**'The Game of the Sea': An Interdisciplinary Educational Board Game on the Marine Environment and Ocean Awareness for Primary and Secondary Students**

**Elena Arboleya-García 1,\* and Laura Miralles 2,3**

	- <sup>3</sup> Department of Environmental Genetics, Ecohydros, 39600 Maliaño, Spain
	- **\*** Correspondence: elenaarboleyagarcia@gmail.com

**Abstract:** Games are a proven tool for learning at all ages and in many contexts. They increase the attractiveness of learning processes through arousing interest and enhancing motivation, and aid with the development of social skills. Educational games provide teachers with different approaches to teaching. 'The Game of the Sea' is an interdisciplinary board game, specifically designed to teach its players about the marine environment, regardless of their age. Through its 68 sections, coloured according to particular topics and organised as a fish shape, players encounter a wide range of questions and activities. Through playing this game, players acquire a broad knowledge of science, the marine environment and its importance, and literature. The game uses an interdisciplinary approach with question cards on a variety of topics (including maths, physics, biology, chemistry, art, etc.). A total of 222 players (111 children, aged 11–15, and 111 adults, aged 18–72) tested the game. These players were enrolled in different formal and non-formal educational contexts and had different educational backgrounds. For a qualitative analysis of game sessions (participant observation), researchers acted as game moderators and, while doing so, made subtle observations of players playing the game. On top of this, the value of the game, as a didactic tool, was evaluated with a test that players took before and after the game. After playing the game, knowledge of the marine environment, increased in both children and adults, with a slightly higher increase in children. Therefore, 'The Game of the Sea' is suitable for teaching all ages about the marine environment. Further, this game can impart to its players the importance of the marine environment and the importance of protecting this environment.

**Keywords:** educational game; game-based learning; board game; learning tool; teaching-learning process; interdisciplinary learning; science learning; marine environment; environmental awareness; skills development

## **1. Introduction**

Games are present throughout all stages of life, from childhood and adolescence to adulthood and old age. Moreover, games have been played throughout the existence of human beings. Indeed, playing games is thought to have been essential for the evolution of civilization [1]. Additionally, by being part of social and cultural activities, games can provide important social experiences. Games can be typically described as fun, voluntary, having prescribed settings in time and space and being constrained by rules and procedures (yet being somewhat, unpredictable) [2,3]. Thus, a wide range of social interactions in which people collaborate and/or compete with the aim of achieving determined goals can be considered games [4].

Games can be categorised depending on their purpose: entertainment or education [5]. Educational games have all the characteristics mentioned before, but are specifically designed to achieve learning goals [6,7], and have been proposed as a mean to prevent

**Citation:** Arboleya-García, E.; Miralles, L. 'The Game of the Sea': An Interdisciplinary Educational Board Game on the Marine Environment and Ocean Awareness for Primary and Secondary Students. *Educ. Sci.* **2022**, *12*, 57. https://doi.org/ 10.3390/educsci12010057

Academic Editors: José Carlos Piñero Charlo, María Teresa Costado Dios, Enrique Carmona Medeiro and Fernando Lloret

Received: 6 December 2021 Accepted: 13 January 2022 Published: 16 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

students failing school [7]. These games try to develop player's cognitive and operational abilities (while reinforcing their social development) through teaching them specific concepts, so that they can understand and expand on these [8]. Therefore, these games should be designed to be teaching materials [9], not just to provide entertainment [10] (although they should be enjoyable too [11]).

Nowadays, educational games are implemented for teaching skills, and academic content, in such different fields as health, business, science, the military, etc., at different levels of education and in different educational contexts (formal, non-formal, and informal) [12,13]. Educational games are sometimes digital [14], though certain scholars think that they should be tangible and face-to-face. Further, non-digital games could supply more, and deeper, interactions among peers and, also, easily allow adaptations of game design to include a wider variety of activities to adapt to different learning styles, or maintain the participant's interest [15]. Gamification is another way in which game elements can be used in education. This does not entail a complete game process, but rather employs whichever elements of games (e.g., badges, game dynamics, etc.) best help players to reach specific goals in their education or improve how they behave with others in non-game contexts [16]. Gamification is employed in fostering students' enthusiasm, by, for instance, providing them with immediate feedback during performance and enhancing recognition of their achievements [17] inside learning contexts.

Both educational games and gamification can be referred to as game-based learning (GBL). GBL uses a learner-centred approach to help learners obtain usable knowledge while developing a wide range of skills [18]. GBL has many benefits. Games have been linked to academic achievement, regardless of the educational stage of the participants [19]. Educational experiences based on GBL allow students to be active participants, rather than passive observers, as they learn through participating in game activities (i.e., problemsolving, making decisions, and reacting to the results of these activities) [20]. GBL gives learners the chance to take risks without real consequences, and reduces their feelings of being exposed as having lower levels of knowledge [21]. Indeed, as games allow players to repeat failed tasks and correct previous mistakes, negative experiences can be transformed into a final success that promotes positive attitudes towards learning through playing [22]. GBL challenges players in a positive way [23], promotes social interactions, fosters attention and concentration, facilitates the construction of long-term memories (through providing continuous and personalized feedback, which also helps tackle misconceptions), and develops emotional skills [24] better than traditional teaching methods [25]. Neuroscience demonstrates further benefits of using GBL. Not only does GBL activate the reward system in the brain, it is also more likely to stimulate retention and engage players toward more effective cognition compared to more traditional methods of education [26,27]. GBL encourages creativity in teaching complex subjects (e.g., sciences) [28]. Games used to teach science subjects can be specifically designed for students' needs so that they can acquire complex knowledge while having fun (thus distracting them from the fact that they are learning [29]).

Despite its many benefits, GBL has some drawbacks. The most common of these is perhaps that games take time and effort, not only to play but also to design, test and implement [18]. This can lead to difficulties in time management and, also, players feeling frustrated if they do not complete the game. Additionally, some players may not take the game seriously. Not only these players may fail to attain the knowledge that they should from the game, teachers might find it hard to determine where they have gaps in their knowledge [21]. An already developed game, aligned with the contents of the *curricula* used in formal education, or the formative program used in informal education, would remove the need for teachers to design and test their own games. Such a game could enable students to reach the same educational goals in less time than traditional methodologies and materials [30].

Board games have been the most popular kind of non-digital games for centuries and, in all age groups, are still the kind most played by people [31]. Board games are also traditionally used, in GBL, for developing academic knowledge and cognitive skills, and have a number of advantages that aid with this. They can address different learning styles [20,32], contents and procedures to be adapted for personalised sessions [33]. They allow players to learn by doing, foster hands-on skills, and promote self-confidence and self-learning [34,35]. They can have clear rules that make it easy to understand, initiate, and sustain game play at an adequate rhythm [36]. They use a combination of tangible materials, turn-taking modes, and face to face interactions among peers or teams [37]. They create a non-threatening environment that supports mutual learning [29] since they provide opportunity for players to receive feedback or clarification, have discussions, and reflect on the game [38], which benefits both peers and game moderators [39]. They involve competition, which can be highly positive, if this motivates players to cooperate with each other and do their best in the game [40]. Nevertheless, success in educational games is based more on aptitude and knowledge than on competitiveness. The above suggests board games to be a powerful educational tool for all ages, across educational contexts [12], in alignment with the longlife learning concept, which implies learning with, and from, other people [20]. Evidence for the success of board games as educational tools include their already frequent use in different educational contexts and in teaching many different subjects. When introduced in university contexts, board games were not considered a childish activity or a waste of time [41]. Such games have yielded excellent results at Undergraduate and Master's levels [42,43]. At the other end of the academic spectrum, playing games is the most frequent learning activity in Elementary and Primary Education [28]. Among the many different subjects taught with board games [44] are architecture [45], astronomy [18,46], biochemistry [47], chemistry [35], ecology [48], electronical engineering [49], environmental sciences [50], healthcare sciences [29,51,52], palaeontology [53], pharmacy [54], chemical engineering [55], and engineering [56].

