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Learning Through Redesigning a Game in the STEM Classroom

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Learning Through Redesigning a Game in the STEM Classroom

Abstract and Figures

Background Play is an important part of the childhood. The learning potential of playing and creating non-digital games, like tabletop games, however, has not been fully explored. Aim The study discussed in this paper identified a range of activities through which learners redesigned a mathematics-oriented tabletop game to develop their ideas and competencies in an integrated STEM (science, technology, engineering, and mathematics) class. Method Third and fourth graders worked as teams to make changes on Triominos over a period of six weeks. Considering what could be changed from the original game, each group provided a different design for Triominos to accommodate the changes introduced. We gathered data through weekly observations of two classes (about 45 learners, ranging from age eight to ten) in a west-Canada school. In this paper, we present the works of three groups of three teammates. Results We found that any change made by learners not only influenced mechanics, dynamics, and aesthetics of the game but also helped engage learners, encourage unconventional ideas, promote learning, and solve problems. Based on our findings, we suggest redesigning games facilitated learners deepen their understanding of mathematical concepts as part of a designed game system in STEM classes.
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Simulation & Gaming
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The Author(s) 2021
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DOI: 10.1177/10468781211039260
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Learning Through
Redesigning a Game in
the STEM Classroom
Farzan Baradaran Rahimi 1 and Beaumie Kim 1
Abstract:
Background
Play is an important part of the childhood. The learning potential of playing and
creating non-digital games, like tabletop games, however, has not been fully
explored.
Aim
The study discussed in this paper identified a range of activities through which
learners redesigned a mathematics-oriented tabletop game to develop
their ideas and competencies in an integrated STEM (science, technology,
engineering, and mathematics) class.
Method
Third and fourth graders worked as teams to make changes on Triominos over
a period of six weeks. Considering what could be changed from the original
game, each group provided a different design for Triominos to accommodate
the changes introduced. We gathered data through weekly observations of
two classes (about 45 learners, ranging from age eight to ten) in a west-
Canada school. In this paper, we present the works of three groups of three
teammates.
Results
We found that any change made by learners not only influenced mechanics,
dynamics, and aesthetics of the game but also helped engage learners,
Research Article
1 University of Calgary, Calgary, Alberta, Canada.
Corresponding Author:
Farzan Baradaran Rahimi, University of Calgary 2500 University Dr. NW Calgary, AB Alberta T2N 1N4
Canada.
Email: farzan.baradaran@ucalgary.ca
2 Simulation & Gaming
encourage unconventional ideas, promote learning, and solve problems. Based
on our findings, we suggest redesigning games facilitated learners deepen their
understanding of mathematical concepts as part of a designed game system
in STEM classes.
Keywords:
Game design, Participatory design, Mathematics, STEM education, Learning
Introduction
Researchers have observed that creating tabletop games could engage learners in
problem-solving, strategic-thinking, decision-making, communicating, and social
learning where learners work and learn together (e.g., Barta & Schaelling, 1998;
Guberman & Saxe, 2000; Saxe, 1992; Squire, 2006). Moreover, playing tabletop
games can provide learners with opportunities to use concepts meaningfully, especially
for mathematics (e.g., geometry of shapes, and logic) and to engage in reasoning
processes, such as, estimating, measuring, classifying, and comparing (Charlesworth
& Leali, 2012; Clements & Sarama, 2014; Jaques et al., 2019). While understanding
numbers and shapes in everyday life is a part of the mathematics curriculum for grade
three and four (Alberta Education, 2005), there are few studies that focus on early
learners’ design of games for using mathematics (e.g., Barta & Schaelling, 1998;
Jaques et al., 2019), especially in an integrated STEM (science, technology,
engineering, and mathematics) classroom. Learners’ creating artifacts by using STEM
concepts can be important as it situates “real-life and domain knowledge and skills in
doing project-like work” (de Vries, 2006, p. 214). When creating artifact is collaborative
and participatory, learning can become even more meaningful for learners — it can
activate collaborative exploration, articulation, reflection, and assimilation or
accommodation for improved knowledge representation (Ke, 2014). When the artifact
that learners make in the classroom is a game, it can engage learners, encourage
unconventional ideas, promote learning, and help solving problems (Amriani et al.,
2013; Enders & Kapp, 2013; Kapp, 2012).
Although play is an important part of the childhood (Almon, 2003; Bloch & Choi,
1990; Csikszentmihalyi, 1981; Kuschner, 2015), the potential that playing and
creating non-digital games, like tabletop games, can bring to learners has not been
fully explored. Particularly, the potential for using mathematics for an integrated
STEM project when learners are both the players and creators of a game has not been
explored as it should. To create a tabletop game, one does not need to start from the
scratch. Learners may create tabletop games by changing an existing game’s struc-
ture like the rules, scoring mechanics, forms, and arrangements (Mattlin, 2018; Poor,
2014). For example, defining new states for winning and losing the game (i.e., rules),
earning bonus points for certain actions newly specified by players (i.e., scoring
Rahimi and Kim 3
mechanics), altering the geometry of the tiles or dice (i.e., forms), and intuitive
categorization of tiles into bonus and regular tiles (i.e., arrangement) are all among
the structural changes that can cause irregularities in an existing game. Such struc-
tural changes to an existing tabletop game may need redesigning the game. What we
consider as redesigning is the process of introducing such changes to an initial state
of a game system and designing to accommodate these changes in a unified and
newly defined state of the game system. A redesigned game by learners can either
serve existing purpose of the original game or a new purpose. In this process, learners
quantify, categorize, and systematize relevant objects, relationships, and actions
(Lesh & Doerr, 2003).
