Abstract
Background
Problem-solving and collaboration occur frequently in serious games. They are also considered necessary skills for students to learn, so many engineering and computer science programs design assignments with them in mind. Understanding the similarities and differences between each scenario would strengthen problem-solving interventions aimed at students.
Aim
This qualitative study examined how engineering and computer science undergraduates (students) and players of Magic: The Gathering (gamers) identified a problem as being complex, used the inquiry cycle for problem-solving, and engaged in proximal processes.
Method
Undergraduates in engineering or computer science and players of Magic: The Gathering’s Elder Dragon Highlander format completed an online questionnaire where they described how they solved a complex problem and how they engaged with others (or why they chose not to engage with others) during each part of the process. Responses were grouped by role (gamer or student) and by gender then coded to identify where each was alike and where they differed.
Results
Gamers and students engaged in the problem-solving process differently, with gamers using more of the inquiry cycle than students did. Proximal processes, however, were used differently based on both group and gender, with female gamers engaging in them most often and female engineers least often.
James Gee argues that serious games are natural environments for both problem-solving scenarios and collaboration. In serious games, players interact with other players, non-player characters, and members of affinity spaces in order to improve their problem-solving capabilities and to share in each other’s achievements (Gee, 2007). In education, communication and collaboration along with problem solving are now considered skills students should learn (e.g., ISTE, 2016), yet the purpose of education is often different than that of games.
This study questioned thirty-four young adults who were either engineering / computer science students (students) or players of the Elder Dragon Highlander variation of Magic: the Gathering (Wizards of the Coast, 2016) (gamers) to understand the similarities and differences in how they collaborate and communicate when solving a complex problem. Complex problems, for this study, are defined as problems which have multiple approaches and multiple solutions. The students were asked to recall a complex problem they had to solve for class and the gamers were asked to recall the last time they built a deck for competitive play. They were each asked questions about the problem-solving process and who, if anyone, they worked with during each stage of the process. Specifically, this study sought to answer: • What similarities and differences exist in the problem solving process between engineering and computer science undergraduates and similarly-aged people who play the Elder Dragon Highlander variation of Magic: the Gathering? • What similarities and differences exist in the proximal process during problem solving between engineering and computer science undergraduates and similarly-aged people who play the Elder Dragon Highlander variation of Magic: the Gathering?
Background
Proximal processes
The interactions between a person and the people, objects, and symbols in their immediate environment over time are known as proximal processes, from which human development, including the development of problem-solving skills, occurs (Bronfenbrenner & Morris, 1998, 2007). In collaborative activities, the interactions between people have the stronger impact on development, while in solo activities the objects, symbols, and settings take precedence (Rosa & Tudge, 2013); although when considered within the context of a given microsystem, such as school, the interactions with people are the most important (Merçon-Vargas, Lima, Rosa, & Tudge, 2020). How these proximal processes affect development varies according to the characteristics of the individual, their environment, their society, and what the developmental outcomes are (Bronfenbrenner & Morris, 1998), but can only be understood when considered within the context of the interactions over time (Merçon-Vargas, Lima, Rosa, & Tudge, 2020; Tudge, Mokrova, Hatfield, & Karnik, 2009).
Collaborative Problem Solving
Problem-solving involves gathering information and applying it to an inquiry cycle, which consists of generating a hypothesis, finding possible solution paths, testing one of the possibilities, and making a decision (Goldman, 1983). Cognitively, one identifies attributes of the problem, explores possible approaches by considering alternatives, evaluates one of these approaches, and either repeats the process or further develops the chosen approach to develop a mental model of the current problem (Zhong et al., 2010). The process is similar in collaborations, except individual knowledge is integrated to form group understanding, which allows each member to explore few possible solution paths in greater depth while collectively ensuring that a larger breadth of possible paths is explored (Warner, Letsky, & Cowen, 2005), and is similar in both informal and formal environments (Cicchino, 2015). The main benefit that collaborative problem-solving has over individual efforts is it can increase the individual’s reasoning and recall skills (e.g., Taylor & McDonald, 2007; van Blankenstein et al., 2011).
