Delta-Phi: Jurnal Pendidikan Matematika, vol. 1, pp. 34–40, 2023
Received 23 Feb 2023 / published 30 Apr 2023
https://doi.org/10.61650/dpjpm.v1i1.39

How can "gamification" help in the
teaching of arithmetic operations as a
didactic tool and digital technology?
Paulo Vitor da Silva Santiago1, and Baiduri2
1. Universidade Federal do Ceara (UFC), Brazil
2. Universitas Muhammadiyah Malang, Indonesia
E-mail correspondence to: paulovitor.paulocds@gmail.com

Abstract
This article is a teaching proposal concerning arithmetic problems of
mathematics to help teachers in initial training in mathematics and
teaching mathematics in the classroom with the use of Gamification.
Thus, the objective of this article is to investigate what contributions
didactic engineering and digital technologies using gamification in fulltime high school teaching can be helpful with the contents of basic
operations. The methodology applied with the games was based and
structured on the Didactic Engineering research methodology, being
exploratory research of a qualitative nature to familiarize the
mathematical problems with the use of Digital Technologies. The results
were categorized based on the phases of preliminary analysis, a priori
analysis, experimentation, and a posteriori analysis and validation.
Conclusions that the use of applied problems brought out the validation
of the strategies applied in the classroom. Therefore, the expected
results were positive in the teacher's view of the way the two games
were planned in Google Presentations and in supporting the students in
the teaching and learning processes of Mathematics.
Keywords:
Didactic Engineering;
Presentations; Mathematics.

Digital

Technology;

Google

Introduction
Digital Technologies (DT) have been significantly changing the
methods of teaching and learning in the classroom, educational
institutions and interactive spaces. (Bzhalava et al., 2022; Inganah
et al., 2023; Lazarenko et al., 2020) recurs "for example, an object
of knowledge is not teachable if we cannot incorporate it into a
teaching progression; if we cannot associate it with exercises for
students; if we cannot find ways to assess its mastery." Remarkably,

such instruments are launching new interactive platforms and
applications that the student establishes with his learning
environment (Ahmed & Kumalasari, 2023; Arif et al., 2023; Nasiha
et al., 2023), with his peers (Rahman, 2023; Sugianto & Khan, 2023),
and with himself (Santiago et al., 2023; Schabas, 2023; Winson et
al., 2023).
The changes in DT evolve rapidly, and the alternatives
becoming dynamic (Darmayanti et al., 2023; Fikri et al., 2023;
Hussain & Xi, 2023; Karim & Zoker, 2023), attractive (König et al.,
2019), and opening educational teaching spaces (Meirbekov et al.,
2022), previously directed in the traditional class with the use of the
whiteboard (Aggleton, 2019), desks, and chairs, currently with the
use of digital resources, allowing several ways to make the teaching
practice assimilative and inclusive, with attractive methods, to seek
the students' attention, increasing the learning opportunities
(Bogoslovskiy et al., 2019; Syaifuddin et al., 2022).
The fundamental arithmetic operations cover the calculations
used to solve problems, which due to the simple way of solving are
important for performing any mathematical calculation in basic
education. In this way, we seek to highlight problematizations with
the basic operations of mathematics (addition, subtraction,
multiplication, division), including the relationship of DTs with the
Google Presentations application. Several authors show
considerations about the use of these technological tools, among
them we highlight the understanding of (Sugianto, Cholily, et al.,
2022), "[...] question the ways in which mathematics can be
produced in school when using DTs; emphasize the humanity and
uncertainty of the subject of mathematics and the use of Digital
Technologies in the classroom.

© 2023 Santiago et al., (s). This is an open-access article licensed under the Creative Commons Attribution License 4.0.
(http://creativecommons.org/licenses/by/4.0/).

Santiago et al. How can “gamifikacation” help... Delta-Phi: Jurnal Pendidikan Matematika, 1, 34-40, 2023
In this statement, the teaching of mathematics is present in
various contexts of students' daily lives, and there are different
meanings between the subject taught in educational institutions
and the interactive one in everyday life (Darmayanti, Sugianto, et
al., 2022; Montiel & Gomez-Zermeño, 2021; Tong et al., 2022). This
reality reflects between the contents and the reality provided by
the knowledge, representations and conclusions of tasks (Nelson et
al., 2021; Zirawaga et al., 2017). Thus, the Brazilian scenario in
external evaluations such as the Basic Education Evaluation System
(SAEB) points out that students of Brazilian Basic Education, at all
levels of education, have difficulties with learning in the subject of
Mathematics (Humaidi et al., 2022; Palinussa et al., 2021; Whitton
& Langan, 2019).

