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"I Just Won Against Myself!": Fostering Early Numeracy Through Board Game Play and Redesign

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Children can develop a variety of mathematical concepts, as well as a positive relationship with mathematics, through playing and redesigning board games. In this article, the authors introduce the process of integrating board game play and redesign into the early mathematics classroom. Presenting cases from a diverse school, they highlight learning opportunities that fostered early numeracy. They discuss how children demonstrated their understanding of integrated numeracy (including subitizing, ordinality and cardinality of number, the area model of multiplication, spatial reasoning, and problem posing and solving). The project not only fostered children’s early numeracy but also helped them to develop a positive relationship with mathematics and social rules and to see themselves as designers, problem solvers and creative people.
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22 Early Childhood Education, Vol 46, No 1, 2019
“I Just Won Against Myself!”:
Fostering Early Numeracy Through
Board Game Play and Redesign
Shayla Jaques, Beaumie Kim, Anna Shyleyko-Kostas
and Miwa A Takeuchi
Shayla Jaques is the math learning leader at an
inner-city elementary school in the Calgary Board of
Education, in Calgary, Alberta. She teaches STEM
(science, technology, engineering and math) to
students in Grades 1–6. She is passionate about not
only exploring new learning approaches for young
learners but also playing and designing board games.
Beaumie Kim is an associate professor of learning
sciences at the Werklund School of Education,
University of Calgary. Her work focuses on
empowering learners to design learning resources and
tools using games. She carries out her work in
collaboration with teachers and students as design
partners and by observing their interactions, discourse
and artifacts.
Anna Shyleyko-Kostas is a kindergarten teacher at an
inner-city elementary school in the Calgary Board of
Education. She is passionate about hands-on, play-
based learning in the early years and believes in
providing authentic experiences for her young
students. She also enjoys playing games and spending
time outside with her family.
Miwa A Takeuchi is an associate professor of learning
sciences at the Werklund School of Education,
University of Calgary. Her expertise and research
interests include equity and diversity in early
mathematics/STEM education and the co-design of
robust learning environments with learners, teachers
and parents.
Abstract
Children can develop a variety of mathematical
concepts, as well as a positive relationship with
mathematics, through playing and redesigning board
games. In this article, the authors introduce the process
of integrating board game play and redesign into the
early mathematics classroom. Presenting cases from a
diverse school, they highlight learning opportunities that
fostered early numeracy. They discuss how children
demonstrated their understanding of integrated
numeracy (including subitizing, ordinality and
cardinality of number, the area model of multiplication,
spatial reasoning, and problem posing and solving). The
project not only fostered children’s early numeracy but
also helped them to develop a positive relationship with
mathematics and social rules and to see themselves as
designers, problem solvers and creative people.
During the early years, children can develop a
wide variety of concepts through everyday
practices. Play is a meaningful context in
which children can develop mathematical concepts,
symbolization and representation (Charlesworth and
Leali 2012; van Oers 2010). Through play, children
develop key concepts such as arithmetic and
counting, one-to-one correspondence, estimating,
spatial reasoning, measuring, understanding shapes,
logical classication, comparing, ordering, and
understanding parts and wholes (Charlesworth and
Leali 2012; Clements and Sarama 2014; Ginsburg,
Inoue and Seo 1999; Ginsburg, Lee and Boyd
2008).
In the context of game play, McFeetors and Palfy
(2018) focused on the development of strategy and
mathematical reasoning in students when they
played games such as Gobblet Gobblers, Othello,
Tic Stac Toe and Go. Centralizing playfulness in
early numeracy can also foster a positive
relationship with mathematics (Takeuchi, Towers
and Plosz 2016). Alberta Education denes
numeracy broadly as “the ability, condence and
willingness to engage with quantitative or spatial
Early Childhood Education, Vol 46, No 1, 2019 23
information to make informed decisions in all
aspects of daily living.”1
In this article, we present a particular context of
early numeracy development—playing and
redesigning board games. Creating artifacts has a
special place in the mathematics classroom.
Children understand new ideas and form their
identities through creating and inventing symbols
and artifacts (Kim, Tan and Bielaczyc 2015). In their
play, they invent rules while developing key
concepts. Game design encompasses both the
creation of artifacts and the invention of rules. In
designing board games, learners use their bodies by
creating game pieces and create a coherent system
in which their invented rules govern the play (Kim
and Bastani 2017), and they also invent alternative
ways to do mathematics (Barta and Schaelling
1998). Learners model, play and revise the invented
system, in which players engage in movements and
actions and make more sense of it through play
(Salen and Zimmerman 2006).
