Advances in Social Science, Education and Humanities Research (ASSEHR), volume 247 International Conference on Science and Education and Technology 2018 (ISET 2018)

Learning Similarity Lawang Sewu using Context for Third Grade Lower Secondary School Students

Achmad Fahrurozi1, Suci Maesaroh2, Imam Suwanto3, Farida Nursyahidah4 1,2,3,4 Faculty of Mathematics and Natural Science Education and Information Technology, University of PGRI , 50125, 4Corresponding author e-mail: [email protected]

Abstract This study aims to produce a learning trajectory by using the context of Lawang Sewu in helping students to understand the concept of similarity. The approach used in this research was Realistic Mathematics Education, in Indonesian version is called by PMRI. Subject of the study is the third-grade students of SMP 37 Semarang, , Indonesia, involving 6 students who were chosen in heterogeneous capabilities. The methodology used is a design research consisting of three phases, namely the preliminary design, the design experiment, and the retrospective analysis. However, this study only shows the results in the design experiment phase, in particular on a pilot experiment. Data collection was done through several techniques, namely: video recordings, photograph, students work result, and students interview during learning. Student learning activities consist of four activities, namely observing the Lawang Sewu video, identifying two similar shapes, identifying the requirements of two similar shapes, and solving a contextual problem related to similarity. The results of this study indicate that through a series of activities that have been designed could help to stimulate students understanding of similarity concept by using Lawang Sewu context.

Key words: Similarity, Design Research, PMRI, Lawang Sewu Context

1. Introduction improved (Abdussakir, 2009). The lack of the Mathematics has an important role in our students to solve the similarity are 1. Students daily life. In addition, Mathematics is a science difficult to determine two similarities or more 2. that has many parts with an unlimited span and Students are able to solve similarity through the depth (Ilgar, 2013). One of the important correct way but the result incorrect. 3. Students learning areas in mathematics and also the oldest are able to solve the question and get a good branches in mathematics is geometry (Fidan, result but incorrect way (Nafiin, 2018). The 2010). Based on the distribution of education difficulty of students in understanding the standards for junior high school, geometry material shown by students is still weak in material has a large portion (41%) compared to understanding the concepts and principles of other materials such as algebra (29%), numbers geometry. Difficulties can be changed by several (18%), and statistics and probability (12%) factors including internal factors (from within (Putra, 2013). Within the knowledge of students) and external factors (external mathematics, the things learned in geometry are environment of students). One of the external shapes and space (Senechal, 1990). In line with factors that influence student difficulties is this, Reference (Sahin, 2008) stated that by teacher-centered learning (teacher center). mastering geometric thinking skills, students Learning that complies with the teacher planning will be able to have an ability of problem- the difficulty of learning goals will reach. The solving, critical thinking, and a better purpose of mathematics learning itself is the understanding of the other subjects in learning process that focuses on children to mathematics. Reference (Ruseffendi, 1991) apply it. This is consistent with (Kemendikbud, asserted that one of beneficial in learning 2016) composing on the modern pedagogical geometry is to developing logical thinking skill dimension of learning, namely using a scientific and making true generalization ability. (scientific) approach. Moreover, the students who acquire the ability To overcome this problem one of the and habit of problem solving in school tend to approaches that can be used in the learning be individuals who can solve the problems in the process of mathematics is Indonesian Realistic social life in their future (Sahin, 2007; Turgut, Mathematics Education (PMRI) by using the 2007). right context. An effective PMRI approach to On the other hand, the ability of students in improve understanding of mathematical learning geometry is still low and need to be concepts because the PMRI approach is a

Copyright © 2018, the Authors. Published by Atlantis Press. 32 This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Social Science, Education and Humanities Research (ASSEHR), volume 247