of classrooms, which is well reflected in the importance given in
this tradition to didactic engineering".
Corroborating Artigue description, French mathematician
Regine Douady, creator of the so-called Board Game, explains the
methodology of DE by comparing the teacher to an engineer.
According to the author, DE happens "in the course of exchanges
between teacher and students, the project evolves under the
students' reactions and according to the teacher's choices and
decisions" (Chen & Chi, 2022; Jamaluddin & Faroh, 2020; Kim et al.,
2020).
Still, according to (Fjællingsdal & Klöckner, 2020), this
methodology has an experimental scheme structured in didactic
situations about the conception, execution, observation and
analysis of teaching sequences, allowing a validation in the a priori
and a posteriori analysis. It goes through the dialectical phases:
previous analysis, conception and analysis a priori,
experimentation and analysis a posteriori and validation.

In this sense, it is observed in the Matrix of Basic Knowledge
(MCB), that arithmetic operations are contained in this, and are
important content to be worked in the classroom (Khoiriyah et al.,
2022; Leton et al., 2019; Sugianto et al., 2017). This practice is a way
to reduce the gaps found in this process in the learning process
from elementary school to high school.

In the Previous analysis (preliminary), the important
information interact creating the intervention strategy, being able
to the epistemological of knowledge, didactic dimension of
teaching and cognitive problems of students. (Ezezika et al., 2021),
describes the inclusion gives, "[...] epistemological analysis of the
current teaching and its effects, of the students' conceptions,
difficulties and obstacles, and analysis of the field of constraints
and requirements in which the effective didactic realization will be
situated".

In view of this, we created the description of a treatment for
the theme directed by some elements of Didactic Engineering (DE)
to organize the research. In this sense, the importance of DI for the
teaching of mathematics included in the classroom that according
to (Casey et al., 2017)) is "[...] an experimental scheme that serves
as a basis for didactic achievements in the classroom, that is, as the
design, realization, observation and analysis of teaching
sequences".

During a priori Conception and Analysis, we select the tools
that can be exposed to the students in order for them to achieve
cognitive asymmetry. However, during this phase we can predict
the students' conjectures and behaviors during the development of
the didactic sequence proposed by the teacher. It is now, that all
the directed activities are planned.

This work is based on gamification for teaching mathematics,
with the following question: how has the learning of basic
mathematics been structured with the use of digital technologies in
Basic Education with students of Integral High School? To ground
this experience report, we included our study in the considerations
of (Cardinot & Fairfield, 2019; Ke & M. Clark, 2020; Qian & Clark,
2016) with Digital Educational Game.

[...] the constructivist theory posits the principle of the
student's commitment to the construction of his knowledge
through interactions with a given environment, the theory of
didactic situations that serves as a reference to the methodology
of engineering [didactics], had, since its origin, the ambition to
constitute itself as a theory of control of the relations between
meaning and situations (Cardinot et al., 2022; Han et al., 2018).

In this sense, we sought to investigate the contributions of
Didactic Engineering with the use of the DTs included the active
methodology of Gamification in the school environment for FullTime High School with the contents of the fundamental arithmetic
operations. In the following topic, the theoretical basis of the work
is presented in detail, subdivided into definitions about Didactic
Engineering and Gamification. It also presents the methodological
procedures, ending with the expected results and the final
conclusions about the theme analyzed.

About the a priori analysis, "[...] the choices made control the
students' behaviors and the meaning of these behaviors. For this,
it is based on hypotheses; it will be the validation of these
hypotheses that will be, in principle, indirectly in play in the
confrontation [...]" (Danilovic & de Voogt, 2021; Wu et al., 2021),
entering in confrontation with the fourth phase (a posteriori
analysis).

Literature Review
Didactic Engineering
Classical or first generation didactic engineering emerged in
discussions of Mathematics Didactics in the early 1980. In mid
1982, the first to study DE were Guy Brousseau, creator of the
Theory of Didactic Situations (TDS) and Frenchman Yves Chevallard
(Liu, 2018; Morschheuser, 2018), author of Didactic Transposition
(DT), then Michèle Artigue in 1989. This theme emerged as a
research methodology capable of elaborating didactic phenomena
in situations closer to a traditional classroom.

At the moment of Experimentation, observation consists in the
execution of the didactic sequence, having in mind the assumptions
shown, the objectives of the activity and its realization during the
research. Thus, it happens "[...] the didactic contract and record the
observations made during experimentation" (Dell’Angela et al.,
2020; Mercier & Lubart, 2021). In this phase, it is performed the
application of the research instrument of the teacher-researcher
and the records of the observations of the subjects (students).