The epistemology of the individuals with respect to the context influences the effectiveness of the collaboration; if an individual believes that knowledge is absolute in a particular context then other perspectives are less likely to be considered (Hofer, 2001). The benefits to the individual in each environment are also affected by that person’s self-efficacy within the environment, perceived expertise by group members, and social connectedness within the group (Hou, 2013; Bluemink, Hamalainen, Manninen, & Jarvela, 2010; Taylor & McDonald, 2007). An individual who is lower in these areas will engage in fewer interactions with peers, which reduces what that individual would learn in the problem-solving process. It is important to note that female engineering undergraduates are lower in these areas than their male counterparts (Christman & Yerrick, 2021; Nagahi et al., 2020; Verdín, Godwin, & Benedict, 2020), while female Magic: The Gathering players may not have the same difficulties unless participating in the online or tournament environments (Falcao, Macedo, & Kurtz, 2021).
Problem Solving in Games
To play a game is to immerse oneself into a culture and way of thinking, creating a situated problem-solving environment (Dede, 2009; Gee, 2007). This environment requires problem-solving strategies that can be transferred to more formal learning environments (Blumberg & Altschuler, 2011). For example, Eseryel et al. (2014) found that playing massively multiplayer online role-playing games (MMORPGs) for a year increased students’ ability to develop mental models and representation for problems which they had not seen before, and which were not related to the game. A key factor in the development of problem-solving skills within games is the talk that occurs during the game with other players, because this talk includes collaboration, giving instructions, requesting assistance, and formulating problems to solve within the game (Danby et al., 2018; Hagstrom & White, 2006). The difficulties with using games more in education, however, involve their costs and their facilitation: Games are expensive to develop and challenging for teachers to use in a traditional classroom (Aqlan & Zhao, 2021). This first difficulty might be circumvented by finding an existing game which addresses the primary instructional skills to be learned, but then one must search through the many titles to find games that not only address those skills but that do so without inappropriate content and with appropriate rigor (López & Caceres, 2010).
Much of the current literature concerning games and problem-solving addresses digital games (e.g., Blumberg & Altschuler, 2011; Danby et al., 2018; Eseryel et al., 2014; Hagstrom & White, 2006; López & Caceres, 2010); there is currently little regarding table-top (non-digital) games, some of which rival the best digital games in terms of complexity. Additionally, much of the literature concerns the improvement of content-specific skills such as arithmetic (e.g., Novak & Soyturk, 2021) or manufacturing processes (e.g., Aqlan & Zhao, 2021) and often uses custom-made or custom-adapted games for that purpose (e.g., Demirel & Yilmaz, 2019; Eseryel et al., 2014; Kang, Liu, & Qu, 2017). No studies were found comparing the problem-solving process in game and non-game environments. This study aims to address this gap by examining the problem-solving and proximal processes used with the table-top game Magic: the Gathering as compared to those used in engineering and computer science education.
About Magic: The Gathering
Magic: The Gathering (MtG) (Wizards of the Coast, 2016) is a collectible card game where players “cast” spells and “summon” creatures in order to battle other players. MtG has several variations, called formats, for play. These formats determine how many cards a player may have in their deck, how many of those cards can be duplicates, and which of the over 20,000 published cards may be used in that deck. The number of possible cards and the rules for gameplay make playing MtG a computationally complex problem, with optimal play being incomputable (Churchill, Biderman, & Herrick, 2019).
Most formats for MtG require players to have a deck of sixty cards built from a subset of all released cards, such as only cards released in the last few years or only cards from the first few sets. In these decks, players have spells, most of which can be included four times, and lands for casting spells, most of which can be included any number of times. Thus the probability of drawing a desired non-land card ranges from 1/60 to 1/15. When one builds a deck for these formats, one can choose a strategy and fill the deck with cards that will work together to support that strategy with a good probability of seeing this synergy during gameplay.
