Search

This paper discusses how 5th-grade students understand quotative fractions division or smaller fractions divided by greater fractions in specific. A context-based mathematics task, making posters, was developed and implemented in two Realistic Mathematics Education (RME)-based lessons involving 6 students and 28 students. The analysis of students’ group discussion and works on the task reveal that the students initially experienced difficulties in determining how many posters can be made using 1/2 of one paper if one poster requires 3/4 of a paper. To support students’ understanding, a task, which carefully sequences fractions division content and utilizes contexts that can be easily modeled, is required.

Agriculture in Bali has profound importance, namely as a natural tourist attraction and is one of the sectors with the most workers absorb as well the largest contributor to regional income for Bali Province. Currently, the agriculture sector in Bali is experiencing the problem of decreasing the workforce due to the reluctance of future generations to continue farming inherited from their families. The purpose of this paper is to identify the factors causing the reluctance of future generations to continue family farming and to study the causality of these factors to the reluctance for continuing family farming. This study uses a variance-based structural equation modeling (PLS-SEM). Internal and external motivation to continue family farming as well the perception of agricultural works are the exogenous variables, and the reluctance to continue family farming is the endogenous variable on the model. The data in this study obtained from interviewing 115 respondents in the Jembrana Regency of Bali. The study’s result justifies that internal factors, external factors, and perceptions of agricultural work influenced the reluctance to continue family farming.

Textbooks used in schools affect the quality of mathematics learning in the country. Indonesian Ministry of Education (Kemendikbud) already lauched students’ and teachers’ textbook that are distributed nationally on 2013; however improvements are needed to revise the textbooks since there are concerns such as the difficulty level of problems contained in the textbooks. The main objective of this study is to compare non-routine problems contained in mathematics textbooks used in Indonesia and Singapore. This is a qualitative research with content analysis design. Researchers compare Singaporean and Indonesian mathematics textbook since Singapore got higher rank in mathematics based on PISA result in 2018. The topic in this study is limited to Pythagorean Theorem. The result of the research shows that Indonesia and Singapore has consecutively 22,1% and 11,3% non-routine problem. Another finding of this study was Singaporean mathematics textbook focused more on developing students’ fluency of solving problems, meanwhile Indonesian mathematics textbook focused more on students’ reasoning ability. The results and findings in this paper are expected to provide input in developing future mathematics textbooks.

Technological improvements in the era of the Industrial Revolution 4.0 can be applied to learning mathematics as a medium of improving teacher performance. In addition, a pandemic situation forces teachers and students to implement online learning. One of the learning media that can help teachers in learning mathematics online is Socratic. The Socratic system generally consists of four basic components: acting humanely, thinking humanely, thinking rationally and acting rationally. For example, the Socratic can provide alternative solutions to the differential equations problems. Mathematics problems can be recorded by the Socratic through three main features:1) home screen, which is used to take pictures of solving the problem needed; 2) search results, the image that has been recorded will be searched for a solution through Socratic's artificial intelligence in internet database, and 3) an explanation, the search results that have been obtained, have their own explanation. Teachers and students as users may find the best solution for each explanation by the Socratic. Meanwhile, this study uses four stages of the literature review process:1) search for relevant literature, 2) evaluation and source selection, 3) identification of themes, and 4) outline of the structure of the writing. This paper systematically investigates the use of the Socratic as a technology application that can assist mathematical problems.

ABSTRAK Seorang investor pada umumnya berharap untuk membeli suatu saham dengan harga yang rendah dan menjual saham tersebut dengan harga yang lebih tinggi untuk memperoleh imbal hasil yang tinggi. Namun, kapan waktu yang tepat melakukannya menjadi tantangan tersendiri bagi para investor. Oleh sebab itu, dibutuhkan suatu model yang mampu menduga imbal hasil saham dengan baik, salah satunya adalah model autoregressive moving average (ARMA). Tujuan dari penelitian ini adalah untuk menerapkan model autoregressive (AR), model moving average (MA), atau model autoregressive moving average (ARMA) pada data observasi untuk menduga imbal hasil saham bank central asia (BCA). Terdapat empat prosedur dalam membangun sebuah model AR, MA atau ARMA. Pertama, data yang digunakan harus weakly stationary. Kedua, orde dari model harus diidentifikasi untuk memperoleh model yang terbaik. Ketiga, parameter setiap model harus ditentukan. Keempat, kelayakan model harus diperiksa dengan melakukan analisis residual untuk memperoleh model yang terbaik. Pada akhirnya, model ARMA (1,1) adalah model terbaik dan akurat dalam menduga imbal hasil saham BCA. ABSTRACT Generally, investor always wish to be able to buy a stock at a low price and sell it at a higher price to obtain high returns. However, when is the best time to buy or sell it is a challenge for investor. Therefore, proper models are needed to predict a stock return, one of them is autoregressive moving average (ARMA) model. The first purpose of this paper is to apply the autoregressive (AR), moving average (MA) or ARMA models to the observations to predict stock returns. There are four procedures which is used to build an AR, MA, or ARMA model. First, the observations must be weakly stationary. Second, the order of the models must be identified to obtain the best model. Third, the unknown parameters of the models are estimated by maximum likelihood. Fourth, through residual analysis, diagnostic checks are performed to determine the adequacy of the model. In this paper, stock returns of BCA are used as data observation. Finally, the ARMA (1,1) model is the best model and appropriate to predict the stock returns BCA in the future.

ABSTRAK Pada artikel ini dibahas sifat-sifat hasil kali matriks (mod 2) terkait graf roda, graf pertemanan, dan graf bunga yang grafikal. Beberapa hasil yang diperoleh, A(Wn)A(Wn)(Mod 2) dan A(Wn)A(Sn)(Mod 2) grafikal apabila n=2k+1 dengan Sn merupakan graf bintang. Selanjutnya, diperoleh A(Wn)A(Go)(mod 2) dan A(Wn)A(G0)(mod 2) grafikal untuk semua n=3 dengan G0 adalah subgraf dari Wn dengan degG0v0=0, degG0vl=degWnvl, untuk 1= l = n. Hasil kali matriks (mod 2) yang grafikal juga diperoleh untuk graf pertemanan dan graf bunga dengan komplemen dan subgrafnya masing- masing. Hasil lebih umum diperoleh untuk kondisi sehingga A(G)A(G)(mod 2) grafikal. ABSTRACT In this paper, we discussed the properties of the wheel, flower and friendship graphs for which the matrix product under modulo 2 was graphical. Let Sn be a star graph and G0 be a subgraph of Wn where degG0v0=0, degG0vl=degWnvl, for 1= l = n. We proved the matrix product A(Wn)A(Wo)(mod 2) and A(Wn)A(Sn)(Mod 2) was graphical for n=2k+1 and the matrix product A(Wn)A(Go)(mod 2) and A(Wn)A(G0)(mod 2) was graphical for all n=3. For the next, a graphical matrix product (mod 2) was also obtained for the friendship graph and the flower graph with its complement and subgraph, respectively. As more general results were obtained for conditions such that A(G)A(G)(mod 2) was graphical.

