58 

 

 
6 (2) (2021)  

 

International Journal of Active Learning 
 

Terakreditasi SINTA 4  
http://journal.unnes.ac.id/nju/index.php/ijal  

 
 
 

Developing Ardgotic Game to Improve Logarithm Learning Outcomes 
 
Rakeltamara Y. Prameshela1, Wahyu H. Kristiyanto2, 3, Helti L. Mampouw1, 3 

 
1Departemen of Mathematics Education FKIP 
2Departemen of Physics Education FSM 
3Center Research of Science, Technology, and Mathematics (e-SisTeM) 

Universitas Kristen Satya Wacana, Salatiga, Indonesia  
 
Info Articles  
____________________  
History Articles:  
Submitted 30 April 2021 

 Revised 11 May 2021 

Accepted 8 June 2021  
____________________  
Keywords:  
ARDGOTIC, logarithm, 

learning media 

_________________________ 

 
 
Abstract  
_________________________________________________________________  
This research aims to produce ardgotic learning media that can improve student learning outcomes 

on logarithm.  This research consists of 5 development steps, namely analysis, design, 

development, implementation and evaluation. Ardgotic is a game developed from an othello type 

board game that requires players to win the games where logarithm is the topic. The results of this 

media validation reached 94.54%. Trials on 32 students of class X SMK showed a practically rate 

of 85.71%, both of which were in the very good category. The use of ardgotic media can improve 

learning outcomes logarithm by 0.697 or a moderate increase. Students find the appearance of the 

media attractives and the media can motivate them to learn logarithms. These results indicate that 

ardgotic media can be used to learn mathematics in different ways.  


 Address correspondence: p-ISSN 2528-505X 
 

Email: helti.mampouw@uksw.edu 
e-ISSN 2615-6377   

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 



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59 

 

INTRODUCTION 

 

Logarithms are found in dalif life. Sinaga et 

al (2017) writes the use of logarithms in the fields of 

electronics, telecommunications, and acoustics. 

Logarithms are used in these fields as the human ear 

expresses sounds heard logarithmically. In 

astronomy, a logarithmic scale magnitude is used to 

measure the brightness of stars as the human eye 

expresses brightness logarithmically. The logarithm 

which is the inverse function to exponentiation has 

the characteristics derived from the properties of the 

exponent. The abstract nature of the logarithm 

learning materials reguires the student’s imagination 

and readiness of conceptual thinking 

 In mathematics, the logarithm is introduced 

as the inversion to exponentiation. This suggests that 

the material is taught after the students have mastered 

the exponential functions, as stated in the math basic 

competency (Permendikbud No.37 tahun 2018) 

related to exponentiation and logarithms.  The 

competency states that students can select and apply 

the rules of exponentiation and logarithm according 

to the characteristics of the problems, verify the steps, 

present realworld problems using algebraic operations 

(i.e., exponential and logarithmic functions) and solve 

the problems using the verified properties and rules. 

By solving logarithmic problems, students learn to 

select and apply the correct logarithmic functions.  

However, some students are unable to use logarithm 

rules according the problems given. Hananta (2019) 

found that students made errors in using logarithm 

rules or properties. Yasin (2017) found that students 

never rechecked logarithm rules or properties they 

used in solving logarithm problems. All of these cause 

the students’ low achievement of logarithm. 

This low achievement was also evident in the result of 

the high school national exam, including that by the 

vocational students of Akutansi dan Penjualan (AKP) 

[Accounting and Marketing] major in 2018/2019. 

Tabel 1 below presents the percentage of the students’ 

mastery of logarithm.  

Table 1 suggests that in the national context, 

the students’ mastery of logarithm is low. The 

mastery of the students in Central Java is better than 

that of the national context. The mastery of the 

students in Salatiga, Salatiga, Boyolali dan Magelang 

(regency) obtains 60 while that in Klaten, kab. 

Semarang dan Surakarta does not yet achieve 60. This 

result indicates that the accounting and marketing 

major students’ mastery on logarithm is below 

expectation. Therefore, there is a need to find a way 

to improve the learning of logarithm in the level of 

vocational schools. 

Table 1. The mastery of logarithm based on the 

national exam result of the vocational students of 

Akutansi dan Penjualan (AKP) [Accounting and 

Marketing] major in 2018/2019 

City/Regency Mastery (%) 

Klaten 55,17 

Kabupaten Semarang 54,13 

Surakarta 54,68 

Salatiga 62,44 

Boyolali 60,75 

Kabuten Magelang 70,11 

Jawa Tengah (Central Java) 57,39 

Nasional (national) 49,88 

 

 One way to improve the students’ learning of 

logarithm is by designing learning media which suit 

the students’ characteristics. Learning media is used 

to encourage and motivate students in learning. 

