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Festarola: a Game for Improving Problem Solving Strategies

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When performing problem solving tasks, teachers need to guide students' activities through the regulation of learning with meaningful resources that exemplify students' daily life. As a contribution to the learning and teaching processes in problem solving in math, we created Festarola, a digital game designed for young children, ages eight to ten, where a team of players is tasked with organizing a birthday party for a group of children. The game fosters both self and shared regulation of learning in problem solving by guiding students through a forethought phase, an execution and monitoring phase, and lastly, a self-reflection phase. A user study was conducted with children from the Portuguese primary education to measure the impact of the game. Children interacted with the game individually and in groups throughout several sessions. Positive results indicate that the game successfully stimulated and developed problem solving strategies in students.
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Festarola: a Game for
Improving Problem Solving Strategies
Ricardo Rodrigues
INESC-ID and Instituto Superior T´
ecnico
University of Lisbon, Portugal
ricardo.rodrigues@gaips.inesc-id.pt
Paula Ferreira
CICPSI, Faculdade de Psicologia, University of Lisbon, Lisbon, Portugal
INESC-ID of Instituto Superior T´
ecnico
University of Lisbon, Portugal
paula.ferreira@campus.ul.pt
Rui Prada
INESC-ID and Instituto Superior T´
ecnico
University of Lisbon, Portugal
rui.prada@tecnico.ulisboa.pt
Paula Paulino
CICPSI, Faculdade de Psicologia
University of Lisbon, Portugal
a.paula.paulino@gmail.com
Ana Margarida Veiga Sim˜
ao
CICPSI, Faculdade de Psicologia
University of Lisbon, Portugal
amsimao@psicologia.ulisboa.pt
Abstract—When performing problem solving tasks, teachers
need to guide students’ activities through the regulation of
learning with meaningful resources that exemplify students’ daily
life. As a contribution to the learning and teaching processes in
problem solving in math, we created Festarola, a digital game
designed for young children, ages eight to ten, where a team of
players is tasked with organizing a birthday party for a group
of children. The game fosters both self and shared regulation
of learning in problem solving by guiding students through a
forethought phase, an execution and monitoring phase, and lastly,
a self-reflection phase. A user study was conducted with children
from the Portuguese primary education to measure the impact of
the game. Children interacted with the game individually and in
groups throughout several sessions. Positive results indicate that
the game successfully stimulated and developed problem solving
strategies in students.
Index Terms—Digital Game, Problem Solving, Collaborative
Learning
I. INTRODUCTION
Students are often cognitively, emotionally and motivation-
ally reliant on their teachers when performing tasks in the
classroom [1]. Teachers tend to use formulas and model pro-
cedures to demonstrate how to solve Mathematical problems,
presenting students with tasks that are completed within a
small amount of time. Therefore, teachers serve as models
who guide students in executing their tasks, often leaving little
room for the latter to self-regulate their learning autonomously.
Within this framework, students tend to formulate beliefs
that Mathematics are bound by a set of fixed skills and that
correctly completing an exercise implies following a series
of rules offered by the teacher [2]. At the same time, when
uses of mathematics are not related with everyday activities,
students tend to assume that mathematics are not part of the
real world, which leads to a lack of understanding regarding
its utility [3].
II. PROBLE M SOLVING IN MATH
In problem solving, one of the most important steps is
understanding the problem itself and what students are being
asked to do [4]. To solve a problem, students should read the
problem,identify the context and what is asked of them, para-
phrase the problem in their own words, take notes of necessary
data, draw diagrams and/or schema that better organize the
data, allowing for better understanding of their connections.
Additionally, articulating thoughts promotes reflection on the
problem and strategies used to solve it, which in turn, leads
to a greater understanding of the problem [4], [5].
A study with Mathematics’ teachers found that most teach-
ers (85.5%) asked their pupils to read the text of the problem
carefully, while 77.5% of them guided their pupils to write
down the data of the problem and the relations between these
data. However, only 61.3% asked the pupils to reword the
problem [4].