ABSTRAK Dalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang dual dari aljabar Lie . Aksi dari grup Lie pada ruang dual menggunakan representasi coadjoint. Hasil yang diperoleh adalah ruang Fase tereduksi tiada lain adalah orbit coadjoint-nya yang buka di ruang dual . Selanjutnya, ditunjukkan pula bahwa grup Lie affine tepat mempunyai dua buah orbit coadjoint buka. Hasil yang diperoleh dalam penelitian ini dapat diperluas untuk kasus grup Lie affine berdimensi dan untuk kasus grup Lie lainnya. ABSTRACT In this paper, we study a reduced phase space for a Lie group, particularly for the 2-dimensional affine Lie group which is denoted by Aff (1). The work aims to identify the reduced phase space for Aff (1) by open coadjoint orbits at certain points in the dual space aff(1)* of the Lie algebra aff(1). The group action of Aff(1) on the dual space aff(1)* is considered using coadjoint representation. We obtained that the reduced phase space for the affine Lie group Aff(1) is nothing but its open coadjoint orbits. Furthermore, we show that the affine Lie group Aff (1) exactly has two open coadjoint orbits in aff(1)*. Our result can be generalized for the n(n+1) dimensional affine Lie group Aff(n) and for another Lie group.

The communication ability possessed by humans, especially Christians, is used to realize God's will. One of them is in carrying out the real Great Commission in the field of education, especially in the learning process. Learning in the classroom must take place effectively so that learning objectives are achieved through the realization of effective communication. Often, teachers have not been able to build effective communication because teachers are not able to manage the class properly through the delivery of appropriate information and according to the characteristics of student development, so that many students are less serious and disciplined in learning. Therefore, this article aims to discuss the importance of delivering the right information in building effective communication to third grade elementary school students as research subjects in this paper. Based on the results of the study, it was found that teachers experienced problems in managing the class, especially in attracting students' attention, giving instructions, conveying and applying class rules and procedures so that effective communication in classroom management had not been achieved, while in delivering subject matter, effective communication was quite built because students actively involved. Submission of appropriate information is very important for teachers to do, especially in building effective communication because it really determines the success or failure of learning activities by considering the characteristics of student development. Christian teachers also act as facilitators who reflect Christian values in every teaching they do. BAHASA INDONESIA ABSTRACT: Kemampuan berkomunikasi yang dimiliki oleh manusia terutama orang Kristen digunakan untuk mewujudkan kehendak Tuhan. Salah satunya dalam menjalankan Amanat Agung yang nyata dalam bidang pendidikan khususnya dalam proses pembelajaran. Pembelajaran di dalam kelas harus berlangsung dengan efektif agar tujuan pembelajaran tercapai melalui terwujudnya komunikasi efektif. Sering kali, guru belum dapat membangun komunikasi efektif tersebut karena guru tidak mampu mengelola kelas dengan baik melalui penyampaian informasi yang tepat dan sesuai karakteristik perkembangan siswa, sehingga banyak siswa yang kurang serius dan disiplin dalam belajar. Oleh karena itu, artikel ini bertujuan untuk membahas mengenai pentingnya penyampaian informasi yang tepat dalam membangun komunikasi efektif kepada siswa kelas III SD sebagai subjek penelitian dalam makalah ini. Berdasarkan hasil penelitian tersebut, ditemukan bahwa guru mengalami kendala dalam mengelola kelas khususnya dalam menarik perhatian siswa, memberi instruksi, menyampaikan dan menerapkan peraturan dan prosedur kelas sehingga komunikasi efektif dalam pengelolaan kelas belum tercapai, sedangkan dalam penyampaian materi pelajaran, komunikasi efektif cukup terbangun karena siswa terlibat aktif. Penyampaian informasi yang tepat sangatlah penting untuk guru lakukan khususnya dalam membangun komunikasi efektif karena sangat menentukan berhasil atau tidaknya kegiatan pembelajaran dengan mempertimbangakan karakteristik perkembangan siswa. Guru Kristen juga berperan sebagai fasilitator yang mencerminkan nilai-nilai Kristiani dalam setiap pengajaran yang dilakukannya.

Reflective learning is one of the actions in which the teacher observes the shortcomings that occur in the classroom. Reflective learning aims to find solutions to every problem that arises when the teacher teaches, so that class management runs well. This reflection process consists of 4 stages: concrete experience, reflective observation, abstract conceptualization, and active experimentation. The focus of the study in this paper is on Christian education, Christian teachers, students, reflective learning, and classroom management. The method used is analysis based on literature study. Reflective learning practices that rely on the Holy Spirit in the progressive sanctification process to become like God in responding to each student's behavior according to the principles of the Christian faith. Reflective learning is important to be applied in the classroom, because through reflective learning the teacher will be more sensitive to problems in the classroom. Based on the results of this study, it can be said that the difficulties experienced by the author during the reflection process; first, student teachers do not see the importance of assertiveness in leading the class. Second, do not give a firm attitude during the learning process. Third, student teachers are not consistent in carrying out discipline in the classroom. It is recommended that in the implementation of reflective learning, teachers need to have sufficient experience and competence, and need to carry out a complete reflective learning cycle to complete the completion of overcoming the class. BAHASA INDONESIA ABSTRACT: Pembelajaran reflektif adalah salah satu tindakan dimana guru melakukann observasi, terhadap kekurangan yang terjadi dalam kelas. Pembelajaran reflektif bertujuan untuk menemukan solusi untuk setiap permasalahan yang muncul saat guru mengajar, sehingga manajemen kelas berjalan dengan baik. Proses refleksi ini terdiri dari 4 tahap: concrete experience, reflective observation, abstract conceptualization, dan active experiment. Fokus kajian dalam paper ini mengenai pendidikan Kristen, guru Kristen, siswa, pembelajaran reflektif, dan manajemen kelas. Metode yang digunakan adalah analisis berdasarkan studi literature. Praktik pembelajaran reflektif yang mengandalkan Roh Kudus dalam proses progressive sanctification untuk menjadi semakin serupa dengan Allah dalam merespons setiap perilaku siswa sesuai prinsip iman Kriten. Pembelajaran reflektif penting untuk diterapkan dalam kelas, karena melalui pembelajaran reflektif guru akan semakin peka dengan permasalahan dalam kelas. Berdasakan hasil dari penelitian ini dapat disimpulkan bahwa kesulitan yang dialami penulis selama proses refleksi; pertama, mahasiswa guru tidak memandang penting sikap tegas dalam memimpin kelas. Kedua, tidak memberikan sikap tegas selama proses belajar. Ketiga, mahasiswa guru tidak konsisten adalam menjalankan sikap disiplin dalam kelas. Disarankan dalam pelaksanaan pembelarajan reflektif guru perlu memiliki pengalaman dan kompetensi yang cukup, serta perlu melakukan siklus pembelajaran reflektif secara utuh untuk memberikan penyelesaian dalam mengatasi kelas.