process that constructs knowledge. This is in designing instruments to evaluate the accordance with the result of some studies learning process (Nursyahidah, 2014; Prahmana, 2012; At this stage HLT designed containing Nursyahidah, 2018; Saputro, 2015) stated that anticipate things that might happen. Before PMRI approach involved in learning that is designing, the researchers set learning goals more concerned with student activities in the or targets will be achieved and the starting learning process in the classroom. Students are point of learning. Some things you do at this able to build their own knowledge of the stage is: (1) review the literature regarding problems that exist in mathematics. the material similarity to the curriculum in There are several contexts used in PMRI 2013 revised edition, 2017, (2) designing the research, for instance, traditional games HLT to the context lawang sewu as the basis (Nursyahidah, 2013; Prahmana, 2012), folklore, of its alleged strategy of beginning students, legend (Widyawati, 2016). In this study, the (3) designing an interactive video that will is context to support the PMRI approach is used as a medium for learning, and (4) Lawang Sewu which is a historical building in discuss with professors, teachers, and Central Java. The Lawang Sewu context is research experts. chosen because not only it has already familiar b. Design Experiment to students in Semarang but also it can represent In this second phase, the researchers similarity of two-dimensional shapes. The shape tested the design as found in the first phase of of the components of that building like doors, activities. The trial is aimed at exploring and windows, pictures, and park as a model that guessing strategy and thinking students allows representing some two-dimensional during the process of the true learning. Stage shape that similar. trial design is divided into two phases, To implement the study, the authors used namely that the pilot experiment and design research method. It consists of three teaching experiment. phases, namely: preliminary design, experiment The pilot phase of this experiment also (a pilot experiment and teaching experiment), referred to as a bridge between the early and retrospectively analyze. But this current phase of learning the experimental stage. The study was limited to the pilot phase of the purpose of this experiment was to test initial experiment. From the above discussion, the HLT. The research will be made up of researchers conduct a research with the aim of several things: a pilot experiment, which developing a theory of learning to assist students tested the HLT has been designed in a small to understand the concept of the similarity using group that involves high ability students, Lawang Sewu context. medium, and low respectively 2 children. Furthermore, researchers did Teaching 2. Methods experiment, which tested the HLT that has The method used in this study is a design been designed, tested on a small group, and research which was designing learning similarity fixed in the actual class that is the subject of material for the third-grade students. The subject research, observation; and perform tests. of this study was 6 students of ninth grade c. Retrospective analysis students of SMP Negeri 37 Semarang. This Some of the steps to be taken at this research was conducted in the second semester stage include: (1) analyzing the data have of academic year 2017/2018. been obtained from the stage of teaching, Design research is a method aiming to experiments, and the results of the analysis develop the Local Instructional Theory (LIT) to are used to plan activities and develop a plan improve the quality (Bakker, 2003). In this of activities in the next learning, (2) study, the developed design was Hypothetical comparing the HLT with students learning in Learning Trajectory (HLT) which contained a the real, the results are used to answer the series of students’ learning activities. According problem formulation. The goal is to develop to (Gravenmeijer, K & Cobb, P. 2006) a theory of local instruments. The techniques instructional design is done in this study of collecting data to answer the research consisted of three phases, namely: problems through observation, interview, and a. Preliminary Design documentation. The main objective at this stage is to The purpose of the observation is to get the develop a sequence of learning activities and idea of dealing with the social norms that apply

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mathematics in the classroom, the teaching apperception by asking, "Is there any one of methods used, class organization, the rules of you who have been there?", "Do you think the classroom, the students' work and the any other forms of two-dimensional shape in allocation of time during the learning process. Lawang Sewu?" This activity makes students Interviews were conducted with mathematics answer the problem with vigor and high education experts, teachers and students. enthusiasm, Interview experts aim to determine the suitability of content and relevance, the application context, interoperability, and ease of material. The language is easy to understand and the adequacy of the time. The goal is to get in- depth information about the difficulties of teachers in teaching materials, the level of understanding of students, teachers experience towards PMRI approach and experience of students toward PMRI approach. The role of researchers in the learning activities are for students ask some additional questions, observe Figure 1. Students watched video of learning activities, coordinate activities and Lawang Sewu make the changes necessary activities to provide relevant information about the research. The teacher then asks the students to Documentation was carried out together with work with a group activity sheet 1. Students the observation to see how the learning process discussed together with the group of the takes place, students strategies and thought activity sheet. In this phase, the teacher acts processes of students from informal stages to as a facilitator to observe the activities of the formal stages in mathematics. students in working groups. The problem that Data analysis techniques implemented is issued in activity 1 is that students are used qualitatively. The data have been collected in the to watching Lawang Sewu videos and initial experiments, pilot, and teach the looking for objects of the same shape and if experimental phase were analyzed on a they are enlarged or reduced in the same retrospective analysis phase. The results of the scale. After completion of work, they analysis of observation sheets, interview results presented the answer. From the answers and the results of the pre-test phase of the pilot presented, the students' understanding of the trial used as a guideline for designing the initial similarities began to be built. Students are HLT. In addition to analyzing the written test able to conclude that two planes if enlarged results of students, analysis of data on study or reduced scale will form a plane that design methods by comparing the observations congruent. The results of students' work in a during the learning process with HLT designed. group can be seen in the figure 2. In figure 2, students are asked to identify 3. Results and Discussion the existing image whether the size is the At this stage, researchers examined the same or not. Furthermore, to find out more instrument that will be used for research. clearly an interview with students was Researchers designed the learning trajectory, the conducted. The results of interviews with implementation plan lessons, teacher guides, students can be concluded that students can student activity sheets, and scoring guidelines. identify the image the same size. From the Learning activity undertaken can be seen as written results and interviews it was proven follows. that the purpose of this activity was achieved. 3.1 Activity 1: Watching Video of Lawang Sewu Activity 1 contains about introducing Lawang Sewu as context for finding the concept of similarity. By using context Lawang Sewu, students are expected to find a common two or more forms. At the beginning of the lesson, the teacher gave Figure 2. The students' answers on 1st activity

