Multiplication and division of integers through cultural approaches of playing dakon

Playing dakon has become a culture in Bengkulu. Since I was in kindergarten, dakon has been a fun game. It has the character of sharing fruit in each dakon convex (or hole). It becomes the starting-point of learning multiplication and division. The purpose of this study was to determine students’ thought processes in understanding the principle of multiplication and the division of integers through the cultural approach to playing the dakon. To achieve the goal, achieved through qualitative-explorative research. The subjects of this study were elementary students in Bengkulu City who were selected based on assignments. It was selected from 30 students who were given assignments about multiplication and division of integers. Students are given instructions using worksheets. After students submit their assignments, they are analyzed to select 2 students who have the thought process in achieving the principle of division and multiplication appropriately. Subjects were interviewed in-depth by researchers. Data were analyzed based on the genetic decomposition of research subjects. The results of this study are the Subject-1 can use the dakon to show the multiplicative properties of positive integers. He demonstrated that 4x3 by inserting it into four small dakon curves and three dakon seeds each. She concluded that multiplication is a repeated sum. Subject-2 uses the dakon to find the concept of dividing two positive integers. Subject-2 shows that 12: 4 by taking dakon seeds from a large curvature containing twelve seeds. She concluded that the division is a repeat reduction. This research concludes that Subject-1 and Subject-2 can build an understanding of operations multiplication and division, including verbal communication, writing, and drawing based on real media from local culture, namely the dakon game.


Introduction
Numeracy is one of the competencies that elementary school students must possess [1,2]. Since elementary level 1, students have been introduced to counting. These competencies involve integer operations. That is part of arithmetic learning. Operations are mathematical objects other than facts, concepts, and principles. Students learn the operations of addition, then subtraction, multiplication, and then division [3]. These are all basic arithmetic operations. The operation is in the universe of talking of a set of real numbers [4,5].
Operations on real numbers are the rules for obtaining a single element from one or more real numbers [6]. Arithmetic operations are operations that involve the addition, subtraction, division, and multiplication of a set of real numbers [3]. The set of real numbers consists of a set of rational and irrational numbers. The set of rational numbers contains a set of integers and fractions. Integers contain 2nd ISAMME 2020 Journal of Physics: Conference Series 1657 (2020) 012030 IOP Publishing doi:10.1088/1742-6596/1657/1/012030 2 natural numbers, zero numbers, and negative integers. For each natural number n, then -n is a negative integer.
The process of connecting mathematics to real life is important. Students who are connected with real-life are generally about numbers, such as counting and shopping. This helps students see the relationship between real life and mathematics [7]. To assist students in mathematical thinking activities, contextual learning approaches are needed [8][9][10]. The teacher should choose a learning strategy that is suitable for the student's intellectual level [11][12][13][14]. Students do the math process easily. They can communicate [15], between ideas in the system thinking, and with peers [16,17]. The teacher assists with scaffolding techniques in the student's distressed zone [18]. This is useful to facilitate students' understanding of the relationships between different mathematical concepts, shown through connections in a set of mathematical problems [19]. There is an increase in students' mathematical processes and connections in the achievement of mathematical concepts and principles. Therefore, learning mathematics with a local cultural approach will make it easier for students to communicate verbally followed by written communication. The local cultural approach results in an increase in students' mathematical abilities, such as mathematical connections, problem-solving, critical thinking, creative thinking, understanding concepts, and other mathematical abilities [16, [20][21][22][23]. Thus, we need to assist with students' mathematical thinking processes during learning.
The extra-mathematical connection approach can reduce the separation between mathematics and reality to give meaning to learning. That is to understand the world through a mathematical perspective and foster a symbiotic relationship between these two worlds [24]. Therefore, learning mathematics with a local cultural approach becomes important. That is often called the ethnomathematics approach [25]. The ethnomathematics approach to the mathematics curriculum can make school mathematics more relevant and meaningful for students. In this context, the application of the ethnomathematics perspective in the school mathematics curriculum helps develop students' intellectual, social, emotional, and political learning by using their unique cultural references to impart their knowledge, skills, and attitudes. Such a curriculum provides a way for students to maintain their identity while succeeding academically [26].
Mathematics teachers are challenged to deal with the cultural diversity of people that occurs in each classroom [27]. Ethnomathematics get an important role, in a meaningful mathematics curriculum. That is to explore various aspects of mathematical literacy. All of this should be implemented in learning mathematics in class. As such, we are interested in utilizing local culture in exploring students' cognitive processes to achieve the concepts of multiplication and division of positive integers.

