particular and powerful way of thinking in evolutionary biology. This means that the students have to learn to rapidly inspect swarms of organisms, observe their traits, perform data analysis and build models [70], detect patterns and tendencies, estimate the cost and benefits of the traits, use those estimates to make predictions, and then contrast those predictions with what really happened, in order to improve for the next round. We analyzed the performance of 181 students from 7 classrooms, where students took a pre- and a post-test on natural and sexual selection. The results provided preliminary evidence of the learning of key components of natural selection.

This interclass tournament has several additional components. It is a game in which all the players are in the same space. Therefore, the interaction and complexity is much greater. It requires the mind reading of many more players. In addition, the player has two different types of control: those that directly control the organisms’ features, and those where the manipulation is through sexual selection.

4. Results

As proposed in the Methodological Approach section, we studied three phenomena. The detection of misconceptions, the introduction of some new teaching strategies, and some ideas for improving the games and tournaments.

4.1. Results of the Machine Learning Interclass Tournament

Throughout the years, together with the teachers, teachers identified several misconceptions in this game (

Table 1. Main detected misconceptions, new teaching practices introduced by teachers, and innovations in the machine learning interclass tournament generated by suggestions from teachers or from interactions with them.

Misconceptions	New Teaching Strategies	Tournament Innovations
Sample size neglect	Record data in tables	Decimals and fractions
Temporal patters	Number line graphs	Bets with rules
Salient features	Record hits and misses	Decision trees in rules
Base rate neglect	Two dim scatter graphs	Rules with inequations
Single discriminator	Align features and classes	Gray bets
Independent test neglect	Check common features	Scoring strategies

). First, sample size neglect is common in students believing that with the results of one or two boxes they already have a pattern. Second, given the random selection of the boxes, there cannot be a pattern over time of the color of the cells besides the proportion of white and black cells. Even so, many students search for these types of patterns. For example, the sequence of white, white, black, white, white, does not implies that the next will be black. Third, there are salient features such as the color of the box. Many students believe that this is why it is a good feature for prediction. Fourth, the accumulated base rate is a good clue, but students ignore it. They tend to use just the outputs of the last turns. Fifth, many students believe that there is only one feature that discriminates. They do not explore the conjunction of two or more features. Sixth, there are also many students who overfit and do not test their hypotheses on independent cases.

Teachers have introduced some teaching strategies to improve the performance of their students. Due to the interclassroom competition, teachers were very interested in how other teachers were training their students. They wanted to know which graphical representations were better to allow a deeper comprehension and allowed faster and more accurate solutions. Some of the main strategies were the following (Table 1): First, teachers designed instructions to help students manage the incoming data and do this efficiently. This means, how to record the information, arranging it into tables where each row corresponds to a new box with its features. Second, they started to instruct students to draw one number line per feature and place on it the boxes’ features and the contents of the included cells. Third, they started to give instructions on how to record hits and misses, and how to graph them on the number lines. Fourth, they started teaching how to draw scatter graphs of attribute pairs and how to do this quickly. Fifth, teachers sought strategies for students to align features of the boxes with the color of the corresponding cell. This seems trivial, but it is not for elementary school students. Sixth, teachers designed strategies for students to quickly verify with others the common characteristics of the features, and thus avoid or rapidly identify errors in records, tables, and graphs.

In the process of implementation, over the years, the tournament has changed. Several innovations emerged (Table 1). First, based on students’ and teachers’ feedback, we adjusted the learning objectives according to the grade level. For example, we introduced decimal numbers and fractions in the features of the boxes. Second, from the interactions with teachers, the idea of including models emerged. This skill was new in the math curriculum, and teachers wondered whether this activity could help to develop modeling skills. Teachers suggested a didactic strategy where the models were autonomous bots and students have to design efficient bots. The task of the students could change to designing bots. Thus, we built a rule design interface. The interface also included the facility to bet with rules. It took the form of selecting variables and adjusting rules. We performed several cycles of improvement, based on the ideas that teachers copied from each other, adjusted to their classes, recombined, and suggested to us. Third, we also introduced decision rules to the interface to design rules. Fourth, we introduced linear equations and inequations to the interface. This means rules with inequations. This was particularly important for middle and high school students. Fifth, we added a gray bet. This means “I don’t know”. This is appropriate for the initial turns of the game. Sixth, we introduced different scoring systems better adjusted to the grade levels and concepts of the curriculum.