Latuheru (1998) stated that learning media were tools 

which had ways to deliver messages in a learning 

teaching activity. The use of media can increase the 

students’ motivation to learn (Hamalik, 1986). 

Learning media can help explain the learning units 

clearly, which helps achieve the learning objectives. 

In addition, using learning media in class, learning 

methods become varied, which makes students 

interested in the teaching learning activity (Sudjana, 

2002). One of the learning media going to be designed 

can take the form of a board game or a physical 

learning medium.   

Board games can help students and teachers 

in teaching learning activities. Some studies suggest 

that board games are efficient in terms of their 

learning usage. Romanica (2018) developed board 

games themed Pasar Tradisional [traditional markets] 

to introduce the art of bargaining in the traditional 

market context. Yunita and Wirawan (2017) used 

board games to enhance the interest of the social 

studies major high school students in the basics of 

accounting. The results showed that board games 

could be developed so as to enhance the students’ 

learning achievement in an interactive wat.  

One board game which can be used for a learning 

medium is Othello. Othello is a famous Japanese 

board game. Othello, which is also called “reversi”, 

begins with placing a pair of white discs and a pair of 

black ones at the center of the board.  This two-player 

game requires a great strategy. Thus, students are 

demanded to develop a great strategy to win the 

game. In addition, playing this game fosters a sense of 

competition in students.  

Othello is the ingredient of logarithm leaning 

media. The learning media developed from Othello is 

named ARDGOTIC. ARDGOTIC is expected to be 



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60 

 

able to enhance the students’ interest and 

achievement of logarithms. The research objective is 

to produce a valid, practical and effective 

ARDGOTIC as a learning medium for improving the 

achievement of logarithms.  

 

METHOD 

 

This research employed Analysis, Design, 

Development, Implementation, Evaluation (ADDIE) 

model.  According to Dick and Carey (1996), ADDIE 

model could be designed for in class learning system. 

ADDIE consists of the analysis stage which analyzes 

the learning problems and the students’ needs, the 

design stage which designs the learning media based 

on the analysis of the learning problems and the 

students’ needs identified in the previous stage, the 

development stage which develops the design to 

attract the students’ interest and improve their 

achievement of logarithm, the implementation  which 

share the media with the students, and, finally, the 

evaluation stage whih reviews and follows up the 

analysis of the media’s benefits and drawbacks. After 

having gone through the five stages, we produced a 

valid, practical, and effective learning medium to use 

in the learning.  

The development of ARDGOTIC requires a 

valid, practical, and effective measurement. 

Therefore, an instrument of data collection was 

designed. This instrument consists of a validation 

sheet, pre-test, post-test, and learners’ evaluation 

sheet. The validation of ARDGOTIC was conducted 

by an expert in math education and learning media. 

The medium’s practicality and the students’ interest 

in ARDGOTIC were based on the teachers’ and 

students’ assessment. The effectiveness of the 

medium was based on the results of pre-test and post-

test, which was calculated using the following 

formula: 

 

𝑁 − 𝐺𝑎𝑖𝑛 =  
𝑝𝑜𝑠𝑡𝑡𝑒𝑠𝑡 𝑠𝑐𝑜𝑟𝑒 –  𝑝𝑟𝑒𝑡𝑒𝑠𝑡 𝑠𝑐𝑜𝑟𝑒

𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑐𝑜𝑟𝑒 – 𝑝𝑟𝑒𝑡𝑒𝑠𝑡 𝑠𝑐𝑜𝑟𝑒
 

 

The calculation result was then verified against the 

assessment category displayed in Table 2. 

 

Table 2.  Classification of N-Gain Category 

N-Gain score Category 

𝐺 ≥ 0,70 High increase 

0,30 ≤ 𝐺 < 0,70 Medium increase 

𝐺 < 0,30 Low increase 

Source: Winarto, 2018 

 

The class and practicality indexes were calculated by 

using the following formula: 

𝑃(𝑠) =
𝑆

𝑁
× 100% 

where 𝑃(𝑠)  is the sub variable percentage, 𝑆 is the 

total score of each sub variable, and 𝑁   is the 

maximum score.  

The result was then classified based on Table 3. 