In this sense, board games could help people better understand how the marine environment and humanity influence each other. This is ocean literacy, conceptualized as 'an understanding of the ocean's influence on citizens and citizens' influence on the ocean' [57]. Accordingly, board games could be used as an effective communication tool to generate environmental awareness [58]. This is important as, with this understanding, people can better communicate information on the marine environment and make conscientious decisions regarding this [59,60]. Through playing board games, players could learn about specific concepts such as sustainability problems that marine ecosystems currently face, as well as how to restore and protect the marine environment. Such education should be present for all ages [61], although children are most likely to change their behaviours in response to it [62]. A better understanding of ecosystems comes from scientific knowledge but arts (in its broader conceptualization as paintings, films, documentaries, etc.) also have the capability to engage people and foster environmental awareness [63].

Here, we present 'The Game of the Sea', a game, suitable for any educational context, regardless of the players age, which focuses on specific *curricula* contents that can lay the foundation for a deeper understanding of the marine environment. 'The Game of the Sea' has an interdisciplinary approach, which integrates information on the marine environment from different disciplines. This differs from a multidisciplinary approach as, while the latter also involves different disciplines, each discipline provides a specific perspective, typically resulting in poor, or null, connections between them [64].

Creating an attractive educational game, which can be successfully used for teaching science, and raising awareness on environmental issues, while holding the players' attention for a long-time, can be difficult [25]. Nevertheless, the development of such games should be encouraged, as they promote the development of important skills. These skills include critical thinking (if the game requires scientific reasoning, decision making and problem solving), collaboration (if players need to work together), creativity (if players need to think outside the box), and communication (if players need to share ideas) [6,65,66]. On top of this, educational games strengthen students' autonomy, self-confidence, and self-esteem. Thus, 'The Game of the Sea' was conceived to teach and learn about marine environment, based on both popular quizzes and board games with a background of sciences such as physics, biology, mathematics, geology, chemistry, or literature.

The 'Game of the Sea' was specifically designed for rising citizen awareness about marine conservation while enjoying and learning. The learning goals of this game are: (1) To enable students to achieve learning objectives (based on the official *curricula* of Spanish Compulsory High School Education) in terms of learning about the marine environment. (2) To foster collaborative learning, regardless of age or educational background. (3) To raise awareness about critical situations regarding our marine environment, and the need to preserve this environment. The learning objectives of the game are for players: (a) To recognise organisms from marine ecosystems. (b) To identify invasive marine species and their environmental consequences. (c) To relate geological concepts to marine phenomena. (d) To apply laws of mathematics, physics, and chemistry to understanding the marine environment. (e) To understand how information about the marine environment that they learnt in schools applies to their daily life. (f) To analyse literary works related to the marine environment. (g) To discuss and compare information about each topic involved in the game. (h) To produce a wide variety of creative works focused on the marine environment. We designed the game based on three main questions that need to be taken into account in educational game design [67]: (1) What are the learning objectives. (2) What materials are needed to reach the learning objectives (i.e., what are the learning contents). (3) How can students learn while playing the game (i.e., what is the learning methodology). To answer to these questions, we trialled the game in different places in Asturias, a coastal region in Northern Spain. People from formal, non-formal, and informal educational contexts, and between the ages of 7 and 72, took part in these trial game play sessions with satisfactory knowledge acquirement results.

#### **2. Materials and Methods**

#### *2.1. Game Materials*

'The Game of the Sea' is a dice-based game inspired by the popular 'Trivia' game model (Figure 1). Playing materials have been specifically designed by authors for this educational purpose. Learning objectives, learning contents, and learning methodology were previously defined and taking into account before designing the game. Learning objectives were enumerated in a list and materials were designed accordingly to reach all of them. Once the goals were defined, learning contents and learning methodology were designed to meet the games learning goals and objectives (listed earlier). The game included elements of physics, biology, mathematics, geology, chemistry, and literature in an interdisciplinary approach, in which different disciplines are used together to improve overall understanding. The game was registered in Spain under the copyright reference 05/2017/329.

'The Game of the Sea' consists of a board on which is printed a fish shape (another marine related shape—an octopus, star fish, or a whale, for instance—could be used instead), divided into 68 sections coloured blue, yellow, red, or green. There is also one additional section where all the individual team pieces are placed, at the start of the game. Inside the shape are four rectangles (blue, yellow, red, and green) on which cards of matching colour are placed.

**Figure 1.** Playing materials needed to play 'The Game of the Sea': game board, question cards, dice, player's pieces, scoreboards, and circular stickers.

The cards (*n* = 80) are the learning content of this game and contain a variety of simple activities (e.g., multiple-choice questions, problem solving, filling gaps, comparing photographs, etc.) to maintain the players' interest. These cards were carefully designed to be easily readable and comprehensible, and are coloured based on which part of the European educational syllabuses they aimed to teach about:


Additionally, required to play the game are one dice, game pieces, scoreboards, and circular stickers. Game pieces (e.g., seashells, painted in different colours) are used to represent each player or team moving along the board. Scoreboards are in the shape of a wave formed by several circles. Each time a player scores a point they place a sticker in one of the circles of the wave score board.

#### *2.2. Rules of Play*

The most dynamic option to play 'The Game of the Sea' is in small groups of two to six players, although the game can be also played individually. The first step is to make teams and get a scoreboard and a game piece per team. Each team puts their piece in the initial square. Then, a player from each team rolls the die. The team with the highest number starts playing by moving their piece as many squares as the number on the die indicates.

Next, one member of the team takes a card of the same colour as the colour of the section their piece lands on. The text on the card should be read aloud, clearly, ensuring the rest of the players (even those from other teams), can understand what is read. In this way, if the first team does not complete the activity on the card, other teams have the opportunity to do so and get extra points.

Players have five seconds to answer the question or complete the activity on the card. This ensures the game has good rhythm and helps players follow it easily. If extra time is allowed (for another kind of activities, such us scientific experiments), this is indicated on the card. Regarding those cards that contain scientific experiments, the team should first choose an answer and then carry out the experiment to test this. When a team scores, they get a sticker to complete the wave printed in their scoreboard. The game will finish when a team succeeds in completing the wave with all stickers.

As a recommendation, the game should have a moderator. This person can not only explain and enforce rules and game timing [58], but also, as they know the solutions to the cards, provide deeper explanations of these and help players come up with solution. However, the moderator ought to allow participants to first try to explain card contents, and solutions, to their team players, before explaining these themselves. Moderators should also encourage collaborative learning and aim to ensure that there is more communication among teams than between the teams and themselves.

#### *2.3. Players*

Pilot studies of how the game could function (duration, audience, etc.) were carried out in two different samples: children from 7 to 15 years old during the educational event on marine environment 'Aula del Mar' and in 'El Pez Escorpión' surf school (both in Salinas, Asturias, Spain), and adults from 24 to 50 years old from the International Workshop ALERTOOLS (Avilés, Asturias, Spain). The principal aim of these pilot studies was to identify possible limitations regarding materials, contents, or procedures [68]. Furthermore, from the pilot study we identified six questions which were used to develop a test to assess the success of our game (see '2.6. Game assessment'). Game sessions in the pilot study and in later assessment lasted between one to one and a half hours, approximately (there was no set time restriction).

After the game was refined based on the pilot studies, two further samples were selected to assess the game as a didactic tool. We had one children sample and one adult sample, thus we could check the appropriateness of the game for different age groups. These samples were selected intentionally [69], according to the interest of instructors from each educational context that the samples came from. One of the samples 'children' (Table 1) was formed by 111 students, between 11–15 years old, from two high schools from Asturias (Spain): IES Escultor Juan de Villanueva (Pola de Siero-Asturias) and IES Salinas (Salinas-Asturias). The other sample 'adults' (Table 2) was composed of 111 people between 18 and 72 years old. These were either university students from Elementary Teaching Degree, High School Teaching Master of the University of Oviedo, who came from different locations, or adults who had enrolled in Lifelong Learning education programmes at the University of Oviedo (Evolution Club) who were from Oviedo and Avilés (Asturias). All participants (*n* = 222) had different educational backgrounds, thus enabling us to assess the effectiveness of this didactic tool on people with a variety of different academic levels and experiences. We tested the game six times in children and six times in adults, therefore we collected data from 12 game sessions in total.

