Design of Realistic Mathematics Education Approach to Improve Critical Thinking Skills

Critical thinking skills are skills needed in the modern era, especially in the industrial era 4.0, as today, having critical skills will facilitate students in solving problems in life. The purpose of this study is to design statistical material for RME-based teaching materials to improve students' critical thinking skills. The method used in this study is ADDIE. In the ADDIE method, there are five stages; (1) Analysis, (2) Design, (3) Development, (4) Implementation, and (5) Evaluation. This research is only limited to analysis and design. The subjects in this study were seventh-grade students at Patuk 4 Public Middle School. Data collection instruments include observation sheets and interview guidelines and validation sheets. The results of this study indicate that the design of teaching materials has been adapted to the characteristic of students using the ADDIE method. The design includes cover, preface, concept map, Core Competencies (KI), Basic Competencies (KD) and Competency Achievement Indicators, table of contents, module activities, evaluation, and summary. Teaching material in statistical learning is based on RME steps to improve students' critical thinking skills. This research can be continued at the development, implementation, and evaluation stages in learning.


Introduction
Critical Thinking is a process that involves reasoning and analysis to conclude [1] [2]. Critical thinking skills are needed in the development of students because they can influence the development of thinking [3]. Critical thinking is one of the foundations of the 21st century's closeness. 21st Century skills are a set of skills that must be possessed by individuals, especially students because it will help succeed in college, work, and life in the information age [4], in this case, schools can become facilitators to instill 21st-century skills. Prepare students for mathematical literacy is equipping them with 21st-century competence [5]. 21st Century skills are also used by students in Thailand in the process of vocational-technical education and training, 21st-century makes students more mature in dealing with problems in the real world [6]. Mathematics is needed in calculations and thinking. The process required individuals to solve problems [7] [8]. Besides, mathematics is a universal language that allows humans to think, record, communicate ideas about elements, and quantity [9]. The importance of thinking skills will have an impact on life because to survive and adapt to the environment is highly dependent on human thinking skills [10]. The skills that can be developed at school are critical thinking. Critical thinking has a great influence in determining one's success in the future compared to IQ [11]. With critical thinking skills, students are expected to think rationally and logically when solving a problem. The lack of critical thinking skills will make it difficult for students to solve High Order thinking Skill (HOTS) type problems. The following skills can identify critical thinking skills: (1) Interpretation, (2) Analysis, (3) Evaluation, and (4) Taking Conclusion [12]. However, the fact that student's critical thinking skills in Indonesia are still relatively low. It can be seen from the results of the 2015 PISA (Program for International Student Assessment). The PISA shows that Indonesia ranks 63 out of 72 participating countries, with a mathematical grade of 386 out of 500 (international value standard) [13]. The cause of the low skills of students in solving problems is the lack of emphasis to develop critical thinking skills in learning mathematics when at school [14]. The teacher has not been able to make learning devices that can make students accustomed to higher-order thinking skills [15]. Based on the results of observations made by researchers, the cause of low critical thinking skills of students, especially in class VII in Patuk Gunung Kidul Middle School can be found. There were several results obtained. Learning is still centered on the teacher so that students become passive. Researchers give the test. The resulting test shows that some students have not been able to analyze the questions and make conclusions due to the lack of learning strategies. The teaching theory that supports thinking skills during the learning process is one of the factors that affect low critical thinking skills. If students do not immediately fix this, they will have difficulty in solving questions with type HOTS. Learning difficulties of students caused by learning disabilities are internal factors, namely neurological dysfunction, and other causes are external factors, including incorrect learning strategies, learning management activities that do not encourage children's learning motivation [16]. Some of the results of the study above state that the critical thinking skills of mathematics from junior high school students who get innovative mathematics learning are better than the critical thinking skills of students who obtain conventional learning. 21st Century skills are needed by students in Thailand in the process of vocational education and technical training [17]. A mathematical model or approach is needed and encourages students to think critically. One approach that can be used is realistic mathematics education. Both the form of teaching theory and learning models are important steps in teaching mathematics. Realistic mathematics education (RME) will make mathematics learning more meaningful and justification. RME brings fundamental changes in the teaching and learning process of mathematics in the classroom. The teacher no longer provides information directly but provides problem assistance and activities. This problem assistance and activities can be used by students to build an understanding of mathematical concepts that lead to the creation of formal mathematical knowledge and empathy. The main principles in RME, namely: (1) Guided discovery, (2) progressive mathematics, (3) Didactic phenomenology, and (4) Self-developed models. In implementing learning, RME provides five principles, namely: (a) use of contexts (b) progressive mathematical (c) contribute to students, (d) interactions, and (e) interrelation. From the principles and characteristics of RME, learning can be made in realistic mathematics learning activities as follows: (a) understanding real problems, (b) solving real problems, (c) comparing and discussing the answers (d) concluding [18]. Although "realistic" in this approach means the "real world" situation at RME, the word itself has a broader meaning [19]. Although "realistic" in this approach means the "real world" situation at RME, the word itself has a broader meaning. This illustrates the problem that students can imagine RME emphasizing learning mathematics, which is ideal by doing mathematics itself. Freudenthal saw mathematics as a human activity. In the learning process, students are expected to rediscover the mathematical concepts learned. Thus, the emphasis on learning is the process. RME-based teaching theory will be easy to understand and attract student's interest because they relate to everyday life, and the tools used are available in the surrounding environment and provide direct benefits to life [20]. Teachers can also use the development of teaching theory that is close to RME as a guide in teaching and effective in improving student's mathematical reasoning [21]. The use of realistic mathematical models can guide students to understand the concepts in solving problems gradually [22]. Also, the use of RME learning models can significantly improve student's mathematical critical thinking compared to conventional learning [23]. The results of another determination also mentioned that the development of learning tools that use realistic mathematics education approaches could improve student's critical thinking skills [24]. Also, realistic mathematics education helps teachers to teach mathematics to students and successfully refine math skills [25]. Some relevant findings regarding the analysis of the characteristics of critical thinking skills and learning with the RME approach provide predictions that learning with the RME approach plays a good role in improving student's critical thinking skills.
With the problems that have been outlined in the background, analyzing the needs of teaching theory that are suitable for students, designing teaching theory that is in line with the RME learning model, and being able to foster student's critical thinking skills. The second is to produce a design of teaching material that is suitable for use.

