Triskelion—In Pursuit of Proficiency Through Immersive Gameplay

Abstract

As technology advances, interest in video games is extending to broader audiences. This makes gamification as a mechanism for improving educational outcomes increasingly attractive. This article reports on a study in which a 3D third-person video game was used to develop proficiency in spatial reasoning abilities relating to symmetry. The video game, called Triskelion, interleaves elements of traditional gameplay with educational elements. Gameplay includes non-violent shooter elements, parkour, searching, and exploring. Educational elements include points, leaderboards, a theme, clear goals, feedback, and a group challenge in the form of a clan-based match. This composition of elements makes Triskelion unique in the genre of academic educational games. Our study compares one Triskelion match to a longer educational sequence consisting of a “practice test”, followed by engagement with a 3D digital experience called the Kessel Run. Analysis of the results using the Mann–Whitney U test revealed (p = 0.9297) that both pedagogical pathways yielded similar proficiency results. This suggests that Triskelion might create a learning environment more aligned with the characteristics of deliberate practice.

1. Introduction

CSCI 1280—Introduction to Computational Science is a freshman-level course taught at the University of Nebraska at Omaha (UNO) that counts towards the fulfillment of general education natural science requirements. The course can be taken by STEM and non-STEM majors alike. Its only prerequisite is college algebra or its equivalent.

CSCI 1230 was designed to have broad appeal, and a wide range of students have enrolled in CSCI 1280, ranging from Computer Science majors to English majors to Math majors. Students learn how to write programs that create 2D and 3D block-based art (e.g., pixel art and Minecraft-like constructions). Figure 1 shows examples of some of the types of artifacts students are required to construct.

To develop these coding skills, CSCI 1280 makes extensive use of interactive web apps whose purpose is to develop specific abilities that support understanding, reasoning about, and creating visual patterns through code. Research has shown that visual/spatial abilities are extremely important to the STEM disciplines. A collaboration between mathematics educators Boaler, Williams, and Montserrat Cordero and neuroscientist Lang Chen has explored the importance of visual thinking to mathematics [1]. Their research has shown that areas of the brain involved in mathematical thinking involve a number of networks and pathways that include both the dorsal and ventral visual pathways. “Neuroimaging has shown that even when people work on a number calculation, such as $12\times 25$, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing” [1].

Analysis performed by Newcombe [2] supports the position that spatial abilities can be developed through practice and that abilities developed are (1) durable and (2) transferable between various kinds of spatial test problems. Activities that can develop spatial abilities include: (1) taking a drafting class, (2) playing Tetris, and (3) pursuing activities in visual arts and crafts. Newcombe endorses a strategy recommended in the National Research Council’s report on Learning to Think Spatially, which calls for existing curriculum to be “spatialized” [3].

Wai, Lubinski, and Benbow report the results of an $11+$ year longitudinal study involving a large student population in which they found that spatial ability played a critical role in the development of STEM abilities [4]. Aligning with such findings, research conducted in the 1970’s by Macoby and Jacklin [5] showed that spatial ability, when compared to either GRE or SAT scores, was a better predictor of success in engineering.

To facilitate the acquisition of spatial abilities relating to symmetry, we have developed a non-commercial video game called Triskelion. Considerable research has shown that video games can have a positive effect on motivation, engagement, and learning outcomes [6,7]. Triskelion builds on these results by creating a rich virtual world where traditional gameplay and educational content are interleaved in the context of a clan-based (i.e., group-based) competition.

Triskelion is relatively unique with respect to how it uses gameplay to pursue educational goals. There are several educational frameworks that teach coding through the construction of video games, which, of course, can then also be played. Scratch [8] is a well-known block-based programming environment suitable for constructing various kinds of 2D video games and animations. Other examples include BootStrap [9] and The Soccer Project [10]. In contrast, Alice [11] is a visual programming language whose goal is to create 3D animations that tell a story. The hope is that by targeting storytelling, Alice will appeal to broad audiences, especially females. Despite their differences, the goal of these systems is to use the creation of a game or animation as the motivator for learning how to code.