Few studies exist that focus on early learners’
design of games for their mathematics learning. A
rare example of engaging children in mathematical
game play and design in the early years is Barta and
Schaelling’s (1998) work on Grades 1 and 2
students’ construction of a Native American
counting game. The children created the counting
game using sticks, played the game and then
generated new rules, becoming vehicles of their own
learning.
Through modelling, learners quantify, categorize
and systematize relevant objects, relationships and
actions (Lesh and Doerr 2003). In this article, we
highlight the experience of redesigning an existing
board game and discuss how children’s early
numeracy was fostered, along with their positive
relationship with mathematics.
Project Context: Board
Game Play and Redesign for
Mathematics Teaching and
Learning
This article is based on a research–practice
partnership in an inner-city school in Alberta. The
school had a diverse population of students, 90 per
cent of whom were English-language learners
(ELLs). The school development plan centred on
teaching ELLs complex concepts through rich tasks,
expanding their understanding regardless of
language.
The school took on the project of playing a
variety of board games in every classroom and
exploring the possibility of redesigning those games
or changing some rules. Through the partnership,
we held co-design workshops with teachers,
researchers, and a professional board game
designer and mathematician (Gord Hamilton).2 We
played and then redesigned a variety of games (Hex,
Codenames, Aggression, Qwirkle); built our
understanding of game play and idea iteration; and
came up with ideas for facilitating a similar
experience for students in the classroom. Giving the
teachers time together to work through the rst
steps of the game redesign process helped them
visualize its place in their own classrooms.
In this article, two teachers recount how board
game play and redesign lived in their classrooms
(Grades 3/4 and kindergarten) in the rst year of
the research partnership. In both classes, students’
activities in terms of progressing their game
redesigns took varying forms, including the
following:
1. Playing games and noticing patterns of winning
or losing
2. Brainstorming new rules
3. Redesigning the game and playtesting
4. Creating rule books
5. Making good copies of the game
6. Inviting others to play (nal showcasing)
Starting with playing the games (before thoroughly
reading the ofcial rules) was important as it
demonstrated the need to understand the rules in
order to participate fully in the game. Some of these
activities were planned, but others emerged as we
worked with the students.
Redesigning Inversé in
Grades 3/4
(Teacher-Author 1)
In my Grades 3/4 classroom, I chose many
games to play. The class’s mathematics learning at
this point focused on arrays and basic multiplication.
My students immediately noticed that many board
games have arrays and grids built into them.
Playing and Noticing
We began playing board games in October, when
I brought in my games (such as Tsuro, Connect 4
and Codenames). We also borrowed some popular
games from the school library (Qwirkle, Triominos,
Guess Who? and Jenga).
The biggest challenge at this stage was ensuring
that the students understood the ofcial rules of the
games. Many groups played with their own house
rules or did not play competitively (for example,
24 Early Childhood Education, Vol 46, No 1, 2019
placing pieces without keeping score, or working
together to create patterns with the pieces). To
tackle this challenge, we played several games as a
whole class. I chose a small group of students to
play with, and the rest watched the game play. We
made an anchor chart of the most important rules
of each game—rules that the students often
misunderstood or overlooked when they played on
their own.
As we incorporated board games into our
classroom culture, students deepened their
understanding of the ofcial rules, as well as the
social rules (such as turn-taking, graceful winning or
losing, and basic game play strategies). They began
to plan a turn or two ahead and to take on their
opponents’ perspectives to develop an effective
defence. Playing a wide variety of games helped
them build up a vernacular around gaming. In
classroom discussions, we began comparing games
based on the balance of luck and strategy, the
number of players, the length and complexity, and
even how the rst player was chosen.
After the students had developed a foundational
understanding of board games, I introduced the
project. We were going to redesign one of our class
favourites, Inversé (Figure 1). Inversé involves a
12-by-12 grid board and wooden blocks of ve
colours and ve shapes, each with a volume of 48
cubic units. The goal is to be the last player to play
a piece, placing it in such a way that your opponent
cannot make a legal move.
FIGURE 1. Two Grade 3 students playing Inversé.
I chose Inversé because it is short (less than two
minutes per game) and simple to teach. It has only
three rules: pieces of the same height can’t touch,
pieces of the same colour can’t touch, and pieces of
the same colour can’t be placed in the same
orientation. It also has lots of depth in terms of
mathematical thinking (spatial awareness, estimating
area and height, and comparing the size and shape
of rectangles).
