=Paper=
{{Paper
|id=Vol-2555/paper27
|storemode=property
|title=FracPotion: An Open Educational Game to Teach Fractions in Brazil
|pdfUrl=https://ceur-ws.org/Vol-2555/paper27.pdf
|volume=Vol-2555
|authors=Josivan P. Da Silva,Rafael Da S. Nogueira,Gabriel T. Rizzo,Ismar F. Silveira
|dblpUrl=https://dblp.org/rec/conf/cisetc/RizzoNSS19
}}
==FracPotion: An Open Educational Game to Teach Fractions in Brazil==
https://ceur-ws.org/Vol-2555/paper27.pdf
FracPotion: An Open Educational Game to Teach
Fractions in Brazil
Josivan Pereira da Silva1, Rafael Nogueira2, Gabriel Rizzo3, Ismar Frango Silveira4
1,4
Mackenzie Presbyterian University, 1,2,3,4Cruzeiro do Sul University
1
josivan.engenharia@gmail.com, 2nightosama@gmail.com,
3
gabrielfoxl@hotmail.com, 4ismarfrango@gmail.com
Abstract. The areas of Science, Technology, Engineering and Mathematics,
called STEM careers, are important fields of knowledge for society nowadays.
Among the basics subjects of these careers is Mathematics, but many young
students present difficulty to understand very basic mathematical concepts and
logical thinking activities. This learning process is very complex and demands a
lot of motivation by part of the students. In this sense, educational games can
act as an interesting and stimulating helping tool for them. In Brazil, the levels
of proficiency on rational numbers in their fractional representation presented
by students aged between 9 and 12 years, in general, are low, mainly because in
local culture the fractional representation is not common at the daily activities.
The educational games to teach this topic in Portuguese are few, so it has
motivated us to develop a game to teach fractions entirely in Portuguese
language, but able to be adapted to other languages of the region, like Spanish.
In this paper, we present such a game, called FracPotion, developed as an Open
Educational Resource to teach about fractions to children. The game was
experienced by a group of students in an elementary school at São Paulo city,
Brazil, and the preliminary results were positive.
Keywords: Open Educational Resources, Open Educational Game,
Mathematics, Fractions.
1 Introduction
STEM (Science, Technology, Engineering and Mathematics) careers are
increasingly becoming each time more relevant for contemporary society. Some
countries are concerned if they really can produce enough skilled workforce on
STEM careers to compete at the global market level for the recent future [1]. Some of
the basics skills to be developed in the context of STEM are on Mathematics, Physics
and Programming, but many young students present difficulty to understand very
fundamental mathematical concepts or to develop logical thinking activities [2], this
one related to the broader concept of Computational Thinking [24]. If we want to
prepare our children and teenagers to have possibilities of work in future STEM
careers, we should offer more didactical and motivational tools and challenges to
them.
Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
According to [3] we should not to force young students to learn with the same
methods their grandparents have been exposed to, because traditional school learning
based on predefined sequential curricula cannot completely meet the requirements for
the 21th century children, so modern tools should be applied to complement these
current requirements. Learning processes are inherently very complex and demand a
big amount of motivation by students. Thus, naturally motivating tools like
educational games can be interesting as vectors of stimuli for students [4]. According
to [5], videogames could be used as support for several pedagogical aspects such as
motivating students and providing attractive and sometimes effective educational
tools.
Mathematics, as any other broad field of knowledge, has many sub-topics that
makes virtually impossible to develop a sole digital game to cover all subjects, so it is
appropriate to choose some specific topic to plan the design and application of
educational games. In Brazil the mean level of proficiency in Mathematics, in general,
presented by students aged between 9 and 12 years, is low; this situation is more
serious when they comes to learn some topics that are not common in their daily
activities, like rational numbers in their fractional representation. Different from its
neighbors in Latin America, in Brazilian culture the fractional representation is not a
commonplace – even ½ is often represented in its decimal form (0,5 – with comma).
Regarding this, the development of a game about fractions would be of great value
to complement the learning of this topic, especially if the game offers some facility of
adaptation by teachers. Therefore, in this paper we present an Open Educational
Game [25] called FracPotion to help students about fractions. The game was applied
to 18 students of an elementary school at São Paulo, Brazil, and the results were
positive.