RefGame [12] is a suite of three 2D games created to teach code refactoring. Games are single-player and have scoring as well as leaderboards. In addition, students are given access to a personal dashboard, allowing them to track their progress. One game in the suite is based on the well-known video game Snake. In this variation of Snake, when the snake eats an “egg”, a popup appears that requires the player to solve a code refactoring exercise. This kind of popup mechanism is similar to Triskelion’s teleportation to puzzles when a player captures a will-o-the-wisp. In contrast to RefGame, Triskelion’s dashboards are available only to teachers and are used to monitor student engagement, proficiency, and improvement. Outside of matchplay, Triskelion’s leaderboards show how well players (i.e., students) perform relative to their clan members. During a match, Triskelion’s leaderboards show the leaderboards for competing clans and clan averages.

Decimal Point [13] is a 2D non-competitive educational game aimed at improving middle school students’ understanding of decimals. Decimal Point provides a collection of mini-games assembled into an amusement park format. Central to the game’s approach to learning is player engagement with erroneous examples. These are step-by-step problem solutions that contain errors that players must correct. Decimal Point tightly integrates gameplay with educational objectives. For example, “Balloon Pop” is a mini-game in which players toss darts at decimal-labeled balloons in order of smallest to largest. In contrast, Triskelion contains elements of pure gameplay, such as wandering through a Celtic Forest in search of will-o-the-wisps or traversing a parkour course to enter a realm.

To advance STEM education in primary schools, Ranosz et al. [14] created a suite for Unity-based 3D games. Two games focus on math, one on biology and ecology, and the last game focuses on image recognition and is a two-player competitive game. One of the math games, called Western Shooter, involves mouse-based shooting. This kind of shooting is similar to that of Triskelion, though Triskelion’s shooting has a broader scope (e.g., hunting and “shooting” will-o-the-wisps in a realm and shooting tiles to solve puzzles).

Several general-purpose 3D virtual environments have been used in (adapted to) educational settings, with Second Life (SL) and Minecraft being perhaps the most widely known. In a K12 educational setting, there are several challenges and concerns surrounding the use of SL. The teachers have found that the initial learning curve for SL is steep and the open world nature creates the risk of students being exposed to inappropriate content [15,16].

In contrast to SL, Minecraft Education provides a comprehensive infrastructure designed for education with a gentle learning curve. The platform natively supports controlled multiplayer environments, provides avatar customization through skins, provides elements that can be used to construct machines, and code-centric elements. A primary activity in Minecraft is constructing artifacts using various types of blocks (e.g., Granite, Dirt, Grass). Artifacts that can be constructed include buildings, farms, roads, and pixel art. These types of constructions make Minecraft well-suited for inclusion in art curriculums [17].

Engagement with a 3D desktop/laptop environment can be a truly immersive experience. However, recent advances in XR has opened up a whole new level of immersion whose educational potential is beginning to be explored [18]. Though Triskelion has been designed to be a desktop/laptop game with a keyboard and mouse interface, it could easily be migrated to a VR setting. However, educational systems (e.g., public K12 education) have limited access to VR headsets at this time.

The closest example of a game in the Triskelion genre is CodeSpells [19], which is a non-competitive third-person role-playing video game where the player is a wizard in a fantasy world populated by gnome-like creatures. Through coding, which is the educational goal of CodeSpells, a player can create various spells to interact with the environment (e.g., moving a boulder).

CodeSpells was designed for extracurricular settings [20]. This is worth noting because learning how to code is a complex task that can take considerable time and effort to acquire. In contrast, Triskelion has a much narrower educational focus and is therefore well-suited to embedding in a curriculum.

Attaining a degree of proficiency in various spatial abilities relating to code-based artifact construction is a desired educational goal of CSCI 1280. To acquire such abilities requires practice. However, not all forms of practice yield equivalent results. Psychologist K. Anders Ericsson defined the term deliberate practice as a form of practice characterized by motivation, focus, and an exerted effort to improve [21].

Research has shown that tasks having the following characteristics are well-suited to effective learning [22,23]:

• Tasks can be understood after a brief period of instruction;
• Immediate feedback is provided;
• Repeated performance of the same or similar task;
• High accuracy is rapidly attained;
• Emphasis is placed on speed.