Materials and Methods
This type of research is development research. The product that will be developed in this research is for improving student's critical thinking skills for class VII, namely designing learning modules based on Realistic Mathematics Education (RME). This research model uses the ADDIE development model. The ADDIE model consists of five stages, namely: Analysis, Design, Development, Implementation, and Evaluation Model (ADDIE), which includes five steps, namely analysis, design, development, implementation, and evaluation [26][27][28][29][30][31][32]. The ADDIE model can be seen in Figure 1 [25] Writing is limited to the design phase to determine module design based on Realistic Mathematics Education (RME) to improve student's critical thinking skills. Data collection techniques use observation, interviews, questionnaires, and literature studies. Observation guidelines are used to retrieve data about the student's needs for learning media and find out what the teacher uses learning models. Interview guidelines are used to determine the use of learning media during the learning process and student's critical thinking skills. A literature study is conducted to find indicators of creative thinking skills and learning models of Realistic Mathematics Education (RME). The subjects of this study were students of class VIII SMP N 4 Patuk 2018/2019 school year.

Analysis Phase
Curriculum analysis of mathematics subjects for seventh-grade junior high school students refers to the 2013 curriculum as contained in the attachment to Permendikbud No. 21 of 2016. Some aspects are analyzed, namely Core Competency (KI), Basic Competence (KD), indicators of competency achievement (GPA), and learning materials. The analysis is used as a guideline in the preparation of teaching materials in the form of an E-Module approached Realistic Mathematics Education to improve critical thinking skills. The lack of teaching materials that integrate critical thinking also becomes one of the causes of the lack of critical thinking in students. Based on the results of interviews with mathematics teachers and some students at SMPN 4 Patuk Gunung Kidul, the writer obtained some data. When explaining the material, the teacher uses teaching materials that are used in the form of books that are already in school and uses conventional methods during the learning process. In terms of the curriculum of teaching materials available are following KI, KD, along with indicators of their achievement, but the teaching materials used do not emphasize the realistic concept. As a result, students do not understand the concepts being taught. The researchers gave questionnaires to 13 students with instructions to fill in the material that was felt to be the most difficult to understand. The result is that statistical material is the most chosen material by students. This can be seen in Lack of understanding of concepts, especially in statistical material, has an impact on student's scores. The average value of statistics material is lower than other materials. This is obtained from interviews with teachers. Furthermore, an analysis of students is conducted. Students still find mathematics difficult. As a result, students cannot focus on learning and even have a chat when learning takes place. Students only hear the explanation from the teacher without being actively involved when learning takes place. Based on the results that have been found, researchers provide a solution that is by providing a model or approach that can encourage students to be active, explore, find ideas, learn independently and improve critical thinking skills. From the analysis of material requirements and learning models from the interview above, it generates an idea that an E-Module with RME approach is needed. With the steps on the RME, the real approach will help students understand material concepts so students can develop critical thinking skills.