Method
This study explores the way students learn multiplication and division of positive integers using the contextual media of dakons. Dakon is one of the children's games that has been entrenched in Indonesian society. That is expected to help students reach concepts in multiplication and division of two positive integers. To achieve these objectives, achieved through qualitative-explorative research. The subjects of this study were elementary school students in Bengkulu City who were selected based on assignments. It was chosen from 30 students who were given assignments about multiplication and division of integers. Students are given instructions using worksheets. After students submit their assignments, they are analyzed to select 2 students who have the thought process in achieving the principle of division and multiplication appropriately. The subjects are Rr and Hf. Subjects were interviewed in depth by the researchers. The interview was recorded with a video recorder. It is used to get complete and accurate data. The subject was asked to play the dakon together and witnessed by another friend. While playing the research team recorded and conducted in-depth interviews. Besides recording, we also make anecdotes to get additional data. Data were analyzed based on the genetic decomposition of research subjects. Genetic decomposition is a structured collection of mental and physical activities that construct certain categories and illustrate how mathematical concepts or principles are developed in individual minds [28].

Results and Discussion
Research involves the full potential of students, ranging from academic potential to play skills. This is a fun technique for students. Learn while playing. The game is very close to their culture. The ancestral culture of the nation that is often used by children to play and have fun is dakon. It is a "congklak" tool. Based on the Indonesian Encyclopedia [29], dakon is one type of game that can be played by boys and girls. Often adults also play it as a means of recreation. Dakon made of wood with a length of 50 cm, width 20 cm, and a thickness of 10 cm. The top of the wood is given a hole with 5 cm in diameter and 3 cm in it. The minimum number of dakon holes is 12. This game requires dakon seeds. Small sapodilla seeds or sapodilla manila are usually used for dakon seeds. Can also, small marbles. The number of players with at least 2 players. The number of dakon seeds is not determined, this is adjusted to the conditions and agreement of the players. Dakon can be seen in Figure 1. Playing dakon is an educational game as local wisdom that can provide excitement for students. It is a game that can improve academic thought processes. This game builds student motivation. Figure 2 shows the happy feelings of girls in playing dakon. This can reduce students' anxiety about learning mathematics. Therefore, this study designed a dakon game to teach multiplication operations and the division of positive integers.
Figure 2 also shows the comfort of children playing dakon. In playing the dakon, the research team asked them to empty 4 small holes and 1 large hole as dakon granaries. We will carry out the process of achieving the multiplication concept, which is 4x3. That is the dakon that can be seen in Figure 3.   Figure 4 shows that students can try to achieve concepts through simple activities. That is done by filling four small holes with 3 seeds each. This is corresponding to the 4x3 multiplication. Pay attention to the sequel to our interview excerpt.  Figure 5.  Figure 5 and the interview footage, it shows that students can make a property of multiplication of two positive integers. He stated that "the multiplication of 4 x 3 is the sum of four times the number 3". That means that 4 x 3 = 3 + 3 + 3 + 3. In another description that rectangular arrays can be used to model multiplication [30,31]. The representation of the multiplication model can be seen in Figure 6.  Based on interview excerpts and Figure 7, it means that students can reach concepts in multiplication operations of two integers. They are able to make the statement that 4 x 3 = 3 + 3 + 3 + 3 = 12. Students state that integer multiplication is a repeated sum. Thus, it can be concluded that through the play of the students' dakon can carry out the process of achieving concepts in the operation of positive integer multiplication that is multiplication is a repetitive sum. Students begin to think critically and rationally in a relaxed atmosphere of the play. That results in a good mathematical process. In line with this, there is an interaction between the development of fundamental arithmetic concepts and relational thinking. Students develop concepts related to arithmetic operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividends, dividers, and profit-sharing [33].