In this study, we explore how learners engage in STEM learning when provided
opportunities to express their creativity when collaboratively redesigning a tabletop
game, called Triominos. We discuss how differences in game redesign can emerge
from learners looking at a single tabletop game through different lenses. In our
research, third and fourth graders (age ranging from eight to ten) in a West-Canada
school transformed Triominos into paper-crafted games and explored how using
different regulations, scoring mechanics, shapes, numbers, and symbols change the
game rules, its look, and the experience of play. We collected qualitative data during
the classroom sessions that spanned six weeks. We took observation notes, video-
recorded the whole class sessions, took photos of students’ progress, collected their
artifacts, and interviewed them and their teachers at the end of the project. We analyzed
the data through different lenses (i.e., mechanics, dynamics, and aesthetics) to position
the activities of redesigning tabletop games (i.e., identifying and modifying their
varying components and aspects) as an approach to disciplinary engagement in the
STEM classroom.
Theoretical Framework
Hunicke et al. (2004) proposed the basic game components of mechanics, dynamics,
and aesthetics (MDA framework). Game mechanics is about designer or developer’s
specifying rules (e.g., what are possible moves in each turn, how to score and win) in
the game. Dynamics portrays how the rules work in action through player interaction
with the game (e.g., how an opponent’s actions influence a player’s ability to score in
a turn). Aesthetics is concerned with how the game influences the sensual and
emotional perceptions of the player (e.g., how a player feels about the progress). MDA
has been useful in allowing game designers to consider the perspective and experience
of players as a meaningful part of the design and development process, especially for
videogames (Kim & Lee, 2015). For researchers, examining how MDA components
work together or influence each other can help understand how players engage in
meaningful play. These three basic game components can influence each other as part
of the design process and through game play (Figure 1). LeBlanc (2004) argued that
“each component of the MDA framework can be thought of as a ‘lens’ or a ‘view’ of
the game – separate, but casually linked” (p. 1724). Mechanics is the lens through
4 Simulation & Gaming
which designers and developers make the game, while players perceive the game
through the lens of aesthetics. Dynamics mediates mechanics and aesthetics lenses.
While Hunicke et al. (2004) proposed MDA for videogames, it is useful in examining
other forms of games, such as board and card games. For example, in a game of chess,
each piece has properties relevant to mechanics, such as possible actions relative to its
position. When a player changes the position of a piece or takes actions to do certain
moves, dynamics emerge. For example, a player’s first move of a pawn influences
how the other player puts certain mechanics and strategies into practice, by choosing
which piece to move. If a player mentions, for example, “it was a weak opening”, the
player refers to aesthetics, an interpretation based on the game play experience.
As interacting and interrelating components, mechanics, dynamics, and aesthetics
work as a unified whole towards a common goal (e.g., entertaining, learning, training,
etc.). Designing a game can help learners to develop systems thinking (Akcaoglu &
Green, 2019) as any change to the game, as a relatively complex system, can intro-
duce disorder, irregularities, and chaos to the system. Redesigning a game can be
considered as the process of introducing a change to an initial state of a game system
and modifying different aspects of it to accommodate the changes toward a unified
and new state of the game system. Many iterations may take place throughout this
process: even a small difference in initial conditions of a game, such as those made
to alter looks, can yield widely diverging outcomes. For example, if the range of the
numbers used in a matching tabletop game increases by adding two more numbers,
the number of the possible combinations of numbers drastically increases as well.
Depending on the situation, such increase may not be reasonable for a game designer
or a game company as producing the tiles will require more time, resources, and
labor. Sometimes, the iterations are related to accommodating a feasible change in a
Figure 1. The reciprocity among the game components of mechanics, dynamics, and
aesthetics (MDA) along with the learning outcomes emerging from the application of MDA
framework in different studies.
Rahimi and Kim 5
better way. For example, a game design team finds that adding bonus tiles to a same
matching tabletop game is feasible. Thus, designers make bonus tiles with a special
sign on top of it to make it different from all other tiles. Then, the design team recon-
siders this after playtesting and decides on changing the color of the bonus tiles as
well, to make them stand out better for the players. The game design process has
always depended on playtesting wherein players’ feedback on the game is pivotal to
the development of the final product. Similarly, playtesting is important in redesigning
a game. It gives opportunities to see how well a change is accommodated in the
redesigned game and at which points the designer needs to go back and refine the
game for another round of playtesting.
Since its inception, the MDA has been used for framing how we understand, design,
and use games in non-game contexts and various disciplines (Deterding et al., 2011).
Amriani (2014), Enders (2013), and Kapp (2012) showed creating games, using MDA
framework in educational research, can support learners in trying unconventional
ideas in solving problems (i.e., motivating actions). Ramesh and Sadashiv (2019) used
MDA framework for game-based learning and analyzing the differences between
traditional method of teaching chemistry and board game-driven learning. Their study
showed “better learning and more in-depth understanding in favor of the board game”
(Ramesh & Sadashiv, 2019, p. 975). Domingues et al. (2013) applied game design
elements in learning management system and found that students who used game
design elements in their practice scored higher marks in practical assignments that
encouraged taking new approaches, such as designing and problem solving, in an
unconventional way.