**Table 1.** 'Children'. Sample formed by people between 11–15 years old.



**Table 2.** 'Adults'. Sample formed by people older than 18 years.

If the players were children, high school science teachers also took part in the sessions. Although they performed a secondary role during the gameplay sessions, their involvement was highly valuable because they could illustrate to their students how material on the game cards linked to their *curricula* contents.

#### *2.4. Ethics Statement*

This study adhered to the European Code of Conduct for Research Integrity. All players were informed that all data would be collected and used only for research, and gave informed consent for this. For children and teenagers under 18, their parents signed a participation permit, and their headmasters and teachers gave us permission to play the game for several sessions that fitted into their high school timetable. Adults from Elementary Teaching Degree, High School Teaching Master and Evolution Club, played the game as volunteers.

#### *2.5. Qualitative Analysis of the Game*

Participant observation was the qualitative research technique employed in different stages of 'The Game of the Sea' development. In particular, it had a relevant implication in those stages referred to test the game during the pilot study first, and its implementation with the sample selected after. This technique consists of the researchers being part of the observed situation. The researchers had access to the information about how phenomena took place, without interactions, in contrast to external observation processes. In this sense, information collected was more accurate than information collected through more obvious external observations [70–72], in which players may have felt scrutinized, would have been.

Researchers obtained qualitative data on the whole gameplay process of 'The Game of the Sea'. The researchers acting as the moderators collected this data by observing the participants as they played the game. They were subtle about doing so, helping players to relax and act naturally. The moderators noted the different ways that players perceived the questions and instructions on the cards and interacted with their peers to respond to these. By doing so, the moderators could not only determine whether game's contents and methodology enabled players to achieve the learning objectives of the game, but also whether collaborative learning took place. Participant observation provided an insight into the whole gameplay process. Data and information collected were registered through field notes.

The analysis of the whole process was focused on learning objectives, learning contents, and learning methodology. The participant observation technique yields interesting information regarding perception of the contents of the questions, and the own answer given to each question by players. Moreover, participant observation contributes to examine the internal team process to choose a response, and also the explanations, discussions, and reflections generated during the gameplay process.

#### *2.6. Game Assessment*

Based on our pilot studies, we created a brief test which, in later game play sessions, we gave to players before ('pre-test') and after ('post-test') playing 'The Game of the Sea' to verify if players achieved the learning objectives of the game and to evaluate if this game was an effective didactic tool.

The test consisted of six questions where the player chose what they thought was the correct answer from multiple options. Players could also indicate if they were unaware of the answer. The six questions related to three topics covered in the game: Biology, Physics, and Literature (Table 3). The test was checked by 10 people, before implementation as a game assessment tool, to ensure clarity and consistency between questions and answers. A time limit of five minutes was given, on both occasions, for the test. Players were not told about the post-test to avoid them attempting to memorise correct answers from the pre-test.


**Table 3.** Test used to assess the success of the Game of the Sea in teaching our learning objectives.

Q indicates a question. A–D are the potential answers the players can choose between. <sup>1</sup> The correct answer for each question is highlighted in bold style font.

Data was collected from the five questions Q1–Q5 on pre- and post- test, and results were coded and tabulated. Q6 was not included in the final study tests because no differences were found between tests on both pilot studies. Researchers found through their participant observation that Q6 did not provide any information, and answers were the same before and after the game. Responses to the tests (Q1–Q5) were classified into three groups: 'success' to cluster all correct answers, 'wrong' to group all wrong responses, and 'unaware' that represent all the 'I do not know' answers.

Descriptive analysis, percentages, frequencies, and statistical analyses were calculated with IBM SPSS Statistics programs to obtain a more complete understanding of this [73], and check whether the patterns we observed were mathematically supported. The nonparametric test 'Pearson chi-square of independence' was considered the most appropriate

to analyse frequencies from two independent samples [74]. This statistical test was used to determine whether the number of correct, and unaware answers differed between the preand post-tests. The analysis was first done on adults and children separately and then in adults and children combined. We used a significance threshold of *p* < 0.05.

Finally, the triangulation of the qualitative and quantitative methods employed was done. This research strategy provides an increment of the validity of data collected and could give a relevant interpretation of the information available [75].

#### **3. Results**

The game was played in 12 sessions, 6 sessions for each group. Every game session lasted approximately between an hour and an hour and a half. During gameplay sessions players, both age groups showed motivation, engagement, and enjoyment during and after the game.

#### *3.1. Qualitative Information*

#### 3.1.1. Learning Objectives of the Game

From observations made as moderators, we verified that all the questions and contents associated with each learning objective were addressed in each game session. Table 4 shows how the questions in the game related to the learning objectives, and classifies them according to the observed level of difficulty encountered by the players during the game sessions. Below, a description of how both samples (i.e., children and adults) performed during the game in terms of different learning objectives.


**Table 4.** How questions in the game related to learning objectives.

**Table 4.** *Cont*.


<sup>1</sup> The correct answer is highlighted in bold style font.

(a) To recognise organisms from marine ecosystems

Marine organisms were fascinating to most people playing the game, regardless of their age, although knowledge and understanding of these organisms varied considerably. For instance, sea sponges were easily identified as animals (Table 4; QA1) by both samples, whereas some players did not know which groups cetaceans, or seahorses, belonged to (Table 3, Q2; Table 4; QA2). This is despite sea sponges, cetaceans, and seahorses- all being common in the Asturian marine ecosystems. Children could explain to each other that cetaceans were mammals; however, the fact that seahorses were fish needed clarification from the moderator.

(b) To identify invasive marine species and their environmental consequences

There are plenty of invasive species in the Asturian region, thus we expected players to be aware of them. Players were aware that invasive species could be both plants and animals (Table 4, QB1). However, differentiating between a common non-invasive edible fish (*Scorpaena scrofa)* and an invasive non-edible one (*Trachinus draco*) was almost impossible for children. This was less difficult for adults (Table 4, QB2). In the children sample, group teachers and/or moderators provided explanations about the differences between both species. Within the adult sample, some people were able to identify the non-invasive species because they had seen it at the fishmongers. In fact, in one of the adults' game sessions, a retired fishmonger explained the characteristics of both species to the other players.

(c) To relate geological concepts to marine phenomena

Participants of all ages knew about the Cantabrian range, where Picos de Europa National Park is located, in Asturias. Most of the players were aware of the existence of marine fossils in these mountains (Table 4, QC1). However, only a few were able to link this sort of land formation with ocean ridges despite this being part of the school *curricula* (Table 4, QC2).

(d) To apply laws of Mathematics, Physics, and Chemistry to understanding the marine environment

Questions based on this learning objective were the most demanding for players in both samples. Of these, those the players found hardest were theoretical questions (e.g., Table 3, Q3) and some questions that involved scientific experiments (Table 4, QD2). Children did better than adults in some questions involving scientific experiments (Table 3, Q3; Table 4, QD1). Providing clear and accurate explanations, for these questions, for their peers was as challenging for children as it was for adults. So, moderators often needed to do this. In all cases, players were pleased to take part in experiments, under supervision, and were delighted with the results observed.

(e) To understand how information about the marine environment that they learnt in schools applies to their daily life

Players understanding of marine phenomena observed in daily life was sometimes less than expected. For example, both children and adults showed poor understanding of what causes tides (Table 4, QE1). Further, only one adult group (that contained a seaman) was able to calculate the timing of the tides (Table 4, QE2). This was despite that there are two high and two low tides and a difference of approximately six hours between a high and low tide is taught at the first level of High School.