Next, we explore the ability of students in the process of achieving concepts for the division of positive integers. Students are triggered by using the media for achieving the concept. They were asked to play dakon by using twelve dakon seeds as shown in Figure 8 for 12 divided by 4. Starting from the dakon as in Figure 8, in the game two research subjects played the dakon based on twelve seeds in a big hole. They play to share it into small holes with each hole as much as four seeds. The following is our interview with the following research subjects. Q : What is the explanation of the next game? Rr : We distributed twelve seeds into the small hole of the dakon ... Hf : ... yes ... this is the first time I am playing the sharing, see as in Figure 9. Based on Figure 10 and the interview excerpt, it was revealed that the 12: 4 division operation is 12-4-4-4 = 0. That means that 12: 4 = 3. The concept in the division operation is a repeat reduction. Other research results that students can use these concepts effectively. Students feel the same sign not only finding results but also as symbols used to build relationships between operations and expressions [33].
According to McLellan et al. [32] that mathematicians seldom use the symbol ÷ for the division. Instead, they use fractional notation. Writing a small portion is another way to write a division. So 12 ÷ 4 is equivalent to writing 12/4, where the numerator, 12, is a dividend and the denominator, 4, is the divisor.
In arithmetic operations, arithmetic priority rules that allow us to do calculations involving parentheses, strengths, +, -, ×, and ÷. Calculations that involve positive and negative numbers, and generate and use rules to add, subtract, multiply, and divide them [34]. In arithmetic learning, verbal information content, and the type of addition and subtraction operations affect student reasoning [35].
After students become fluent with the concepts of multiplication and division the symbolic notation, x for multiplication, and ÷ for division can be introduced. Initially, ideas will be explored through conversation, then written into words, followed by a combination of words and numbers, and finally using numbers and symbols. At each step, when the child is ready, the use of symbols can reflect the child's ability to deal with abstract concepts [32]. Thus, the process of achievement by students in multiplication and division operations can be done well by students. It is utilizing media that is close to their culture. They play dakon in a relaxed and highly motivating way to play while learning.
The results of this study indicate that Subject-1 subjects can use dakon to show the multiplicative nature of positive integers. He demonstrated the 4x3 by inserting it into four small dakon curves and three dakon seeds each. Next, he gathered all the dakon seeds into a large tub and he stated the number of twelve seeds. Subject-1 concludes that 4 x 3 = 3 + 3 + 3 + 3 = 12, and multiplication is an iterative number. Subject Subject-2 uses the dakon to find the concept of dividing two positive integers. Subject-2 shows that 12:4 by taking dakon seeds from a large curvature containing twelve seeds. He took four seeds and then placed them in a small basin, four more seeds, and placed it in a small basin as well, and so on until the seeds in the large basin were used up. Subject-2 states that there are three small tubs, each containing four seeds. He concluded that 12: 4 = 3, because 12 -4 -4 -4 = 0, and division is a repeat reduction.

Conclusion
The need for learning with an ethnomathematics approach becomes very important to be applied in the abstraction process of mathematical concepts. Like dakon toys as one of the cultures that are close to students, it becomes a learning media for multiplication and division 2nd ISAMME 2020 Journal of Physics: Conference Series 1657 (2020) 012030 IOP Publishing doi:10.1088/1742-6596/1657/1/012030 8 of positive integers. This study concludes that Subject-1 and Subject-2 can build an understanding of learning messages, including verbal communication, writing, and drawing based on real media from local culture, namely the dakon game. That is to produce the correct concept of multiplication operations as repetitive addition and division is an iterative subtraction.