Learners engagement in a participatory game design project can take the forms of
seeking inspiration from beyond the classroom or learning from peers (Baradaran
Rahimi & Kim, 2019; B. Kim et al., 2015). In redesigning games, the inspirations may
come from a game that learners play and be used for changing mechanics, dynamics,
and aesthetics of another game. For instance, adding bonus tiles to a matching game,
wherein having bonus tiles is not defined, alters the mechanics of matching as a bonus
tile may be played with any tile and at any moment. Learning from peers can take
place in the exchange of thoughts and feedbacks within a team. For example, a learner
may see an idea in a single way but when this idea is shared with teammates, the
learner may see it from different perspectives through the feedbacks received from
teammates. Participatory game (re)design projects may encourage a variety of new
approaches (Baradaran Rahimi & Kim, 2019; Jenkins, 2009; Resnick, 2007). To
exemplify, experimenting with tile shape, finding new ways of combining tiles, and
tinkering or refining solutions to accommodate changes in the game system in a
matching tabletop game can motivate actions and get learners to actively learn systems
thinking (Baradaran Rahimi et al., 2020). Promoting learning can take different shapes
in redesigning a game depending on the topic of the course. For instance, redesigning
a game in a mathematics classroom may promote and pave the way for exploring
complex topics in math like division, combination, and topology1. Moreover, the
social interactions within and between the teams can promote learning in terms of
6 Simulation & Gaming
giving and receiving feedback as well as group decision making (Baradaran Rahimi &
Kim, 2019; Zimmerman, 2009). The main problem that learners solve in redesigning
a game is that they introduce a change to the game system of an existing game (initial
state) and accommodate these changes within a new game system (new state) through
design and playtesting (Baradaran Rahimi et al., 2020). The changes can be made to
the game mechanics, dynamics, and aesthetics, each introducing a sub-problem to be
solved by learners. For example, implementing new rules, reformulating matching
mechanism, developing a new scoring system, or changing shape and looks of the tiles
in a matching tabletop game, each introduce a sub-problem that are related to one or
more of the game components (MDA) and influence the initial state of a game system.
Research Design
The study was conducted in an inner-city elementary school in western Canada, after
obtaining the ethics approval for the study from the Conjoint Faculties Research
Ethics Board at the University of Calgary. We worked with a teacher who was
facilitating STEM classes across different grades. Her STEM classes were intended
for learners to use their disciplinary knowledge from their regular classroom
meaningfully through various projects. Based on her previous experiences, the teacher
selected the game, Triominos for learners to play and redesign, in order for them to
engage in STEM learning. Triominos has 56 triangular tiles with three numbers
(between 0 and 5) in three corners. Two to four players compete to reach 400 points
and win the game by matching two numbers on one side of the triangle and earning
points. The redesign process took six weeks for three and four graders (two or three
45-minutes sessions per week). Learners made several paper-crafted versions of the
game. The process started with an introduction to Triominos’ rules followed by a
discussion of strategy versus luck in Triominos. In a following session, the teacher
discussed the changes that could be done to the game with learners (Figure 2). They
considered the changes in shape, size, rules, scoring system, the symbols appearing on
Figure 2. Students and the teacher decided to change several aspects of Triominos.
Rahimi and Kim 7
each tile, and interactions like how to draw tiles for redesigning Triominos. Learners
began with working on their individual ideas for redesigning Triominos. The teacher
then teamed up the students based on the similarity of their individual ideas in groups
of two to four students. As teams, learners and the teacher discussed board-game
design and made a rough version of their tiles and developed the rules for their game.
Later, the teacher provided learners with a printed checklist to determine if their tiles
are created identical in terms of shape and size, if the symbols, letters, or numbers are
organized consistently, and if their rules and scoring systems work properly. Learners
play-tested their games and adjusted their games. After discussing what they would
need in a rulebook, the teacher provided a template for students to start recording the
rules as they play-tested.
Our data collection combined intrusive and obtrusive approaches. Influenced by
research methods in anthropology, the intrusive approach involves researchers
building rapport and interacting with participants, whereas in the obtrusive approach
researchers only observe the participants and take notes without interactions (Bernard,
2017). For obtrusive data collection, one researcher was a silent observer taking
detailed notes on all the students within their groups while video-recording the
progress of the learners. The teacher carried a GoPro to record her interactions with
team members. Learners were informed about videorecording by the GoPro, but it did
not change the interactions between the teacher and the students based on our observa-
tion. This was useful since the GoPro could record the organic and natural interactions
of the learners. For intrusive data collection, another researcher made conversations
with learners while video-recording the progress of redesigning Triominos. Data
collection was followed by a semi-structured interview with the teacher and learners
at the end of the sixth week. Data analysis included transcribing the interviews and
logging observational videos. Video logging was event-based to note ongoing interac-
tions. Textual materials, including the video logs, transcriptions, and observation
notes, were initially analyzed using margin coding approach (Baradaran Rahimi &
Kim, 2019; Bertrand et al., 1992).
We took an open coding approach and thematically analyzed data that we collected.
There was no master list of competencies for us to create codes and themes. Instead,
we expected that STEM learning would emerge differently in each group as learners
bring their own interest and ideas. As we progressed through the analysis process, we
could link the codes and themes to those competencies we identified from literature
(Figure 1). One researcher was responsible for coding, categorizing, and interpreting
the data in line with the research goal (i.e., exploring how learners engage in STEM
learning by redesigning a tabletop game). Another researcher independently checked
the interpretations, and then researchers discussed the interpretations for consensus.