We found that there was a great learning opportunity in the idea that students bet by writing rules. The rules use several learning objectives of the curriculum, such as a mix of categorical and numerical attributes, inequalities, scatter graphs, and linear and nonlinear equations and inequations. These changes were signs of a process of cultural evolution that was emerging in the community. In addition, analyzing students’ behaviors, in [63], we found evidence of a diffusion process of strategies. Students learned different modeling strategies from other students, at least in the case of simple patterns. A statistical analysis [63] suggested that during the preparation for the tournament, some teams learned how to detect patterns, how to express them with rules (models), and then internally diffused those strategies. Students were successful in sharing only the simplest types of hidden input–output patterns.

In summary, we observed a diffusion process throughout classrooms in the tournament. Through feedback from teachers, we incorporated pedagogical instructions and adjusted the user interface of the game to promote learning. Additionally, we introduced the idea of autonomous bots, where the students had to design efficient bots. Through cycles of improvement, we observed a process of cultural evolution emerge in the community, with students using categorical and numerical attributes, inequalities, scatter graphs, and linear and nonlinear equations and inequations.

4.2. Results of the Conservation of Momentum Interclass Tournament

There are several well-known and documented misconceptions regarding basic physics. For example, that heavier objects fall more rapidly. However, there is not much experience in teaching the notion of momentum, also called quantity of motion. Therefore, misconceptions about this topic are not that well known. The left column of

Table 2. Main detected misconceptions, new teaching practices introduced by teachers, and innovations in the conservation of momentum interclass tournament generated from suggestions from teachers or from interactions with them.

Misconceptions	New Teaching Strategies	Tournament Innovations
High friction physics	Do measurements	Model with skateboards
No inertia	Compare measurements	Model with toy carts
Only visible forces	Draw experiments	Model with springs
No mass in momentum	Analogic reasoning	Trigger mechanism
Impulse from water	Explain verbally	Pressure meter
Only initial impulse	Modeling	Change rocket performance

lists some misconceptions that the teachers identified. First, students’ notion of forces are the typical of horizontal motion of a vehicle in an environment with high friction. Someone has to be pushing the vehicle. Second, related to the previous point, they do not systematically include inertia in the predictions of motion. Third, they only include visible forces in their analysis. For example, someone or a motor is pushing the vehicle. The question is then how the rocket elevates if no visible force is pushing it. At this moment, students think of initial impulse and start to consider inertia. Fourth, they do not include mass in the quantity of motion. They tend to think initially that heavier objects moving at the same velocity do not have a higher momentum. Fifth, they think that more water inside the rocket means more energy, which helps to elevate it. Sixth, they think that motion is due to the initial impulse. They do not consider that the water continues leaving the rocket, or they do not know how to consider this effect.

Teachers also introduced several teaching strategies. The center column of Table 2 lists some of these strategies. First, teachers started to put more time and emphasis on measurements and to give instructions on performing more measurements with more precision. For example, measurements of displacements. Second, they also promoted making comparisons of measurements obtained by different students, finding the sources of errors, and finding options to control errors. Third, they suggested students draw the experiments and the setups. Figure 5 shows a sample of a fourth-grader drawing. Fourth, teachers promoted analogic reasoning. For example, imagine that the air inside the bottle was something like a spring mounted in the cart, and that the water was like the ball that the spring pushed once released. Fifth, teachers asked students to verbalize the explanations and compare the explanations of the different students searching for new ideas. Sixth, teachers started to talk about models. Where the different experiments were models that helped in understanding the motion of the rocket.