One of the main goals of school education is developing
problem solving skills [6]. Students who tend to be more
self-regulated usually have more success in problem solving,
mainly because the development of problem solving skills is
related with acquiring self-regulation strategies that allow the
learner to understand what to do,how to do it and why do it
[7].
III. THE RE GU LATION OF LEARNING IN PRO BLEM
SOLVI NG
Self-regulated learning refers to the degree with which stu-
dents motivationally, meta-cognitively and behaviorally man-
age their own learning [8]. If self-regulation is tied to the way
students regulate their own learning, sharing this regulation
refers to the way students, together, regulate the processes of
learning to reach a common objective [9].
In sharing the regulation of learning, students may develop
self-regulation strategies, pro-social skills (e.g., conflict res-
olution strategies) and an assertive communication style by
having opportunities to verbalize their thoughts and strategies
to solve problems [10]. Nonetheless, the coordination of a
collaborative learning task is a demanding process due to the
fact that each element of a group is an agent with varying
levels of self-regulation, individual objectives, cognitions and
emotions, which in turn, creates challenges to the maintenance
of motivation in contexts of social interaction [11].
During the executing of tasks, such as, a problem to solve,
the elements of a group must be responsible and capable of
regulating their own learning (i.e., self-regulation learning);
support colleagues in the regulation of learning to reach
their objectives (i.e., co-regulation of learning); and, together
regulate the learning processes of the group to reach a common
objective (i.e., shared regulation of learning) (e.g., [12]).
Additionally, the success of a student during this process
seems to depend on the success of the whole group, making it
essential for different elements to trust the team and recognize
a common direction [13].
Independently of whether a problem-solving task is per-
formed individually or in group, the regulation of learning
implies various cyclical phases, such as forethought, perfor-
mance and self-reflection [8]. These phases are in line with the
problem solving phases proposed by Polya [14]. Specifically,
these phases include understanding the problem, planning how
to solve it, carrying out a plan and reviewing the process [14],
a self-regulated process which may lead to better problem-
solving accuracy in math.
IV. GAM ES FOR TH E REG UL ATI ON O F LEARNING IN
PROB LEM SOLVI NG
In parallel with the self, co and shared regulation of
learning, the literature has highlighted the role of games
in developing learning skills. Games, problem solving, and
learning are part of everyday life [15]. Games in particular, are
seen as a tool to think [16], to learn [17], and to learn to think
[18]. Digital games require diverse skills considered essential
to learning [19], such as: attention, research, planning, com-
munication, creativity, and self confidence (e.g., [20]–[23]).
Additionally, games promote problem-solving skills, as they
are challenging, accessible and cognitively demanding [15].
Digital game-based learning has been a focus of education
professionals in various fields, such as mathematics [24], [25],
to improve learning effectiveness and efficiency in motivating
and ludic learning environments. The literature has highlighted
that games can make specific subjects, which are often per-
ceived as difficult, more accessible [26]. Digital games have
also been specifically used to support children’s learning [27].
In terms of problem-solving specifically, some of the litera-
ture has indicated that digital games are user-centered in devel-
oping problem-solving strategies while promoting challenges,
cooperation and engagement [28]. Shih et al. [29] demon-
strated how a game designed to help elementary school stu-
dents solve problems, fostered collaboration during problem-
solving, and thus, better learning effectiveness. Yang [30]
investigated the effectiveness of Digital Game-Based Learning
(DGBL) on 9th-grade students’ problem solving, learning
motivation, and academic achievement. Results revealed that
DGBL was effective in promoting students’ problem-solving
skills and motivation. Additionally a recent study [31] with
6th and 8th grade students using a programming game found
that problem solving behaviors were significantly associated
with students’ self-explanation ability.
DGBL also has the potential to develop and assess chil-
dren’s self-regulatory capabilities [32]. A recent study [32]
provided evidence that a digital assessment tool integrated in
daily classroom activities has the potential to promote self-
regulation in children.