Triskelion Matchplay Aligns with These Characteristics

At UNO, it is not uncommon for freshman-level courses to have a higher DWF rate than sophomore, junior, and senior-level courses. CSCI 1280 is no exception. In the course, requiring students to “practice” until sufficient proficiency is attained is a challenging task. To address this challenge, we have developed a variety of interactive web apps that provide instant feedback. We have also developed puzzle-like exercises. And lastly, we have developed immersive 3D educational video games.

Through EdTech, of the kind described in the previous paragraph, the acquisition of various abilities is distributed across many short assignments. This has given rise to an additional challenge—students would like fewer assignments.

In this article, we compare two learning sequences, LS1 and LS2, that have been designed to develop proficiency in a visual-based understanding of horizontal and vertical reflection symmetry, as well as 2-fold and 4-fold rotation symmetry. The learning sequences we will compare are shown below.

LS1	lecture	2 quizzes	test, Kessel Run	⋆ test ⋆
LS2	lecture	2 quizzes,	Triskelion	⋆ test ⋆

To compare the effectiveness of LS1 and LS2, we analyzed response time data using a Mann–Whitney U test, which indicated no significant difference in response times between LS1 (Mdn = 189.5 s) and LS2 (Mdn = 232.5 s), p = 0.93, suggesting that both sequences achieve similar levels of proficiency.

$H_0$:	The distributions of response times are the same
$H_1$:	The distributions are different

2. Materials and Methods

A study involving 44 students was conducted at the University of Nebraska at Omaha (UNO) spanning two semesters: Spring 2021 (20 students) and Spring 2022 (24 students). In this paper, we will refer to the Spring 2021 students as Group A and we will refer to the Spring 2022 students as Group B.

The educational content provided was the following:

• Group A:

• Introductory content consisting of a lecture and two quizzes.
• A practice test consisting of 10 problems randomly selected from a problem bank. Solving a problem requires creating an artifact that is appropriately flipped or rotated through mouse clicks on a grid. It is important to mention that such tests are generated on an individual basis, meaning each student is provided a unique test of 10 randomly generated problems drawn from the problem bank.
• Playing a 3D game called the Kessel Run [24]. Though the Kessel Run is a video game, it consists primarily of solving symmetry problems. In the Kessel Run, there is no traditional gameplay.
• A final test consisting of 10 problems randomly selected from a problem bank. Solving a problem requires creating an artifact that is appropriately flipped or rotated through mouse clicks on a grid. The problems in this test are drawn from the same problem bank as the practice test. So this can be viewed as taking a test for the second time (i.e., a repetition).

• Group B:

• Introductory content consisting of a lecture and two quizzes.
• Playing a Triskelion match, which is a group-based competition. In contrast to the Kessel Run, Triskelion interleaves elements of standard gameplay with solving symmetry problems. Furthermore, Triskelion provides a clan-based competitive environment, a distinction we feel to be important.
• A final test consisting of 10 problems randomly selected from a problem bank. Solving a problem requires creating an artifact that is appropriately flipped or rotated through mouse clicks on a grid. This final test (of randomly selected problems) is the same test that is given to Group A.

The goal of the experiment described in this paper is to compare the performance of Group A and Group B on the final test. Specifically, we are interested in the speed (and accuracy) at which students can complete symmetry-related problems in the final test.

2.1. Introductory Content

Both groups were given a lecture on symmetry, followed by two 10-question quizzes. Quiz questions are multiple-answer quests that ask students to identify all forms of symmetry in a given 2D artifact. Figure 2 is an example of the type of artifact students were being asked to analyze.

Students were allowed to take these two quizzes as often as desired (e.g., until they obtained a perfect score). This provides another opportunity for practice. The difference between Quiz 1 and Quiz 2 was that the artifacts in Quiz 2 were slightly more complex than the artifacts in Quiz 1.

2.2. Practice Sequence for Group A: A Practice Test and the Kessel Run

The practice sequence for Group A consisted of a practice test and an engagement with an educational video game called the Kessel Run [24].

The practice test consists of 10 symmetry problems randomly selected from a problem bank. Tests were created using a test generator, and each student had an instance of a generated test. In other words, students were not all given the same set of problems.