As we implemented these activities, the teachers gave suggestions to make them closer to the curriculum, to make them more attractive to students, and to facilitate their implementation in the classroom. The teachers were interested in knowing how other classrooms implemented the activities. How much were those students learning? How did those students do on the post-test? What were the differences with their students? Why did the differences occur? Teachers copied the most successful teaching strategies and recombined them. Thus, the experimental activity underwent several changes. Initially the activity was mainly launching rockets. Then, we started to introduce a explanations section to the tournaments. Then, with suggestions from teachers, we introduced several innovative experiments. The goal was to help understand how the rocket elevates. First, among the important innovations was the model with skateboards and with different weights in the backpack. The idea was to understand the role of mass in addition to velocity. Second, came the innovation using toy carts with balls. Third, we introduced the spring to push the balls instead of using gravity. This way, the balls gained velocity. Fourth, there was an interaction with students’ fingers. Therefore, there was a need to have a trigger mechanism isolated from other interactions. Then, after several trial and error developments, a spring release mechanism emerged. The idea was to use a string that holds the contracted spring and set it on fire with a match. The fire moves slowly and burns the string until it cuts it. This causes the spring to loosen. This phenomenon generates a lot of expectation. This causes great excitement in the students, as it resembles a bomb fuse. Fifth, we introduced the measurement of pressure while pumping air. We instructed releasing the rocket at a given pressure. Sixth, we changed the performance score for the rocket. We incorporated launching the rocket at a certain angle (45 degrees, for example) and not straight up. This makes measurement easier. Another idea that emerged was to improve safety with skateboards. Initially, it was easy for some students to slip, which can lead to accidents. Over time, various didactic strategies emerged to maintain a certain level of order in the class and achieve the participation of all in the experiments.

Thus, teachers made various adjustments to the experimental activity to make them more engaging, closer to the curriculum, and safer. These adjustments created a lot excitement in the students and improved the maintenance of order in the classroom. The teachers also discussed how other classrooms implemented the activity, the learning outcomes, and the differences in learning between their students. In this way, they copied and recombined the most successful teaching strategies.

4.3. Results of the Word Problem Interclass Tournament

The synchronized interclassroom competitions not only attracted the students, but also the teachers. The tournaments encouraged the search for strategies to teach how to efficiently solve word problems and strategies for moving beads on the board. There was a process of comparison and imitation among teachers. Then, each teacher adapted the didactic strategies to the reality and level of her course.

This process of imitation, recombination, and diffusion of didactic strategies allowed us to improve the tournaments. It also led to an increase in the number of students who were attracted to solving the word problems and to do it with greater accuracy and speed.

Teachers identified and discussed between them and us different misconceptions about the word problems.

Table 3. Main detected misconceptions, new teaching practices introduced by teachers, and innovations in the word problems interclass tournament generated from suggestions from teachers or from interactions with them.

Misconceptions	New Teaching Strategies	Tournament Innovations
Always more means +	Pattern of word problems	Include word problems
Always minus means −	Search for metaphors	Include irrelevant numbers
Always divide means:	Use a concrete case	Include fractions in words
All numbers have to be used	Thinking with balls and boxes	Include fraction operations
Word order is not important	Check solution is integer	Include translations
Fractions are not numbers	Additions as translations	springboard sequences
Multiplication increases		How many times does it fit?
Division decreases		Financial elements

lists some of these. First, students automatically assign an addition to the presence of the word “more”. However, this is not always true. For example, in “How much more is 12 than 8?”, the student has to subtract. Second, the same happens with the word “minus”. For example in “What number minus 3 equals 1?”. Third, something similar happens with “division”. For example, you have two bacteria. After they divide, how many do you have? Fourth, there is a strong impulse to use all the numbers mentioned in the question. Fifth, word order is not important. For example, they think that the square of the successor of a number is the same as the successor of the square of a number. Sixth, fractions are processes not numbers. Therefore, they do not have a position on the number line. Seventh, multiplication increases. This could come from the idea that multiplication is repeating. However, we can have repeating half a time or turn. Eight, division decreases. This idea may come from the fact that dividing is dividing equally. However, if we use the idea that dividing is how much the result fits into the dividend, we can see that half a sack of flour fits twice in a sack.