2 Learning Fractions: The Brazilian Reality
The National Basic Education Assessment System (SAEB) of 2001 [6] reveals that
only 35% of Brazilians students were able to solve simple problems involving
fractions; many of those that failed had problems with the part-whole relation, which
is considered the most basic concept in this topic. The São Paulo State Performance
Assessment System (SARESP) in 2005 [7] revealed that only 37% of students
answered simple questions regarding such a topic. The results of the Programme for
International Student Assessment PISA (2012) [8] showed that two out of three
students do not know how to work with simple operations involving fractions.
A survey recently conducted by the International Student Assessment Program in
(2015) [9] showed a drop in scores in the three areas assessed: Science, Reading, and
Math. The drop in scores also reflected Brazil's drop in the world ranking: the country
ranked 63rd in science, 59th in reading and 66th in Mathematics. The Figure 1 shows
the results of proficiency in Sciences, Reading and Mathematics of the Brazilian
students in elementary schools, according to OCDE and PISA 2015 [9].
Fig. 1. Results of proficiency in Sciences, Reading and Mathematics of the Brazilian
students in elementary schools, according to OCDE and PISA 2015 [9].
There are three very important aspects to the practice and learning of fractions
[10]: first, the practical aspect, in which fractions in their different representations,
appear, often in several situations related to the expression of measures and quantities
– this fact highlights the need for extension of the set of natural numbers. Second, the
psychological aspect, since working with fractions appears as a privileged opportunity
to leverage and expand mental structures necessary for intellectual development.
Finally, the Mathematical Perspective aspect, since it will be precisely the first studies
with the fractions that will ground more complex ideas such as operations.
We believe that an Educational Game that presents fractions and give player the
task of reorganize them can offer experiences that address the three aspects mentioned
by [10]. Since learning fractions requires a reorganization of numerical knowledge,
such a game would allow for a better understanding of numbers than it is commonly
gained through experience with natural or integer numbers [11].
About the third aspect explained by [10], many authors show different approaches
to the mathematical perspective in the teaching of fractions. According to [12] the
focus of mathematical programs should be on fractions as quantities, to allow students
to make a correlation with their previous knowledge of natural numbers as quantities.
[13] suggests that teachers need to introduce a variety of fractional interpretations for
students, as students whose fraction learning was previously focused on regular
fractions of tend to have an impoverished understanding of the rational numbers. In
[14] there is an experiment with elementary school students that analyzed how
students think to determine larger or smaller fraction values and make the order of
fractions conform> This experiment was performed with pieces of paper, but it could
be easily achievable as a digital game, which would allow player to interact with the
fractions trying to reorder them.
3 Digital Educational Games to Teach and Learn Mathematics
3.1 Educational Games Overview and Applications to Teach Mathematics
Today we live in a world that offers many technology tools for children and young
people; usually these young people’s first contact with electronic equipment happens
through Digital Games [3]. These can be defined as engaging, interactive
environments that capture player attention by offering challenges that require
increasing levels of dexterity and skills [15] [16].
Many teachers believe that regardless of whether a digital game has or not some
educational purpose, it could contribute to psychomotor skills, development of
analytical skills and computational skills of the player. This is mainly due to the
difficulties faced during the game, the need to create new strategies (when strategies
used before are no longer good), the pressure to develop strategic thinking, among
other common aspects.
3.2 Related Works
Educational games could be effective learning resources, mainly when applied to
courses such as Mathematics or Science, often considered as difficult, abstract
courses. They also have the potential of influencing students’ social and daily life,
affecting their behavior with colleagues [18]. However, many authors – like [26] and
[27] suggest that educational games need more empirical evidence of effectiveness,
requiring more evidences in this field. According to [20] the research field of
educational games still has a limited quantity of empirical evidence about the
effectiveness of games, especially in the domain of Mathematics. Some other works,
like [19], bring stimulating results regarding to the use of digital games in the specific
topic of fractions.