To establish the trustworthiness of our findings, we triangulate our findings from
multiple sources of data between the researchers. After we went through this process
multiple times a systematic analysis of the findings using mechanics, dynamics, and
aesthetics categories was conducted and both researchers discussed the codes and
categories as well as the interpretations for the consensus. After we went through this
8 Simulation & Gaming
process multiple times, the codes, categories, and comments were selected for inclu-
sion in this paper.
Findings
While starting from the same game (i.e., Triominos), learners’ redesigned games were
diverse in their components and elements. Using the lens of mechanics, dynamics, and
aesthetics as basic game components (Hunicke et al., 2004), we analyzed the changes
made by different groups to some elements in Triominos, such as rules and shapes. We
also explored how decisions made by learners on components and elements of the
Triominos resulted in different versions of the game and how thinking about scoring
system, game rules, and tile shapes could expand the capacity of students for learning
mathematics. Although we sent out consent forms through the school authorities to all
the parents, we only received consents from the parents of 11 learners. We were able
to select three groups of three participants with consent. In the following sections, we
discuss these three groups who redesigned Triominos, paying attention to the actions,
discussions, and learning that took place in each group through the lens of mechanics,
dynamics, and aesthetics. To protect confidentiality and anonymity, all names used in
this paper are pseudonyms.
‘Squareominos’ and the Creative Strategies and Rules
This group (one girl and two boys) decided to go with rectangle (square shape) for the
tiles. This decision and selection of shape added another corner to the triangular tiles
of the original game. Primarily, learners wanted to use numbers, one to eight, on their
tiles. Discussing this with their teacher, learners discovered that they needed to make
too many tiles based on the numbers they chose and the number of the corners their
tiles had:
Teacher: Do you remember how many tiles are there in Triominos?
Mimas: Like 56.
Teacher: Yes. How many numbers they have on Triominos?
Mimas: 1 to 5.
Teacher: I think it is 0 to 5. Remember that 5,5,5 is the biggest tile and 0,0,0 is the
smallest tile. So, in Triominos with 3 numbers on each tile going from 0 to 5 there
are 56 tiles. So, think about you are doing square and choosing to go up to 8. How
many tiles do you have?
Mimas: Oh, a lot.
Rahimi and Kim 9
Understanding that they needed a lot of tiles, learners considered reducing the numbers
and adding a few shapes. They wanted to match the number of sides that a shape has
with a number written on other tiles (Figure 3). For example, number four could match
with a square or three with triangle. However, this solution did not really reduce the
large number of tiles they needed, and the game was still complex to create:
Teacher: Over here I can see that you started planning to put circles and squares
together on your tiles. You need to come up with a system to include all combinations.
Are you planning to do some tiles with shapes and some with numbers?
Mimas: Yes, like circle with zero, triangle with three, square with four.
Yoda: No, I do not want.
Teacher: It is easier to go with one of them and if you still want the numbers, you
can add them later.
Based on the feedback received from the teacher, learners reduced the complexity of
the game by only keeping shapes on all the tiles (Figure 3). They started with five
shapes (circle, square, star, triangle, and hexagon). Later, in another session, they
decided to remove hexagon after group discussions about the number of sides that a
hexagon has. After removing hexagon, they eventually listed 35 different combinations
of their tiles (Figure 3). The process of listing all the combinations on a piece of paper
was suggested by the teacher to several groups.
To define the player who starts the game, the shape drawn on the tile and the
number of the edges for each shape was important. For example, star has ten points as
it has ten edges. Square has four points as it has four edges. Triangle has three points
as it has three edges and circle has one point as it has one edge. Each player gets five
tiles and a player with the highest points for a tile starts the game. For instance, a
player having a tile with four stars on it begins as there is no tile with a higher score
than 40. In the game, players score the points of the edges (both sides) that they match.
As figure 3 shows, a player matching stars on both edges gets 40 points. If players
create a bigger rectangle (4 regular square tiles or more) the one who puts the last tile
gets all the points on the bigger square or rectangle (Figure 3). There was a score
Figure 3. Making shapes and scoring bonus point (left). Pairing edges and scoring 40 points
(middle). Partial listing of different tiles combinations (right).
10 Simulation & Gaming
keeper role in this game marking the scores of the players on a blank paper. When all
players ran out of the tiles, the score keeper adds up the scores earned by each player
and defines the winner based on the highest points earned.
These observations show that learners developed the matching rule of the game
based on the shape they chose for the tiles. Making connections between the chosen
geometrical shapes and the matching rule of the game provided opportunities for
students to think mathematically through the game redesign. Changing the tile shape
implicitly changed one of the main rules of the game and encouraged learners to think
about all the combinations they may have by increasing or decreasing corners. In this
case, redesigning the game helped learners familiarize themselves with the complex
topic of combination in mathematics in a simpler way: writing down the combinations
on a piece of paper. Changing the shape, not only influenced the mechanics (i.e.,
matching rule) but also the dynamics and aesthetics of the game. More corners and
one additional edge to the tiles meant more opportunities for matching. Moreover,
such a change could make the game more complex and time consuming as more
corners and wider range of numbers on the tiles makes score calculation more complex.
