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DESIGNING LEARNING ROTATION USING THE CONTEXT OF BAMBOO WOVEN MOTIF

An essential part of learning transformation geometry is rotation. Before learning more about other parts of the transformation geometry topic, such as translation, dilation, and reflection, firstly, students are required to understand well about rotation. However, several students have not been able to understand this subject properly due to the stages of learning in the rotation has not been appropriately arranged. Thus, this study aims to design a student learning trajectory in learning rotation, which develop from informal to formal level through the Indonesian Realistic Mathematics Education (IRME) approach. Furthermore, researchers used a design research method divided into three stages, namely preliminary design, design experiments, and retrospective analysis. This study describes how the bamboo woven motif contributes significantly to 31 ninth-grade students understanding the rotation concept. As a result, the woven bamboo motif's context can stimulate students' understanding of rotation. It is proven based on the strategies and models of students during their learning process which contributes to their fundamental knowledge of rotation.


INTRODUCTION
Rotation is a circular motion that moves points by rotating these points to a central point of rotation (Maryati & Prahmana, 2019). Furthermore, Risdiyanti & Prahmana (2018) show that learning about transformation geometry, especially rotation, can be used to design learning using the local contexts such as culture or other things that are easily found in students' daily activities. On the other hand, students can understand mathematical concepts easily, fun, close to daily activities, and affordable to students' imagination (Zulkardi, 2013;Adams & Cook, 2017;Clarke & Roche, 2018). Thus, it would be made it easier for students to be able to solve the problems encountered in students' daily life.

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Designing learning rotation using the context of bamboo woven motif Maryati, Prahmana The Program for International Student Assessment (PISA) results analyzed by Stacey (2011) shows that Indonesian students still have difficulty in formulating problems in daily life into mathematical models. One example is interpreting the context of real situations into mathematical models, understanding mathematical structures, including order, relationships, and patterns (Edo, Hartono, & Putri, 2013;Revina & Leung, 2019). One contributing factor is the process of learning mathematics, which tends to use practical formulas and has not connected mathematical concepts with students' daily activities (Naidoo, 2012;Arisetyawan, Suryadi, Herman, & Rahmat, 2014). Therefore, meaningful learning activities are needed so that students can master the concepts and traits of rotation easily and fun.
One of the learning approaches that can connect the learning subject with daily life is the Indonesian Realistic Mathematics Education (IRME) (Sembiring, Hadi, & Dolk, 2008). The IRME is an adaptation of Realistic Mathematics Education (RME) and has been developed in accordance with the context, cultural values, or local wisdom in Indonesia (Lestariningsih, Putri, & Darmawijoyo, 2015). The IRME places more emphasis on the processes that occur during the learning process so that they are not only concerned with the final results (Sembiring et al., 2008). Thus, IRME could be used as a solution in a learning approach that wants to connect a mathematical material with daily student activities. IRME is one of the learning approaches that will lead students to understand mathematical concepts by constructing themselves through prior knowledge related to daily life (Revina & Leung, 2019;Risdiyanti & Prahmana, 2020). Furthermore, by discovering the concept by themselves, the students' learning process will become more meaningful. In addition, one of the developments in IRME was carried out with research aimed at improving classroom learning practices through an interactive analysis of hypothetical learning trajectory of what would happen in the classroom and its implementation, the research was design research (Cobb & Gravemeijer, 2006).
As an innovation in learning mathematics and as an implementation of the 2013 curriculum which is oriented to the relationship of mathematics to the conditions of reality and culture of students, researchers designing learning rotation using the context of the woven bamboo motif through the IRME approach. This context was chosen because it is close to students and easily found in students' daily lives. Through this design, it is expected to be an innovation in learning mathematics that can facilitate students in understanding the concept of rotation and be able to solve everyday problems related to the concept and further concept in transformation geometry, such as translation, dilatation, and reflection.