V. OBJECTIVE
Considering the previously discussed impact of self, co and
shared regulation, as well as games for learning to solve
problems, we developed a digital game named Festarola
designed for young children, ages 8 to 10. With this game
we aimed to fulfill the following objectives:
1) Develop problem solving strategies in students. These
strategies are based on processes of self-regulation of
learning, applied in several phases, namely: (a) under-
standing the problem; (b) elaborating a plan to solve it;
(c) executing the plan; and (d) reflecting on the obtained
results – these phases were based on the global heuristics
of Polya [14] that presented 4 phases to guide problem
solving. Moreover, these phases were in accordance with
the processes for the self-regulation of learning [33].
2) Provide students with diverse ludic and appealing learn-
ing scenarios to foster motivation and knowledge in
problem solving, bridging Mathematics and a real world
scenario.
3) Improve students’ autonomy in regulating their learning
individually and collaboratively during problem solving
by providing options for solving the problem through
interactive scenarios.
VI. FE STA ROLA,THE GAME
Fig. 1. Festarola cardboard mockup.
The game evolves around the activity of organizing a party
for a group of children. The player is part of the organizing
team, which, is constituted by two to four players (it is also
possible to have a single player experience). The team needs
to perform some tasks in a sequence that highlights different
processes of problem solving, as described previously in the
objectives (see section V).
The overall goal is to please the guests of the party. To
organize the party, the team needs to decide on a proper theme
for the party, buy food and drinks, props and hire entertainers,
while dealing with budget and time restrictions.
The activity is divided in three main phases. The first phase
is performed in group and includes choosing the theme for
the party and defining a plan for the team, which consists of
a list of things to buy, rent or hire. Defining the plan includes
assigning individual responsibilities to players. Different shop-
ping lists are defined (one per team member) and part of the
overall budget is assigned to each player. In the end, players
need to agree on which list each one is responsible for.
The second phase is performed individually. Each player
performs the concrete shopping actions in the town shops
according to the items on their shopping list and the assigned
budget. However, this activity does not impose strong restric-
tions, as players can buy different things and go over budget.
Actions in town take time, hence, there is a limited number
of actions that players can perform in this phase.
The third phase is played in a group again. The team meets
to share the items they bought. This provides them with the
have opportunity to check the initial plan and revise their
shopping options by returning some items if they choose to.
These decisions are made together and once an agreement is
reached, the game advances to the set-up of the party. In this
activity, the players distribute the items in the room where the
party will take place. Once they finish, the party starts and the
final score is presented.
The game is designed to promote the regulation of learning
in problem solving in math through face to face discussions
and to be used in classes at school. The first and third phases
are played at the same computer. Players gather around the
computer during the activities and are invited to move to a
different computer once the second phase starts. That is, one
player stays at the initial computer and the others go to a
different one. When the second phase ends, players go to the
first computer again.
A. Detailed gameplay
1) Game start: In the beginning, players are asked to
choose a character and give it a name. This character serves as
the player’s avatar during the game. Once all players are happy
with their avatars, they must choose a name for their team. The
main idea of this action is to reinforce the establishment of the
team, but the team name is used to support the save and resume
mechanism as well. After initialising the game, which starts
after the definition of the team name, players have the option
to resume a previously saved game. Saving is automatically
performed after each activity.
2) Gameplay activities: The game unfolds in a sequence
of five activities:
1 – Choosing the party theme (in group). In this activity, the
players take time to explore the interests of the party’s guests
and choose a theme for the party. The party has a total of eight
guests. Each has up to four likes and dislikes from a set of four
different themes: medieval, space, farm and sea. For example,
Fig. 2. Festarola screenshots. The top images refer to the first phase. On the
left is the theme selection, while on the right is the definition of the team
plan. The bottom left depicts a shop (phase two) and the figure on the bottom
right shows an example of the revision of the execution (phase three).
a character may like the medieval theme and dislike space
and sea. The challenge of the team, in this activity, is to select
the theme that will please most guests. Players have to count
the number of guests who like/dislike each theme and pick
the theme that maximizes the like/dislike ratio. This activity
presents a numerical challenge and enables perspective taking,
as players should consider others’ preferences. This choice
is presented in the remaining activities to support the team’s
future decisions, however, it does not enforce any decision.
For example, if medieval is the theme selected, players can
still buy a pirate cake (from the sea theme) if they choose to.