 

Quantitative score range 

(x)  

Qualitative category 

(x) 

81% ≤ 𝑠𝑘𝑜𝑟 ≤ 100% Very good 

61% ≤ 𝑠𝑘𝑜𝑟 < 81% Good 

41% ≤ 𝑠𝑘𝑜𝑟 < 61% Fair 

21% ≤ 𝑠𝑘𝑜𝑟 < 41% Poor 

Source: Winarto, 2018 

 

RESULTS AND DISCUSSIONS 

 

ARDGOTIC is an Othello-based board 

game which was developed to help students achieve 

the expected competency in logarithms.  The 

development lasted for seven months starting from 

June until December 2020, involving 32 students of 

Akutansi dan Penjualan (AKP) [Accounting and 

Marketing] major of SMK Negeri 2 Salatiga. 

Although the research was conducted during the 

Covid-19 pandemic, the research procedure obeyed 

the government health protocols. The development of 

ARDGOTIC is explained as follows. 

 

Analysis 

 The initial stage of ARDGOTIC 

development is to obtain information related to the 

nature of the learning materials, the characteristics of 

the students, and the condition of the learning. 

Logarithms are compulsory materials in semester 1 of 

for tenth graders of vocational schools. The 2013 

curriculum, 2017 revision and Permendikbud No.37 

tahun 2018, states that the basic competency in 

logarithms is the students’ ability to select and apply 

logarithm rules and solve real problems related to 

logarithms using the properties of logarithms. The 

vocational students’ characteristics were obtained 

through direct observations and interviews with the 

teachers and students. The information obtained 

suggests that vocational students are less interested in 

maths. Mathematics is considered difficult, rigid, and 

abstract. Logarithms are considered not directly 

connected to the world of work. Vocational students 

tend to emphasize practical things.   

The learning medium developed must be 

able to draw the students’ interest, improve the 

students’ learning interaction, make enjoyable 



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61 

 

learning atmosphere, challenge the students to learn 

more, as well as motivate them to make a good 

practical strategy to solve problems.  

 

Design 

 An Othello-like board game was selected 

based on the result of the analysis stage. This type of 

game was selected as it foster students’ interaction 

through the game.   The procedure of logarithm 

learning and the selection of software to design the 

images, characters, and fonts were then completed.  

ARDGOTIC is a board game consisting a board, 

discs, question cards, and the game guidebook which 

also serves as the answer key or solution manual. The 

graphic design software used was CorelDraw 2019. 

This software works with Windows XP, Windows 7, 

and Windows 8. Figure 1 shows the ARDGOTIC 

logarithm.  

 

 
Figure 1. Steps in ARDGOTIC 

 

The basic board design is green and white. 

The board is equipped with a score box.  The question 

cards are in orange. The logo and one question and its 

answer or solution is printed on each card. The 

guidebook and answer key are in green. The color 

selection was based on the eye health and aesthetic 

aspect. 

 

Development 

 A detailed design process was conducted by 

using CorelDraw 2019. The design paid attention to the 

aesthetic aspect as well as showed friendliness. The 

games rules were developed as to be played easily, to 

highlight interactions, and to help students master 

logarithms. CorelDraw 2019 was used to deign the 

board, discs, and quetions cards. The game rules were 

designed by using Microsoft Word from Microsoft 

Office for Windows. 

ARDGOTIC requires player teams to obtain 

the highest score by answering questions printed on 

the question cards, related to the logarithm properties. 

Figure 2 displays the board.  The score boxes are 

placed on the upper part of the board to ease the 

competing teams to see their scores.  The questions 

cards are cards containing questions on the logarithm 

properties. Each card is made of a 10x15 cm paper.  

Figure 3 displays a sample of a card design. This game 

comes with a guidebook for teachers to teach their 

students how to play ARDGOTIC. Figure 4 diplays 

the front page of the guidebook. 

 

 

 
(a) 

 
(b) 

Figure 2. The board and the variation of the discs’ position: (a) scattered, (b) centered  

 

 

 
(a) 

 
(b) 

Figure 3. Question card: (a) front, (b) back 

  



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62 

 

 
Figure 4. The front page of ARDGOTIC guidebook 

 

Learning logarithms begins with forming 

two competing teams of players. At first step, the 

teacher places two pairs of discs in the middle of the 

game; one pair of black discs and one pair of white 

discs. The discs care diagonally placed are shown by 

Figure 1.(b). 

 Next, the players decide who play first. The 

job of the players is to surround opponents’ discs. For 

example, the white discs must surround black discs as 

shown by Figure 5.(a).  The surrounded or outflanked 

discs are then flipped over to the opposite color. For 

example, the surrounded black discs as show in 

Figure 5(a) are flipped to white as shown by Figure 

5.(b).  

If a player can surround at least three 

opponent’s discs, he or she gets a question card. If the 

player can correctly answer the question, he or she 

gets points as many discs as he or she flanks or frames. 