The format this study focuses on is Elder Dragon Highlander (EDH), commonly called “Commander,” and is generally considered the most complicated MtG format, not only because the gameplay is more difficult but because building one’s deck is a complex problem (e.g., Darrenhabib, 2017; Mookie, 2019; TCGnoobkin, 2018). Unlike other formats, an MtG:EDH deck consists of one hundred cards, of which only the basic lands may be duplicated. Thus, the probability of drawing a desired card is only 1/100. One card is considered the Commander, typically a multi-colored card, and all other cards must be either colorless or using only colors that match one or more in the Commander. Additionally, MtG:EDH allows one to use nearly all of the published cards (only seventy-six are banned from competitive play), which increases the difficulty when choosing which cards to use in the deck.
Methods
This qualitative study used an online questionnaire to discover the similarities and differences between engineering / computer science undergraduates and players of the Elder Dragon Highlander variation of Magic: The Gathering (MtG: EDH) (Wizards of the Coast, 2016) when engaged in complex problem-solving. This research was approved by my institution’s Institutional Review Board. All participants gave written consent prior to completing the questionnaire.
Participants
College undergraduates majoring in engineering or computer science (students) and similarly-aged people who played MtG: EDH (gamers) were invited to participate. The students were recruited using posted flyers at two universities with strong engineering programs in southern United States. The gamers were also recruited at these universities and through an online forum for MtG: EDH. The questionnaire was open for three months and generated 72 responses. Each response was given an identification number before analysis; participants were then identified as “gender group number” (e.g., female gamer 1). Because the students ranged from 18 to 25 years of age, responses by gamers outside of that age range were removed. Responses with less than 60% of the questions completed were also removed. Forty-five responses remained: 22 students (13 male, 9 female), 12 gamers (6 male, 6 female), and 11 who were both (all male). Because those who were both students and gamers were all males, and because how they approached one problem might influence how they approached the other, they were also removed from analysis, leaving 34 participants.
Instrument
Questions asked of participants.
Analysis
Responses were separated into four cases: female students, male students, female gamers, and male gamers. Each response was then coded using initial coding to allow for later comparing of similarities and differences between the cases (Saldaña, 2012, p. 100). Codes that addressed the problem-solving process were then separated from codes addressing proximal processes and themed within each case to address each of the research questions. These themes were then compared between the cases to determine what similarities and differences existed.
Role of the researcher
I teach undergraduate computer science courses and have played MtG for over ten years, including the EDH format. Because of my experience in both areas, I chose to utilize the online questionnaire to minimize influencing participant responses.
Limitations
The data gathered from the questionnaire is self-reported; no participants were observed or asked to contribute supporting data, which would have improved context and trustworthiness for this study. A larger number of participants and recruiting from more than two universities would also have strengthened the findings.
Findings
Recognizing a complex problem
Both students and gamers recognized that they were working on a complex problem because it had multiple parts to it. Female participants were more likely to mention the multiple parts than males, however, with over half of the females and only 21% of the males mentioning this aspect. The students were not explicit in describing what these steps were, saying simply, “There were multiple parts that require extensive calculations, teamwork, input, research” (female student 1), while the gamers were more likely to list the different parts they had to consider, such as, “There are many complicated strategies to consider, including theme, resource management, mana curves, the balance of threats and responses, the presence (or lack thereof) of combos, etc.” (female gamer 52).
Both groups also recognized it was a complex problem because of the amount of knowledge needed; this aspect was mentioned equally by both genders. The students added that they might not have, or might not be proficient, in this knowledge. As one student said, “It involved assembling something with parts and tools that I had never used before” (male student 38). Only one gamer mentioned having too little knowledge for the problem.
The students also recognized they were solving a complex problem because they could not get to a solution easily. Sometimes this recognition came from simply thinking about the problem, such as, “Usually I get the basic structure to solve from the beginning to end. If any problem I can't prepare a structure by mind I consider it as a complex problem” (male student 30), and sometimes during the planning process: “I tried writing it out/making a diagram and I couldn't get to the solution” (female student 29). In each case, this recognition came when they realized that the problem had aspects that were not obvious at first: “Taking a non-powered system and making it powered seemed simple at first; but upon further thought; taking rotational motion and changing its direction twice is a difficult thing” (male student 35).