The choice of the theme will change the main decoration of
the party room shown in activity 5. It is in this first phase
also that students are asked to interpret the information that
is being given to them and what is being asked of them
(What information do you have and what do you have to do?).
Students may write a response on the computer.
2 – Defining the team plan (in group). In this activity, the
players create several shopping lists and assign each one to
a different player. The shopping list contains a set of items
and is built around 10 different categories (e.g. drinks, cakes,
entertainers, activity items, cup-cakes). The challenge in this
activity is to define a set of lists with a good distribution
of items. A good distribution assigns a similar number of
categories to each list and places items of similar categories
in the same list. Additionally, it should include enough items
for the eight guests. The main idea is to distribute the items
in a way that all members use a similar amount of time to
perform the shopping task while avoiding that they travel to
the same shops, hence, minimizing the total travel time of
the team members. An additional concern in this task is the
distribution of the budget. The team receives a limit to the
amount of money they can spend (e.g. 100C). That amount
needs to be distributed by the lists. This brings an additional
challenge to the players to foresee which list contains the most
expensive items. There is no direct scoring in this activity, but
the planning will influence the performance of the players in
activity 3. A good balance in the plan leads, for example, to
players spending less time travelling and shopping and hence
getting higher score in the end. At the end of this phase,
students are asked why they chose to proceed the way they
did. Students may write a response on the computer.
3 – Performance - Executing the plan (individual). In this
activity, players navigate in the town and enter shops to buy the
items needed, according to the plan. Players can consult their
assigned shopping list anytime during the activity. Movement
actions (i.e. entering a shop) and buying actions take time.
Players receive a time budget (equal to all) and need to buy
everything before the time runs out. Players may return items
if they wish to with no money penalty, but this action takes
time. The challenge in this activity is to buy all the items in
the list taking into account the party theme and the budget
restriction. Note that the list specifies generic items, such as
cakes. However, the stores sell items of the different themes
as well, such as, a farm cake or a pirate cake. Players need to
make the buying decisions carefully to match the party theme
and the interests of the guests. However, themed items are
more expensive than generic ones and players should meet
the budget. The actions that players may take in this activity
are not limited by any means. Players can buy items that are
not on the list and are not forced to buy items of the chosen
theme. Additionally, they may spend any amount of money
over the budget. This freedom is included in the gameplay to
allow players to perform mistakes and to make them actively
responsible for following the plan. Players may leave the town
as soon as they feel that their part of the plan is concluded.
However, they are forced to leave if the time runs out. At the
end of this phase, students are asked why they bought what
they did.
4 – Revising performance (in group). In this activity, players
see the items that all members of the team bought and decide if
they keep them all or if they return some items. They can check
the initial plan to support the decision. The team may only
finish this activity if the total cost of the items kept is equal to
or lower than the limit of the budget. The team incurs in no
monetary costs for returning the items, but will be penalized
for the number of items they return (check the budget scoring
bellow). The challenge in this activity is to reach an agreement
on the items to keep and to ensure that the cost is lower than
the budget. A good decision keeps the items that will please
the guests more without overspending. Note that, if the team
defined a good plan and its members performed it well, this
activity will not present any challenge as there is no need to
return any item. Then, students are asked to reflect on their
score and explain why they received that score individually
and in group.
5 – Setting up the party (in group). In this activity, players
may distribute the items they bought throughout the room
where the party takes place. The room starts empty with base
decorations according to the chosen theme. The players may
select items and place them in the room. There is no restriction
on the placement and there is no need to place any items at all.
This activity is not a challenge per se, as it functions more like
a gratification and cool-down activity. It presents a playful and
fun experience where players express themselves and imagine
the party setting. The team may discuss the options to take,
nevertheless. Once they feel that the set-up is ready, the party
starts and they receive the feedback from the guests and the
final scoring.
Fig. 3. On the left is an example of the party set-up activity. On the right is
a sample of a party scoring.
3) Scoring: The score in the game has three different
components: the success of the party, the budget spent and
the time taken while shopping for items.
