The research results show that Mathematics GASING makes a real contribution to students' understanding and mastering the concept of the multiplication operation. Based on some of the issues mentioned above, the research question of this study is how the learning trajectory of multiplication in Mathematics GASING has developed among the students of the rural area. The learning process ensures that students learn easily, fun and enjoyable in Math GASING (Shanty and Wijaya, 2012).
The results of this study indicate that learning design of multiplication operation in Math GASING plays a very important role as the starting point and improves students' motivation in learning. First, teacher introduced the concept of multiplication by playing some games using Math GASING learning aids. In designing this study, researcher used the learning steps of multiplication in Math GASING as shown in Table 1.
In the dialogue, students seem to feel that learning multiplication in Math GASING seems so easy and so much fun. Researcher can conclude that learning multiplication operation in Math GASING plays a very important role as the starting point and improves students' motivation in learning multiplication.
Paper ID: 9257]
The results of the research show that GASING of mathematics has a real contribution for students in understanding and mastering the concept of multiplication operations. This situation underlies the researchers of this present study to try to map the learning trajectory on number operations in Math GASING for rural area students originating from Serui, Sorong Selatan and Ambon, Papua. Therefore, the focus of this study is to describe the learning activities on students' performance to do multiplication in mathematics GASING.
The learning process makes student learning easy, fun and enjoyable in Math GASING (Shanty & Wijaya, 2012). Math GASING as one of the innovations in learning mathematics offers a critical point in its learning process. As a result, the students were able to master the multiplication operation in Math GASING, as shown by the results of the final evaluation, and most importantly, the learning of Math GASING could be detected from the comments of the students who wanted to abandon the old way to learn math.
The results of this study indicated that learning design of multiplication operation in Math GASING has a very important role as the starting point and improvement in the. A set of activities for learning multiplication in Math GASING is design-based learning trajectory and thinking process of students who made hypothesis. In designing this study, the researchers used the learning steps of multiplication in Math GASING as shown in Table 1.
Therefore, it can be seen that learning the multiplication operation in Math GASING can be used to improve students' understanding of integer multiplication operations, or in other words, the design of this study can be used as a starting point for learning multiplication. Researchers can conclude that learning the multiplication operation in Math GASING plays a very important role as a starting point and improves students' motivation in learning multiplication. In addition, activities designed in such a way that students find the concept of multiplication, starting from understanding the concept of multiplication to mastering the concept of multiplication from 1 × 1 to 10 × 10, which is a critical point in learning multiplication in Math GASING. .
This situation is the reason for the researcher to try to design a learning path on number operations in Math GASING for rural students from Serui, Sorong Selatan and Ambon, Papua. Therefore, the focus of this study was to describe the learning activities on students' performance in doing multiplication in Mathematics GASING. As a result, students were able to master the multiplication operation in Mathematics GASING, as shown by the results of the final evaluation. They were happy to hear that Mathematics GASING is reflected in the comments of students who want to leave the old way of learning mathematics.
It was found that learning the multiplication operation in GASING mathematics plays a very important role as a starting point and improves students' motivation in learning multiplication. Commented [WU7]: How does the math in this study compare to Shanty and Wijaya.
THE INNOVATION OF LEARNING TRAJECTORY ON
MULTIPLICATION OPERATIONS FOR RURAL AREA STUDENTS IN INDONESIA
There is a critical point that we have to pass called GASING's critical point when we study a topic in Math GASING. As a result, the students were able to master the multiplication operation in Math GASING as shown by the results of the final evaluation and more importantly, the learning of Math GASING could be detected from the comments of the students who wanted to abandon the old way. The results of this study indicated that learning design of multiplication operation in Math GASING plays a very important role as the starting point and improvement in the students' motivation in learning.
Therefore, it can be seen that teaching the operation of multiplication in Math GASING can be used to increase students' understanding of multiplication of whole numbers. This situation underlies the researchers of this present study to try to map the learning trajectory in number operations especially for multiplication operation in mathematical GASING for students of rural areas originating from Serui, Sorong Selatan and Ambon, Indonesia. Therefore, the focus of this study is to describe the learning activities on students' performance to do multiplication in GASING of mathematics.
Finally, the research question of this study is how the learning trajectory of multiplication in Mathematics GASING has evolved and how the students' understanding of multiplication in the rural area has evolved from informal to formal level. The critical point of GASING means the condition that students must meet during the learning process and studying a subject in Mathematics GASING. This study uses Math GASING to describe the learning outcomes of rural students in learning multiplication as a repeated addition and to see student responses.
Moreover, other results indicate that the design of multiplication learning operations in Math GASING plays a crucial role as a starting point and increases students' motivation in learning. There are some differences between the multiplication process in Math GASING and the multiplication process in general. During the discussion, students seem easy, fun and enjoyable in learning multiplication in Mathematics GASING.
Their experience supported by Math GASING learning tools can get students past the critical point of multiplication so that students can master multiplication as a whole. Surya and Moss (2012) stated that the student would be able to master the mathematics subject related to the mathematics GASING after passing the critical point of the subject. Therefore, it can be seen that the teaching of the multiplication operation in Math GASING can be used to increase students' understanding of the multiplication operations of whole numbers or in other words, the design of this study can be used as a starting point for teaching multiplication .
Learning multiplication operations in Math GASING plays an important role as a starting point and improves students' motivation in learning multiplication. Activities start from understanding the concept of multiplication to mastering the concept of multiplication from 1 × 1 to 10 × 10, which is a critical point in learning multiplication in Math GASING.