Teachers tried various teaching strategies. First, the most common was to detect patterns of problems and teach how to solve those problems. Second, teachers tried to use metaphors or analogies. For example, in finding the number that when subtracting 3 from it the result is 5, the strategy is to locate the position of 5 in the number line and then look for the position to place a small object that when moving it to the left 3 positions the object would reach the position of 5. Third, the teachers developed various strategies to translate to specific cases. For example, how much more is 8 than 6, translates into putting 8 blue candies in a row and comparing them with 6 red candies in a row, then putting them in pairs blue and red, and then counting how many candies remain unpaired. Fourth, thinking with balls and boxes. For example, for the number that when subtracting 3 gives 5, it can be thought of as a box with sweets that when removing 3 sweets is left with 5 sweets. Then the idea is to reverse the actions. Fifth, check that the solution is an integer and not a decimal, since then you have to move one of the beads in an integer number of positions. Sixth, imagine addition and subtraction as translations on the number line.

This tournament evolved incorporating several innovations radically different from the original version. Each player does not respond or advance independently of the others, as in a race, a pattern bet, or a knowledge test. Now, the student must make decisions taking into account what her opponent can do. Thus, in this tournament, there is a phenomenon of mind reading. Each student has to guess what her opponent will do. In the language of game theory, it is a true game. On the one hand, the word problem comes out randomly, but according to the learning objectives of the curriculum selected by the tournament coordinator. A solution is always a number between 1 and 20. These are the number of positions that the player can advance. However, next comes the risk factor. The student has to choose which bead to move. In certain positions, the opponent can more easily attack him, and there are others where he can attack his opponent more successfully. On the other hand, there are movements that have a greater benefit than others do. There are more coins to collect. This combination of chance, deterministic problems, mind reading, risk, and reward establishes a connection with the world of financial decisions.

Over the years, this tournament has undergone several significant changes. In the beginning, there were no word problems. Originally, teachers used the game for students to practice basic math concepts. For example, counting and arithmetic operations. However, some teachers suggested looking at how to include other learning objectives in the curriculum. One of the most demanded was the resolution of word problems. Given the attractiveness of the game and the students’ weaknesses in solving word problems [68], we worked with some teachers on different strategies to include them. We tested on several classrooms. A second innovation was to introduce superfluous numbers, in order to signal to students to try for more comprehension. Third, we incorporated an increasing number of learning objectives from the curriculum and adjusted these to the strands and grade levels. An important topic in the curriculum and one that represents a great teaching challenge is fractions. We introduced fractions as words. This means expressions such as one out of four. Fourth, we also introduced operations with fractions. In the game, by its nature, the result must be an integer from 1 to 20. This is an important restriction. Fifth, we introduced additions as translations with trampolines on the board. Sixth, we also included the option to detect strategies with springboard sequences. Seventh, we introduced problems asking how many times one quantity fits into another. At the suggestion of teachers, we also included elements of a financial nature that support new learning objectives in the curriculum.

4.4. Results of the Natural and Sexual Selection Interclass Tournament

During the more than 10 years of implementing this game, teachers have detected various misconceptions. Many of them are known in the literature on the teaching of natural selection. However, the teachers were unaware of these misconceptions. One explanation for this is that teachers do not teach natural selection or sexual selection. They only teach the evolution of the species very superficially, without emphasizing the underlying mechanism.