The success of the party depends on the number of pleased
guests. Guests are pleased if there are more items in the party
that they like than items that they do not like. Big items count
more than small items (e.g., an inflatable castle counts more
than a princess cupcake for the Medieval theme). Also, there is
a demand on themed items according to the number of guests
that like a theme. This means that if most guests like a theme
like space, for example, the party needs several space items
as one is not enough to please them all. Despite the choice
of the party theme, the computation of the amount of guests
that are happy takes into account all likes and dislikes. The
decision is made for each guest, according to the following:
ItemsLike ItemsDislike >=K, then the guest
is pleased with the party
ItemsLike ItemsDislike <=K, then the
guest is not pleased with the party
Otherwise, the guest is neutral towards the party.
The ItemsLike represents the weighted amount of items
of the themes that the guest likes, while the ItemsDislike
represents the same for the themes that the guest dislikes.
The constant K is introduced to control the challenge. The
higher the value of K the more difficult it is to move the
guests from the neutral state. For example, imagine a scenario
with 2 guests. One likes the space theme and dislikes the
farm theme, the other likes the space theme and dislikes the
medieval theme. If the party includes 2 items of the space
theme and 1 item of the medieval theme, for K=1, the first
guest if pleased (as he gets one item he likes and no dislikes,
hence 10=1>=K) and the second one is neutral
(as he get one item he likes and one item he dislikes, hence
11=0< K ). In the case of K=2 both guests will be
neutral. More items of the space theme would be needed to
please the first guest.
Each pleased guest accounts for 1 point in the score and
each guest who is not pleased accounts for -1 point.
The budget score is computed based on the number of
items returned in the revision of the teams’ performance
(activity 4). There is a base number of points (e.g. 10) that
is decremented by one for each item returned. The rationale
behind this scoring mechanism is the fact that the main reason
for returning items is overspending beyond the limits of the
budget.
The time score has a similar mechanism. There is a base
score (e.g., 10) that is decremented for each player that runs
out of time.
There is an additional score feedback in the form of stars
attributed to the performance. The party can get zero to three
stars. It gets one star for each condition: the team had no time
penalties, the team returned no items, and there are more than
five participants pleased.
Fig. 4. On the left is a character presenting the overall goal of the game.
On the right is a character asking for the reason for cancelling the changes
performed in the revision activity.
4) Guiding and Reflection: The game includes two ad-
ditional characters to guide players in the activities and to
prompt them to reflect on their decisions. At the beginning
of each activity, one character presents a description of the
activity. During the activity or at the end, another character
asks players to justify their actions and decisions. For example,
players should justify the choice of theme, the way they
divided the tasks in the plan, the reasons for their shopping
actions in town, and why they returned items (or not) during
the revision activity. These justifications are written in a text
box and are in most cases a team responsibility. Therefore, a
discussion among the group of children is expected.
5) Defining new scenarios: The game was developed to
be a tool used by teachers and researchers. For this reason,
it records all actions performed in the activities and all
texts written by the students to allow future analyses to be
performed.
Additionally, different scenarios may be presented in the
game by configuring a set of features. It is possible to change
the set of interests of the party’s guests, thus, changing the
difficulty of the overall challenge. For example, if most guests
share common interests, it will be easier to reach a good
solution regarding the theme of the party. However, in case
of conflicting interests, it will be harder. It is also possible to
define the budget limit and time limit for actions in town. By
doing this, teachers can define different levels of pressure and
flexibility in the task. For example, allowing more exploration
and correction actions if the time limit is higher. Finally, the
prices of the items in the shops can be changed as well. This
may change the nature and difficulty of the math calculations
needed in the game. For example, if the prices are all in round
small (e.g., one figure) numbers, it will be easier for the players
to estimate the overall costs of buying actions rather than if the
numbers in the prices are higher (e.g., two figures) or include
decimals.
VII. USE R STU DY
To understand the impact of the Festarola in young students,
two user studies were conducted in which participants were
tasked with completing the phases of the game in different
sessions.
A. Samples
This user study involved 269 primary school students,
spanning over 17 classes, from the 3rd and 4th grades, in
Lisbon’s public schools, with ages ranging between 8 and 11
years old.