RESEARCH METHOD
This study's research method is design research, which is an appropriate way to answer research questions and achieve research objectives, starting with a preliminary design, design experiments, and retrospective analysis (Cobb & Gravemeijer, 2006;Prahmana, 2017 Therefore, to what extent the design process and implementation of this rotation learning design would be explored in this research.

RESULTS AND DISCUSSION
The results obtained in this study in the form of learning trajectories in learning rotation using the context of the bamboo woven motif through the PMRI approach. The following is an explanation of the learning process of rotation material in class IXA

The Early Learning Phase
Learning begins with giving assignments in groups (4-5 people per group), namely working on the Student Worksheet (SW) entitled "Activity 2". This activity aims to bring up the language or understanding of students about the concept of rotation. Describing the activities in this learning process begins with the teacher instructing all students to gather with their respective groups. Next, the teacher gives assignments to each group to work on the SW

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Designing learning rotation using the context of bamboo woven motif Maryati, Prahmana entitle "Activity 2" about the concept of rotation. Activities in the SW start from preparing the Anyaman and ornaments, as shown in Figure 1.

Figure 1. Students make the ornaments using manila paper
The Informal Phase At this stage, students do activities based on the steps or instructions on the SW entitle "Activity 2" which starts from preparing the woven and ornamentation. After all, students are ready with their weaving and ornaments, and the teacher instructs each group to record the initial coordinates and the final coordinates after they are rotated according to the instructions in the worksheet. In Figure 2, students are seen rotating the ornaments according to the instructions in SW "Activity 2" to get a starting point and endpoint.

The Phase of Model For
At this stage, students analyze the change from a starting point to an endpoint and make interpretations related to the concept of rotation with their own language, as shown in Figure   4.

Formal Phase
At this stage, students make mathematical modeling in the form of a rotation formula according to their respective understanding. The results of students' mathematical modeling can be seen in Figure 5.

Figure 5. Student mathematical modeling results related to the rotation formula (formal)
A class discussion is needed to classify the results of student answers listed in the worksheet. Therefore, the teacher invites each group to present their work. Students are seen presenting the concept of rotation, as shown in Figure 6. worksheet. It is caused by the position of the ornamental starting point that is different from each discussion group so that the position of the ornamental endpoint will also be different.
Furthermore, the teacher guides students to have five common perceptions of the concept of rotation. Firstly, if the starting point is rotated 90 degrees to the right with a center point (0.0), then the endpoint will be the opposite, but the back is negative. Secondly, if the starting point is rotated 90 degrees to the left with the center point (0,0), then the endpoint will be the opposite, but the front is negative. Thirdly, if the starting point is rotated 180 degrees to the right and to the left with the center point (0,0), then the endpoint will be the same that is to be all negative. Fourthly, if the starting point is rotated as far as 270 degrees to the right with the center point (0,0), then the endpoint will be the opposite, but the front negative. Lastly, if the starting point is rotated 270 degrees to the left with the center point (0,0), then the endpoint will be the opposite, but the back is negative.
In addition, some researchers have also made mathematics learning design using IRME approaches and cultural contexts, such as learning number pattern using "Barathayudha" war stories (Risdiyanti & Prahmana, 2020), rotational learning designs using kawung batik motifs (Risdiyanti & Prahmana, 2018), the design of transformation learning using Sidoarjo written batik motifs (Lestariningsih & Mulyono, 2017), and learning number operation using traditional Indonesian game "Tepuk Bergambar" (Prahmana, Zulkardi, & Hartono, 2012). Therefore, the role taken from the results of this study is to enrich the study of mathematics learning design that is a rotational learning design using the context of the woven bamboo motif.

CONCLUSION
Learning trajectories that can support the concept of rotation from informal to formal level include the activity of recording the starting and ending points of ornamentation on the webbing field, analyzing and interpreting the change of the starting point into an endpoint using their own language, and writing the rotation formula. The context of the woven bamboo motif can stimulate students' concept of rotation.