Table 4. Main detected misconceptions, new teaching practices introduced by teachers, and innovations in the natural and sexual selection interclass tournament generated from suggestions from teachers or from interactions with them.

Misconceptions	New Teaching Strategies	Tournament Innovations
Essentialism	Population thinking	Behavioral traits
Organism needs to change	Graph histograms	Concrete to digital
Only physical traits	Blocks for histograms	Loss of traits
Cooperation is impossible	Trends in histograms	Sexual selection
No loosing traits	Cost–benefit tradeoffs	Graphs
Competition across species		Instructions to herds
Teleological conceptions		More generations
Evolution is progressive		Predict traits distribution
		Rock–paper–scissors ecology

lists the main misconceptions. First, students have a strong essentialist bias, where things have a true underlying nature, and therefore species have fixed essences. This essentialist bias can distort judgments about a wide range of evolutionary phenomena, such as the concepts of variation, inheritance, adaptation, domestication, speciation, and extinction. Second, students believe that organisms change because they need to change to survive. They do not conceive of it as a blind mechanism, completely independent of the needs or will of an organism. Third, students think that natural selection only operates on physical traits. Fourth, students and teachers think that Darwinian competition is incompatible with cooperation and altruism. Fifth, students think that natural selection explains the appearance of new traits, not the loosing of traits. Sixth, students think that the competition in natural selection is against other species, not of organisms within the specie. Seventh, students have a teleological view of evolution and have severe difficulties in understanding the blind mechanism of natural selection. Eight, students think evolution is progressive. These misconceptions are deep-rooted and not easy to eradicate. Thanks to the game and the tournaments, the teachers began to place emphasis on teaching the mechanism of natural selection, and therefore they began to detect these misconceptions.

During the years of implementation of the tournament, the interaction with teachers facilitated the development and implementation of various teaching strategies. The first was to promote population thinking. The idea is always to reason about a population of organisms of a species and not about single individuals. Second, the teachers began to train the students to construct histograms with the distribution of traits in the population. This was not common in biology classes. Third, for elementary school students, teachers began using plastic blocks to make histograms of traits and then translated them into graphed histograms on paper. Fourth, teachers began to instruct on how to visualize trends in traits across generations. Fifth, teachers began to promote reasoning about cost–benefit analyses and tradeoffs of the different traits.

We introduced several innovations during the years of implementation. During these years, teachers gave various feedback to the game development team. In the first years, the tournament started as a game between teams within classes. It was not computer-based but used only concrete material. In the first two versions, students played a game of natural selection of physical traits. The first version was about the natural selection of color. The second version was about the natural selection of beak size. After these successful experiences and the feedback received from several teachers and their classes, we developed a natural selection game of a non-physical trait. This was the first conceptual innovation. Introducing behavioral traits generated a fertile discussion among teachers. In the teachers’ training and in the years that they taught biology, they had done very little instruction on natural selection, and if they included it, it was only of physical traits such as height or hair color. Therefore, the introduction of behavioral traits generated confusion among teachers. However, after successive cycles of trial and error, the conversation turned to how to teach the evolution of behavioral traits. Some teachers suggested starting by illustrating common behaviors close to students’ daily life. This included the domestication of dogs and horses. Professional breeders artificially selected them. In other words, the behavioral trait was aggressiveness. Another behavioral trait introduced was cooperation. Students used hooks, some one-sided and others two-sided, with hooks at both ends [13]. The hooks represented birds. The hooks hunted fishes, represented by Christmas baubles. One-sided hooks fished alone, whereas two-sided hooks could hook onto each other, in order to reach the baubles that were deeper down. The second innovation was the development of a digital version of the game. The digital version facilitated holding interclass tournaments. The third innovation was the introduction of the possibility of losing traits. The fourth innovation was the introduction of sexual selection. This is difficult content and most teachers do not teach it. Students have male and female organisms, with the typical reproduction conditions of mammals. Human females mostly have only one child at a time, but males can have many. Students have to select mates for each of their organisms. The fifth innovation was the displaying of graphs in the game. The number of traits of the organisms increased considerably. Thus, students needed a lot of time to graph. Therefore, we introduced the facility to select variables and the game automatically displayed the graphs. Students had to rapidly interpret the graphs and use them to make decisions. The sixth innovation was the introduction of a facility to give instructions to the herd. Thus, each student has four control variables defined at the birth of the generation. The seventh innovation was to increase the number of generations. The greater number of traits and the number of control variables other than sexual selection made it difficult to see trends in three generations available in the original game. The eighth innovation was the facility for predicting the distribution of traits. Since there are six traits, each student predicts a pair of traits. Therefore, that is 15 combinations of different pairs of traits. Each student receives a pair to predict. Thus, in a typical course there are only two or three students who must predict the same pair. The ninth innovation is the introduction of rock–paper–scissors ecology [71]. One of the questions that arose was whether generations could exist in a nontransitive relationship. In other words, species A preys on species B, species B preys on species C, and species C preys on species A. This led us to include three species in this rock–paper–scissors relationship.