B. Resources
To allow us to better measure the impact of the game in
students, we used the following resources listed below. We
used a mediated assessment approach to dynamic assessment,
which has been found to be appropriate to use with children
[34].
1) The four phases of the regulation of learning in the
game. During gameplay, after some phases, the students
were asked to justify their actions through written text.
The replies were coded by phase as follows:
Choosing the party theme: 1 = no response; 2
= irrelevant information for the resolution of the
problem; 3 = information provided of what students
were asked to do; 4 = information provided, and
students mention what they were supposed to do.
Defining the team plan: – 1 = no response; 2
= irrelevant information for the resolution of the
problem; 3 = explanation as to why students planned
the way they did (e.g. “we divided the budget evenly
so we could all have time to go shopping”).
Performance: – 1 = no response; 2 = irrelevant
information; 3 = information provided is according
to the game’s overall objective of organizing a
party (e.g. “we bought things for the party”); 4
= information provided is according to the team’s
specific plan to organize the party (i.e. “I respected
the budget I planned with my colleagues.”).
Revising performance: – 1 = no response; 2 = irrel-
evant information; 3 = general self-evaluation with
no criteria (e.g. “we did well”); 4 = specific self-
evaluation with criteria (e.g. we did well because
we bought only what we had planned to.”).
The users’ in-game responses revealed a reasonable
reliability of α=.71. These phases were used as the
independent latent variable of the regulation of learning
in problem solving in a structural equation modeling
analysis.
2) Performance in the game. Game performance was an
objective measure of performance and evaluated the
number of items students returned (in the gameplay
activity 4), as this indicated students were either not
able to execute the task according to their plan , and
overspent money, thus, not respecting their budget or
did not define a good plan. This served as one of the
dependent variables and was recoded from 1 (returned
more items) to 5 (returned less items).
3) Mathematical Problem on paper. With the aim of better
understanding students’ performance with regards to
problem solving, they solved a mathematical problem
on paper, which was created by a team of primary
education teachers. The math problem served as an
objective measure of performance and revealed a reason-
able reliability of α=.71, and was used as another de-
pendent variable reflecting students’ performance. Since
this mathematical problem evaluates the same construct
as the performance in the game, it serves as a concurrent
validity.
4) Questionnaire for the evaluation of the game by the stu-
dents A questionnaire with open-answer questions was
created to gather the students’ self-reported perceptions
of the game (i.e., “What I learned form the game was...”;
“What I most liked about the game was...”; “What I
least liked about the game was...”). Thematic analysis
was performed with the data [35].
5) Questionnaire for the evaluation of the game by the
teachers A questionnaire was created to gather the
teachers’ perceptions of the game, namely its impact
and potential as a pedagogical tool. Thematic analysis
was performed with the data [35].
C. Procedure
This study included 2 workshops with teachers (one at the
beginning and one at the end of the study) and 8 sessions with
each class of students (128 sessions total). Each session lasted
around 60 minutes. An extra 4 sessions were performed for
the pilot test. The workshops occurred as follows:
Session 1: First workshop with teachers. This workshop
was performed with the objective of presenting the theoretical
context of the project and create awareness of the themes and
contents of the game. Furthermore, a pilot test was performed
to test the game and evaluation procedures (e.g., detect bugs
and errors in the game).
Sessions 2 and 3: Introduction to the intervention in problem
solving. Presenting the game to students. Students could view
and play around with the game to learn how to use it.
Sessions 4 and 5: Understanding the Problem and Planning.
In this session students played the first and second stage of
Festarola,Understanding the problem and Defining the team
plan, respectively. The students also needed to reflect on how
they thought and what strategies they used.
Session 6: Executing and monitoring the plan. In this session
students played the third stage of Festarola,Executing the plan
by shopping in the stores in town.
Session 7: Revision of the performance. In this session
students played the fourth and fifth stage of Festarola,Revising
their performance and Setting up the party, respectively. The
students discussed their results and reflected on the successes
and/or failures of their tasks, self-evaluating their performance.