We spent a couple math classes honing our
Inversé skills, playing tournaments and keeping
track of the success of various strategies. We
documented how many times the rst player was
the winner, and how many times the person who
played the yellow piece rst was the winner. This
deeper understanding of the system of Inversé was
combined with continuous but more-focused playing
and noticing.
Brainstorming New Rules
I challenged my students to nd a way to make
Inversé a two-dimensional game, and I asked them
what rules would have to change and what rules
they could potentially keep. For example, we had
learned that the Inversé pieces do not all t on the
board at once, and the students realized that they
would have to consider the relationship between the
board size and the number of pieces. As a whole
class, we brainstormed possible variations, such as
using a shape other than rectangles, adding a third
player or changing the rules about which tiles could
touch. I recorded the students’ ideas during this
brainstorming session (Figure 2).
FIGURE 2. Recording student-generated ideas during
the brainstorming phase.
We also spent time brainstorming the
mathematics we saw in Inversé and which of those
skills might transfer to the students’ redesigns. We
Early Childhood Education, Vol 46, No 1, 2019 25
explored questions such as, “Which piece is the
biggest?” Students learned about measurement and
estimation, and they were able to verbalize their
estimates of arrays and areas. (For example, one
student said, “I don’t think my piece will t there.
That spot is too skinny.”) Students then practised
mathematical vocabulary, such as longest, widest
and tallest. They measured the area, the length and
even the volume of the pieces by rebuilding them
with unit cubes. Inversé also allowed them to
practise their spatial reasoning as they oriented the
pieces in different ways and visualized how pieces of
different sizes might t together.
After our initial class discussion about redesigning
the game, I gave the students time to individually
brainstorm new rules and components. Then I
placed them in groups of two or three, based on
their initial ideas.
Redesigning and Playtesting
We spent several classes redesigning Inversé by
rening the students’ initial ideas; creating rough
copies out of construction paper; and playtesting
and adjusting the rules, pieces and boards (Figure 3).
FIGURE 3. One group’s paper rough copy of their
Inversé redesign.
The redesign process is complicated, even more
so when children are in heterogeneous groups, with
a range of language, math and social skills. This
project allowed for scaffolding, as students had
agency over the complexity of their designs and
could lean on their group members when they felt
challenged by particular aspects of the project.
The biggest challenge as a teacher was keeping
the groups on track to nish their games on time;
some groups spent multiple class periods debating a
single rule, whereas others were nished and ready
to create a good copy of their game after just a few
days. The strategy I used to help the students move
forward and make progress every day was to
provide checkpoints and deadlines, without taking
away their agency and choice. For example, after
the rst week I said, “By the end of today your
group should have decided on whether you are
creating pieces to be placed or using a blank board
that the players can draw on.” This gave them a few
options and left the project open-ended enough for
customization, while also narrowing their focus so
that they could make a choice and move on to the
next step. This process was organic and responsive
rather than premeditated; when I felt that most
groups were ready to move on, I presented the
deadline and the choices to the remaining groups.
When many of the groups were struggling to
make a decision about the same component of the
game, we talked as a class and wrote down all their
ideas. This gave them a jumping-off point, and each
group could then zero in on the idea that would
work best for their game.
It was essential for the students to playtest their
games as often as possible so that they could adjust
the games when they were too easy or too difcult,
or if they found that the rst player always won.
Creating Rule Books
Once all the groups were happy with their new
game designs, we moved on to creating rule books.
The students learned how to articulate the
mechanics of their game, the procedures of a
player’s turn and the special placement rules they
had chosen. As they playtested their games over
and over, they constantly revised their rule books,
adding more details to clarify the systems of their
games.
Many groups who found the complex language
and layout of traditional rule books challenging
chose to explain the rules of their games through
photos or drawings (Figure 4). These ELL students
used symbols such as a check mark and an X to
clarify which moves were allowed and which were
against the rules.
FIGURE 4. A rough copy of a rule book, with
headings, pictures and symbols.
26 Early Childhood Education, Vol 46, No 1, 2019
After nishing rough copies of their rule books
and receiving feedback from me and from their
Grade 6 buddies, my students worked with the older
students to type up the rule books and print them
out (Figure 5).
FIGURE 5. One group’s rule book, using photos and
symbols, created with the help of an older student.
Creating Good Copies of the Games
With their rule books complete, students moved
on to creating good copies of their games out of
materials that were more durable.
This proved to be challenging, as many of their
rough copies had been created using tiny pieces of
construction paper. They wanted to make a game
that was as engaging to play as the original Inversé,
which uses large, brightly coloured wooden blocks.