Making a game more complex or giving extra opportunities for matching tiles by a
single change could influence the dynamics of how players interact with the matching
mechanics and rule of the game. The changes that learners made in terms of scoring
system, rules of the game, and creating tiles not only influenced the mechanics,
dynamics, and aesthetics, but also provided a context for understanding how a
seemingly small change could destabilize the game system and motivate learners to
further modify the game.
‘Rhombinos’ (Wild Edition) and the Iterative Process of Redesigning Game
This group (three boys) decided to change the triangular shape of the Triominos tiles
to rhombus. Primarily, learners within this group had different ideas for the tiles’ shape
based on their individual ideas. However, after discussions within themselves the
teammates agreed to go with rhombus:
Teacher: What is going to be your scoring rule?
Aron: Adding up all the numbers on the matching tile.
Kia: Adding up the numbers on the matching edges.
Dennis: The edge that you match you get the points for.
Teacher: Can you write this rule in the rule book please and draw a picture to show
what that means.
After group discussions, they came up with an agreement on using rhombus tiles and
a numbering system from zero to six where they put a number on each corner of a tile.
Rahimi and Kim 11
These numbers were used for matching tiles and scoring points equal to the numbers
written on a matching edge. All these decisions, changes, and discussions influenced
the dynamics of the game where the behavior of the rules and mechanics in play are
different from Triominos. The scoring system underwent several iterations and
developed over time (Figure 4). Based on our observation, the scoring rule change had
three main benchmarks. Switching among different rules was often facilitated by the
discussions within group, between group and teacher, as well as game playtesting. The
three rules that Aron, Kia, and Dennis mentioned above are shown side by side on a
single frame in figure 4. In the first scoring rule, players got the points of the edge that
they match (i.e., the edge of the tile that they put down). The second rule was that the
player adds up and scores all the numbers written on the tile that s/he plays. The third
rule was that a player gets the points of the edges (both tiles) that s/he matches.
Rhombinos had 24 regular tiles (in black) and six wild cards (in green) with each
player getting three tiles to start with:
Teacher: Can we play an example of your game?
Aron: Three pieces for each player.
Teacher: Why do you only start with three?
Aron: Because we did this, we have 24 pieces. 3, 6, 9, 12, 15, 18, 21, 24.
Dennis: If we started with more pieces there were less pieces left on the floor to
continue with.
Teacher: I see. so, you select small number that more people can play your game.
Kia: And there are more tiles to draw from.
This conversation shows that the learners wanted the number of tiles in Rhombinos to
be divisible by three maybe as their team had three members and this could make the
game very specific to three players. The wild cards (in green) could be used everywhere,
and players could match it with all the tiles in the game regardless of their numbers.
Figure 4. Various tried scoring system, first (left), second (middle), and third rules (right).
12 Simulation & Gaming
When a player matched a wild card with another tile, s/he gets five points for each edge
(Figure 5). Another way to score bonus point in Rhombinos was completing a star
shape (6 rhombuses) with a regular black tile to score 50 points or completing a star
shape (6 rhombuses) with a wild card, to score 40 points. Whenever a player did not
have a matching card s/he had to draw a card from the stacks of the cards and lose a
point per draw. Moreover, a player would lose one point when placing a card that does
not match and must skip the turn. For the score keeping, the players wrote down their
points in each turn on a blank paper until a player earned 200 points (winning state).
As per these observations, there was a range of shapes that a player could create
with the tiles to get a bonus point in this game (Figure 5), including two- and three-
dimensional geometries like star (2D) and cube (3D) or hexagon (2D). Thinking about
a certain number of the tiles to be divisible by three in the redesigned game implied
learners to touch upon a more complex topic in mathematics, divisibility. Losing
points in this game was a new mechanics, that influenced its dynamics as well as
aesthetics by requiring players to be more meticulous in their matches and score calcu-
lations. The three benchmarks in developing the scoring system fall into those changes
made to mechanics. Changes in the way that players score points can influence the
complexity and difficulty of the game as a result. Moreover, the iterative process of
developing the scoring system provided learners with a context to familiarize
themselves with the iterative process of game design and how it can evolve to
overcome complexity and disorder.
Figure 5. Scoring bonus points: matching a wild card with two regular cards and scoring 5
bonus points for each matching edge (left), completing a star with a regular card to score 50
points (middle), and completing a star with a wild card to score 40 points (right).
Figure 6. Random numbers in the middle of tiles indicates the points that a player gets when
s/he matches (left). Using ruler (middle) and a cardboard template for tracing and cutting the
tiles (right).
Rahimi and Kim 13
Type-Ominos' and the Incorporation of Inspirations and Ideas
This group (three boys) decided not to change the triangular shape of the Triominos
tiles and used this shape for the tiles. The game included 35 regulars and five Star tiles
(bonus). Regular tiles had different symbols on their corners and a number in the
middle. The number in the middle of each tile showed the points each player earned
when matching tiles (Figure 6). The Star tiles had a star in the middle.
Learners chose six symbols to go onto their tiles: grass, star, water, fairy, steel, and
lightning. Except the star that went on top of the star tiles (bonus), these were placed
on the corners of the regular tiles. Based on the rule book of this game, players get six
tiles to begin with (i.e., mechanics):
Teacher: What system did you use to create your pieces? I do not see steel, steel,
grass and steel, steel, star. I think you guys do not have all the pieces made yet.