The term "didactic engineering" was structured on the didactic
work compared to the work of an engineer who, in order to start a
project, bases himself on scientific knowledge of his area of activity,
accepts to insert himself in a scientific type of moment, that is, he
is obliged to work with more complex objects than the objects
studied in science, therefore, to achieve, with all the supports he
has, problems that science does not or cannot apply (Aranda et al.,
2019). In view of this, a trinomial relationship arises: teacher,
student and knowledge.

In the last stage, the a posteriori analysis and validation is a set
of data obtained throughout the third stage (experimentation), as
an example, the students' writings, records during observation and
audio and video recording, as mentioned above. In this phase, the
confrontation between the second phase (a priori analysis) and the
a posteriori analysis of the didactic situation takes place.
This research is structured in the four stages of DE, preliminary
analysis, a priori analysis and design of the didactic situation,
experimentation and a posteriori analysis and validation for an
application of teaching the basic operations of mathematics
(addition, subtraction, multiplication, division) with the use of
Gamification in the classroom.

(Valiero, 2020), report that French didactics allows that "they
allowed to develop didactic research in close interaction between
researchers and teachers, as well as in close contact with the reality

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Santiago et al. How can “gamifikacation” help... Delta-Phi: Jurnal Pendidikan Matematika, 1, 34-39, 2023

Gamification

environment into learning spaces.

The problem approached in the classroom is challenging,
interactive, and shows a universe of fun games, demanding basic
knowledge of mathematics from the students' resolutions.
However, materials already made by other teachers are generally
used, i.e., those evidenced for download on the internet. (Fauza et
al., 2022; Lin et al., 2018; Sugianto, Darmayanti, et al., 2022) in the
intervention with the "[...] game, it is possible to learn to negotiate
in a rules environment and postpone the immediate pleasure. It is
possible to work in teams and be collaborative, to make decisions
for the best available option."

Games provide, in various ways, to advance their stages in
education, acquiring rewards as challenges are conquered. (Kaddari
et al., 2021), talks about the ways of teaching, inspiration and
involvement with a differentiated learning. In this sense,
Gamification can increase the number of student participation in
front of the enjoyable and fun elements of games in a way adapted
to the teaching of mathematics. Therefore, (Mosalanejad et al.,
2020) shows that the fact of delivering activities does not
characterize gamification, but the means used in the classroom,
seeking interaction with everyone, making a pleasant environment
for teaching and learning.

In this same bias, the teacher and students adapt with
Gamification in Google Presentations online version (Hu & Shang,
2018), the starting point will be the alternatives to be selected
during the application in the classroom and by which learnings
should follow for the resolution. (Gündüz & Akkoyunlu, 2020)
reports on attractive teaching materials in the eyes of the subjects,
making a major challenge for educational institutions, but also for
other professionals in basic education, who need to turn the school

(Hu & Shang, 2018), includes "the insertion of games in the
context of teaching-learning implies advantages and
disadvantages" and worked in the literature specialized in the
theme, and should be thought and assumed by teachers, when
considering structuring a virtual pedagogical object, with
technological games. The author's contributions in the context of
the following aspects are evidenced in Figure 1.

Figure 1. Advantages and disadvantages of games in teaching and learning
(Grando, 2000)

These considerations above delineate necessary and important
aspects in the inclusion of games in the context of teaching and
learning, proposing to the teacher a reflective thought with the
methodological assumptions, planned in his school pedagogical
planning, observing a coherent conception, present in the action of
applicator in the classroom. (Tsai et al., 2020; Wen et al., 2020)
discussed about "digital games favor the response to user activity,
making it more immediate and instantaneous. There are simulation
situations in which a game can direct the learning of skills needed
for its improvement, opening space to be used in education."

reason, integrate and engage, as well as engage and motivate to
achieve goals.
Based on the theoretical and methodological aspects explained
above, the next topic discusses the methodological approach taken
in the research.

Research Methode
The methodological path carried out in the complete work that
was realized by the phases of the DE (preliminary analyses, a priori
analysis and design, experiment and a posteriori analysis and
validation), however, only some results will be included for
exposition in the text. In the first phase of Preliminary Analysis, a
study was created based on two aspects: I) a brief epistemological
explanation about the teaching of the four basic operations of
mathematics and; II) analyses of textbooks on the content of basic
operations to choose questions about the content exposed in
Gamification to be addressed in the research.