In [21], an educational game called “Animo Math” was developed to help 5-7
years old children to learn Mathematics. The game has five levels with different
difficulties, beginning with calculus that uses only single digit numbers (0-9) to
teach/reinforce addition and subtraction operations; the other levels present more
digits and different difficulties in calculus. In this work, there were expected the
following four benefits in his game:
1. Make children more interested in positive learning in Mathematics.
2. Gain more of children’s attention by using cartoon animations and fun sound
effects.
3. Enable children to see the fun of Mathematics.
4. Parents perceive how to use modern digital technology and computers for
children in mathematical learning.
In [20] an educational game was developed to teach about decimal numbers. In this
game the students are introduced to a group of some fantastic characters that act as
guides to Decimal Point Game and encourage students to play, congratulating them
when they correctly solve problems. The game is composed by several mini-games
inside a kind of Amusement Park. However, the game does not present numbers in
factionary format. After playing a mini-game and correctly solving the problem, the
student was prompted to explain his or her solution, by choosing possible pre-listed
explanations from multiple-choice options available.
4 The FracPotion Education Game
FracPotion is a 2D educational game that was created for elementary school
students. It is expected to evaluate whether students find the game funny and whether
they can better identify, practice and understand educational content about fractions.
For the game to be better accepted by students, a narrative was created that justified the
need to work with fractions in the game. In this sense, a wizard is proposed as a
character since he employs fractions to combine potion ingredients that allow player to
have progress in the game, when potions are properly created with the correct
fractional quantity calculations. The background history to support the narrative
follows:
“The game takes place in a kingdom called Camelot, ruled by Arthur. This kingdom
is being threatened by a wicked witch named Morgana who, along with an army of
wizards is heading toward Camelot to defeat Arthur and rule over humanity, but with
the help of Merlin and his apprentice Arthur intends to defeat her with Magic potions.
For the creation of potions, it is necessary to define the right dose that is in the form
of fraction and thus create the potion to defeat Morgana and save the kingdom from
destruction.”
4.1 Game Overview
The game FracPotion is a simple adaptation of the classic history of King Arthur
and his knights, where to defeat the villain Morgana, the player (as an apprentice) will
have to hit the right amount of ingredients to complete the potion represented by
fractions. This kernel of the game is explained (in Portuguese) on screen of game
illustrated in Figure 2.
Fig. 2. Screen explaining the story behind the game.
Players are not punished for their mistakes, they only earn stars according to the
number of attempts they used to reach the required amount of ingredient that was
thrown into the cauldron. Figure 3 is an exhibition of the first level of the game.
Contains a question the player must answer to complete the potion. In Figure 3 we
can see the score markers, error markers and the elapsed time. The character is the
wizard in the lower right corner of the screen and the alternatives A, B, C and D are
the possibilities to complete the potion in the cauldron.
Fig. 3. First level of the game
It must be noted that, even though the game was conceived in Portuguese
language, it can be easily translated to any other language, as well as it is possible to
modify most of its aspects, given that it was designed as an Open Educationa
Resource. Source code is available on GitHub and is made available under open
source license.
4.2 Development of the Game.
The Game uses a 2D view and was developed in JavaScript and WebGL to
facilitate the visual work that forms the look-and-feel of the game. Game’s target
audience is composed by students who want to discover or review contents about
basic fractions.
Cocos2D-x is a multi-platform framework for developing games and graphic
applications [22] – the “x” letter in the name of the framework means that it can be
changed by one between several languages supported; in our case, the chosen
language was JavaScript (JS). This framework is a branch of another framework with
a similar name called Cocos2D, which is focused on development for Apple devices
running the IOS operating system. The big advantage of Cocos2D-x was to bring
improvements to the then Cocos2D:
It has a simple but also very powerful phase creator.
Accessible through all major operating systems.
Make it possible to publish games, for various platforms such as Windows,
Mac OS, Linux, Android, iOS and also to the Web, in any HTML5-
supported browser.
Possibility to create your applications through various programming
languages, such as C++, Lua, JavaScript, Objective-C, Swift, C#.
Figure 3 exposes de Cocos2D-x framework used in this paper.