Session 8: Improving self-regulation strategies and problem
solving. In this session students were tasked with playing the
full game individually with a higher difficulty - party guests
would have conflicting tastes in themes.
Session 9: Problem solving (class). In this session students
solved a mathematical problem on paper and discussed how
they solved it. The students also evaluated the game.
Session 10: Second workshop with teachers. In this session
the teachers were asked to evaluate the game and its impact.
VIII. RES ULTS AN D DISCUSSION
In this section we will present our objectives (see section
V) and the results from our user study.
A. Developing problem solving strategies in students
This objective focused on the development of problem solv-
ing strategies through processes of self-regulation of learning.
Results seem to suggest the achievement of this objective,
not only by the teachers’ input after filling the questionnaires
regarding the questions on problem solving, but also through
the in-game explanations given by the students regarding
stages 1 and 2 of the game (session 3) and the performance
in the game and in the math problem on paper.
1) Teachers’ input on problem solving strategies: Teachers
pointed to positive changes in the students, mainly regarding
mathematical reasoning, in particular the “explanation of re-
sults, data sorting, strategy planning, the steps to follow in
problem solving and development of mental calculation”. The
majority of teachers also reported an increase in the awareness
of the students regarding the problem solving phases, shown in
the verbalization of the different tasks regarding understand-
ing,planning,executing and revising. Furthermore, teachers
also reported an improvement in students’ calculations (in
particular mental calculus), memorization capabilities, and the
ability to follow and apply clues throughout problem solving
tasks, which were presented during classroom activities.
2) The impact of the regulation of learning in problem
solving in math: The phases of the regulation of learning in
problem solving in the game were used to measure their impact
on students’ performance. Structural equation modeling (SEM)
was computed with AMOS 24.0 software package (IBM,
SPSS, Amos 24). The chosen causal model presented a good fit
[36] to the data with the independent variable of the regulation
of learning in problem solving (i.e., the phases presented in the
game) and the dependent variable of performance in problem-
solving in math (problem on paper and game performance)
[χ2(10) = 1.36,CF I =.98,T LI =.97,IF I =.98,
RM SEA =.03,LO =.00,H I =.08,p > .05].
Bootstrapping confidence intervals were used, and the p-
values were calculated. The model proposes that students’
performance accuracy in problem-solving in math is predicted
by their self-regulated learning phases presented in the game
(problem to solve on paper, β= 0.28; performance in the
game, β= 0.41). All trajectories were positive and statistically
significant. Students who were more self-regulated in solving
problems in math, attained better problem-solving accuracy.
B. Providing diverse learning scenarios to foster knowledge
on problem solving strategies
Our objective was not only to foster knowledge on problem
solving strategies, but also to present students with a ludic
way to solve problems by using the game to present different
scenarios for training strategies in an appealing manner.
The teachers’ opinion of the game was quite positive,
stating that the game offers a learning dynamic that favors the
development of mathematical reasoning. The use of this type
of technology is perceived by teachers to be advantageous,
since it makes the tasks more appealing and motivating. The
value of the game was particularly highlighted for money
management, conflict resolution and decision making. The
ability to play games and perform teamwork in a collaborative
learning context was considered beneficial for the students’
growth on a personal and social level. In the teachers opinions,
the game “educates through respect and mutual aid”, since
students “need to learn to give in, hear others’ opinions, respect
ideas, and listen to others’ strategies”, which fosters positive
“relationships, help and sharing among colleagues”. The game
is overall described as “very stimulating”, “fun, important”, “a
motif for learning”, “positive”, “motivational”, “beneficial”.
Students mentioned that Festarola showed them the dif-
ferent phases of problem solving, enabled them to practice
throughout the sessions, and transfer this knowledge to dif-
ferent problems (“I learned that when I am going to solve a
problem it is necessary to understand, plan, solve and review
it”; “I learned to review the problems”; “I learned to plan be-
fore doing”). This was visible in the traditional math problem,
as the regulation of learning in the game predicted students’
performance. Students also mentioned that tasks performed
in-game allowed them to reflect on the importance of some
topics lectured in class, such as the mathematical operations
and the explanation of the solution (“I learned to divide
the money”; “I learned how to write a complete answer”).