Understand the economic, social and historical relationships
between these dimensions of social practice, through the course
understand concepts as relational systems of concrete totalities
intended to explain, understand and (Azizah et al., 2021; Gulo,
2020).
Essentially, gamification is a way of using the form and
reasoning of games to motivate, engage and facilitate learning, in
this way gamification can be applied in two ways: with or without
digital technology; the mechanism does not necessarily depend on
technical or digital means (Barbosa, Pontes & Castro, 2020). From
these exposed elements, it can be noted that gamification is not
defined simply by the creation or use of games, but assimilates a
global culture that creates challenges that allow students to

In aspect I, the basis was in authors such as (Holanda, Freitas &
Rodrigues, 2020) and (Jacomelli-Alves & Sabel, 2022) when they
work on the teaching of basic operations and the difficulties
encountered in the four basic operations, as well as their approach
in observing the behavior of students during the application of the
questionnaire, realized that one of the important factors in

36

Santiago et al. How can “gamifikacation” help... Delta-Phi: Jurnal Pendidikan Matematika, 1, 34-40, 2023
mathematical problems is the lack of interest and discouragement
in the face of insufficient results acquired after the resolution, the
basic operations were exposed in an insufficient manner or not
included during the school year studied in previous years to the
current ones, which is added to the context where the DT is a reality
that can no longer be excluded from teaching and learning.
Already in aspect II, it was observed in all books approved in
the National Textbook Program (PNLD) 2018, that the contents of
the basic operations is little, mostly is found a short explanation. Of
the 3 (three) volumes analyzed, only (Balestri, 2016) volume 1
exposes in the initial chapters some problematizations. It was also
analyzed how the contents are explained to high school students,
following the traditional teaching with some applications of the
GeoGebra software, often stimulate the mechanization of learning
by repetition. These patterns are considered, according to (AN
Vidyastuti et al., 2022; Scott et al., 2022)), exploring the contents
about the use of symbology in teaching the proposed activities.

Figure 2. Virtual game in Google presentations, Google (2023)

In the phase of the a posteriori analysis and validation
(internal), the analyses of the data obtained in the game
resolutions were performed, comparing them with the a priori
analysis whose purpose was to reach the objectives and
hypotheses present in this work, in addition to analyzing the
inclusion of arithmetic problems solved by them and their
observations regarding Gamification applied in the classroom.

Research Methode

In the a priori Analysis and Design of the didactic situation, an
interactive gamification was structured and planned with basic
contents of high school to recompose the learning of mathematics.
In this case, gamification, as a multimodal approach, should help
the mismatch between education and the contemporary world and
its digital culture with such a great impact on society, as the
dispersion of knowledge and the multiple ways to access it leads to
the need to rethink teaching, restructure existing rules and review
entrenched and conservative paradigms. Stay focused on your
educational goals, free from the extreme effects of distance or
proximity to the digital world.

As a result of this work, two educational games were produced
by the mathematics teacher of the classes with the support of the
Google Presentations platform. All games had a common goal: to
show the Mathematics subject in an interactive and fun way to
obtain better results in internal and external evaluations. The
application happened with 32 students in the Mathematics subject
of the Assis Bezerra Full Time School, located in the city of
Quixeramobim - Ceará - Brazil. The application took place during
the math teacher's time, with the participation of the students
present on the day of the Gamification.

The methodology of the work was exploratory research of a
qualitative nature. The inclusion of exploratory research is justified
because there are few studies using Gamification for High School
outlined in Action Research. (Eriksson et al., 2021; Sah RWA et al.,
2022), exploratory research aims to familiarize the problem by
trying to make it as explicit as possible for those involved.
Qualitative research presents a reality that cannot be treated or
quantified with the subjective items of reality with the research
(Darmayanti, Baiduri, et al., 2022; MM Effendi et al., 2022). In view
of this, it is considerable to analyze the data without the due
statistical treatment of the students, because it seeks to
understand the reality of the school (Ezezika et al., 2021; Tsai et al.,
2019).

The problems included in the game were taken from the
analyzed textbooks referring to the content of basic operations in
mathematics. These small problems should emphasize the
mathematical calculation of open and interpretative questions that
can be presented as students' previous knowledge. Basic Math
Museum - is a game that had as a reference the labyrinth and called
Labyrinth, aiming to encourage mathematical reasoning, in a
playful way and Stop Egypt is a game with a roulette wheel and
figures on the side that can be turned to find out which math
subject will be answered by students. Game 01 - Presents several
mathematical problems with basic operations for students to
answer, taking place in various scenes of the virtual environment
and passing through random phases during the game. Game 02 - A
mathematical logic reasoning game, whose objective is to select a
figure displayed on the screen containing 4 by 4, totaling a total of
16 different questions and adding to the left side a choice of any
number to solve the question. Right after that, based on the
didactic proposal, the interactive groups discuss the problem
situations exposed in the classroom. Next, we present the two
computer games built in Google Presentations (Figure 3).