Design
The author makes a module design that is composed of cover, preface, table of contents, to a bibliography. The design of this module is based on indicators of practicality and validity. The author decides the module with the RME approach to improve student's critical thinking skills. The design can be seen in Figure 2. The syntax that has been presented in Figure 2 shows five stages, namely: the use of context, progressive mathematics, student contribution, interactions, and interrelation. In the use of context, the teacher gives problems relating to the real world and the activities of students observing what is conveyed by the teacher so that in this process, there will be analysis activities by students. In progressive mathematics, mathematics was built through models. With this activity, students try to solve problems through models created or developed as mathematization so that they can foster analysis activities in the process. In student contributions, the students play an active role in the learning process. That means that all thoughts or ideas of students are considered. The activities of students can be in the form of discussion in the process of students who will foster interpretation. In interactions, there are interactions between teachers and students as well as students with students as well as students. The student interaction occurs in the form of comparing answers and others. At this stage, an evaluation process occurs to evaluate the credibility of the statement. In interrelation, the aim is to address the linkages between topics and the teacher who guides students to exploit, so that the learning process is meaningful. In this case, the activities of students are to made conclusions.

Cover
The cover is the outside, which consists of a title, author's name, and the image that represents the contents. The following is the cover design, which can be seen in Figure 3.

Preference
The introduction contains a statement of thanks to those who have helped complete the student worksheet. The introduction can be seen in Figure 4.

Concept Map
The concept map contains an outline of the mapping of material to be studied. The concept map can be seen in Figure 5

Learning Activities Based on Realistic Mathematics Education
In learning activities, some activities adjust to the syntax of RME. The use of context or realistic problems is used as a starting point for learning. Context is something that can be imagined by students. The goal is that the concepts conveyed can be understood. Figure 7 is an example of a part of the contexts. In progressive mathematical, which is building mathematics through models, the use of models is regarded as a link from real-world knowledge to the world of mathematics. Figure 8 is an example of a part of a progressive mathematical model. In the contribution of students, students are allowed to develop various informal strategies that are used in the process Interactivity of solving problems. In realistic mathematics, learning mathematics is a social activity. Listening to what others find and discussing the findings, students will get ideas for solving their problems. Figure 9 is an example of a part of the results of student construction and interactivity. Next, to show the relationship, the teacher plays an important role in directing students to gain knowledge. Figure 10 is an example of part of the interrelation.  Table Content Table of contents is the page that is a guide to the contents in the book along with the appropriate page number. The table of contents can be seen in Figure 11.  The summary contains conclusions about the statistical material in a nutshell. The summary can be seen in Figure 12.

Evaluation
The aim is to evaluate the learning outcomes of students in understanding the material that has been learned. The evaluation in this study can be seen in Figure 13.  The background is too colorful, so it prevents text material in teaching material.

Background replaced
The author designs a design. The design is developed, and a media expert validates the design. Some suggestions are obtained. The researcher improves by the advice given by the expert. The list of improvements that have been given by media experts can be seen in Table 2.
After getting comments/suggestions from experts, the researchers then followed up on improving teaching theory, so that they would be better in the learning process, the following improvements have been made;

Cover
Repairing the cover that is too flashy, the font used by the cover, to make it more comfortable when viewed, can be seen in Figure 14.

Layout
Correcting the layout of the module that is not suitable, the improvement results can be seen in Figure 15   The research data obtained were converted into qualitative values by comparing scores from media experts with ideal scores calculated using the provisions in Table 3: The results of the questionnaire assessment by media experts can be seen in Table 4. Based on the results that have been obtained, it can be seen that teaching theory is declared feasible by getting an average grade of 4.6 with very good criteria.

Conclusions
This study resulted in the design of modules based on Realistic Mathematics Education (RME). Module design based on the Realistic Mathematics Education (RME) model to improve student's critical thinking skills with the method used is ADDIE. The results of the research in the design phase consist of several components arranged in a module, at the beginning, namely (cover, preface, table of contents, instructions for use, concept map, IC and basic competency), content section (learning and evaluation activities) and closing (glossary and bibliography). The development of critical thinking skills is found in problem training and evaluation. The module contains steps for RME and indicators of critical thinking skills. Furthermore, the module design is validated and then repaired according to the advice given by the validator so that the product can be declared valid and is suitable for use.