Fig. 3. Framework hierarchy
The way the framework works is by using the concept of a director and scenes,
being each object on the screen a node in a component tree. Everything that will be
drawn is controlled by a class called CCDirector, where it has the ability to modify
the order of how components will be drawn and also change the game scenes, being
responsible for defining the initialization of the components that are requested by the
framework calls. The Cocos Creator tool tends to hide most of this complexity.
Cocos Creator is an editor that works on top of the Cocos2D-JS framework,
assisting in the development of the graphical application whatever it is, showing the
properties of the components, also providing a preview of what the game scene will
be at the moment that it is loaded and a way to graphically manage the files and
scripts that will be within the game. The scenes within Cocos2D-x are the most basic
component of each game window, within each scene, will be all the components,
effects, texts and images of the game being then managed by the Director.
5 Evaluation Of The Game And Educational Content
For the evaluation of the game FracPotions, an experiment was carried out with
elementary school students. As we wanted to evaluate the experience of the children
under a qualitative approach, we studied two different frameworks in the evaluation
process. The first one was the generic ITU BT500 assessment
(https://www.itu.int/rec/R-REC-BT.500) –and the other one was the MEEGA+ model
[23]. After we have analyzed these two assessment models, we have chosen the
second one, so the MEEGA+ model was used to evaluate the quality of the game and
educational content, since it is directly focuses in educational game evaluation instead
the generically approach of the ITU BT 500 for all type of software.
5.1 Experiment
The experiment was carried out with elementary school students. The participants
of the research were 18 students and the criterion of choice was that they already
knew the basic concepts of fractions learned in the classroom. The profile of the
students of the experiment presented a mean age of 12 years, there was a balance with
respect to gender, but the girls slightly predominated on boys; 92% of volunteers
make regular use of digital games - 47.6% on a daily basis and 9.5% weekly. Players
first had an experience of interacting with the game, without the help of any
instructor. Soon after, they answered a survey about the aspects of the game,
involving the visual characteristics of the game, the interface, the easiness that the
game possibly presents and other aspects of usability of the game. In addition, the
survey had extra questions about the educational content presented and its relationship
with the game, as a way to verify if the game met the educational purpose regarding
fractions. The students answered the questions using five possible responses in a
Likert-like scale (Too little, Little, Neutral, Very, and Very much).
The questions to evaluate the educational content of the game were:
1) How motivated did you feel to learn about fraction with this game?
2) Did you learn about fractions with this game?
3) Would you recommend this game to a friend?
4) Would you rather learn fractions using this Game?
5) Did you feel challenged by this Game?
5.2 Results Obtained
The combination of texts, colors and sources were pointed out as good
combination and consistency by 62% of the interviewees and the other 14% answered
neutrally (neither agree nor disagree). As for the game being intuitive and easy to
adapt 30% agreed with this aspect and 43% responded with neutrality. As for the
easiness to understand rules, 53% judged them easily understandable and the other
28% responded with neutrality. About the questions regarding the educational
content, the students have answered to the question (1) positively or neutral 61% (11
students); question (2) have 56% of positive answers (10 students); third question (3)
had 94% of positive or neutral answers (17 students); question (4) 78% (14 students);
and question (5) had 67% of positive or neutral responses(12 students).
6 Conclusions and Future Work
The teaching and learning processes in the field of Mathematics require an
important effort on building knowledge over a very abstract body of knowledge, but
with many practical applications in real-world situations. Fractions, for instance, tend
to represent an extremely abstract concept, mainly when local culture do not make
regular use of this kind of representation in common situations – which is the case for
Brazilian culture, which have adopted the floating point decimal representation in
detriment of the fractional one. Tools that help to stimulate students to keep
motivational aspect when learning such subjects are potentially useful to these
process.
This paper presented a game designed to support students to learn or revise some
basic fraction concepts. Regarding the group to which this game was applied, the
players/students showed interest in game’s subject and they reported to have enjoyed
the learning process supported by the game. However, the results point out that more
research is needed in order to improve the game itself and to apply it in other study
groups. Further work includes the development of other games for different subjects
in Mathematics and other STEM areas. The current game is in its beta version; as
improvements, new phases are to be developed with other types of fractions and
operations, as well as the translation and adaptation capabilities of the game as an
Open Educational Resource are to be tested.
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