Mathematics is a subject that is considered a scourge by most students. They think that mathematics is difficult, complicated, and boring. However, if we look at the process of creation, everything in this universe (including mathematics) is God's creation and everything is really good. This truth needs to be revealed to students by the mathematics teacher. Unfortunately, many math teachers make students dislike mathematics. Therefore, this paper aims to describe the role of Christian mathematics teachers to guide students in viewing mathematics according to God's perspective. The research method used is the literature study method. The results of this study indicate that the role of Christian mathematics teachers includes: (1) appreciating and exploring mathematics first; (2) developing the four teacher competencies; and (3) understand the objectives of learning mathematics. Christian mathematics teachers also need to be careful not to fall into the sin of idolatry and pride by asking the Holy Spirit for help to be enabled in each of their ministries. BAHASA INDONESIA ABSTRACT: Matematika merupakan salah satu mata pelajaran yang dianggap momok oleh siswa. Siswa menganggap bahwa matematika itu sulit, rumit, dan membosankan. Namun jika melihat pada proses penciptaan maka segala yang ada di alam semesta ini (termasuk matematika) merupakan ciptaan Allah dan semuanya sungguh amat baik. Kebenaran ini perlu disingkapkan kepada siswa oleh guru matematika. Namun, banyak guru matematika yang justru membuat siswa tidak menyukai matematika. Oleh sebab itu, tulisan ini bertujuan untuk memaparkan peran guru matematika Kristen di dalam menuntun siswa dalam memandang matematika sesuai dengan cara pandang Allah. Adapun metode penelitian yang digunakan adalah metode studi kepustakaan. Hasil penelitian ini memaparkan bahwa peran guru matematika Kristen meliputi: (1) mengapresiasi dan menjelajahi matematika terlebih dahulu; (2) mengembangkan keempat kompetensi guru; serta (3) memahami tujuan pembelajaran matematika. Guru matematika Kristen juga perlu berhati-hati agar tidak jatuh ke dalam dosa penyembahan berhala dan kesombongan dengan meminta pertolongan kepada Roh Kudus agar dimampukan dalam setiap pelayanannya.

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty 9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

Physics and mathematics are the two most closely related natural rudimentary subjects. In the study of physics, often need to rely on mathematical rigorous reasoning and argumentation and need to use a variety of mathematical methods for investigation, reasoning, calculus, test, discussion, but students often appear in these difficulties. To explain the influence of mathematics achievement on physics achievement from the high school mathematics achievement and physics achievement. The results of math and physics in the first semester of 6 classes of senior high school student's grade 12 were selected, and the data were analyzed with SPSS.22 software, and three students of different learning abilities were interviewed in detail. The innovation of this paper lies in the use of hierarchical research methods to compare classes of mathematics achievement and physics achievement. The conclusions are (1) in objective level, there is a positive linear relationship between math achievement and physics achievement; (2) on the subjective level, students accept the view that the performance of mathematics can promote the performance of physics; students' subjective cognition will affect their cognitive structure and learning behavior, to actively seek for the relationship between mathematical knowledge and physical knowledge, and then slowly affect the objective level of students, and then in mathematics and physics performance, and (3) applying mathematical thinking to physics learning can improve the efficiency of learning physics. Use mathematical knowledge of trigonometry to solve the force analysis problem of physical movement. This shows that math scores play a very important role in physics scores. Remind us that in the process of teaching, we should pay attention to the integration of mathematical ideas into physics learning, and help students to learn physics knowledge better with mathematical ideas.

Abstrak Penelitian ini merupakan penelitian pengembangan dengan maksud mengembangkan modul geometri analitik bidang dan ruang materi konikoida berdasarkan Teori Van Hiele yang valid, praktis, dan efektif. Penelitian ini menggunakan model pengembangan Plomp yang terdiri atas empat fase, yaitu: fase investigasi awal, fase desain, fase realisasi, dan fase tes, evaluasi, dan revisi. Instrumen yang digunakan adalah lembar validasi, lembar observasi keterlaksanaan pembelajaran, angket respon mahasiswa, angket respon dosen, lembar observasi aktivitas mahasiswa, lembar observasi kemampuan dosen mengelola pembelajaran, dan tes pemahaman konsep. Hasil penelitian menunjukkan modul yang dihasilkan valid, praktis dan efektif, dengan rata-rata kevalidan untuk bahan ajar dan semua instrumen penelitian adalah 4,5. Praktis, dengan rata-rata lembar observasi keterlaksanaan pembelajaran 1,56, rata-rata persentase angket respon mahasiswa 82,68 dengan kategori positif dan rata-rata persentase angket respon dosen adalah 86,94. Efektif, rata-rata persentase aktivitas mahasiswa adalah 80,125, rata-rata persentase kemampuan dosen mengelola pembelajaran adalah 4,00, dan persentase ketuntasan belajar mahasiswa adalah 75%. Abstract This research form development that refers to development geometrical module analytics field and matter conicoid materials based on Van Hiele Theories which is valid, practical and effective. This research used development of Plomp models that consists of four phases : Investigation phase, design phase, realization phase, and test phase, evaluation and revision. Instrument that used are paper of validation, paper of observation characteristic of learning, questionnaire response of students, questionnaire response of lecture, observation papers activity of students, observation papers the ability of lecture to manage the subject and comprehension test of the concept, result of research show module that valid. Practically and effective. Dengan rata-rata the validation to substance of teaching and all the instrument of research is 4,5 practically. With range observation of papers the characteristic of learning 1,56, range of questionnaire presentation of students response 82,68 for the positive of category and range questionnaire presentation of lecture response is 86,94. Effective, range presentation activity of students is 80,125, range the ability the presentation of lecture to manage the subject is 4,00, and completeness presentation student learning is 75%.

Web-based inquiry is an intermediary medium that supports broad sharing of data and ideas, in visualizing, analyzing, and offering knowledge integration. This study aims to analyze the scope of scientific research related to web-based inquiry using bibliometric studies starting from the last 10 years. Database information is obtained from Scopus indexed papers, via the Publish or Perish application. Based on the search and selection results, 65 articles were obtained which were then reviewed with Zotero and processed with the VOS viewer. The analysis used is based on the title area, according to web-based inquiry in supporting science education research. Overall, this study provides information regarding research opportunities in science learning with web-based inquiry, especially during this pandemic. This research also illustrates the publication opportunities in various countries that have a high interest in the topic of inquiry. The mapping of the bibliometric results also supports the scientific explanation between the theory and the evidence of probability. Therefore, the literature is expected to be a reference for further science research.

Quantitative literacy is an important skill needed by individuals in solving problems with quantitative situations in daily life. Thus, this paper aimed to identify quantitative literacy in solving the PISA problem based on gender differences. This study used descriptive research with a qualitative approach. Research subjects in this study were two tenth-grade students in middle school. They were one male student and one female student who have the similar mathematical ability. Data were collected by giving the Program for International Student Assessment (PISA) problem, especially mathematical literacy, and using the interview method. The research results showed that the quantitative literacy of male student in solving PISA problems is by using fewless symbols to represent time and incomplete algorithms and procedures. In comparison, the quantitative literacy of female student in solving PISA problems is by using a more detailed description, more mathematical operations, and solving the problem according to algorithms and procedures. Furthermore, both students have quantitative literacy aspects, including interpretation, calculation, representation, assumption, analysis, and communication skills. Therefore, the quantitative literacy ability of students can be used as a reference for teachers to determine the modeling activities conducted by students in solving the PISA problem.