Gamers did not mention arriving at a solution easily, but did mention that their problem, building a deck, had multiple solutions. As one gamer explained, “The restrictions of what can be included; the singleton nature of the format; both items require one to take in a lot of options and narrow down to the most enjoyable/efficient options” (female gamer 49).
They also mentioned that building a deck was a complex problem because it had to be prepared for multiple, unknown, scenarios. “Commander is a multiplayer game, and each player is likely to have a different deck. Therefore, your deck must be able to deal with multiple competing strategies every game” (male gamer 56).
Neither multiple solutions nor multiple scenarios were mentioned by the students.
The problem-solving process
Planning (Generating a hypothesis and finding possible solution paths)
None of the students reported having to generate a hypothesis; instead, they stated that the assignment’s requirements already suggested what the hypothesis should be. The gamers, however, only started with a goal, to win the game, and most developed their hypothesis around a strategy they wanted to implement (5 females, 3 males, 67%). The remaining gamers, however, preferred to find possible solutions by designing their deck around a specific card they wanted to use as their Commander (1 female, 3 males, 33%) because “Commanders have specific abilities that can be easily outlined to help formulate a deck” (male gamer 54).
All but one female student reported sketching or writing plans to find possible solutions. Some of these plans were quite detailed, such as, “I listed my given requirements, then brainstormed different ways of solving. Once I found the approach I wanted to use, I listed in order and great detail what steps I needed to take and approximately how much time I would spend on each step” (female student 42).
Seven of the male students did as well, but six reported only planning a little in their head or recording a few ideas, with one explaining, “I have a general idea of what will be needed for the project” (male student 23). Most of the gamers (4 female, 4 male, 67%) said they only recorded a few ideas or planned in their head.
Once they had possible solution paths, the gamers (4 female, 5 male, 75%) reported conducting research before trying to solve their problem more than the students (3 female, 0 male, 14%) did. The gamers’ research typically involved getting a better understanding of the resources (cards) available, but some gamers also considered experienced opinions: “I researched many other peoples' decks online to see how similar decks were built and which cards were used. I then compared those decks to the one I was trying to build. I looked at these decks to see if there were any cards that would work really well in mine that I was not aware of, and I asked more experienced players to look at my deck to see if the cards I chose worked well together” (female gamer 52).
Only a few female engineers conducted research, and their research was on the problem or a part of the problem instead of resources.
Testing a possible solution
The most common form of testing used by all groups was trial and error. The students (6 female, 6 male, 55%) simply called it “trial and error” while the gamers (4 female, 3 male, 58%) said they tried their decks against other players to see how it worked. The remaining participants mostly reported using some form of modeling or simulation (2 female students, 3 male students, 2 female gamers, 3 male gamers). Students used technology to create the simulation, such as computer-aided design/manufacturing (CAD/CAM) software, while gamers used a combination of online game simulators and a hands-on modelling technique known as “goldfishing,” which is when one plays their deck against zero opponents.
Making a decision
The students determined that their solution was viable when it met, or mostly met, the requirements of the assignment. Most of them (7 female, 8 male, 68%) reported having to change their solution path because their initial solution was not meeting those requirements, with five of them (2 female, 3 male) attempting a completely different approach and the rest making adjustments to their initial idea. All the gamers stated that they determined they had a viable solution if they had fun with their decks and could win with them. Only one (female gamer 49) determined that the solution did not work and deconstructed the deck without recording her ideas, intending instead to try a different solution path, while three gamers (1 female, 2 male) felt their solution was completely viable, although they each still believed that their solution could be improved upon. The rest of the gamers reported that their solutions mostly worked, because they were fun to play, and had plans to adjust them. Four males shared specific issues they wanted to improve, such as the pacing of the deck during play (male gamers 53 and 56) or how to take advantage of specific mechanics (male gamers 54 and 55), while the four females who wanted to adjust their solutions stated that they wanted other players’ opinions on what to improve. “My friends who also play love to help with my decks and give good advice” (female gamer 52).