With the interclass competition, teachers became interested in knowing how teachers from other sections or schools introduced these ideas. They also wanted to know the responses and learning of the corresponding students. There was copying of concrete materials, stories, and teaching strategies. Natural selection is one of the central themes of biology. It is a great challenge to develop and learn effective teaching strategies that manage to dismantle deep-rooted misconceptions. Then, we developed an online version with many more features, both physical and behavioral. The feedback from teachers and students guided the inclusion of game features. This is an example of a cultural evolution process of multiple micro-adjustments and innovations throughout years of interactions.

In summary, the teachers gave various feedback to the game development team on introducing behavioral traits, such as aggressiveness and cooperation, into the game. Their experience with natural selection was limited and it was restricted to physical traits. Sexual selection was also not part of their instructional goals. Through trial and error, they discussed strategies to exemplify common behavioral traits in domesticated animals. We used the feedback of teachers and students to guide the development of an online version of the game with these more challenging and deep concepts. Teachers learned from each other what worked best. This is an example of a cultural evolution process, guided by multiple micro-adjustments and innovations over time.

5. Discussion

According to UNESCO’s Sustainable Development Goal 4, by 2030, we have to ensure that all learners acquire the knowledge and skills needed for global citizenship. In particular, a great challenge is learning to integrate disciplines. Another challenge is to learn to cooperate with known and unknown people. However, classrooms are isolated from each other. This generates very little cooperation between teachers. A way to try to achieve more integration and collaboration is with effective learning environments. In this paper, we reviewed how feasible it is to connect classrooms with the help of technology and hold tournaments between classes. Does this facilitate collaboration and the dissemination of effective practices?

According to [72], in cooperative learning, the most important element is positive interdependence; students should believe that they sink or swim together. With synchronous online interclass tournaments, there is a common goal. All students share this common target. The platforms explicitly highlight this key element by posting class rankings as students compete against other classes. The platform permanently publishes the class score, reminding students of the shared target. Another key element is individual and group accountability [72]. In these four types of tournament, the platforms track the performance of each student. The games also includes instant feedback and metacognition. For example, in training sessions, the teacher can freeze the game, as in basketball games, and can pose open-ended questions that promote a deeper reflection. The teacher thus becomes a coach, constantly providing cognitive and emotional support to the class.

From the teachers’ point of view, they quickly build a community that remains highly connected throughout the tournament. Teachers discuss their strategies with tournament organizers, as well as with other teachers of the tournament community.

Additionally, the coordinator of the tournament also has a fundamental role in promoting metacognition. This role is particularly intense in training sessions. She comments on the strategies developed by students from different classes, encourages comparison of strategies, and encourages them to reflect on mathematical concepts and methodologies. Finally, after several years of implementation, the community of teachers has generated ideas that allow improvements to the games for the next year’s tournaments.