In this paper, we present a novel approach to data-driven neuro-fuzzy modeling, which aims to create accurate monthly inflow and outflow forecast of money (M0) in Bali Province. The data is monthly time series included some religious ceremony identification variables and a monthly dummy variable from January 2011 to March 2019. Well known, Bali Province has unique cultures, the only one province which Hinduism majority religion in Indonesia, and listed as top tourism destination in the world. The neuro-fuzzy models were created using ANFIS architecture and sliding window time series analysis, then simulated using walk forward validation, interpreted using MAPE, and NRMSE. Based on the simulation of the last 24 months, the model of inflow obtained MAPE 23.33% (worth considering) and NRMSE 18.68% (accurate). Meanwhile, the model of outflow obtained MAPE 19.24% (accurate) and NRMSE 8.71% (very accurate). These models and their pieces of information could assist the central bank in Bali Province to prepare cash for money (M0) outflow and managed technic for counting money (M0) inflow.

The purpose of this paper is to forecast the room occupancy rate (ROR) of star hotels by utilizing Google Trends data, in addition to historical ROR data. The data used is the ROR (%) which comes from the Badan Pusat Statistik-Statistics Indonesia and the Google Trends query index using the search word "hotel". The method used is the ARIMAX model. The results of this study indicate that the ARIMAX model has excellent forecasting capabilities. This is shown by the MAPE value which reached 6.541%, which means the added value of the hotel sector in the first quarter of 2021 is not expected to increase significantly.

Diberikan dua graf $G_1$ and $G_2$, bilangan Ramsey multipartit himpunan $M_j(G_1,G_2)=t$ adalah bilangan asli terkecil sedemikian sehingga setiap faktorisasi graf $K_{t\times j}:=F_1\oplus F_2$ senantiasa memenuhi kondisi berikut: atau $F_1$ memuat $G_1$ sebagai subgraf, atau $F_2$ memuat $G_2$ sebagai subgraf . Pada paper ini, akan ditentukan nilai eksak dari bilangan Ramsey multipartit himupnan $M_3(P_n,K_{1,t})$ dimana $P_n$ adalah suatu lintasan dengan $n$ titik, $2\leq n\leq 3$, dan $K_{1,t}$ adalah suatu bintang dengan $t+1$ titik.

Demam Berdarah Dengue (DBD) merupakan kasus penyakit yang sudah tidak asing lagi bagi masyarakat Indonesia. Kasus ini memperoleh perhatian khusus dari pemerintah karena sering berakibat kematian karena keterlambatan penanganan. Dari segi jumlah, setiap tahunnya kasus ini selalu mengalami peningkatan, sehingga banyak dilakukan penelitian terkait dengan kasus DBD, baik dari segi usaha untuk mengurangi kasus penyakit ataupun untuk memprediksi masa yang akan datang. Paper ini akan memodelkan jumlah kasus DBD di Kabupaten Majalengka tahun 2016 dengan menggunakan regresi TELBS. Regresi TELBS merupakan metode regresi linier berganda untuk kasus pencilan. Keberadaan pencilan akan menyebabkan asumsi Gaussian tidak terpenuhi, sehingga jika dipaksakan dengan metode kuadrat terkecil akan menghasilkan model yang tidak baik. Regresi TELBS menghasilkan model yang dapat mewakili sebagian besar data. Hal ini ditunjukkan oleh nilai ketepatan model berdasarkan koefisien determinasi yang besar. Dengan menggunakan data sekunder dari BPS model yang dihasilkan berdasarkan metode TELBS menunjukkan bahwa 94,7109% jumlah kasus DBD di Kabupaten Majalengka ditentukan oleh faktor-faktor persentasi angka bebas jentik nyamuk, persentasi angka penduduk miskin, ketinggain daerah dari dasar dasar laut, fasilitas yang dibina dari kesehatan, kepadatan penduduk.

Partisi bilangan bulat merupakan salah satu cabang ilmu yang berkembang sangat pesat di bidang teori bilangan. Suatu partisi dari bilangan bulat positif n adalah barisan tak naik atas bilangan bulat positif sedemikian hingga jumlahnya adalah n. Beberapa kelompok peneliti mengkaji partisi dengan tambahan sifat tertentu. Salah satu kelompok tersebut adalah Andrews, Lewis dan Lovejoy yang memperkenalkan partisi dengan penjumlah ditandai. Suatu partisi dari bilangan bulat tak negatif disebut partisi dengan penjumlah ditandai jika setiap penjumlah dari partisi tersebut ditandai tepat satu. Selanjutnya PD(n) menyatakan banyaknya partisi dari dengan penjumlah ditandai. Kelompok lain, yaitu Chen, Ji, Jin dan Shen, mengkaji 3-diseksi dari PD(n) menggunakan sifat-sifat pecahan kubik kontinu Ramanujan. Di paper ini ditunjukkan bukti alternatif dari 3-diseksi dari PD(n) yang diperoleh oleh kedua kelompok tersebut.

Paper ini membahas model matematika tentang kestabilan titik ekuilibrium endemik terhadap Human Papillomavirus (HPV) pada model SIS dengan populasi berbeda. Model SIS Terdiri dari dua kompartemen, yaitu kompartemen rentan (Susceptible) dan kompartemen yang terinfeksi (Infected) dengan populasi yaitu subpopulasi perempuan dan subpopulasi laki-laki . Titik ekuilibrium endemik pada model SIS ini dapat dilakukan dengan melakukan substitusi atau manipulasi aljabar terhadap asumsi-asumsi pada model SIS Human Papillomavirus (HPV). Selanjutnya, kestabilan endemik dinyatakan stabil asimtotik dapat di uji menggunakan matriks Jacobian dengan syarat terpenuhi. Kemudian, model SIS Human Papillomavirus (HPV) dianalisis dengan simulasi numerik dengan hasil kestabilan titik ekuilibrium endemik itu stabil asimtotik jika . Dan ini menjelaskan bahwa subpopulasi terinfeksi akan memungkinkan menginfeksi atau menularkan virus kepada subpopulasi rentan. Artinya virus masih ada dalam populasi.

This study investigated the use of a free GeoGebra application, where the ability of a GeoGebra software application had the potential to simplify and help the teaching and learning process in the informatics management study program, Medan State Polytechnic. The focus of this research was the incorporation of conventional method-based teaching, namely using the assistance of writing instruments such as pencils, pens, and paper when describing the Venn diagram in mathematical logic courses with the help of the GeoGebra application which made it easier for students to drew circles and determine the slices and combinations on the Venn diagram. The resulted of this study were obtained from the scores of student assignments and the results of interviews conducted online with the number of respondents consisting of 44 students who successfully uploaded assignments through the SIPADI application. The value analysis obtained was compiled into tables then processed using the SPSS application using the pair test and linearity test. Based on the output obtained, it was known that the GeoGebra value obtained the average value of learning outcomes or the mean of 75.9773, while for the average learning outcomes using conventional methods or the mean of 68.9091. The number of respondents or students who took the test amounted to 44 people, Std. Deviation for GeoGebra method was 5.800092 and conventional method was 5.56909, and Std. Error Means. Based on the results of descriptive statistical tests, the average value of the GeoGebra method > conventional method was 75.9773> 68.9091, so descriptively there was an average difference between the GeoGebra method and the conventional method.