(f) To analyse literary works related to marine environments

Players from both samples remembered a literary work featured in this game called 'The pirates' song', from their elementary education (Table 4, QF2). Despite experiencing positive emotions upon remembering this song, players still found it difficult to identify the name of the author and the title of the poem, and also to fill in gaps in its paragraphs. Players found information from more recent literary works easier to recall.

(g) To discuss and compare information about each topic involved in the game

Climate change and how this affects the Earth, in particular the oceans, was discussed by both children and adults. The question relating to how much of the surface of the Earth is covered by oceans was answered successfully in almost all cases (Table 4, QG1). This led several players to comment on the risks of ice melting and the subsequent rise in sea levels. Furthermore, both groups entered into discussions about invasive marine species. However, nobody was able to identify floating rubbish, or the use of vehicles (such us merchant ships), as vectors by which invasive species could enter the marine ecosystem (Table 4, QG2).

(h) To produce a wide variety of creative works focused on the marine environment

Team creativity was not evident in some groups (Table 4, QH2). We found that adults (especially women in their seventies) tended to be more creative and got more involved in creative activities than children. Nevertheless, all players enjoyed using pieces of newspaper to make boats, for instance. Although some children did not know how to do this, they were taught how by their peers.

#### 3.1.2. Collaborative Learning

Players communicated successfully with their peers, which led them acquiring knowledge from the game.

Initially, children were more likely to interact when there was a moderator present. However, as the session progressed peer interaction within the teams increased. This may have been due to the reward of extra points when team members could provide a correct answer to the question.

Adults performed somewhat differently to children. This is possibly due to their different academic and occupational backgrounds. A high level of peer interactions, both within and across the adult teams, was observed. In this case, moderators were only required to clarify concepts, keep the game moving along, or provide materials needed to solve questions.

#### *3.2. Game Assessment Tool*

Data collected from pre- and post-test is presented in Table 5. How the number of 'correct', 'unaware' and 'wrong' answers changed between the pre- and post-tests is analysed in the next section.


**Table 5.** Absolute frequencies of correct, wrong and unaware answers for the questions used in our game assessment test.

#### 3.2.1. Analyses of Correct Answers

Children only had one question in the pre-test (Q4), in which they had a frequency of correct answers higher than 50% (93 correct answers mean 83.78%; Table 4). In adults, the frequency of correct answers in the pre-test was higher than 50% for all questions, apart from Q3 (for which the frequency of correct answers was 38, it means 34.23%; Table 4).

In both age groups, the post-test mean frequency of correct answers was significantly higher than the pre-test mean frequency of correct answers (Table 6). Standard deviation was lower in the pre-test than in the post-test, for both samples, and, in both tests adults had more homogenous answers than children (Table 6).


**Table 6.** Descriptive statistics for frequency of correct answers in the pre-tests and post-tests.

Significant differences between pre-test and post-test in each subsample and within each question were detected. Children differences between pre-test and post-test were highly significant (Chi-square = 60.848, *p*-value = 0.000). Correct answers increased from less than 30% in the pre-test, to over 70% in the post-test (Table 7). In adults, Chisquare also yields significant differences between pre-test and post-test correct answers. (Chi-square = 15.711, *p*-value = 0.003). The increment between the pre- and post-test was from 39.6% to 60.4% (Table 7).

**Table 7.** Correct answers cross table: percentage (%) of correct answers within each question and whole tests.


CH: children; AD: adults.

The question on which both age groups achieved the highest scores in the post-test (and the highest increase in scores between pre- and post-tests) was Q3 (Table 7). There were also significant differences in the frequency of correct answers between the pre-tests and post-tests, for both age groups, for Q1 (Chi-square = 16.495, *p*-value = 0.000), Q2 (Chi-square = 10.483, *p*-value = 0.001), Q3 (Chi-square = 13.891, *p*-value = 0.000) and Q5 (Chi-square = 4.613, *p*-value = 0.032) but not for Q4 (Chi-square = 3.359, *p*-value = 0.067).

#### 3.2.2. Analyses of Unaware Answers

The frequency of unaware answers was significantly lower than the frequency of correct answers in general. Descriptive statistics (Table 8) show that unaware answers were more frequent in pre-test than in post-test and this pattern was more pronounced in children than in adults. First, children were more likely to give an unaware answer for each question compared to adults (Table 8). Second, children had a larger decrease in the number of unaware answers between pre- and post-tests than adults, this decrease was significant for children (Chi-square = 18.116, *p*-value = 0.001), but not for adults (Chi-square = 4.354, *p*-value = 0.360).

**Table 8.** Unaware answers descriptive statistics in each test and subsample.


Q1 and Q5 were the questions which both age groups were most likely to give an unaware answer to (Table 4). For Q4, the number of unaware answers increased between the pre- and post-tests, from one unaware answer in the pre-test to three unaware answers in the post-test (Table 4).

Overall, considering both samples together unaware answers decreased sharply between the pre- and post-tests (Table 9). However, there were significant differences in the

frequency of unaware answers between the pre-tests and post-tests, for both age groups, only for Q4 (Chi-square = 8.000, *p*-value = 0.005), but not for Q1 (Chi-square = 0.897, *p*-value = 0.343), Q2 (Chi-square = 0.204, *p*-value = 0.651), and Q5 (Chi-square = 2.674, *p*-value = 0.102).

**Table 9.** 'Unaware' answers cross table: percentage (%) of correct responses within each question and whole tests.


CH: children; AD: adults.

#### 3.2.3. Analyses Considering Each Topic Separately

Knowledge increase occurred in all the three topics covered by the test (Figure 2). Children's knowledge increased substantially in Biology and Physics, and they show considerably higher scores in the post-test, compared to the pre-test, in the literature. Adults showed a high and similar post-test percentage of correct answers regarding Physics questions compared to the children.

**Figure 2.** Knowledge (%) in the three main topics of 'The Game of the Sea': Biology, Physics, and Literature, comparing pre- and post- tests data of both studied samples (children and adults).

Unaware answers decreased in each age group and in each topic (Figure 3). The sharpest decrease in unaware answers, particularly in children, was in Biology. There was also a decrease in the number of unaware answers in terms of Literature questions. More adults gave unaware answers to Physics question in the pre-test compared to children, but were less likely to do so, compared to children, in the post-test. Overall, adults were less likely than children to give an unaware response in the whole post-test.

**Figure 3.** 'Unaware' percentage (%) in biology, physics), and literature in each subsample (children and adults), before and after playing 'The Game of the Sea'.

#### **4. Discussion and Conclusions**

'The Game of the Sea' gave players the opportunity to acquire knowledge on a wide range of topics related to the marine environment. Sometimes scientific communication is not clear and/or not accessible enough to citizens [76]. Board games can, therefore, play an important role in scientific communication by simplifying complex scientific concepts, or environmental issues, to make the salient points understandable to citizens [8,33,37,58]. As well as being educational, some of the cards used in our game appeared to be thoughtprovoking [77], creating much discussion among players, who were regularly surprised by their contents, and inspiring them to find out more about specific topics. Two of the most discussed topics were marine invasive species and the sea level rise.

Previous studies suggest that game-based learning (GBL) engages participants and significantly increases knowledge [18,78,79]. 'The Game of the Sea' supports these findings, further demonstrating that board games, and GBL in general, can be important in educational contexts. Game elements which were specifically designed for 'The Game of the Sea' (such as an overly sized die, seashells as playing pieces, or sticker points) made the game more enjoyable for players. This, in turn, made players more self-confident while playing [53], which contributed to them achieving the learning objectives of the game [52]. Different participants played the game with different attitudes, which often changed over the course of the game. At the start of the game, players often showed high levels of competitiveness towards each other, in each sample. It decreased as the game progressed and players increasingly worked together to find the right solutions. This working together attitude produced collaborative learning which certainly contributed to the game success in improving players' knowledge about marine ecosystems [35], and showed that this game could be an efficient didactic tool for both children and adults [80,81]. As well as fostering collaborative learning, the discussions and interactions that took place in the game, generated by the game cards fostered other important skills, such as critical thinking, scientific reasoning, decision making, problem solving, collaboration, and creativity.