However, the relationship between the size of the
pieces and the size of the game board was vital to
making their games work.
I gave the students time to struggle with this
problem before introducing some tools that might
help, including graph paper in various sizes, rulers
and unit cubes. One group gured out how to
measure the size of their pieces with the smaller-
sized graph paper and then count out the same
units on the larger-sized graph paper to ensure that
the ratios were intact. The rest of the class gathered
around to watch them use this method and then
went back to their own games. Some groups
borrowed this idea, and others used it as inspiration
and went on to use rulers and multiplication to
create larger versions of their pieces.
Showcasing Our Games
After six weeks of playing, noticing, planning,
designing and creating, students nally had games
they were proud to produce. We talked about how
designers get their ideas and products out to the
public, and many students suggested using yers and
brochures.
We created an invitation to send out to families,
asking them to participate in our board game night.
Many families and staff members showed up after
school one afternoon, and the students were thrilled
to teach them the rules of their games and see the
games being played by members of the community.
Since then, these student-created board games
have been added to our school library’s games
collection, and children can sign them out to play at
home or at school.
Outcomes
This game redesign project changed how my
students approached mathematical tasks, design
thinking and group work. They learned that creating
high-quality work takes time, and they felt a sense of
satisfaction when they were able to produce and
showcase that level of quality.
They also showed growth in specic mathematics
skills. As a result of the nature of the design project,
each group of designers produced a different type of
game that targeted different mathematics skills.
For example, a group of three that included a
recent Chinese immigrant student created a game
combining the principles of the traditional Chinese
game Go with the area-based themes of Inversé. In
their game, players were to roll two dice and create
a rectangle with the area shown on the dice, trying
to surround their opponent’s rectangles (Figure 6).
These learners developed a deeper understanding of
the relationship between area and side length as
they worked out the best ways to orient their
rectangles.
FIGURE 6. A game designed using the principles of
the Chinese game Go.
Early Childhood Education, Vol 46, No 1, 2019 27
Meanwhile, another group developed a three-
player game in which the goal was for players to ll
the space with their own pieces and not leave space
for opponents (Figure 7). This group explored the
concepts of shape composition, combining area and
arrays.
FIGURE 7. A three-player ll-the-space game.
Redesigning Connect 4 in
a Kindergarten Classroom
(Teacher-Author 2)
In my kindergarten classroom, I introduced the
game Connect 4 to my students. Through play, we
were able to use mathematics vocabulary, and the
children’s redesign ideas emerged from their own
need to be playful.
Playing and Noticing
I had Connect 4 set up on a table when the
students arrived. As they approached the table,
some commented that they had the game at home.
Some said, “I know this game!” Others picked up
the coloured playing chips and started dropping
them into the grid.
In a short time, the sense of excitement grew as
the students took turns at the table, and many
gathered to watch what their peers were doing.
Something about Connect 4 connected with this
group of children more than the other games I
introduced. They would go to the Connect 4 table
rst (despite having other activity options), watch
their peers play while waiting for their turn, and
sound joyful when talking about the game.
In the beginning, I gave the students time to
interact with the game and play it in their own way.
Some talked about the rules with each other, stating
the rules as they understood them. Others enjoyed
dropping chips at random into the grid and hearing
the clinking sound. Others used the chips to make
patterns or stacked them to build towers.
Soon, I brought more copies of the game into the
classroom to allow more students to interact with it.
We had many small-group conversations about
game rules (for example, how the rules one student
played by could be the same as or different from the
rules another student played by), as well as social
rules (such as what players should do with their
hands while waiting for their turn, whether it is OK
for players to cover the opening of the grid with
their hands and how to win gracefully). We also
talked about the object of Connect 4 and what it
means to win the game. This led to larger group
conversations and documentation so that children
had a shared understanding of all aspects of the
game.
There was also mathematical vocabulary to teach,
like grid, line, vertical, horizontal and diagonal
(Figure 8). The students’ interactions with each
other and with the game guided the conversations
and learning intentions in our work.
FIGURE 8. Connect 4 game board with mathematical
vocabulary.
Once the children were familiar with Connect 4
and satised with playing in their own ways, we
began talking about our thinking while playing the
game. I encouraged them to talk as they played (that
is, to think out loud). This led to their play becoming
more purposeful, allowed for more observation and
documentation of their understandings, and began
shaping their strategies for playing the game.