Moreover, other learning topics were also mentioned, such as
money management and teamwork (“I learned to work in a
group”; “I learned to manage my money”). The game also
provided the students with awareness to important factors to
achieve a good performance, such as effort, responsibility,
and organization (“I learned to use the time set and to do
everything correctly”).
C. Improving the students’ autonomy in regulating their learn-
ing in problem solving
An objective of this project was to improve students’
autonomy in regulating their learning individually and col-
laboratively during problem solving by providing options for
solving the problem through interactive scenarios. To measure
the success of this objective students answered a questionnaire
to provide feedback on the game and describe their experience
of solving problems with it.
The majority of the students mentioned feeling involved in
the execution task (i.e. shopping in town, setting up the party)
and appreciated the look of the game. Students stated that
they felt capable of solving the tasks presented by the game
autonomously, and that they gave more importance to numeric
calculus and its written explanation in order to better verbalize
their mental processes throughout the stages of the game. The
opportunity to play the game in a team, and to manage money
were points equally considered positive and motivational to
the students.
In a previous user study, Marques et al. [37] used Festarola
to study the relation between students’ perceived support
(by their team members) and shared regulation of learning
in problem solving (among their team members). Perceived
Support referred to the way students perceived the support
given by their team members in order to adapt to challenges
imposed by different contexts [38]. Their work aimed to better
comprehend how perceived support in a group affected the
shared regulation of the task, and how students understood
the task’s potential to foster self and shared regulation. They
evaluated groups of children by using Festarola as a way to
present tasks which may be solvable in a group. Results from
this work revealed that when students felt support from their
group, they tended to better regulate their tasks within their
group. These results suggest that Festarola has the potential
to foster not only self-regulation, but also shared regulation of
learning in problem solving in math.
IX. CONCLUSION
Festarola was designed to promote the regulation of learning
in problem solving and to foster both self and shared regulation
of learning. The regulation of learning was used as basis for
the four stages in the game: (1) understanding the problem –
learning each party participants’ likings and selecting a theme
for the party; (2) elaborating a plan to solve it – deciding what
each player will purchase or rent for the party; (3) executing
the plan – visiting the town and obtaining the previously
planned items; and (4) reflecting on the obtained results –
revising the items brought by each player, having the option
to return items if the total cost is higher than the budget. A
final stage, Setting up the party, was added for enjoyment of
the players, where they could arrange the items bought in a
room where the party would be held.
A user study was performed with 269 primary school chil-
dren from ages 8 to 11. In this user study, children interacted
with the game throughout several sessions, allowing for the
evaluation of each stage separately. Positive results indicated
that the game successfully stimulates and develops problem
solving strategies in students and provides diverse learning
scenarios to foster knowledge on problem solving strategies.
These results, as well as the findings reported by Marques
et al., (2019), suggested that Festarola has the potential
to improve students’ autonomy in regulating their learning
individually and collaboratively during problem solving by
providing options for solving the problem through interactive
scenarios.
In conclusion, Festarola was shown to be an appealing game
that allows children to develop skills not regularly developed in
schools and improve their competences not only in problem
solving, but also collaborative work and other skills needed
later in life. This study served as an example and to test
possible trends of performance with the game, so that future
research with different study designs (e.g., with a control
group) may find our results useful to confirm the findings
presented.
X. AC KN OW LE DGEME NT
This work was financed under the participative budget of
the Lisbon City Council. It was partially supported by national
funds through Fundac¸˜
ao para a Ciˆ
encia e a Tecnologia (FCT)
with ref. UID/CEC/50021/2019; SFRH/BPD/110695/2015.
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... In fact, students who tend to be more self-regulated usually have more success with problem solving because the concept involves various phases and different intellectual processes, such as accessing prestored information and applying problem-solving strategies [1]. The development of problem-solving strategies is related to acquiring selfregulation strategies that allow the learner to understand what to do, how to do it and why [2]. ...
... The work presented herein is an extension of the paper presented at VS-Games 2019 [2] with further details on the game design and user studies. ...
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