The Kessel Run was our first experiment with immersive educational video games. In the Kessel Run, a player must solve a symmetry problem on a platform in space. When a problem is solved, a portal opens, allowing the player to teleport to the next platform. Figure 3 shows a platform in the Kessel Run.

A test problem consists of an artifact in a grid, an empty grid, a color palette, verbal instructions describing the artifact to be created in the empty grid, and a submit button. Each problem focuses exclusively on a single transformation. There are 5 possible transformations to choose from: horizontal flip (reflection), vertical flip (reflection), 90-degree clockwise rotation, 90-degree counterclockwise rotation, and 180-degree rotation. Figure 4 shows an example of a test problem.

In the Kessel Run, each platform has a single problem that must be solved to reach the next platform. The goal is to reach the last platform as fast as possible. It was our impression that playing the Kessel Run was more engaging to students than simply practicing symmetry problems using “pencil and paper”. However, student feedback indicated that the competitive element of the Kessel Run—individual scores that then mapped to letter grades—was unappealing. It was to improve the competitive element of this kind of interaction that was one of the reasons behind the creation of Triskelion. Triskelion also departs from the single-minded pursuit of problem-solving in the Kessel Run by incorporating elements of traditional gameplay.

2.3. Practice Sequence for Group B: Triskelion

Triskelion is a 3D, third-person single-player clan-based video game that combines educational elements with elements of traditional gameplay. Triskelion is implemented in Unity. Its leaderboards and player-tracking metrics are implemented in PlayFab. A YouTube video giving an overview of Triskelion can be found at the following URL: https://www.youtube.com/watch?v=qKIukNjz9mk (accessed on 10 December 2024).

To play Triskelion, one must first create a username (i.e., gamer tag). To align with privacy requirements, Triskelion’s gamer tag is associated with the machine on which it is created. It is not associated with an email address. In addition, Triskelion employs a profanity checker to reduce the likelihood that a player creates a gamer tag deemed inappropriate.

Upon its creation, a valid gamer tag can be used to login and play Triskelion on the machine on which the gamer tag was created. Initially, all players are members of a default clan called Mercenary. Players can request to join another clan. The request will be honored if the clan exists and if the clan is not currently in a match.

2.3.1. Triskelion from the Perspective of a Student

The Triskelion universe consists of 3 realms connected by an Otherworld called the Upsidedown (see Figure 5). The game begins in a Celtic forest scattered with ruins of ancient Druids. This forest is also inhabited by will-o-the-wisps, which are glowing orbs that move around in unpredictable ways.

Gameplay involves wandering through the forest in search of will-o-the-wisps. When a will-o-the-wisp is found, it can be collected by casting a magic spell. Spellcasting is a shooter-style interaction in which a player points their magic wand at a will-o-the-wisp and then, via a mouse click, casts a lightning spell. When a will-o-the-wisp is touched by lightning, it moves to the player decreasing in size as it approaches. The type of interaction was inspired by how Dumbledore collected the light from street lamps on Privet Drive in the first Harry Potter movie (see Figure 6).

Research has shown that playing shooter-style games has cognitive benefits. However, most shooter games are typically also violent. We wanted Triskelion players to have the cognitive benefits of shooter games, but without the violent element typically accompanying such interactions. Capturing will-o-the-wisps is a non-violent activity involving tracking and targeting moving objects. This was done so that Triskelion would appeal to broad audiences.

When a player captures a will-o-the-wisp, they are teleported to a magic realm (see Figure 7) where they must solve a symmetry problem. These problems are drawn from the same problem bank that test problems are drawn from.

Triskelion’s scoring function takes into account the accuracy and speed at which artifacts are created. In order to provide dynamic gameplay, problems are randomly selected from a problem bank. Thus, the gameplay is continuously varying.

When all the will-o-the-wisps in a realm have been captured and their corresponding puzzles solved, the player is teleported to an Otherworld called the Upsidedown. To give the effect of being upside down, the Druid ruins from the Celtic forest are displayed upside down and appear above the player. Aside from the Druid ruins, the Upsidedown is a black void.