28 Early Childhood Education, Vol 46, No 1, 2019
Brainstorming New Rules
When considering how Connect 4 could be
redesigned, I intended to listen to the students and
allow the redesign concept to come from them.
Being present with a small group of children playing
the game allowed me to make observations, ask
questions and document their experiences. I
watched for any changes they might make to the
game on their own. I did not have to wait for long.
During table centres, groups of children were
playing Connect 4. One child didn’t have a partner
because he kept winning against everyone. So he
decided to play the game by himself. After a few
minutes of dropping chips of alternating colours
into the grid, he declared, “I just won against
myself!” A few children and I laughed after hearing
that, since by having control of both colours of
chips, he had, of course, allowed one colour to
make a winning line. We used elements of this
discovery in our Connect 4 redesign.
Redesigning and Playtesting
We played around with this concept of Connect 4
as a one-player game, keeping all other rules in
place. Players were to play one chip at a time,
alternating colours, and the way to win was to form
a vertical, horizontal or diagonal line with four chips
of the same colour.
I gave the children a paper copy of the Connect4
grid so that they could document their game play by
recording the moves they made with the red and
yellow playing chips. This became the answer key.
As an example, the key in Figure 9 reads as “Yellow
goes rst, with 11 moves, and red must win.” The
balloons (three circles connected with lines) indicate
the celebratory winning.
FIGURE 9. One kindergarten student’s answer key
for one-player Connect 4.
In this process of redesigning and playtesting, the
children encountered the concept of cardinality and
ordinality of numbers. In other words, they counted
the number of red and yellow chips on the board,
but they also counted the order in which the chips
were placed.
Creating Rule Books
Creating rule books went along with playtesting
the new game. The students realized that it was
difcult to remember which playing chip they had
placed rst, second, third and so on. They also
realized that various arrangements of the playing
chips could all result in a given colour forming a
winning line.
This led to their making starting cards with a
limited number of playing chips coloured in on the
paper grid. The remaining chips were placed on
instruction cards that told the player which colour to
start with and how many moves were needed to
make a given colour win. (See Figure 10.)
FIGURE 10. A kindergarten student playing with a
starting card (top) and an instruction card (bottom).
Creating Good Copies of the Game
I laminated the starting cards and the instruction
cards that the students and I had made together.
These became the good copies that we kept so that
we could play our redesigned Connect 4 game over
and over.
Showcasing Our Game
The students shared their game cards with each
other to play in class. We showcased our redesigned
Connect 4 game at a math night so that students’
families could see our work.
Conclusion
This article highlighted learning opportunities that
fostered early numeracy by introducing narratives
from a kindergarten classroom and a Grades 3/4
classroom in a linguistically diverse school.
Early Childhood Education, Vol 46, No 1, 2019 29
These narratives depict how children used and
demonstrated their understanding of integrated
numeracy (including subitizing, understanding
ordinality and cardinality of number, the area model
of multiplication, spatial reasoning, and problem
posing and problem solving). These various aspects
of early numeracy were integrated and emerged
under the goal of board game play and redesign.
The children were engaged in holistic learning
throughout this process. They developed early
numeracy through play and design, and they formed
a positive relationship with mathematics by creating
games that they themselves enjoyed playing and
that they were proud to share with their families.
Moreover, the social aspects of game play and
redesign allowed them to talk about and create
social rules for playing games and to position
themselves as designers, problem solvers and
creative people.
Notes
This project was funded by a Research Partnerships Program
grant from Alberta Education’s Alberta Research Network. The
authors are listed alphabetically, as they engaged in this writing
collectively and collaboratively.
1. See https://education.alberta.ca/media/159477/
numeracy-denition-poster-colour.pdf (accessed October 11,
2019).
2. Gord Hamilton’s website (http://mathpickle.com/
puzzles-and-games/) has a range of puzzles and games that are
highly relevant to mathematics learning (accessed October 11,
2019).
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Article
Designing games from the ground up is a popular activity for helping students think in designerly ways. Despite their benefits, such game design activities may place higher-than-anticipated demands on cognitive and institutional resources. In an effort to alleviate these demands, this study explored how playing and fixing partially completed games may elicit engagement with designerly thinking. This paper reports on the results of examining participants' talk during a playfixing activity in which, rather than designing wholesale, participants mended incomplete or “broken” tabletop games. Results suggest participants focused on problem identification, demonstrated quick and sustained engagement with thinking like designers, and drew from designerly modes non-linearly. These results illustrate that broken games may hold potential as accessible alternatives for helping learners think in designerly ways.
Article
Full-text available
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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