Have you tried playtesting your game?
Bob: we will try.
Teacher: So, you have six different symbols same as in Triominos. How many tiles
are in Triominos?
Bob: fifty…
Teacher: There are 56 tiles in the Triominos. You have the same number of symbols,
and your tiles are the same. But because you are placing one of your symbols (i.e.,
star) on the whole tile, you have fewer than 56… There is only one star piece?
Bob: There are five.
Teacher: I see you did some matches here. How did you play your game?
Winston: weird because this one is like a random number; we do not know what to
do with this one.
Teacher: Often, there are handful of pieces in front of me and I cannot play any
of them. right? That happens a lot in games and that is why you have to draw. So,
that is ok.
Teacher: Playtesting is not just playing the pieces that are matching. Playtesting
would be dividing up your pieces and taking turns to play them to make sure there
is enough to choose, make matches, and draw to make matches.
Winston: There are two pieces that match here.
Teacher: Yes, there are times that you can choose between two pieces that work.
What strategy we use to say which piece is better to play?
14 Simulation & Gaming
Winston: Highest.
Teacher: Exactly. the highest.
In this game, a player with the lowest number written in the middle of a tile started the
game. This rule is different from the original rule in Triominos wherein the player with
the highest combination of numbers on a tile starts the game. When a player matched
regular tiles, s/he got the points written in the middle of the tile that s/he played. A
player could put a wild card anytime and anywhere to earn 20 points since it could go
with all the tiles. Players could also attach any tile to a Star tile. Matching a Star tile
with a regular tile had 20 bonus points. Making a shape (e.g., rectangle) with the tiles
earned a player 10 extra points. The game continued until there was no more tiles to
play. Consequently, a player with the highest score was the winner.
Although their redesigned game has similarities with Triominos, changing scoring
system, rules of the game, and conceptual inspirations from other games, like
Pokémon, transformed the mechanics, dynamics, and aesthetics of the original game.
One of the researchers overheard the learners within this team talking about Pokémon
among themselves. They were also excited to show us Pokémon and explain the
types during the interview. As such, the changes in rules and mechanics of the game
were inspired by the aesthetics, their enthusiasm toward the symbols adopted from
Pokémon types. This observation was supported by the teacher’s remark that Winston
is an artistic person. This skewed enthusiasm about aesthetics came with its own cost
as learners struggled to incorporate the idea of having types in the game. Matching
different symbols (types) added to the complexity of play while adding Star tiles
increased the possibility of playing when there is no matching tile. Switching from
the numbers in Triominos to the types in Type-ominos implicitly involved learners
with a more complex topic in mathematics, equivalence relation. Instead of matching
numbers, different symbols (i.e., types) were considered equivalent and were paired
by players for scoring points. Although learners did this accidentally, it also demon-
strates that redesigning the game could expand the capacity of students for learning
mathematics.
Discussion
We observed that engaging in the game (re)design process with different components
of MDA model is associated with STEM learning. The changes that learners made to
the game may appear simple or cosmetic (e.g., change in shape, size, and symbols).
The uniqueness in the redesigned games, however, can emerge from looking at the
changes through different lenses. The three redesigned games discussed in this paper
demonstrate how even one change made by learners to the shape, or the symbols
drawn on the tiles can eventually change the mechanics, dynamics, and aesthetics of a
game, while learners’ choices could encourage learning (Table 1). For example,
changing the shape or the symbols on the tiles engaged learners in creating new rules
(e.g., starting the game with three tiles in Rombinos), scoring systems (e.g., scoring
Rahimi and Kim 15
Table 1. Activities, outcomes, and competencies emerging in three groups thrughout the (re)
design process
(Re) designed
game Learners’ activities
STEM related
outcomes Competencies
Squareominos Changing tiles’ shape
from triangle to
rectangle
Understanding the
geometry of shapes,
similarities, and
differences
Systems thinking
Using four sides and
corners for the game
Understanding and
reformulating the
matching mechanism
Tinkering with
rules and rening
solutions
Considering numbers
from one to eight as
well as ve symbols
to go on tiles
Understanding the
complexity of com-
binations by writing
them down
Controlling the
complexity by
reducing the used
symbols to four and
not using numbers
Playtesting the game Understanding and
modifying the system
of scoring for the game
Connecting reac-
tions to design
decisions
Introducing a change
of tiles’ shape and
combination simulta-
neously to the initial
state of Triominos
Understanding the
impact of changes on
Triominos leading to a
(re)design
Promoting learn-
ing (i.e., exploring
complex topics like
combination, topol-
ogy, and game design)
Rhombinos Experimenting with
rhombus tiles to shape
star (2D), cube (3D),
and hexagon (2D)
Understanding the
relationship between
scoring system and
geometry by match-
ing tiles
Experimenting with
new tile combina-
tions
Negotiating different
ideas for matching
and scoring points,