In the Upsidedown, the player initially appears on a platform at the bottom of two staircase-like paths leading in opposite directions. At the top of each staircase is a portal, one blue and one red. The staircase is a simple parkour course that can be climbed by moving and jumping (via mouse clicks) at the proper time. If a player falls, they are respawned at the bottom of the staircase.

When a player passes through a portal, they are teleported to a realm. The blue portal teleports the player to an Alice in Wonderland-like realm, and the red portal teleports the player to a desert wasteland. Gameplay in both realms is similar to that of the Celtic Forest, where players search for and collect will-o-the-wisps and solve corresponding problems. When all the will-o-the-wisps and puzzles have been solved in the second realm, the game is completed and a leaderboard is displayed showing the player’s score as well as the scores of other players in the player’s clan.

2.3.2. Triskelion from the Perspective of a Teacher

A Triskelion administrator can elevate a player to a chieftain. A chieftain can create a clan and give it a name (e.g., clan Blue). A chieftain is the leader of their clan and therefore has special capabilities. For example, a chieftain has control over the educational content their clan members will encounter during gameplay.

Triskelion’s clan configuration screen is shown in Figure 8. In the figure, only Level 1 Horizontal Reflection puzzles are selected.

Triskelion offers five types of symmetry puzzles and two levels of difficulty. To configure the educational content of a clan, all a chieftain (i.e., teacher) needs to do is check the boxes of the puzzles they want included in the game.

Chieftains can also access a metrics dashboard displaying the following.

• High Score—The high score of each player in their clan. This can provide insight into the level of mastery a student has with the educational material. However, it should be noted that very high scores can only be attained by individuals having exceptional shooter skills (quick and precise mouse movements targeting desired objects).
• Low Score—The low score of each player in their clan. This can provide insight into a student’s improvement over time. For example, a student initially may have a very low score. As they improve, their scores will increase. Thus, in some sense, the difference between a player’s low score and high score approximates a player’s improvement.
• Average Score—The average score of each player in their clan. This can provide insight into whether a student’s progress has stabilized (e.g., reached a plateau where additional gameplay might only yield minor improvement). Consider a situation where there is a large difference between the low score of a student and their high score. In such a situation, if the average score is close to the high score, the student’s learning might have stabilized.
• Games Played—This metric provides insight into the level of engagement of the players in a clan. This metric can be especially useful if students are able to play Triskelion outside of the school day (e.g., at home in the evenings or on weekends).
• Play Time—This metric measures how much time a player spends in-game not engaging with educational content. For example, some students may spend much of their time exploring the Celtic Forest and the ancient Druid ruins.
• Puzzle Time—This metric measures how much time a player spends engaging with educational content. For example, a student who is struggling with the puzzles (i.e., problems) might spend a lot of time engaging with puzzles relative to the time they spend collecting will-o-the-wisps.

2.3.3. Clan Competitions

A Triskelion administrator can temporarily elevate two chieftains to pendragons (see Figure 9).

Two chieftains whose status have been elevated to Pendragon may challenge each other to a match. Triskelion employs a handshake-style protocol for creating a match that requires one Pendragon to issue a challenge and the Pendragon being challenged to accept. The match becomes active when this protocol is completed.

A match is in effect until it is concluded by one of the Pendragons. During a match, clan members can play multiple games and only their high score will be used. When a clan member completes a game, they are shown the leaderboards for both clans. Displaying the leaderboards for both clans was done for motivational purposes.

When a match is concluded, the clan with the highest average score is victorious. Using the average score of players compensates for differences in clan size and also takes pressure off of individual players. Our goal when designing a match was to make it competitive but not overly competitive. A metrics dashboard is available to Pendragons, similar to the metrics dashboard available to chieftains. The metrics dashboard for Pendragons contains data exclusive to the match.

Lastly, when a clan is involved in a match, it cannot accept new players. This was done to prevent “ringers” from joining a clan that is losing a match.

3. Results

After both groups completed their practice sequence, they were given a symmetry test. This test consisted of 10 problems randomly selected from a collection of problems. It is worth mentioning that Group A was given such a test twice, once at the beginning of the practice sequence (i.e., the practice test) and once after completing the practice sequence (i.e., the final test). Repetition is a way to improve proficiency in solving symmetry problems. However, students may perceive pure repetition as being tedious or boring, which has a negative impact on learning outcomes.