Another important characteristic of interclass tournaments is synchrony. Students play interclass tournaments at the same time and with announcements from the organizers that highlight synchrony. Interpersonal synchronization is important for many cooperative tasks. Reference [73] found that synchrony has significant positive social influences, such as a greater sense of similarity and affiliation. An example of the social impact of synchrony is in the evolution of language. Originally, it comes from grooming between peers. Next, it started collective laughter that synchronizes small groups. In a third stage, it started collective singing and dancing. This moved synchronization to a higher level. This new stage increased social cohesion and collaboration [74]. In addition, with the enjoyment triggered by synchronization, we are more willing to change our behavior. This is a great motivator to integrate and feel part of a community, accept feedback, and transform our practices.

We have analyzed our experience of more than a decade with four different types of interclass tournament. They connect mathematics and computational thinking topics with other STEM disciplines. We found that interclass games are feasible to implement in schools. These are tournaments between classes from different schools with topics from various disciplines. In each case, the whole class participated in teams or as a whole, and students learned central themes of each discipline. They also used and practiced some crosscutting concepts, such as data and patterns, and crosscutting skills, such as argumentation, cooperation, and teamwork. Moreover, we found that the tournaments generated improved student motivation and that students not only enjoyed them but learned some basic citizen values and attitudes, such as fair competition with anonymous others and unknown teams.

To what extent do interclass tournaments help develop educational activities that integrate various disciplines? The integration of different disciplines is a great challenge. However, interclass tournaments offer a platform to help spread activities across disciplines. The innovative environment and lively atmosphere created facilitate trial and error. This helps teachers open their class to introduce core concepts from other disciplines. In the four types of tournament shown in this work, there are some integration components. These successful experiences showed us that this mechanism can be a strategy that helps to overcome the barriers to integration. There are 10 difficult barriers to face, described at the beginning, but interclass tournaments seem to be a technique that makes it easier to lift those barriers.

To what extent do interclass tournaments help to innovate educational strategies? We have studied the evolution of four types of online interclass tournament. They represented a unique opportunity to track changes, as they are recorded specifications for the game software used in tournaments. For each tournament, we studied three types of change. First, there are the major misconceptions that teachers spotted. Given the novelty of the contents in tournaments and the integration of disciplines, these were not always the domain of teachers. Thus, teachers were just learning and spotting misconceptions they had never encountered before. This was very clear, for example, in the games about machine learning. Teachers had never taught machine learning before. The same was true of the momentum game, which had a strong component of engineering and reasoning by analogy. This caused changes in the teaching strategies and requirements for upgrades in the games. Second, there were changes to the teaching practices. On the one hand, it was necessary to address misconceptions. On the other hand, there were new concepts. We listed the most significant changes. For example, a new way of thinking in biology: population thinking. Similarly, completely new problems appeared in the word problem game. This was particularly challenging for fractions. Third, we documented changes to games and tournaments. These were translated into specifications for software changes. For example, being able to bet with models in the machine learning game. Other changes were tweaks to physical devices, such as the trigger mechanism to release the spring and thus shoot the ball.

The four examples of online interclass tournaments presented in this paper show evidence that there was a constant process of cultural learning and innovation. Throughout the years, the nature of the games experienced some changes. Most of the feedback came from trial and error with different features, the reactions and performance of the students, and suggestions from teachers.

6. Conclusions

Until now, scaling new educational strategies has been a major challenge and one that remains. In recent decades, progress in mechanisms for educational scaling has been very limited. Although the technological development of the internet and social networks has allowed a much greater dissemination of information, this has not translated into changes in teaching practices. ICT has an enormous potential to improve quality in education, as proposed in the UNESCO’s Sustainable Development Goal SDG 4 [75], and to address the challenges of large-scale teacher professional development [76]. Both the coverage and speed of propagation of educational information, new curricula, seminars, webinars, educational websites, etc. have skyrocketed. However, this diffusion does not translate into changes in educational behaviors or educational beliefs [28].