In the Experimentation stage, which was applied with two high
school classes of the Assis Bezerra Full Time School, 54 students
were enrolled and 32 of them were able to participate in the game.
The research instrument of this work is composed of the grade of
the first period of the subject of Mathematics, following three
stages: 1st stage - Bibliographic review of the textbook, school
curriculum and matrix of descriptors of SAEB; 2nd stage Development of games on the Google Presentations platform; and
3rd stage - Application of Gamification with the two classes.
In the first stage, bibliographic research of the textbook on
digital platforms that facilitate students' reasoning was surveyed.
The second stage included interactive workshops with games in the
form of slides. Finally, in the third stage, the digital games created
in the Google Presentations platform were applied with the two
classes, reporting the rules, the beginning and the end of
Gamification in the classroom. In the workshop interactive groups
were divided to facilitate the learning of Mathematics content. In
this way, digital games were also made to obtain from the students
the mathematical thinking and reasoning and apply it in
Gamification.

Figure 3. Games applied in the classroom

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Santiago et al. How can “gamifikacation” help... Delta-Phi: Jurnal Pendidikan Matematika, 1, 34-40, 2023
During the application of Gamification, the teacher provided
the rules of the game and which steps to follow for the completion
of each game. One can observe the students' initial contact with
the game and the information contained in the teacher's
explanation, so that they can begin their attempts at solving each
problem. With this, we included the data collected from the
students' conversations, being named E1, E2, E3, E4, and so on, due
to not inserting their real names, considering the norms of the
Ethics Committee when working with human beings. In this
context, all care was taken during the insertion of data and their
analysis in the description of the text of this work. In view of this,
subject E8 presented the following question to interactive group
03.

basic operations and measures of central tendencies, through the
application Presentations. Therefore, this investigation included
mathematical problems adapted with the help of Google
Presentations, providing teachers with a digital didactic model
based on the DE that provided, in the classroom, a methodology
that differed from the traditional and repetitive teaching of
concepts worked by textbooks, as well as making available the
responsibility of the student for the construction of his reasoning
and mathematical knowledge.
It is hoped that the methodology discussed in this work will
serve other teachers and classes as teaching material to explore
basic mathematics with other related contents. Since this is an
ongoing research, the goal is to (re)apply other didactic models in
the Presentations application during the school year to collect
other data and observations

"E8: I observed that at each stage of Game 01 we can learn the
step by step of solving the basic operations of mathematics,
because when observing the first stage of the museum, we visualize
the basic operation of addition, already in the other stages are
complemented by subtraction, multiplication and division. So, I
made sure to analyze each short problem with my previous
knowledge acquired in previous years of teaching".

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The lecturer continued the game by questioning the other
students in relation to the exposed questions. Subjects E23, E31,
E10 responded as follows.
"E23: Teacher, I was in doubt when arriving at the division
stage, I did not have the necessary knowledge to solve these
questions, after your speech I realized how to solve them
differently and use in future problems".
"E31: I was able to solve some and I am trying to learn how to
solve the other more difficult ones in the two games."
"E10: I thought Game 02 was better, because it had fewer
alternatives and the text was closer to the reality experienced
in elementary school.
It was observed that each student explained his difficulties and
ways of learning consistent with the two games, substantiating the
stages of EE. These reports go through the construction of each
student's intuitive idea, which leads them to choose a learning that
can generate the necessary knowledge for other types of
questions. It is worth noting that the interactive moment with
students provided the organization of relevant information
structured in the previous step, addressing a formal mathematical
language in order to validate the conjectures built in the games, the
validation phase was established, which, according to (HassingerDas et al., 2017) states that dialectical situation seeks a solution
that the actors determine the validity of the knowledge acquired in
the didactic situation. It was also realized that the two games
adapted in Google Presentations enabled the use of DT, through
the dynamization of gamification in the classroom, the
development of student autonomy facing the digital technological
tool in the use of their basic knowledge of mathematics in relation
to the proposed content.

Conclusion
During the application of this work, it was observed in the
epistemological and didactic investigation about the relationship of
the fundamental arithmetic operations applied with interactive
games using the methodology of DE, the need to work this
application with other classes of Comprehensive High School,
through Gamification workshops with the basic concepts of
mathematics.
The application Google Presentations was also used as a
technological tool that helped the teacher in the didactic
transposition of the proposed problems, allowing a better
understanding of the content of some issues explained in both
games, as in the ability to understand which methods to use in
solving each problem situation.
In this way, this work seeks to investigate the results obtained
in the mathematics grade and the contents little worked on in
elementary school, for a better understanding of the elements of

38

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