In this study, the problems that make up a symmetry test were drawn from the following problem banks:

• Horizontal Reflection II;
• Vertical Reflection II;
• 180 Degree Rotation II;
• 90 Degree Clockwise Rotation II;
• 90 Degree Counterclockwise Rotation II.

Symmetry problem banks have two difficulty levels. Difficulty level I involves the consideration of artifacts that fit on a $3\times 3$ grid. Difficulty level II involves artifacts that fit on a $5\times 5\dots 7\times 7$ grid. Figure 10 shows an example of a Level I and Level II problem.

Each problem bank (e.g., Horizontal Reflection II) consists of 28 problems. The artifacts used in these problem banks were intentionally designed to encourage students to visualize and manipulate artifacts in their entirety, seeing the artifact as a whole in their mind’s eye. We specifically sought to avoid creating artifacts whose manipulations involve/require consideration of individual cell positions in insolation. An example of such an artifact is a random set of (unconnected) cells. To encourage visualizing artifacts as a whole, the artifacts in the problem banks consist of connected cells and correspond to recognizable shapes (e.g., the letter “h” or a downward pointing arrow). Color is also used to give a point of reference for the manipulation. This encourages an approach where a key cell of the artifact is manipulated first. The remainder of the artifact can then be constructed relative to this reference point. It is by making this approach to manipulation easy that we hope to encourage visualization in the mind’s eye.

The testing app we developed records the overall score, the total time taken, which problems were selected from the problem bank, and the individual score and time taken for each problem. Figure 11 shows a submission in which the student obtained 9 out of 10 problems correct and took 167 s (2.78 min) to take the test. This final test can be taken as many times as desired, and the student can submit their best performance.

Figure 12 shows the averages for Group A and Group B for Quiz 1, Quiz 2, the Practice Test (Group A only), and the Final Test. The data show that Group A performed better than Group B on both Quiz 1 (9.7/10 versus 9.66/10) and Quiz 2 (9.88/10 versus 9.67/10). It is worth noting that for both groups, their performance on Quiz 2 was better than on Quiz 1. However, in the case of Group B, this improvement was minimal. Nevertheless, this improvement trend is interesting because Quiz 2 problems are more difficult than the Quiz 1 problems. More specifically, the artifacts analyzed in Quiz 1 fit on a $5\times 5$ grid, whereas the artifacts analyzed in Quiz 2 fit on a $7\times 7$ grid and are therefore more complex.

Enrollment in CSCI 1280 is open to all students at UNO, provided they have taken college algebra or its equivalent. This leads to some variability between different sections of the course. In particular, the demographics of the students in Group A and Group B can be different. This raises the question as to whether Group B might (through random chance) consist of students whose background and abilities make them inherently better at solving symmetry problems. However, given the similar performance of both groups on the symmetry quizzes, we postulate that had Group B been given a (practice) test alongside Group A, Group B’s average score and time would have been similar to the average score (9.8) and time (346.1) recorded for Group A.

After completing its practice sequence, Group A’s score and time on the final test was 9.9 and 268.1. After completing its practice sequence, Group B’s average score and time on the final test was 9.83 and 271.2. The final test (and practice test) has no time limits; students can spend as much time as they desire on each problem. The final test (and practice test) can also be taken as often as desired. This accounts, to some extent, for the high test scores, which is the goal behind this pedagogical approach.

Allowing multiple test retakes makes using the score as the basis for comparing the proficiency between both groups problematic. In addition, problems were designed to be relatively easy. However, the average time taken to complete a test does provide insight into proficiency. Gauging proficiency in this manner is similar to timed math tests, where students are given 100 simple math problems to solve in 5 min. Such tests are frequently and repeatedly given in elementary school. In this study, our approach to assessment is conceptually similar. A key difference is that, in our approach, though we record the time taken to solve problems, we do not subject our students to time pressure.

These metrics suggest that Group A’s practice sequence and Group B’s practice sequence achieve similar results with respect to proficiency, which in turn suggests that Triskelion matchplay might have accelerated the learning process, allowing Group B to achieve in one test iteration what Group A achieved after an additional practice test and Kessel Run sequence.