Proximal processes
Male students and female gamers engaged the most with other people throughout the problem-solving process, however the roles they assigned themselves during these interactions differed greatly. The male students regularly identified as an equal (n = 12, 92%), stating that they had an idea and simply wanted feedback. Although most sought feedback from others directly by asking what someone thought of their approach, one stated he used these discussions to increase his own reasoning: “If you’re talking to someone about something, you’re sort of forcing yourself to work it out step by step to convince that person, so you’re also convincing yourself” (male student 28).
Even when they were not sure of their understanding, the male students acted confident during these interactions: “We kept going back on forth, me asking him what do you think, etc. And then we tested it and it worked. But it was kind of a heated discussion because we didn’t know. I wasn’t quite sure that it would work, but I was trying to persuade them” (male student 38).
The female gamers instead identified as a learner (n = 5, 83%) and used these interactions to gain advice. As one explained, “Others might have more experience with a certain archetype or play style. There are also so many cards to choose from, someone else might know of cards I never would have thought of” (female gamer 52).
The vast number of cards to choose from was cited as a reason to seek advice by all five female gamers: “Other people just think of different things! They either know cards that I don't know about, or they think of ways to use cards that I wouldn't have thought of on my own” (female gamer 50).
Only one male gamer mentioned the number of cards available as a reason to interact with others early in the problem-solving process. The remainder restricted their interactions for later in the process (n = 5, 83%), identified as an equal during these interactions (n = 5, 83%), and justified this restriction by saying it would diminish their enjoyment (n = 4, 67%). As one gamer stated: “I believed communicating with others in the context of a new deck was possible, but undesirable, to an extent. Much of EDH is social and discovering a unique solution to your ‘problem' (your commander) is, personally, a large part of the fun and engagement. Showing off a new commander deck holds greater social value if it's your own personal creation” (male gamer 53).
All gamers, females and males, tested their solutions by playing against other people. Only one male, however, asked for his opponents’ opinions about his solution after the game, stating, “More opinions can give me more ideas to modify and improve” (male gamer 54). Four of the six female gamers also asked for opponents’ opinions.
Female students interacted with other people the least, and usually only in the beginning of the problem-solving process. When considering possible approaches to the problem, seven of the nine female students (78%) mentioned they sought others to get a different perspective or opinion on the problem. After this initial planning, however, only one (female student 43) continued to interact with others. The remainder recognized that they could have sought more interactions, but said it was too difficult to find people who knew enough to help (n = 6, 67%). One student also mentioned, “I felt like I had bothered them enough” (female student 29), even though she reported not seeking others after the initial problem-solving stage. When females did interact with others, they identified themselves as learners (n = 7, 78%).
Eleven of the twelve gamers (6 male, 5 female) mentioned using online resources in addition to people they knew during the problem-solving process, although only two (1 male, 1 female) included discussion forums and one (1 female) included a simulator with these resources. Thirteen students (7 males, 6 females) also used online resources, with only one (male) mentioning discussion forums. None who used discussion forums stated if they were contributors or observers. Five students (3 males, 2 females) also used publications, including textbooks, and one (female) used materials from previous coursework.
Discussion
The Partnership for 21st Century Learning (2019) places communication and collaboration equal to critical thinking skills as necessary for learning and innovation. Collectable card games such as Magic: The Gathering provide rich problem-solving and potentially collaborative environments (Norton, 2015). The findings in this study suggest that these games may provide similar problem-solving experiences as those cultivated by engineering and computer science undergraduates. Both groups believed they were working on a complex problem because it had multiple parts to it and required more knowledge to solve. The gamers also believed that having multiple solutions was also a characteristic of a complex problem, while the students believed that not being able to arrive at a solution easily was a characteristic. These beliefs suggest that both building a deck for competitive play and project/problem-based coursework in engineering or computer science have the potential for engaging young adults in the problem-solving process. The skills developed in one environment would likely transfer to the other (Blumberg & Altschuler, 2011; Eseryel et al., 2014).