Faculty members of a private Christian Teachers College in Tangerang have been assigned to integrate faith and learning. The purpose of this research was to describe Biology, Physics, Chemistry and Mathematics lecturers’ practices of faith learning integration on their teachings. Five lecturers including two lecturers teaching Physics, and the others each teaching Biology, Chemistry and Mathematics were involved in this research. Two student teachers contributed as well in the research. The data were derived from interview with five faculty members and collecting their course syllabus along with the interview with two student teachers. Descriptive qualitative research with a case study approach was employed. The data were described and analyzed in the light of the current literatures. The findings showed that those five faculty members have been implementing faith learning integration on their teaching with a pedagogy of transferring new information. This paper suggests faculty to go beyond faith learning integration and to focus on learning as formation of heart and desire.

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners’ procedural and conceptual knowledge of algebra has not been well explored. This research paper examined the relationship between Grade 11 learners’ procedural and conceptual knowledge of algebra. Data for the study was collected using an algebra test administered to 181 grade 11 learners in Gauteng province, South Africa. Descriptive statistics and Pearson’s correlation coefficient were used to analyse the data in SPSS. The study revealed that the learners have low levels of both procedural and conceptual knowledge of algebra. However, they displayed better procedural knowledge than the conceptual knowledge of algebra. In addition, a statistically significant moderate positive linear relationship was found between the learners’ procedural and conceptual knowledge of algebra.

We consider Susceptible-Infected-Recovered (SIR) models of infectious disease spread without and with vital dynamics. We recall some existing analytical approximate iterative methods for solving these models. We observe that all these methods solve the models accurately only for points close to the initialisation. These methods produce inaccurate, and even, unrealistic solutions to the SIR models if the time domain is sufficiently large. In this paper, our research objective is to propose an analytical-numerical iterative method, which is able to solve the SIR models accurately on the whole domain. The research method used is quantitative mathematical modelling with simulation. By implementing this analytical-numerical iterative method into a finite number of small consecutive subintervals of the domain, our research results show that the proposed method produces accurate solutions to the SIR models on the whole domain.

The purpose of this research finds a link between adaptive reasoning, mathematical problem solving, and cognitive style. This research is a literature study. This paper showed the relationship between adaptive reasoning, mathematical problem solving, and cognitive styles. In particular, field-independent (FI) and field-dependent (FD) cognitive styles. Adaptive reasoning in mathematical problems is the legitimacy of problem strategies. Whereas the cognitive style provides opportunities for students to give reasonable arguments according to the tendency of the cognitive style. Mathematical problem-solving in the FI and the FD can vary according to students' cognitive styles. It was found that adaptive reasoning, mathematical problems, cognitive styles (FI, FD) have a strong stylistic relationship where adaptive reasoning will be able to give direction to students in solving math problems. Therefore, the basis for researching the adaptive reasoning profile of students in solving mathematical problems in terms of FI and FD cognitive styles is our understanding of the relationship between adaptive reasoning, mathematical problem solving, and cognitive style

In this article, the notion of (α,β)-intuitionistic fuzzy ideals (briefly, (α,β)-IF ideals) of ternary semigroups is described using ”belong to” relation (ϵ) and “quasi-coincidence with” relation (q) connecting two objects, i.e., an intuitionistic fuzzy point (IFP, for short) and an intuitionistic fuzzy set (briefly, IFS). Throughout this paper, α∈{ϵ,q,ϵ∨q} and β∈{ϵ,q,ϵ∨q,ϵ∧q}. The main purposes of this research are to construct the definition of (α,β)-intuitionistic fuzzy ideals of ternary semigroups and to investigate the relations between some types of these ideals. To achieve these goals, we use literature review method to study previous researches regarding (α,β)-fuzzy ideals of ternary semigroups and (α,β)-IF ideals of semigroups. As a result, we find the conditions for an IFS and an ideal of a ternary semigroup to be classified as an (α,ϵ∨q)-IF ideal of ternary semigroup. Relations between some types of (α,β)-IF ideals of a ternary semigroup are also discussed here.

This paper discusses topics in the symmetrized max-plus algebra. In this study, it will be shown the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra. Eigenvalue decomposition is shown by using a function that corresponds to the symmetrized max-plus algebra with conventional algebra. The result obtained is the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra and its application to determine eigenvalues and eigenvectors.

Given a graph with n points and m lines. If each vertex is labeled, then it can be constructed many graphs, connected, or disconnected graphs. A graph G is called a connected graph if there is at least one path that connects a pair of vertices in G. In addition, the graph formed may be simple or not simple. A simple graph is a graph that does not contain loops or parallel lines. A loop is a line that connects a point to itself, and a parallel line is two or more lines that connect the same pair of points. This paper will discuss the relationship between the formula patterns for calculating the number of connected graphs labeled with vertices of order five and six without loops.

Abstrak Dalam makalah ini dikaji kemampuan atau keterampilan yang diperlukan untuk menghadapi era society 5.0 dan cara mengembangkan kemampuan/keterampilan tersebut. Dari hasil kajian literatur diperoleh bahwa keterampilan yang diperlukan untuk menghadapi era society 5.0 ialah keterampilan abad 21. Keterampilan tersebut meliputi kemampuan berpikir kritis, berkreasi, dan berinovasi, berkomunikasi dan berkolaborasi, menerapkan teknologi, menggunakan media dan informasi serta keterampilan hidup dan berkarir. Keterampilan abad 21 dapat dikembangkan melalui pembelajaran matematika. Pembelajaran yang digunakan harus berpusat pada siswa, pembelajaran kolaboratif, dikaitkan dengan konteks yang relevan dengan kehidupan siswa, dan melibatkan siswa dalam lingkungan sosialnya. Selanjutnya untuk mengembangkan karakter sebagai keterampilan hidup dan berkarir dapat dilakukan baik secara langsung terintegrasi dalam pembelajaran maupun secara tidak langsung dimana guru sebagai model atau menerapkannya dalam kegiatan sehari-hari. Abstract In this paper, we examined the skills needed to face the society 5.0 era and how to develop these skills. From the results of literature studies obtained that the skills needed to face the era of society 5.0 is the skills of the 21st-century. These skills include critical thinking, creating, and innovating, communicating and collaborating, applying technology, using media and information as well as life and career skills. 21st-century skills can be developed through mathematics learning. The learning used should be student-centered, collaborative learning, associated with context relevant to student life, and involve students in their social environment. Furthermore, to develop the character as a life and career skills can be done either directly integrated into learning or indirectly where the teacher as a model or apply it in daily activities.