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In Figure 4, students are correct in 3.2 Activity 2: Identify Two Forms of the identifying the similar two-dimensional Same shapes. They solve the problem by In the second activity, students are asked comparing the corresponding sides and to find two forms the same contained in angles. Student answers are in line with the Lawang Sewu. In this activity, students are learning trajectory that has been designed. asked to measure the image that has been 3.4 Activity 4: Solving Contextual Problems provided by using a ruler to find the same related to Similarity picture or not. Furthermore, students are In this activity students were asked to asked to compare the third image. From this solve contextual problems related to the comparison, students can discover which similarity of two-dimensional shapes. picture is the same or not. Answer students Students were able to resolve the problem can be seen in Fig. 3. with the concept learned in previous material. In addition, the results of the students' answer is shown in Figure 5.

Figure 5. The students' answers on 4th Figure 3. The students' answers on 2nd activity activity Figure 5 shows that the students are already familiar with the concept of Based on Figure 3, with the help of similarity so they can solve the contextual images, students can identify two forms problems given related to similarity. whether it is similar or not. The PMRI approach is very well applied 3.3 Activity 3: Identifying Requirements of in mathematics learning because by using Two Similar Forms this approach students are asked to find their In the third activity, students were asked own concept of similarity material with the to identify the requirements of two similar help of contextual problems surrounding the forms contained in Lawang Sewu. In this students. It is in line with the several studies activity, students were asked to compare the (Nursyahidah, 2013; Nursyahidah, 2014; sides and corresponding angles of the image Nursyahidah, 2018; Nursyahidah, 2018; that has been provided by using a ruler to Widyawati, 2016) asserted that using PMRI find the requisite the similar two forms. From approach in learning process by using the comparison of corresponding sides and appropriate context can help students angles, students can find the prerequisite of understanding the concept learned. With the two similar forms. Answer students can be help of the context of Lawang Sewu which is seen in Figure 4. a historical building where students are familiar with which is packaged in an interactive video so students are enthusiastic and more active in learning process that is why they can understand the concept learned deeply.

4. Conclusion The hypothetical learning trajectory resulted in this study consist of four Figure 4. The students' answers on 3rd activities, namely watching the Lawang Sewu activity video, identifying two similar shapes, identifying the requirements of two similar