However, if the player is unable to answer the 

question, the points are rewarded to the opponent. 

The game is over when the board is full of discs or the 

players can no longer surround their opponents’ discs. 

The players with the highest points win the game. 

 

 
(a) 

 
(b) 

Figure 5. Discs’ position on the board: (a) White discs surround or outflank black discs and (b) the 

surrounded black discs turn to white 

  

Implementation 

 A validated “ARDGOTIC” game was 

played by teams of 32 students of SMK Negeri 2 

Salatiga. Before the game began, all students were 

expected to recall logarithm requirements in order to 

know how to learn through ARDGOTIC.  Before the 

teams were complete, the teacher simulated the game 

to emphasize the rules of the game.  Then, the 

students learned logarithms through the ARDGOTIC 

team competition. While the students were playing, 

the teacher was observing, explaining logarithms, and 

collecting data. At the end of the impementation 

stage, the teacher had already acquired the data on the 

pre-test, post-test, and students’ evaluation on 

ARDGOTIC and the overall learning.   The data were 

then analyzed.  

 

Evaluation 

 The evaluation was conducted to find the 

contribution of to the students’ logarithm mastery. 

The scores of the students’ pre-test and post test as 

well as the students’ evaluation on the medium were 

used to find out if the learning medium was effective 

in improving the students’ learning achivement. Table 

4 shows the recapitulation of the pre-test and post-test 

of 32 vocational students in Salatiga  

 

Table 4. Description of students’ pre-test dan post-

tes scores 

Description Pre-test Post-test 

Numbers of subjects 32 

Average 4,3 7,8 

Standard deviation 2.53 1.00 

Total score 136 250,5 

Minimum score 0 6 

Maximum score 10 10 

 

The result of the effectiveness testing was 

taken from the result of pre-test and post-test. N-gain 

formula was employed to measure the increase. The 



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63 

 

N-gain calculation suggests that the students’ learning 

achievement has an increase of 0,697, which is 

classified as a medium increase. Therefore, ardgotic is 

said to be an effective learning medium.  

The analysis of the students’ opinion also shows that 

ARDGOTIC is interesting and that it makes the 

students interested in learning logarithms. Overall 

comments show a positive response for ARDGOTIC. 

One student’s response states that ARDGOTIC is fun 

as it makes students learn through the game 

questions. 

The validation result of the pre-test and post-

test instruments shows that: (1) the questions are in 

line with the research objective, (2) the test directions 

are clear, (3) the question objectives are clear, (4) the 

questions are likely to be answered by the students, (5) 

the language uses the correct and appropriate 

Indonesian language, dan (6) the questions use simple 

words and sentence structures which are easy to 

understand. The validity testing result of the pre-test 

and post-test obtains an index of 93.3%, which means 

very good. 

The validity index of ARDGOTIC is 

94.54%, which means very good. This is because 

ARDGOTIC has some benefits, one of which is its 

interesting design addition, this game requires 

students to develop a good strategy and learn. 

ARDGOTIC receives a percentage of 85.71% in 

terms of practicality, which is classified as very good. 

This is due to the fact that the board is not too big to 

carry anywhere. 

The analysis result of the students’ opinion 

suggests that: (1) ARDGOTIC has an interesting 

display, (2) ARDGOTIC can motivate students to 

learn mathematics, (3) ARDGOTIC can serve as an 

alternative to learning mathematics.  

Most students agreed if ARDGOTIC was 

used in the learning and if it was also designed for 

learning other topics. ARDGOTIC can ease the 

students’ learning as they learn logarithms through 

playing. The analysis result of the students’ opinion 

shows that the students gave a positive response to the 

use of ARDGOTIC. 

The result of the observation shows that the 

students were quite enthusiastic about learning media 

which let students play and about board games which 

fostered a sense of competition in them.  The teachers 

also stated that this type of media could be used as 

they helped students learn while playing.  

 

CONCLUSION 

  

The research findings conclude that 

ARDGOTIC is a valid, effective, and practical 

learning medium which can used to improve the 

students’ learning achievement of logarithms. The 

validity testing result of ARDGOTIC yields a validity 

index of 94.54%, which means very good. The result 

of ARDGOTIC practicality testing shows a 

percentage of 85.71%, which means very good. The 

N gain score of the vocational students in Salatiga 

shows an increase of 0.697. Therefore, ARDGOTIC 

is concluded to be an appropriate learning medium. 

ARDGOTIC can be further developed to teach 

different learning materials. The use of learning 

media is not only for learning the materials but also 

for fostering a sense of competition in students.  

 

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