This study aims to analyze the location of students' errors in problem solving and the causal factors based on Watson's criteria. This type of qualitative descriptive research, with the subject of three students of class X AKL 1 taken based on certain considerations according to the criteria or can be called purposive sampling technique. Data collection techniques include direct observation in schools, interviews with subjects and documentation. Triangulation techniques used for data analysis include data reduction, presentation and conclusion drawing. From the results of the analysis, it was found that four types of errors were located inimproper procedures, indirect manipulation, missing data and missing conclusions. The cause of the error is students lack understanding of material concepts, being careless in reading questions, forgetting formulas, being in a hurry, and new factors are found, namely students use other paper to write down the completion steps. The results of the study can explain in detail the errors made by students in solving problems, so that it can minimize the occurrence of similar errors and improve the learning process of mathematics.

Abstrak Ujian Nasional yang dilaksanakan setiap tahun di Indonesia telah menghasilkan banyak data, termasuk di Provinsi Lampung. Pada rentang tahun 2015 sampai dengan tahun 2018, telah terkumpul kurang lebih 11 juta data hasil ujian nasional. Data tersebut tentu dapat memberikan banyak informasi untuk perbaikan Pendidikan Indonesia di masa mendatang. Tulisan ini membahas tentang pengelompokan mata pelajaran pada Ujian Nasional SMP di Provinsi Lampung dengan tujuan untuk memetakan hubungan hasil belajar Matematika, IPA, Bahasa Indonesia, dan Bahasa Inggris. Tujuan pengelompokan tersebut sebagai analisa lebih jauh agar perbaikan pendidikan juga dapat mulai masuk pada ranah non-teknis, seperti penjadwalan, penyeusaian waktu belajar di kelas sampai dengan waktu pengerjaan tugas, serta perbaikan pada penentuan mata pelajaran yang menjadi syarat pelajaran lainnya. Analisis klusterisasi dilakukan dengan menggunakan Algoritma Kruskal berdasarkan graf maximum spanning tree (MST) dengan bantuan teknik statistik deskriptif dan inferensial. Data yang digunakan adalah hasil Ujian Nasional di Provinsi Lampung tahun 2017 dan 2018 sebanyak 15876 data. Graf MST ditentukan menggunakan algoritma Kruskal dan koefisien korelasi ditentukan menggunakan nilai koefisien korelasi Pearson. Hasil eksperimen menunjukkan bahwa Matematika, IPA, dan Bahasa Inggris memiliki korelasi yang paling kuat. Mata pelajaran yang paling kuat korelasinya dengan Bahasa Indonesia adalah Bahasa Inggris. Oleh karena itu, pemetaan mata pelajaran dapat disusun menjadi dua kelompok yaitu Matematika-IPA-Bahasa Inggris dan Bahasa Inggris- Bahasa Indonesia- IPA. Hasil tersebut dapat bermanfaat sebagai dasar pengambilan keputusan pada berbagai aspek teknis untuk mengoptimalkan hasil belajar siswa SMP khususnya di Provinsi Lampung. Kata kunci: Klusterisasi, Lampung, Ujian Nasional Abstract National exams carried out every year in Indonesia have produced a lot of data, including in Lampung Province. In the span of 2015 to 2018, approximately 11 million national exam results have been collected. This data can certainly provide a lot of information for the improvement of Indonesian education. This paper discusses the clustering of subjects on junior high school national exams in Lampung Province with the aim of mapping the relationship of learning outcomes in Mathematics, Sciences, Indonesian, and English. The purpose of the clustering is as a further analysis so that educational improvements can also begin to enter the non-technical realm, such as scheduling, adjusting class and assignment time, and also determine prerequisite subjects. Clustering analysis is performed using an algorithm based on maximum spanning tree (MST) graphs with the help of descriptive and inferential statistical techniques. The data used are the results of national exams in Lampung province in 2017 and 2018 totaling 15.876 data. The MST Graph is determined using Kruskal’s algorithm and the coefficient of correlation is determined using Pearson coefficient of correlation value. The experimental results show that Mathematics, Natural Sciences, and English have the strongest correlation. Subject that has the strongest correlation with Indonesian is English. Therefore, the mapping of subjects can be arranged into two groups namely Mathematics- Sciences- English and English-Indonesian- Sains. These results can be useful as a basis for decision making on various technical aspects to optimize junior high school student learning outcomes, especially in Lampung Province. Keywords: Clusterization, Lampung, National Examination

During the Covid-19 pandemic, online learning became a new way of teaching and learning which utilized electronic devices, especially internet networks. However, in practice, online learning often encounters obstacles. With online learning, teachers need to know the causes and indicators of these difficulties. Efforts can then be made to alleviate them, namely that teachers become facilitators of online learning activities. In their role as facilitators, teachers can provide their students with supportive learning resources and media, encouragement and motivatation, and time outside of school hours to help students understand well. In this case, the author used a literature review and case study methods as the basis for preparing research instruments with the purpose of this paper being to explain the role of the teacher as a facilitator in overcoming learning difficulties of students during online learning. The author is aware of the limitations that humans have so the learning difficulties that students experience can be seen as an opportunity for teachers to serve those students. Teachers are also required to be more responsible for themselves and their students as a form of gratitude to God. The author suggests that the teacher as a facilitator can continue to learn to better understand the various strategies in overcoming learning difficulties and have a sense of responsibility towards students. BAHASA INDONESIA ABSTRACT: Dalam masa pandemi seperti ini, pembelajaran daring menjadi cara baru dalam proses belajar mengajar dengan memanfaatkan perangkat elektronik, khususnya jaringan internet. Namun dalam pelaksanaannya, pembelajaran daring sering mengalami kendala. Dalam pembelajaran daring yang dihadapi, guru perlu mengetahui faktor penyebab dan indikator kesulitan belajar daring. Kemudian, upaya dapat dilakukan yaitu guru diharapkan mampu menjadi fasilitator dalam kegiatan pembelajaran daring. Dengan perannya sebagai fasilitator, guru memberikan pelayanan berupa menyediakan sumber dan media pembelajaran yang mendukung, serta memberi semangat dan motivasi, serta meluangkan waktu di luar jam sekolah agar dapat membantu peserta didik memahami pembelajaran dengan baik. Dalam hal ini, penulis menggunakan metode kajian pustaka dan studi kasus sebagai dasar dalam penyusunan instrumen penelitian, dan tujuan penulisan paper adalah untuk menjelaskan guru sebagai fasilitator dalam mengatasi kesulitan belajar peserta didik selama pembelajaran daring. Penulis menyadari akan keterbatasan yang manusia miliki, sehingga melalui kesulitan belajar yang peserta didik alami dapat dilihat sebagai kesempatan untuk dapat melayani peserta didik. Guru juga dituntut lebih bertanggung jawab terhadap diri sendiri maupun peserta didik, sebagai wujud ucapan syukur kepada Tuhan. Saran penulis adalah agar guru sebagai fasilitator dapat belajar terus untuk lebih memahami berbagai macam strategi dalam mengatasi kesulitan belajar dan memiliki rasa tanggung jawab terhadap peserta didik.