The problem-solving process includes gathering information, generating a hypothesis, finding possible solution paths, testing one of the possibilities, and making a decision (Goldman, 1983). In this study, the gamers followed this process closer than the students. Most of the gamers generated a hypothesis on what a winning strategy would be for their deck, conducted research on the cards available, tested their decks, and made their decision based on how fun their deck was to play. Additionally, they believed that their solution could be improved upon. The part of the process gamers appeared to do the least was finding possible solution paths because few reported doing any planning other than considering a few ideas in their head. None of the students reported generating a hypothesis, believing instead that the assignment’s requirements were the hypothesis. These requirements also formed the basis on which students made their decisions; if their solution met most or all requirements then they considered their solution complete. Similarly, only three female students reported conducting any research on the problem. These findings suggest that students are less engaged in the problem-solving process than gamers are, perhaps because building a deck for play is more open-ended and less high stakes than school assignments are and are thus more supportive of the problem-solving process (Gee, 2007), or because games encourage a wider variety of problem-solving strategies (Blumberg & Altschuler, 2011).
Collaborative problem-solving can increase reasoning and recall skills (e.g., Taylor & McDonald, 2007; van Blankenstein et al., 2011), but only if the individual has self-efficacy and a sense of belonging in the environment (Hou, 2013; Bluemink et al., 2010; Taylor & McDonald, 2007) and does not believe that knowledge is absolute in the given context (Hofer, 2001). These beliefs of the individual help explain the differences in how and when participants used proximal processes. The female students reported the fewest interactions with others, saying they wanted help but did not believe they could find someone with enough knowledge. This belief is like the findings of Danby et al. (2018) and Hagstrom and White (2006), who found that young children often use talk during game play to seek assistance. The main difference between these studies and the current one suggests that young children believe others can give assistance, while female engineering / computer science students are not as certain. When this finding is contrasted with the male students, who interacted with others throughout the process but did so by trying to convince others to their way of thinking, it suggests that neither group benefited from collaboration. The males did not act as though they believed they could gain knowledge this way, suggesting that they believed knowledge was absolute (Hofer, 2001), while the females suggested a feeling of isolation in their environment by not having a network of more-knowledgeable people they could turn to (Hou, 2013; Bluemink et al., 2010; Taylor & McDonald, 2007).
Interestingly, the female gamers did not appear to share in this sense of isolation because they reported regular interactions with more-knowledgeable people throughout the problem-solving process. Although only about 38% of MtG players (Elliotte, Farris, & Andry, 2019) and 20% of engineering and computer science undergraduates are female (AAUW, 2019), the findings of this study suggest that females may have a greater sense of belonging and/or self-efficacy in the gaming context than in engineering or computer science programs. The competitive nature of gaming, however, appears to inhibit male gamers from collaborating. They reported a possessiveness about their ideas and did not want to share them with others, even to learn how to improve, until it was time to test their decks (solutions) in gameplay. This study did not ask if the male gamers helped others to improve their decks; doing so may have shown they develop problem solving skills more by giving instruction rather than collaborating or seeking help (Danby et al., 2018; Hagstrom & White, 2006).
Implications and future research
Further research is needed to better understand the role gender plays on collaborative problem-solving, especially when the genders are not equally represented in the environment, but this study does suggest a few implications for practice and research. First, it suggests that one may be able to use collectable card games, such as Magic: The Gathering, to develop problem-solving skills in students, especially since engaging in complex games improves the ability to develop accurate mental models of a problem (Eseryel et al., 2014), a requirement for solving complex problems (Zhong et al., 2010). Since there are several such games currently available, and for various age groups, it would be interesting to determine if one could use these games to teach problem-solving skills to younger learners. Second, the findings concerning the females of both groups support other research (e.g., Brown et al., 2020) that has shown positive effects on female engineering undergraduates from mentoring or other social-support systems are in place. Female gamers in this study were more likely to engage in proximal processes than female students, possibly because they felt they had the social support needed. Third, because males in both groups were reluctant to collaborate, or used collaboration to confirm their own ideas, it may be beneficial for engineering and computer science programs to teach collaboration skills early in their college careers.
The literature regarding problem solving in table-top (non-digital) games is limited and often concerns traditional games like chess, which may not easily support collaboration. Thus, the primary implication for research that this study suggests is to further investigate the problem-solving practices, skills, and transferability that occurs outside of the digital realm.