Interclass tournaments encourage a large community of classes, with their teachers and all their students, to interact under four conditions. First, the interaction is synchronous. This means an atmosphere of increased engagement, motivation, effervescence, and cooperation. Second, this environment makes it easier for the organizer to disseminate messages, strategies, and concepts. This synchronous interaction also makes it easy to receive feedback from teachers and students. Third, homophily. Students and teachers of the same grade level interact. They are students with similar interests and learning goals. Their teachers have to focus on teaching the same topics and doing this in practically the same weeks. Fourth, reiteration. Many times in preparatory events, as well as in the tournament, students and teachers from different schools are interacting. These repeated exchanges facilitate the creation of friendships and close and permanent social networks [36].

The combination of these conditions facilitates the spread of ideas, innovation, and change of strategies. This is a mechanism of cultural evolution different from that of standard teacher professional development and lesson study. In our experience, interclass tournaments, are an alternative worth exploring and further developing. They are an alternative mechanism for enhancing and accelerating cultural evolution didactic strategies.

Online interclass tournaments provide social interaction and learning opportunities between different schools. Teachers and coordinators can imitate more successful ideas and strategies. Online interclass tournaments help teachers to modify activities and test variants for improved teaching of core concepts. They are a new type of academic activity, unprecedented before the digital age. They connect entire K12 classrooms through digital communication, allowing for the exchange of ideas and strategies for a deeper integration of core math and science concepts, crosscutting skills, and meaningful learning. These tournaments promote imitation and recombination of didactic strategies. They are feasible to implement in schools and have the potential to improve student preparation for the challenges of a fast-changing and smarter society. Furthermore, in interclass tournaments, all students participate. This characteristic creates an environment fostering interaction between students of different abilities, accelerating students’ learning. This environment helps reduce the isolation between teachers from different schools. Now, the teachers are more aware of each other, they communicate and learn from each other.

This work has several limitations. The first limitation is that the number of different tournament types is very low. They are only four. It is necessary to increase this number and verify the replicability of the main findings. However, this will take many years, so it is a great challenge. The second limitation is that each tournament was followed for a few years. In the future it would be important to carry out continuous monitoring of each type of tournament for many more years. A third limitation is in the degree of granularity of the documentation of changes in teaching practices. More granularity requires a more detailed class observation. Thus, observations of the sessions and the corresponding classification of them according to a certain protocol should be included. For this, it would be necessary to video record the sessions. Then, given the large volume of sessions that would be recorded, analysis could be facilitated with automated analysis tools.

For future work in my laboratory, we foresee several lines of work. First, we plan to analyze innovations in educational materials. For example, changes in the nature of digital materials. With AI and natural language processing tools, changes to textbooks and lesson contents and structures can be easily monitored [77]. The conversion of text paragraphs into vectors through vector embedding facilitates the detection of patterns and the formation and evolution of clusters. Second, we plan to study thousands of classes. Machine learning tools make it easy to automate the classification of events according to different classroom observation protocols [78]. This, in turn, makes it possible to detect clusters of lessons and their evolution [79]. Third, an area of great interest is to detect changes in the types of open-ended questions posed by teachers and the evolution of the corresponding students’ answers. Machine learning tools and large language models make these analyses possible [80]. Fourth, another area of great interest is student teamwork. Machine learning makes it possible to automate part of the analysis. We plan to start monitoring changes in team strategies and their innovations over the years. We already have some promising preliminary results [81]. Fifth, we are planning to study changes in students’ attitudes and socio-emotional behaviors. For example, interpersonal behaviors, intraclass versus interclasses collaboration, and the structure and cohesion of the different social networks that naturally emerge in the classrooms.