School math learning is part of the educational process that provides students with a mathematics learning experience through a planned set of activities to achieve established goals. The goal of learning mathematics in schools in Indonesia is oriented towards achieving a balance between the cognitive, affective, and psychomotor domains. In fact, learning mathematics in schools in Indonesia so far has focused on efforts to achieve high scores from the cognitive domain. But along with the development and change of curriculum, affective and psychomotor domains are receiving more priority to develop. In this paper, the author wants to examine the affective domain by conducting a study of character values in school mathematics learning through an analogy approach. This paper aims to contribute ideas related to the development of affective domains in learning mathematics through the study conducted. The research method used is a literature study. While the strategy for conducting the study is an analogical approach that is associated with the understanding of quantitative and qualitative relationships. Based on the results, it is evident that in school mathematics learning implied character values are learned. The author hopes that this study will be useful to math teachers in developing the affective domain of math learning in schools. The implication is that the goal of learning mathematics, namely the balance between the cognitive, affective, and psychomotor domains, can be achieved. BAHASA INDONESIA ABSTRACT: Pembelajaran matematika sekolah adalah bagian dari proses pendidikan yang memberikan pengalaman belajar matematika kepada siswa melalui serangkaian kegiatan yang terencana untuk mencapai tujuan yang telah ditetapkan. Tujuan pembelajaran matematika sekolah di Indonesia berorientasi untuk mewujudkan keseimbangan antara domain kognitif, afektif, dan psikomotor. Pada kenyataannya pembelajaran matematika sekolah di Indonesia selama ini menitikberatkan pada upaya pencapaian nilai yang tinggi dari domain kognitif. Tetapi bersamaan dengan pengembangan dan pergantian kurikulum, domain afektif dan psikomotor mendapat prioritas untuk dikembangkan. Oleh karena itu, dalam paper ini penulis ingin mengembangkan domain afektif dengan melakukan kajian nilai-nilai karakter dalam pembelajaran matematika sekolah melalui pendekatan analogi. Penulisan paper ini bertujuan untuk memberikan kontribusi pemikiran terkait pengembangan domain afektif dalam pembelajaran matematika. Metode penelitian yang digunakan adalah studi literatur. Sedangkan strategi melakukan kajian adalah pendekatan analogi yang dikaitkan dengan pemahaman hubungan kuantitatif dan kualitatif. Berdasarkan hasilnya dapat diketahui bahwa didalam pembelajaran matematika sekolah terdapat nilai-nilai karakter yang tersirat untuk dipelajari. Harapan penulis, kajian ini bermanfaat untuk guru matematika dalam mengembangkan domain afektif pembelajaran matematika di sekolah. Implikasinya tujuan pembelajaran matematika yaitu keseimbangan antara domain kognitif, afektif dan psikomotor dapat tercapai.

During the Covid-19 pandemic, learning was carried out online. It takes student activeness with the right approach and method to provide maximal learning experiences and learning outcomes. The purpose of this paper is to describe the application of the facilitated e-learning approach combined with the 5E method on student activeness in learning. This paper used the descriptive qualitative research method. Students are imagebearers of God so a teacher should view students as special and valuable. Students have reason and ability so it can be said that they are active individuals. Therefore, a teacher should always encourage their activiteness during the learning process. Implementing the facilitated e-learning approach with the 5E method is the right solution because the students carry out learning activities independently with the teacher in the role of facilitator. This has the potential to encourage student activeness in online learning so that students can get the maximum learning experience and learning outcomes and teachers can provide God-centered learning. In applying these approaches and methods, a teacher needs careful and measured preparation in order to provide the maximum learning experience even though it is carried out online. BAHASA INDONESIA ABSTRACT: Selama pandemi covid-19, pembelajaran dilaksanakan secara daring. Dibutuhkan keaktifan siswa dengan pendekatan dan metode yang tepat untuk tetap memberikan pengalaman belajar dan hasil belajar yang maksimal. Tujuan penulisan dari penelitian ini untuk memaparkan penerapan pendekatan facilitated e-learning dikolaborasikan dengan metode 5E terhadap keaktifan siswa dalam pembelajaran. Penelitian ini disusun dengan metode penelitian kualitatif deskriptif. Hasil pembahasan dari penelitian, siswa merupakan gambar dan rupa Allah sehingga seorang guru hendaknya memandang siswa istimewa dan berharga. Siswa memiliki akal dan kemampuan sehingga siswa dapat dikatakan sebagai pribadi yang aktif. Maka dari itu, seorang guru hendaknya dapat selalu mendorong keaktifan siswa dalam proses pembelajaran. Kesimpulannya, menerapkan pendekatan facilitated e-learning dengan metode 5E merupakan solusi yang tepat karena siswa melakukan aktivitas pembelajaran secara mandiri dengan guru memiliki peran sebagai fasilitator yang berpotensi mendorong keaktifan siswa dalam pembelajaran daring sehingga siswa dapat mendapatkan pengalaman belajar dan hasil belajar yang maksimal serta guru dapat memberikan pembelajaran yang berpusat pada Allah. Disarankan seorang guru dalam menerapkan pendekatan dan metode tersebut perlu memberikan persiapan yang matang dan terukur agar dapat memberikan pengalaman belajar yang maksimal meskipun dilaksanakan secara daring.

This paper investigates student learning activeness as an important part of the formation and development of student potential. The aim of this paper is to describe the use of quizzes in lesson plans (practice questions) to encourage student activeness in online learning. Doing a field practicum program online presents its own challenges for teachers. One of them is related to the responses of students who are less active in learning. The solution applied is to use technology media for learning, namely using Quizizz to do practice exercises online. Divided into 10 implementation steps, the initial 8 steps are general steps such as making an online quiz on Quizizz while the last 2 steps are an adaptation done by the teacher himself. The implementation of this media in doing exercises shows that students are encouraged to be actively involved in learning. It can be seen in the attitude of those who are actively discussing (question & answer). This emphasizes the real practice of a Christian teacher in living his salvation through holistic learning design, for example by utilizing technology in the classroom to encourage active student involvement. This research has many weaknesses such as data validity, problem deepening, and technical problems in using Quizziz. This can be an evaluation and input for writers and readers. BAHASA INDONESIA ABSTRACT: Paper ini dibuat untuk melihat hubungan keaktifan belajar siswa dalam pembelajaran sebagai bagian penting dalam pembentukan dan pengembangan potensi siswa. Tujuan paper ini adalah untuk memaparkan pemanfaatan Quizizz dalam pembelajaran untuk mendorong keaktifan siswa dalam pembelajaran online. PPL yang dilaksanakan secara online memberikan tantangan tersendiri bagi pengajar, di antaranya: berkaitan dengan respons siswa yang kurang aktif dalam pembelajaran. Solusi yang diterapkan adalah memanfaatkan media teknologi untuk pembelajaran yaitu menggunakan Quizizz untuk melakukan latihan soal secara online. Dibagi menjadi 10 langkah penerapan, 8 langkah awal merupakan langkah umum seperti membuat kuis online pada Quizizz sedangkan 2 langkah terakhir merupakan adaptasi yang dilakukan oleh pengajar sendiri. Pengimplementasian media ini dalam melakukan latihan soal menunjukan adanya dorongan untuk siswa dapat terlibat aktif di dalam pembelajaran. Terlihat dari sikap mereka yang aktif berdiskusi (tanya & jawab). Hal ini menekankan praktik nyata seorang pengajar Kristen dalam menghidupi keselamatannya melalui perancangan pembelajaran yang holistik misalnya dengan memanfaatkan teknologi di kelas untuk mendorong keterlibatan aktif siswa. Penelitian ini memiliki banyak kelemahan seperti kevalidan data, pendalaman masalah, serta gangguan teknis dalam penggunaan Quizizz. Hal ini dapat menjadi evaluasi dan masukan bagi penulis maupun pembaca.