As well as being a tool for teaching about the marine environment, 'The Game of The Sea' has other positives attributes. First, all the materials for the game are accessible on request, can be handmade, and can be replicated at a low cost (less than EUR 20). This makes 'The Game of the Sea' an easy to replicate and affordable, didactic tool, available to different educational levels and situations. Second, the cards used in this game are very versatile, allowing the contents of the game to be adapted for use in various situations, without modifying the format of the game. This, along with that the game is determined by how players interact, increases its unpredictability, making it more interesting.

Pre- and post-test questions were used to verify if players achieved the learning objectives of the game. What players got out of the game, in terms of knowledge acquisition, could have been influenced by their age and background (both academic and occupational). Although both age samples showed significant increases in the number of correct answers between pre-test and post-test results, this was more pronounced in children than in adults. A potential explanation for this is that all the information contained in the game cards is taught in official educational programs in Europe. Thus, adults would have finished their education on these topics while children may not have yet. Therefore, this game could be considered as a noteworthy didactic tool (in terms of knowledge acquisition) for an interdisciplinary approach of those scientific contents related to marine environment from the official *curricula* of Spanish Compulsory Elementary, Middle and High School Education.

Players did not necessarily find different questions on the same topics to be of similar difficulty. For example, children found Q4 (If we have two balloons, one with air and the other one with some water, and we heat them, which one will blow out first? R4: The balloon only with air) the easiest to answer in the pre-test, and adults found Q3 (Where does the speed of a sound go faster? R3: In the water) the hardest, despite both questions being Physics questions. One explanation for why players were much more likely to know the answer to Q4 than Q3 is that Q4 is more easily tested with an experiment than Q3. There was little increase in the number of correct answers in Q4 between pre- and post-tests (most players got it right both times), which suggests that players may have already seen this experiment, or a similar one, prior to playing the game. When children and adults were considered together, Q3 showed the greatest increase in the number of correct answers between pre- and post-test. Peer interaction contributed to this, Q3 was, overall, one of the most clarified questions. In general, the discussions which took place during gameplay among players and with moderators, allowed for clarification of misconceptions, thus enabling players to successfully reach the learning objectives of the game [39].

Through playing 'The Game of the Sea' players improved their interdisciplinary knowledge on the marine environment and critical situations facing this environment. Thus, the game achieved its 3 main goals: (1) To enable students to achieve learning objectives (based on the official *curricula* of Spanish Compulsory High School Education) in terms of learning about the marine environment. (2) To foster collaborative learning, regardless of age or educational background. (3) To raise awareness about critical situations regarding our marine environment, and the need to preserve this environment. Achieving this third goal was especially important. Nowadays, policies to protect the marine ecosystems are not well enforced/often overlooked [82], and politicians and lawmakers appear to have little concern for the marine environment. Thus, marine ecosystems increasingly rely on the general public to help protect and preserve them. Consequently, raising public awareness of the situations our marine environments face (e.g., through board games, which can simultaneously educate and entertain people from many walks of life [63]) can positively contribute to achieving marine conservation objectives [83,84]. In this study 'The Game of the Sea', was shown to facilitate learning [13] about the marine ecosystems, thus enhancing awareness, in all ages, of the importance of preserving this environment.

#### **5. Patents**

'The Game of the Sea' has been registered at Intellectual Property Registry of the Principality of Asturias in Spain with the copyright reference 05/2017/329.

**Author Contributions:** Conceptualization, E.A.-G. and L.M.; methodology, E.A.-G. and L.M.; validation, E.A.-G. and L.M.; formal analysis, E.A.-G.; investigation, E.A.-G.; resources, E.A.-G.; data curation, E.A.-G.; writing—original draft preparation, E.A.-G.; writing—review and editing, E.A.-G. and L.M.; supervision, L.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki. The protocol was approved by the high schools IES Escultor Juan de Villanueva and IES Salinas, and the University of Oviedo where the research took place.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors acknowledge 'Surf, Music & Friends Festival' and the surf school 'El Pez Escorpión', in Salinas (Asturias, Spain) the opportunity to play and test the game as a pilot study therein. It was also played in ALERTOOLS International Workshop. We have collected data thanks to the interest in the game of teachers and students from IES Escultor Juan de Villanueva and IES Salinas; students from Elementary Teaching Degree, High School Teaching Master of the University of Oviedo, and participants in Evolution Club of University of Oviedo. This research is part of Elena Arboleya García thesis from PhD Programme in Education and Psychology. Laura Miralles holds a Torres Quevedo grant from the Government of Spain (PTQ2018-010019).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Similarities in Procedures Used to Solve Mathematical Problems and Video Games**

**Juan Antonio Antequera-Barroso 1,\*, Francisco-Ignacio Revuelta-Domínguez <sup>2</sup> and Jorge Guerra Antequera <sup>2</sup>**


**Abstract:** Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality. We took advantage of this recreational aspect of video games when investigating whether there are similarities between the procedures used to pass a video game level and those used to solve a mathematical problem. Moreover, we also questioned whether the use of video games can reduce the negative emotions generated by mathematical problems and logical–mathematical knowledge in general. To verify this, we used the Portal 2 video game as a research method or tool. This video game features concepts from the spatial– geometric field that the students must identify and relate in order to carry out the procedures required to solve challenges in each level. The procedures were recorded in a questionnaire that was separated into two blocks of content in order to compare them with the procedures used to solve mathematical problems. The first block pertains to the procedures employed and the second block to the emotions that the students experienced when playing the video game and when solving a mathematical problem. The results reveal that the recreational aspect of video games is more important than the educational aspect. However, the students were not aware of using the problem-solving procedures they learned at school to solve different challenges in the video games. Furthermore, overcoming video game challenges stimulates positive emotions as opposed to the negative emotions generated when solving mathematical problems.

**Keywords:** mathematical problem-solving; video games; emotions; Portal 2

## **1. Introduction**

Current technological developments emerge in all social, cultural, and educational contexts. Among these developments, digital whiteboards or didactic software are examples of applications and hardware designed for the educational context. However, there are also digital elements that, despite not being designed for the teaching–learning process, have been used for this purpose. In light of this, video games could be considered based on the same essence as traditional games. McGonigal [1] states that a video game must be based on the premise of overcoming a challenge and being motivated to do so. Therefore, when interacting with these recreational applications, the individual must: (a) analyse the challenge that appears before them and determine what its purpose is; (b) analyse which elements in the game represent support (power-ups) or which elements are negative (enemies, traps, or penalties); (c) discover how to progress or gain experience; (d) consider action sequences by trial-and-error exercises; and (e) put decision-making skills into practice [2]. A careful analysis of the previously mentioned skills reveals that they are similar to those used in problem-solving.

**Citation:** Antequera-Barroso, J.A.; Revuelta-Domínguez, F.-I.; Guerra Antequera, J. Similarities in Procedures Used to Solve Mathematical Problems and Video Games. *Educ. Sci.* **2022**, *12*, 172. https://doi.org/10.3390/ educsci12030172

Academic Editor: José Carlos Piñero Charlo

Received: 27 December 2021 Accepted: 26 February 2022 Published: 1 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Based on this, problem-solving is one of the most relevant areas in logical–mathematical knowledge. In fact, problem-solving can be applied to the field of mathematics as well as to aspects of daily life: when people encounter situations that require a solution in their daily lives, they unconsciously apply the problem-solving method they learned in school. In this manner, mathematical competence is developed through problem-solving exercises. According to Gorgorió and Albarracín [3]:

*Mathematical competence is the ability to use mathematical knowledge in a cross-cutting manner in mathematical and non-mathematical situations and contexts. Mathematical competence goes beyond procedural knowledge; it is manifested in the use of conceptual knowledge in different practical situations.*

#### (pp. 116–117)

In view of this definition of mathematical competence, it could be stated that video games are included in these non-mathematical contexts. However, the question would be whether video games can be used in mathematical contexts, such as classrooms, during mathematics or science classes. According to the literature on this topic, the answer is yes. Various studies describe the use of these elements in the classroom—for example, using the Angry Birds video game to develop mathematical knowledge [4–6] or physical knowledge [7–11].