Table 1. Mann–Whitney analysis results.

	Accuracy			Response Time
	Mean	Std	Median	Mean	Std	Median
Group A	9.9	0.45	10.0	268.10	269.74	189.5
Group B	9.83	0.48	10.0	271.25	127.29	232.5

Mann–Whitney U test p-value: 0.9297.

shows that both learning sequences achieved high accuracy (LS1: M = 9.90, LS2: M = 9.83 out of 10), and the Mann–Whitney U test revealed no significant difference in response times between the sequences (p = 0.93). Given that response times for LS1 (Mdn = 189.5 s, SD = 269.74 s) and LS2 (Mdn = 232.5 s, SD = 127.29 s) were comparable, and that LS2 showed more consistent performance (lower standard deviation), these results suggest that the Triskelion-based assignment (LS2) achieves similar proficiency levels while requiring fewer assignments.

The Mann–Whitney U test p-value of 0.9297 provides very strong evidence in favor of keeping (i.e., not rejecting) the null hypothesis of our study. Recall that $H_0$ states that both learning sequences produce similar proficiency as defined by response time.

We would like to remark that because CSCI 1280 is open to all majors, the study described in this paper involved students from diverse academic backgrounds, including both STEM and non-STEM majors. The response time data revealed several extreme outliers, particularly in Group A, with some students taking more than twice the median time to complete the test. Though they represent authentic student experiences, these outliers substantially influence the statistical analysis. This difference in variability is particularly noteworthy given the diverse academic backgrounds of the participants.

When extreme outliers (defined as values exceeding 1.5 times the interquartile range above Q3) were considered separately, the patterns became more pronounced. These outliers, predominantly found in Group A, represent important cases where students struggled significantly with the task. Group B showed fewer extreme cases, suggesting that Triskelion might be particularly beneficial for students who would otherwise find the task challenging.

4. Discussion

The video game industry has acquired a deep understanding of how to develop complex skills needed to effectively play advanced modern games like Fortnite [25]. These games can be so compelling that it is not uncommon for individuals to devote considerable time to playing their favorite video games. In fact, well-designed games are so captivating that video game addiction has become a problem [26].

Gamification seeks to leverage proven techniques for developing complex skills discovered by the video game industry and apply them to the development of specific skill sets. In 2011, Deterding et al. defined gamification as “the use of game design elements in non-game contexts” [27]. Gamification in education aims to enhance learning by incorporating game-like elements such as immersion, points, levels, challenges, and rewards into the educational experience. It is hoped that the gamification of educational content will yield increased engagement, persistence, motivation, competition, and collaboration.

A large number of studies report that gamification, when done properly, yields positive results [28]. However, this is not automatic. When gamifying educational content, it is important to “know your audience” and design an appropriate gamified digital experience [28,29].

For our target audience and educational goals, we believe that interleaving elements of traditional gameplay with educational elements is beneficial. Gameplay provides a cool-down period of sorts between problem-solving interactions. Triskelion incorporates points, leaderboards, a theme (of sorts), clear goals, feedback, and challenge (in the form of match play). It is an immersive game with randomized elements providing rich and varied gameplay. While Triskelion has shooter elements, it sidesteps the violence typically associated with shooter games, thereby making it appropriate for broader audiences. It is this design and combination of game elements that makes Triskelion unique in the genre of academic educational games.

Triskelion player accounts are associated with a machine, not an email address, and a profanity checker is used to prevent students from creating inappropriate usernames. The ability to configure the educational content for a clan allows for handicapping creating a wider range of match opportunities. This makes Triskelion well-suited for K16 environments. Furthermore, the findings reported on in this study suggest that Triskelion might provide a more direct path to proficiency for problems related to symmetry, creating a learning environment more aligned with the characteristics of deliberate practice.

From a technical perspective, Triskelion has been designed so that gameplay and educational elements are compartmentalized. In effect, Triskelion is parameterized on educational content. This design creates the possibility of including other types of educational content in the game. This parameterization has the potential to enable Triskelion to be extended, allowing it to encompass a wide range of educational goals.

We believe Triskelion could be improved by creating a more meaningful connection between gameplay and educational content. This element of game design is an area of future work.