such as adding up all
the numbers on a tile
vs. matching edges
Understanding the
gaps of their matching
system and lling it by
adding wild cards with
bonus points
Problem solving
Not considering all
the tile combinations
Understanding the
value of keeping the
number of tiles divis-
ible by the number of
players (3)
Implementing new
rules and deepen-
ing learning about
divisibility
Introducing a change
of tiles’ shape and
scoring mechanism
simultaneously to the
initial state of Triominos
Understanding the im-
portance of accommo-
dating any issues caused
by decisions they made
in a (re)design
Promoting learn-
ing (i.e., exploring
complex topics like
game design)
(continued)
16 Simulation & Gaming
(Re) designed
game Learners’ activities
STEM related
outcomes Competencies
Type-ominos Keeping the trian-
gular tile shape but
introducing types to
Triominos
Understanding
matches and scoring
points based on types
and xing matching
issues by bonus tiles
Finding new ways
of making and xing
and problem solving
Getting inspirations
from the Pokémon
types
Understanding the
relevance of (re)de-
signing game to their
interest in another
game’s matching sys-
tem and scoring bonus
points
Noticing something
useful
Using ruler and
cardboard template
for tracing and cutting
the tiles effectively
Understanding the
values of using tools
in making accelerable
and consistent tiles in
a shorter time
Motivating actions
(i.e., exploring
unconventional ways
of doing)
Showing Pokémon and
explaining the types
during the interview
Understanding the
relevance of giving
context to others to
better connect with
the (re)designed game
Increasing participa-
tion
Introducing a change,
inspired from Poké-
mon to the initial
state of Triominos
Understanding anoth-
er game, they already
played and mapping a
few systems onto the
(re)design project
Promoting learn-
ing (i.e., exploring
complex topics like
equivalence relation
and game design)
bonus points by making star shape in Type-ominos), and matching mechanisms (e.g.,
matching symbols with numbers in Squareominos). Consequently, dynamics were
developed based on these mechanical changes during the playtesting. For instance,
learners found that adding one more corner to the shape and extending the range of the
numbers that can go on top of the tiles, could result in more tiles. Thus, they found
ways of handling this by reducing the range of the numbers and symbols (e.g., in
Squareominos and Type-ominos) or keeping the number of tiles divisible by the
number of players instead of including all the combinations (e.g., Rhombinos). Such a
dynamical change could result in aesthetical changes and influence the experience of
player. By reducing the range of the numbers going on top of the tiles on some
occasions and keeping it divisible by the number of the players or by adding bonus
tiles (e.g., in Type-ominos and Rhombinos) made the games less complex and more
fun for the players as we observed and played these games in the interview sessions.
Table 1. Continued
Rahimi and Kim 17
It seems that when learners are involved in (re)designing a non-videogame irregu-
larities and changes in any of the mechanics, dynamics, and aesthetics can open doors
for further changes on all aspects of the game and encourage learning subjects like
mathematics while paving the way for developing certain competencies and engaging
in various activities (Figure 7). Some of these activities and competencies emerged
when learners worked on mechanics (Figure 7). For example, implementing new
rules, reformulating the matching mechanisms, and developing new scoring systems
in all the three games that learners redesigned targeted the mechanics of the Triominos.
Some other activities, such as experimenting with new tile combinations, numbers,
and symbols were complemented by the playtesting sessions where learners could put
the changes into play (Figure 7). Moreover, when learners discovered that a change in
the shape or symbols on top of the tiles can cause other problems to solve (e.g., larger
number of tiles than expected), they found new ways of making their game and dealing
with the new problem by reducing the number of symbols and combinations or prior-
itizing divisibility of the number of the tiles by the number of the players. Tinkering
with rules and refining solutions also emerged from the dynamics specially when the
learners play tested their game. For instance, learners who worked on Rhombinos
refined the method of scoring points when matching tiles during a playtesting session
and conversation with their teacher. A series of competencies emerged when learners
focused on the aesthetic aspects of their games (Figure 7). Learners’ activities and
developing competencies were associated with controlling for the complexity of the
game by keeping it simple but entertaining and connecting emotional feedback and
reactions from other players of the game to the design decisions. For example, in
Figure 7. Authors’ assumption of different components of MDA model encouraging learning..
18 Simulation & Gaming
Type-ominos, one of the learners (i.e., Winston) expressed that their game acts “wired”
on some occasions during the play. Yet, the teacher explained that it is very normal for
the games to act like this. Their conversation shows that a learner as a designer and
player had an emotional response to the game and looked for external emotional
responses from others. These discussions also show that even though a change may
seem cosmetic at the first glance, such as changing the shape of tiles, it can profoundly
engage the players in thinking critically and designerly about the mechanics, dynamics,
and aesthetics of the game.