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shapes, and solving a contextual problem Nursyahidah, F., Ilma, R., & Somakim. related to similarity. The results of this study (2014). Instructional Design of indicate that through a series of activities that Subtraction Using PMRI Approach Based have been designed could help to stimulate on Traditional Game. SEA-DR. students understanding of similarity concept Palembang: Universitas Sriwijaya. by using Lawang Sewu context. Nursyahidah, F., Saputro, B. A., & Rubowo, M. R. (2018). Supporting Second Grade 5. References Lower Secondary School Students’ Abdussakir. (2009). Pembelajaran Geometri Understanding of Linear Equation System dan Teori Van Hiele. [Online]. Tersedia: in Two Variables Using http://abdussakir.wordpress.com/2009/01/ Ethnomathematics. IOP Conf. Ser.: Inter. 25/ [21 Februari 2011]. Cof. On Math., Sci, and Edu, 983 012119. Bakker, A. (2003). Design Research on How Nursyahidah, F., Saputro, B. A., & Rubowo, IT May Support The Development of M. R. (2018). A Secondary Student’s Symbols and Meaning in Mathematics Problem Solving Ability in Learning Education. Freudenthal Institute, Utrecht Based on Realistic Mathematics with University, Netherlands. Ethnomathematics. JRAMathEdu. Cobb, P., Stephan, M., McClain, K., & Semarang: Universitas PGRI Semarang. Gravemeijer, K. (2001). Participating in Putra, H. D. (2013). Pembelajaran Geometri Classroom Mathematical Practices. The Dengan Pendekatan Savi Berbantuan Journal of the Learning Sciences. 10 Wingeom Untuk (1&2), 113-163 Meningkatkankemampuan Generalisasi Cobb, Confrey, J., Sessa, A., Lehrer, R., & Matematis Siswa SMP. Bandung: STKIP Schauble, L. (2003). Design Experiments Siliwangi. in Educational Research. Educational Ruseffendi, E. T. (1991). Pengantar Kepada Researcher. 32(1),9-13 Membantu Guru Mengembangkan Fidan, Y., & Türnüklü, E. (2010). Kompetensinya dan Pengajaran Examination of 5th-grade students’ levels Matematika Untuk Meningkatkan CBSA. of geometric thinking in terms of some Bandung: Tarsito. variables. Pamukkale University Journal Sahin, O. (2008). In- & pre-service of Education, 27, 185-197. elementary school teachers? Van Hiele Gravenmeijer, K & Cobb, P. (2006). Design reasoning stages. Master Thesis. Research From A Learning Design Kocatepe University, Institute of Social Perspective. Educational Design Sciences, Afyon Research. 17 – 55. Sahin, A. A. (2007). Determining the Ilgar, L., & Gülten, D. Ç. (2013). Matematik problem-solving strategies for the konularinin günlük yasamda kullaniminin students aged 13-14 years. Master Thesis. ögrencilere ögretilmesinin gerekliligi ve Balikesir University, Institute of Natural önemi. Istanbul Zaim Üniversitesi Sosyal Sciences, Balikesir. Bilimler Dergisi, Güz. Saputro, B. A., Prayito, M., & Nursyahidah, Kemendikbud. (2016). Lampiran F. (2015). Media Pembelajaran Geometri Permendikbud Nomor 24 Tahun 2016 Menggunakan Pendekatan Pendidikan Tentang Standar Kompetensi Isi dan Matematika Realistik Berbasis GeoGebra. Kompetensi Dasar Pendidikan Dasar dan Kreano, 6(1), p. 33-38 Menengah. : Kemendikbud. Senechal, M. (1990). Shape. In L.A. Steen Nafiin, M., W., & Budiarto, M., T. (2018). (ed.), On the Shoulders of Giants; New Analisis Kesalahan Peserta Didik dalam Approaches to Numeracy (pp. 139-182). Menyelesaikan Soal Kesebangunan. Washington DC: National Research MATHEdunesa. Surabaya: Universitas Council. Negeri Surabaya Turgut, U.M., & Yilmaz, S. (2007). Geometri Nursyahidah, F., Ilma, R., & Somakim. derslerine nasil giris yapardik? Ilkögretim (2013). Supporting First Grade Student’s matematik ögretmen adaylarinin Understanding of Addition up to 20 Using görüsleri. Bilim Egitim ve Düsünce Traditional Game. IndoMSJME, Vol.4, Dergisi, 7(4). No.2. 212 – 223. Widjaja, W. (2008). Local Instruction Theory

36 Advances in Social Science, Education and Humanities Research (ASSEHR), volume 247

on Decimals: The Case of Indonesian Pre- (2016). Desain Pembelajaran Sudut service Teachers. Disertasi. Melbourne Menggunakan Konteks Rumah Limas di Graduate school of Education, The Kelas VII. JINop. Vol.2, No.2. University of Melbourne, Melbourne. Palembang. Widyawati, W., Ilma, R., & Somakim.

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