#### *1.1. Problem-Solving*

Problem-solving could be considered one of the most important curricular activities in all the stages of a country's educational system. Analysing the current legislation, one can see that, in all cases, problem-solving is oriented towards problems in children's daily lives. Focusing on Spain (whose legislation stipulates that problem-solving be present from the earliest stages of education), self-confidence, the capacity for initiative, and problemsolving are developed from early childhood education onwards [12]. In primary education, problem-solving competencies are also developed within the field of mathematics, together with others, such as reading, reflection, planning processes, establishing resolution strategies, and designing and evaluating procedures [13]. In both stages, problem-solving is based on the development of different skills that allow students to address the situation and/or problem while developing skills related to personal development, personal autonomy, confidence, and motivation to overcome situations in their daily lives.

The logical–mathematical skills to be developed are established sequentially through a series of phases. As a result of these phases, a methodology for solving mathematical problems that is applicable to any situation is established. One of the most well-described and frequently used methodologies is that of Polya [14], which outlines four phases to pose and solve a problem through a series of questions set out in a method (Table 1).


**Table 1.** Polya's problem-solving phases.

Source: own elaboration based on Polya [14].

Mason, Burton, and Stacey [15] described another method of phased problem-solving, which is divided into three phases—entry, attack, and review. As with the previous method, in each of its phases, a series of questions are posed that allow the individual to progress (Table 2).


**Table 2.** Summary of Mason, Burton, and Stacey's problem-solving phases.

Source: own elaboration based on Mason et al. [15].

Within the description of the method presented by Mason et al. [15], as well as the phases, there are processes such as specialising—typical of the entry and attack phases—and generalising—typical of the attack and review phases. The method introduces the concepts of STUCK! and AHA!—concepts related to the manner of dealing with problem-solving and the learning possibilities that can be extracted from solving the problem.

Being in the STUCK! phase leads to many cases of frustration and a lack of motivation to move forward. Recent studies [16] introduce a new phase in problem-solving methods, in which the identification and control of emotions that arise when solving a problem play an important role. Di Leo et al. [17] indicate that the main emotions that students experience when solving a mathematical problem are frustration and confusion, which are negative emotions. Managing negative emotions, such as confusion, can lead to positive emotions that help with solving the problem. According to Caballero, Blanco, and Guerrero [18], it is necessary to introduce emotional aspects as well as cognitive aspects in mathematical problem-solving. By doing so, we can develop techniques, such as relaxation or breathing techniques, that allow us to transform negative emotions, such as anxiety, into positive emotions. Hannin and Nieuwenhoven [19] found a reduction in negative emotions in students who had developed cognitive and emotional aspects versus those who had only received training in problem-solving, although the cognitive levels were equivalent. Therefore, it is necessary to take into account cognitive and emotional changes as a whole, rather than individually, to understand students' performance when solving mathematical problems [20]. These changes move students from the STUCK! phase to the AHA! phase.

#### *1.2. Video Games for Problem-Solving*

A series of logical–mathematical skills are employed when solving a mathematical problem. These skills can be used to overcome the challenges posed by the different phases of a video game, thus providing a number of opportunities to put mathematical knowledge into practice [21]. Among these skills are observing the elements of the screen or level, differentiating useful elements or accessories, designing strategies, and anticipating results from the objects [22–24]. Visuospatial and spatial–geographical skills are also required to interpret plans or areas of the screen. As such, video games provide an opportunity to develop mathematical logic and to establish processes of observation, relation, and operation or transformation.

#### *1.3. Research Questions and Objectives*

Considering the relationship that exists between the use of video games and logical– mathematical knowledge, we have posed the following research questions and their corresponding objectives.

Research Question 1. Are the procedures that students use to pass a level in a video game and to solve a mathematical problem comparable?

Objective 1. To verify if the mathematical problem-solving procedures used by students are similar to those they use to pass a level of a video game.

Research Question 2. Do students experience similar feelings when passing a level in a video game and solving a mathematical problem?

Objective 2. To compare the feelings that students experience while playing a video game with those they experience when solving a mathematical problem.

Based on the previous paragraphs, the aim of this study is to discover whether the procedures used to complete video game levels are similar to those used in problem-solving, and to compare whether there are any similarities between the main characteristics of a video game and the characteristics of a mathematical problem. Furthermore, we also aim to observe the emotions students experience when playing video games and compare them with the emotions they experience when solving a mathematical problem.

#### **2. Materials and Methods**

#### *2.1. Population and Sample*

This study was carried out at the University of Cadiz, in the Faculty of Education Sciences. The participants were 170 trainee teachers taking the subject "Mathematical Knowledge in Early Childhood Education" of the bachelor's degree in early childhood education (*n* = 170). We chose to select students taking this subject because it involves developing the first of the three pillars that constitute didactics—that is, logical–mathematical knowledge, in which they develop their own discourse on the construction of this knowledge.

#### *2.2. Method*

In order to answer the research questions posed, we decided to use a video game that we know as a research method or tool. We chose the Portal 2 video game, developed by the Valve Corporation, to work on problem-solving with our students. We chose this video game because we were aware of its potential to impart logical–mathematical and spatial–geometric knowledge, which allows students to improve visuospatial competence, and, therefore, to identify shapes or objects that appear in the scene. By looking for the relationship between the shapes and objects that appear on the screen, students obtain information and develop a strategy to pass the level. Portal 2 is a platform/action game with puzzles that appear in the form of a series of riddles on the walls and objects to solve in order to pass to the next level. Hence, we considered it an interesting option to compare the students' perception of both the video game and solving a mathematical problem, in accordance with Shute et al. [25,26] and Avry et al. [27].

Chorianopoulos and Giannakos [28] highlight the existence of four basic principles in video games that relate them to mathematical knowledge. The following table (Table 3) shows the principles and their relationship with the chosen video game, Portal 2, and mathematical problem-solving.


**Table 3.** Relationship between the basic principles of video games and problem-solving.

Source: own elaboration based on the principles of Ref. [28].

Once the video game had been selected, the students were given a brief presentation on the video game, its context, how to install it, its controls, and the instructions in order to carry out the task correctly. Then, the class was divided into groups of four or five students, and the furniture was rearranged so that the students could work collaboratively. This facilitated both the development of the activity individually and, at a later stage, the sharing of findings and the discussion of relevant questions or doubts that the students had encountered during the activity. This configuration was chosen because group work favours dialogue, critical reflection, and sharing ideas through negotiation. It also allows the teacher to intervene as a dialogue guide or advisor, sharing reflections or doubts with the students and enriching the activity and its result.

The implementation of the task was divided into three parts. The first part consisted of a period of individual free play so that the students could set up the controls to their liking and get used to the dynamics of the game in the first levels, which had a tutorial function. Once the students understood the dynamics of the game, the second part of the task focused on passing the different levels by looking for the procedures required to solve them. At this part, a dialogue was established on various occasions between the students as doubts arose about how to solve the puzzles, the clues, or the handling of the main character. The third part was carried out as a way of closing the activity. At this stage, the students completed a questionnaire that was divided into different blocks. In the first block, descriptive data were collected, such as sex, age, previous studies, if they were a video game player, and the number of hours they spent playing video games. In the second block, they were asked to describe the procedure they followed to pass the different levels. They were asked to describe, step by step, what they had done, what they had looked at, and what decisions they had made in order to solve the problem. In another session, the answers given were analysed and compared with the problem-solving models of Polya and Mason et al., providing an opportunity for the students to analyse and reflect on their findings as a group. Finally, in the last block, they had to express their impressions, feelings, or emotions regarding working with logical–mathematical knowledge in this way. In order to do so, they used a Likert scale and recorded their degree of agreement or disagreement with the statements shown. The statements used in the questionnaire were written according to both the opinions expressed by the students and the objectives set out in this task. The students were also asked to include a brief comment justifying their answer to each of the statements in the questionnaire. Table 4, with the distribution of the work during the various sessions conducted, is presented below.


