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 35 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 37 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". Reference Aggleton, J. (2019). Defining digital comics: a British Library perspective. Journal of Graphic Novels and Comics, 10(4). https://doi.org/10.1080/21504857.2018.1503189 Ahmed, M. A., & Kumalasari, N. (2023). ANDIN-MU: Development of Android-Based Descriptive Text Interactive Multimedia Materials in High School English Subjects. Assyfa Learning Journal, 1(1), 49–59. 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"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 Santiago et al. How can “gamifikacation” help... 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