The changes that learners made to Triominos not only engaged them in the process
of game design but also encouraged learning simple and complex mathematical
concepts, ranging from addition and subtraction to division, combination, and
topology. For example, the triangular shape of the tiles in Triominos changed to
rectangle in Squareominos and Rhombinos. Topologically, triangle and rectangle are
homomorphic (Lawson, 2003). This means that, if a point in the triangle be mapped to
by some point in the rectangle, no other point in the rectangle maps to the same point
in the triangle (Armstrong, 2013). Moreover, any point in rectangle should have some
point in triangle that maps to it (Armstrong, 2013). This does not mean that learners
knew about topology, but it shows that it is possible to contextualize and facilitate
learning complex mathematical topics in game (re)design practices. Another example
is the concept of combination that was practiced by learners in a simple way when the
teacher asked them to write down all the possible combinations of symbols on their
tiles. For Triominos with triangular tiles and numbered from zero to five (i.e., six
numbers). the number of multisets of 6 (n) items taken 3 (k) at a time equals 56,
according to the following equation (Benjamin & Quinn, 2003):
n
k
nk
k
=+−
1
If we use the same equation for Squareominos, the number of multisets of four items
(i.e., symbols selected by the learners in this group) taken four at a time (i.e., as each
tile has four corners in squire) equals 35. As data shows, the number of tiles that
learners reached by writing down all the combinations – as per teacher’s suggestion
– that could go on top of their tiles was also 35. The case for Type-ominos was a bit
different. This group had six selected symbols to go on top of the tiles. However, as
they kept one symbol only for bonus tiles, the number of multisets of five items (i.e.,
remaining symbols selected by the learners in this group) taken three at a time (i.e., as
each tile has three corners in triangle) equals 35. Adding the five bonus tiles with the
star on top, the total number of tiles for Type-ominos equals 40. As data shows, learners
reached the same number of tiles (i.e., 40) by arranging and making matches during
the playtesting. As per Rhombinos, this team used another strategy for making tiles
that was connected to divisibility rule in mathematics. According to the data, this
group selected six symbols to go on top of their tiles with four corners. This makes the
number of possible combinations 126. However, they only made 24 regular tiles and
six bonus tiles for their game. The reason was that this game was designed by learners
Rahimi and Kim 19
for three players, and as data shows, learners tried to keep the number of tiles to start
with and the total number of regular and bonus tiles divisible by three.
Conclusion
In this study, we positioned the activities of redesigning a tabletop game, (i.e.,
Triominos) as an approach to disciplinary engagement in a STEM classroom. In this
study, we attended to how learners’ activities could encourage different disciplinary
learning and social engagements within and around the classroom. Redesigning game
gave learners opportunities to express their creativity and generate ideas collaboratively.
In our research, third and fourth graders (age ranging from eight to ten) in a
West-Canada school transformed Triominos into paper-crafted games and explored
how using different shapes, numbers, and symbols change the game rules, looks, and
experience of the game. The outcomes show that any changes, even trivial at the
beginning, can fundamentally influence aesthetics, dynamics, and mechanics of the
game. Learners engaged in various activities and developed competencies, such as
tinkering with rules and refining solutions. The outcomes from this study demonstrate
the role of redesigning games in deepening their understanding of design and
mathematics in STEM classrooms. The outcomes help teachers identify strengths of
redesigning games in encouraging learning complex mathematical concepts, such as,
topology, combination, and divisibility rule. Instead of solving prefabricated math
problems, learners were engaged in solving problems that were composed throughout
the process of redesigning Triominos. One may consider learning through redesigning
a game as an open-ended way of encouraging learning mathematics. This resonates
with the open-ended nature of redesigning a game wherein there is no ending for the
possibilities to change game components and accommodate the changes in a new state
of the game components. In a deeper level, this project can help teachers develop an
improved curriculum for mathematics and STEM classrooms based on redesigning
tabletop games. The outcomes also show the differences between the approaches that
children take for redesigning a same game with the same assumptions.
The scale of this study was small as only about a quarter of the parents provided
their consents for including data collected from the learners within both classrooms
(i.e., 11 out of 45) in the study. This introduced another limitation in terms of the
participants’ gender as three groups with complete consents had dominantly male
students. As such, discussions of gender and its influence on the results remained out
of the scope of this research. Moreover, conducting the research in an inner-city
elementary school in western Canada, might make it specific to location, and influ-
ence the generalizability of the study. Future studies may focus on the application of
this approach in other K-12 grades, with more diverse groups in term of gender and
geographic locations. The role of the teacher in guiding the projects and providing
feedback is another area to pay attention to in the future studies. Although several
times the guidance from the teacher encouraged learners to develop their work, we
observed few occasions that learners lost their interest because of the feedback they
20 Simulation & Gaming
received from their peers and teacher. Thus, a deepening their understanding of the
role that these guidelines and feedbacks can shed light on the individual differences of
learners and their development over time in the classroom. It is interesting to study
how other games can offer opportunities for redesigning and learning subject-specific
matters. This research paves the way for further studies and opens the door for more
question to be answered in the future studies.
Acknowledgments
We thank the teachers and the students who participated in this research. Special thanks to
reviewers and the research team members at the University of Calgary who contributed to the
project.
Declaration of Conflicting Interests
The author(s) declared no potential conicts of interest with respect to the research, authorship,
and/or publication of this article.
Funding
The author(s) disclosed receipt of the following nancial support for the research, authorship,
and/or publication of.this article: This research was supported by Government of Alberta,
Canada and the University of Calgary.
Note
1. Topology is the study of intrinsic, qualitative properties of geometric forms that are not
normally affected by changes in size or shape (Armstrong, 2013; Lawson, 2003).
ORCID iD
Farzan Baradaran Rahimi https://orcid.org/0000-0001-5938-0181
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Author Biographies
Dr. Farzan Baradaran Rahimi, is an interdisciplinary researcher, educator, and designer at
the University of Calgary, Canada. His research incorporates emerging technology, STEM
education, museology, and integrative design. Previously, he worked as a registered architect
and lead designer of public buildings in Iran and served as the Director of Gallery Future Media
at the University of Calgary.
Dr. Beaumie Kim is Professor of the Learning Sciences at the Werklund School of Education,
University of Calgary, Canada. Her research is focused on engaging learners in playing and
designing games that model ideas, concepts, and systems, and also express something about
themselves. Her research work is carried out in collaboration with teachers and students as
design partners, and by observing their interactions, discourse and artifacts.
ResearchGate has not been able to resolve any citations for this publication.
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