#### **Table 4.** Timetable of sessions.

Source: own elaboration.

#### *2.3. Instruments*

The instrument used was a questionnaire prepared for the study with blocks relating to descriptive data, video game consumption and typology, general knowledge about video games, questions about the activity carried out, and the didactic possibilities of Portal 2 (Figure 1).


**Figure 1.** Screenshot of the questionnaire (bit.ly/2Z08sbd). (Late date of access: 28 January 2022).

Questionnaire: Teach with Portals: This questionnaire has been designed for the students of the bachelor's degree in early childhood education at the University of Cadiz in order to analyse their experience of using logical –mathematical knowledge when playing the Portal 2 video game.

#### *2.4. Data Analysis*

Data collection was carried out following a mixed methodology approach—both quantitative and qualitative—in order to observe the data and thus gain a better understanding of the usefulness of the activity from different perspectives, as indicated by Creswell [29] (p. 18). Qualitative aspects were employed when analysing the problem-solving phases used by the students to pass the levels and comparing them with those indicated by Polya [14] and Mason, Burton, and Stacey [15]. Quantitative aspects were employed when analysing the students' emotions or feelings towards this logical–mathematical knowledge. Employing both analyses allowed us to provide more in-depth answers to the research questions posed and to fulfil the objectives of this study. Furthermore, to show the validity or internal consistency of our analysis, we carried out a study of the correlations between the different answers our students gave to the statements shown in the third block of the questionnaire. In order to do so, the statistical software Jamovi v.1.8.4 was used.

#### **3. Results and Discussion**

The distribution of students by sex shows that the majority of our students were women, 95%, and the rest were men. In terms of their ages, they were between 19 and 24 years old, although there was one 50-year-old student (Table 5).


**Table 5.** Distribution of the students in the 2nd year of the bachelor's degree in early childhood education by sex.

Source: own elaboration.

One of the questions the students responded to in the questionnaire was related to what Novak and Tassell [30]—citing Stevens and Bavelier (2012)—indicate regarding whether video game players of action games exhibit greater memory, spatial, and geometric skills than non-video game players. These players focus their attention on relevant facts or data and ignore irrelevant information, which is a characteristic that is important when solving mathematical problems. Novak and Tassell [30] also indicate that players improve this characteristic after several hours of gameplay regardless of whether or not the game is an action one. In the case of this study, 46 individuals considered themselves to be video game players. The rest either did not define themselves or did not consider themselves to be video game players because they did not have an established playing routine (Table 6).

**Table 6.** Distribution of the students in the 2nd year of the bachelor's degree in early childhood education according to whether or not they consider themselves to be video game players.


Source: own elaboration.

In light of this response, one might think that students have the logical–mathematical skills to solve the challenges or problems posed, as Novak and Tassell [30] commented. In the second block of the questionnaire, the students had to reflect on the procedures they followed to pass different levels of the Portal 2 video game. Considering the procedures described by the students, we were able to distinguish or codify three types of players. The first type of player (J1) passes the levels without difficulty, with (J11) or without (J12) requiring external help. The second type of player (J2) is stuck because of not being able to find the clues. This type of player is further divided into two types—those who managed to continue the game despite being stuck (J21) and those who required some kind of help to continue playing (J22). Finally, there are those players who declined to continue playing regardless of whether they refused to continue without help (J31) or with help (J32).

Below are the answers given by our students, Tables 7–12, analysed from the point of view of the two problem-solving models.

**Table 7.** Procedures followed by students to pass the level following Polya's model (1989).


Source: own elaboration.

**Table 8.** Procedures followed by students to pass the level following the model of Mason et al. (1992).


Source: own elaboration.

**Table 9.** Procedures followed by students to pass the level following Polya's model (1989).


Source: own elaboration.

**Table 10.** Procedures followed by students to pass the level following the model of Mason et al. (1992).


**Table 11.** Procedures followed by students to pass the level following Polya's model (1989).


Source: own elaboration.

**Table 12.** Procedures followed by students to pass the level following the model of Mason et al. (1992).


Source: own elaboration.

*3.1. J11-Type Player. Player Who Does Not Need External Help to Pass a Level*

The section below shows the J11- type player, the one who does not need external help to pass a level.

#### *3.2. J21-Type Player. Player Who Is Stuck but Passes the Level without External Help*

The section below shows the J21- Type Player, the one who despite being stuck, manages to pass the level without external help.

Two concepts described by Mason et al. [15] appear in this type of player: STUCK! when they start going around in circles opening portals following themselves, and AHA! when they return to solving the problem after getting lost between portals.

#### *3.3. J31-Type Player. Player Who Gets Stuck on a Level and Does Not Continue*

The section below presents the J31 type player, the one gets stuck on a level and doesn't continue.

Responses from the types of students who needed help (J12, J22, or J32) or who relied on their peers to advance in the video game have not been included. The answers they offered were very similar to those presented in Tables 7–12, except for the fact that they indicated they required help from their classmates in order to continue to advance in the video game.

Furthermore, by analysing the students' answers in Tables 7–12, we can see not only how the answers conform to the different phases described by Polya [14] and Mason et al. [15] but also how aspects related to mathematical problems appear, such as the statement of the problem, the data that appear, the unknown data, and the possible procedures to link the known and the unknown in order to pass the level, i.e., to overcome the challenge posed. These aspects are in line with the principles indicated by Chorianopoulos and Giannakos [28] that link video games and problem-solving. In the last block of the questionnaire, the students were given a series of statements where they were asked to indicate their degree of agreement (1 = Strongly disagree, 2 = Somewhat disagree, 3 = Somewhat agree, and 4 = Strongly agree) after having played and passed the different levels. The first statements were related to their feelings or emotions towards mathematical knowledge. The following statements were related to the video game and its use with respect to the resolution of mathematical problems. Finally, there were statements related to the emotions experienced during the activity.

The first statement (S1) they had to respond to was: 'Everything related to mathematical knowledge makes me feel overwhelmed or stressed'. Figure 2 shows that the majority of our students responded 'Strongly agree' to the statement (3.71 ± 0.25). This result was linked to the second statement (S2): 'When I do a task that involves mathematical knowledge, I feel nervous or afraid'. The percentages were very similar in both statements. Figure 3 shows that, once again, the students responded 'Strongly agree' (3.81 ± 0.26) to the statement about negative feelings that arise when solving any task involving mathematical knowledge. These behaviours, as Gómez-Chacón [31] indicates—citing different authors are due to two fundamental aspects: beliefs and emotions; indicating that an important factor is how students learn and use mathematics, or how they see themselves as learners.

**Figure 2.** Students' degree of agreement with the stress or distress that mathematical knowledge causes them.

**Figure 3.** Students' degree of agreement with their negative feelings when carrying out a mathematical task.

The following statements from the questionnaire were related to the video game itself and its relation to problem-solving. The first statement (S3) was: 'To pass a level of the video game, I must apply the same phases as in problem-solving'. In this case, the students answered mostly 'Somewhat disagree' or 'Somewhat agree' (2.61 ± 0.17), as can be seen in Figure 4. The students indicated that the main aspect they saw in video games was the recreational aspect or that of diverting from reality, and that they did not think about whether or not the procedures were mathematical when passing a level. The procedures they used were those they knew to be effective in passing the level regardless of the type of game they were playing.

**Figure 4.** Students' degree of agreement with the use of problem-solving procedures to pass to the next level in a video game.

The fourth statement (S4) was: 'There is a relationship between the situation presented in the video game and solving mathematical problems'. The answers given by the students (Figure 5) show that they do not believe that there is a relationship between playing video games and solving mathematical problems. The students mostly disagreed with the statement, with the most popular response being 'Somewhat disagree' (2.08 ± 0.18). Similar to their answer to the previous statement, they justified this by saying that they viewed video games as a distraction to be used for recreational purposes rather than educational purposes. Few students found or justified relationships such as those shown by Chorianopoulos and Giannakos [28]. The students recognised that a problem arose that they had to solve, but it did not correspond to the type of problems they are used to solving in the different educational stages they have gone through.

**Figure 5.** Students' degree of agreement with the comparison of the situations posed in a level of the video game with the situations posed in a mathematical problem.

The final statements that were put forward concerned the emotions or feelings that the students experienced during the game and compared them with those they experienced when solving a mathematical problem. The first of the statements (S5) was related to their emotional state when playing the video game: 'I felt good when playing the video game'. The majority answered 'Somewhat agree' (2.74 ± 0.17), as can be seen in Figure 6. Most of our students found playing the video game to be a pleasant experience that broke from the usual routine of the class. Once again, they highlighted that the recreational aspect of the video game lacked the pressure that accompanies regular classroom activities. However, there was a small number of students that responded 'Strongly disagree' to the statement. These students argued that they did not understand the game, that they got disoriented, that they did not manage to pass the level, and that, when they did, it was with the help of their classmates. The argument regarding the disorientation caused by the video game was also put forward by those who answered 'Somewhat disagree' as they felt it was easy to get lost and slightly difficult to refocus on the game.

**Figure 6.** Students' degree of agreement with the emotions experienced when playing the video game.

The last statement (S6) was: 'The emotions I have experienced while playing the video game are the same as those I experience when solving a mathematical problem'. The students mostly disagreed with the statement (1.99 ± 0.19)—which was expected given their responses to the previous statement on the comparison of mathematical problemsolving and passing a level of the video game, as can be seen in Figure 7. Once again, the recreational aspect took precedence over the educational aspect. The students believed that the stress they suffered when carrying out any mathematical activity was not comparable to playing a video game.

**Figure 7.** Students' degree of agreement with the comparison of emotions when playing a video game and when solving a mathematical problem.

Based on the data obtained from the Likert scale for each of the statements, we carried out a correlation analysis on the different statements, shown in Figures 2–7. As can be seen in Figure 8, the correlation between statements 1 (S1) and 2 (S2) shows a strong Pearson's correlation coefficient (0.81, *p* < 0.001), indicating that the students' negative feelings towards mathematical knowledge are transferred to any task that involves the use of such knowledge. This result could be justified by students' opinions such as "I am not good at mathematics" or "I do not like mathematics". Focusing on the second block of statements related to the use of video games and their relationship to problem-solving (S3 and S4), we also observe a strong Pearson's correlation coefficient (0.80, *p* < 0.001). Although both statements S3 and S4 relate video games and problem-solving procedures, when relating them to statements S1 and S2 from the previous block, we discovered that the relationship is no longer direct; instead, we observed an inverse relationship with a negative Pearson's correlation coefficient (S1 with S3, r2 = −0.36, *p* < 0.001; S1 with S4, r2 = −0.40, *p* < 0.001; S2 with S3, r2 = −0.48, *p* < 0.001, and S2 with S4, r2 = −0.50). As indicated above, the students mainly consider video games to be something fun, separate from mathematics, whose recreational aspect takes precedence over other aspects. Analysing the answers given to the last two statements (S5 and S6), we see that S5 shows a good correlation with S3 (0.55, *p* < 0.001) and with S4 (0.56, *p* < 0.001). This exhibits a direct relationship, as would be expected, since the recreational aspect of video games takes precedence over any other aspect, hence the positive emotions they elicit. However, when comparing S5 with S1 (−0.30, *p* < 0.001) and S2 (−0.35, *p* < 0.001), we see that there is an inverse relationship as the emotions related to mathematical knowledge are negative, while those related to the use of video games are positive, with the recreational and relaxing aspects of video games taking precedence. Statement 6 (S6), however, exhibits differences to all the previous statements. It presents very weak correlation values with a significance (*p*-value) greater than 0.1. This could be due to the fact that emotions are highly conditioned by the type of video game chosen and by the interests of the students themselves when playing a video game. Video game choice preferences manifest themselves as more complex relations, according to Ref. [32], and even vary from one time period to another [33]. The possible impact on video game players, their benefits, or their effects on behaviour and emotions must also be considered, as indicated by Ref. [34].


**Figure 8.** Correlation matrix and heat map shown in the statements (S1 to S6) shown to students.

#### **4. Conclusions**

Since they became a recreational–cultural element, video games have had a strong presence in people's daily lives. This means that video games can be used as a medium through which to build didactic experiences, or to be implemented as support tools in the classroom in order to generate learning. Although they were not conceived as a curricular tool, they can be used as a didactic element following a previous treatment and adaptation with respect to the teaching–learning process in which they will be employed.

The objective set out in this study involved aiming to take advantage of the potential provided by video games when analysing whether the techniques or procedures used to overcome a level in a video game are analogous to those used to solve a mathematical problem. We also aimed to analyse whether the situations posed by a video game can be equivalent to those described in a mathematical problem. Based on the results obtained in the answers given by our students, we can state that the students were not sure whether or not they were really using such procedures or whether they are comparable situations. That is, the students were not able to determine their applicability and theoretical transposition to a virtual context and vice versa. However, when describing the procedures they used to pass a level, they conformed to the procedures learned at school. They described in detail each of the phases they went through, which are equivalent to those described for problem-solving in the methods of both Polya [14] and Mason et al. [15]. These seemingly contradictory results lead us to believe that video games are perceived in a purely recreational sense, but the students were not able to discern their didactic potential. Moreover, from their answers, we observed that the feeling of stress or fear that any activity related to mathematical knowledge produces is still present during the problem-solving process.

Our second objective was related to the emotions that students experience when playing a video game and when solving a mathematical problem. We found that, in particular, the Portal 2 video game elicits mixed feelings. We found that there were students who had been challenged, which led them to become more involved in passing the levels despite the different tests and perspectives presented by the video game. That is, it provided extra motivation when facing the proposed challenge. However, other students stated that the movement through the levels of the video game—with recurrent changes of perspective—seemed quite complex to them as they were unable to orient themselves and even felt disoriented.

In conclusion, we can state that the procedures for solving mathematical problems and for passing a level in a video game are the same. However, unlike mathematical activities—which cause students to experience negative feelings—video games promote positive emotions. Video games are considered to be recreational, relaxing, and can provide a means of diverting from academic aspects as they are unrelated to the mathematical knowledge that causes students so much stress or feelings of fear.

The world of video games allows us to take advantage of all their potential for educational purposes by orienting them to work on knowledge that—despite being part of students' lives—causes them stress and uncertainty when using traditional methodologies and tools. For future lines of research, we could implement the use of video games as a tool to facilitate knowledge by creating a gamified environment in the classroom, as indicated in Ref. [35], in such a way as to encourage students' commitment and motivation towards mathematical knowledge.

Similarly, taking advantage of video games as a tool for working on logical–mathematical knowledge, we could gain a deeper understanding of the emotions that students experience when faced with logical–mathematical knowledge and whether the use of the video games modifies these feelings.

**Author Contributions:** All authors participated in the theoretical framework, data collection and analysis, and discussion. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Informed consent was obtained from all subjects involved in the study.

**Informed Consent Statement:** All students agreed to participate at the beginning of the research.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available at the participants' requests.

**Acknowledgments:** To the students of the 2nd year of the Early Childhood Education Degree at the University of Cadiz, Spain. Academic year 18/19.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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