Konsep green supply chain (GSC) banyak diterapkan dalam mengatasi permasalahan limbah industri, seperti pengerajin tekstil tradisional Jumputan Palembang. Proses pembuatan kain jumputan menggunakan air dan menghasilkan limbah cair yang berpotensi membahayakan lingkungan. Penerapan konsep teknologi ramah lingkungan dalam pengelolaan rantai pasokan bisnis dapat mengatasi hal tersebut jika dikelola dengan optimal. Paper ini menyajikan hasil analisis jaringan GSC dalam bentuk model proses dan prototipe sistem informasi yang dapat digunakan oleh pengerajin untuk mengolah data pengadaan, produksi, dan penjualan produk jumputan mereka, serta yang tidak kalah pentingnya adalah pengelolaan data limbah cair. Limbah cair ini akan diproses menjadi air bersih kembali oleh pengerajin secara bersama-sama. Dihasilkan beberapa model GSC yang dapat digunakan oleh peneliti, pengerajin maupun pemerintah untuk mengatasi permasalahan dampak lingkungan dari limbah proses pembuatan kain jumputan. Model analisis yang dihasilkan dapat digunakan untk mengoptimalkan proses produksi dan penjualan kain jumputan oleh pengerajin. Di saat yang sama juga dapat dihasilkan model bisnis baru terkait pengolahan limbah produksi ini, yaitu dengan menghadirkan atau membuat unit bank limbah. Konsep model bank limbah ini dapat mengoptimalkan pengendalian dampak lingkungan akibat limbah cair produksi jumputan di kawasan industri pengerajin jumputan, dan hasil ini dapat direplikasi di kawasan industri yang lain dalam bentuk yang sejenis.

In this paper we study the existence and uniqueness solution for a first kind fractional Volterra boundary value problem involving Hadamard type and three-point boundary conditions. Our analysis is based on Krasnoselskii-Zabreiko’s fixed point theorem and Banach contraction principle. As an application we discuss a Hadamard type boundary value problem with fractional integral boundary conditions. We emphasize that our results are new in the context of Hadamard fractional calculus and are well illustrated with the aid of examples.

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.

This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers. The purpose of this paper is to describe the commutation matrices obtained in relation to the matrices in this group. The commutation matrix is a permutation matrix that associates the relationship between the vec and vec of the transpose matrix. Based on the classification of matrices in the Kronecker quaternion group, there are 16 classification of commutation matrices for the matrices in this group.

Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 and to do a simulation study to observe the probabilities that parameters are contained in the confidence intervals. We do not assume any parametric form for the intensity function except that it is periodic. We consider in the observed there is only one realization of the cyclic Poisson process in a bounded interval. The main results are two theory about confidence intervals for parameters. The simulation shows that the probability values of the observed parameters contained in the confidence intervals are in accordance with the theory.

Information data protection is necessary to ward off and overcome various fraud attacks that may be encountered. A secret sharing scheme that implements cryptographic methods intends to maintain the security of confidential data by a group of trusted parties is the answer. In this paper, we choose the application of recursive algorithm on Shamir-based linear scheme as the primary method. In the secret reconstruction stage and since the beginning of the share distribution stage, these algorithms have been integrated by relying on a detection parameter to ensure that the secret value sought is valid. Although the obtained scheme will be much simpler because it utilizes the Vandermonde matrix structure, the security aspect of this scheme is not reduced. Indeed, it is supported by two detection parameters formulated from a recursive algorithm to detect cheating and identify the cheater(s). Therefore, this scheme is guaranteed to be unconditionally secure and has a high time efficiency (polynomial running time).

Under classical statistics Hotelling 〖 T〗^2 control chart is applied when the observations of quality characteristics are precise, exact, or crips data. However, in reality, under uncertain conditions, the observations are not necessarily precise, exact, or indeterminacy. As a consequence, the classical Hotelling〖 T〗^2control chart is not appropriate to monitor the process for this condition. To tackle this situation, we proposed new Hotelling 〖 T〗^2 monitoring scheme based on a fuzzy neutrosophic concept. Neutrosophic is the generalization of fuzzy. It is used to handle uncertainty using indeterminacy. The combination of statistics based on neutrosophic Hotelling 〖 T〗^2 and classical Hotelling 〖 T〗^2 control chart will be proposed to tackle indeterminacy observations. The proposed Hotelling 〖 T〗^2 statistics, its call neutrosophic Hotelling 〖 T〗^2 (T_N^2 ) control chart. This chart involves the indeterminacy of observations, its call neutrosophic data and will be expressed in the indeterminacy interval. T_N^2 control charts consist T_N^2 lower chart and T_N^2 upper chart. In this paper, the neutrosophic Hotelling T^2will be applied to individual observations of glass production and will be compared by using classical Hotelling T^2 control chart. Based on T_N^2 control charts of glass production, nine points fall outside of 〖UCL〗_N of lower control chart and 24 points outside from 〖UCL〗_N of upper control chart. Whereas using classical Hotelling T^2 control chart, just one point outside frim UCL. From the comparison, it concluded that the neutrosophic Hotelling T^2 control chart is more suitable for the indeterminacy of observations.

The research in graph theory has been widened by combining it with ring. In this paper, we introduce the definition of a non-braid graph of a ring. The non-braid graph of a ring R, denoted by YR, is a simple graph with a vertex set R\B(R), where B(R) is the set of x in R such that xyx=yxy for all y in R. Two distinct vertices x and y are adjacent if and only if xyx not equal to yxy. The method that we use to observe the non-braid graphs of Zn is by seeing the adjacency of the vertices and its braider. The main objective of this paper is to prove the completeness and connectedness of the non-braid graph of ring Zn. We prove that if n is a prime number, the non-braid graph of Zn is a complete graph. For all n greater than equal to 3, the non-braid graph of Zn is a connected graph.

In this paper, we consider the boundedness of the operator families in whole space for Navier-Lame model problem in bounded domain of N dimensional Euclidean space (N≥2). To find the boundedness of the operator families, first of all we construct model problem in the form of the resolvent problem by using Laplace transform. Then, using Fourier transform, we get the solution formula of the model problem. In this paper, we use the qualitative methods to construct solution formula of velocity (u). This step is fundamental stage to find the well-posedness of the model problem. As we known that fluid motion can be described in partial differential equation (PDE). Essential point in PDE are finding existence and uniqueness of the model problem. One methods of investigating the well-posedness is R-boundedness of the solution operator families of the model problem. We can find the R-boundedness of the solution operator families not only in whole-space, half-space, bent-half space and in general domain. In this paper we investigate the R-boundedness of the solution operator families only in whole space. By using this R-boundedness, we can find that the multipliers which form of the operator families are bounded with some positive constant.

Some conjectures related to the radical theory of rings are still open. Hence, the research on the radical theory of rings is still being investigated by some prominent authors. On the other hand, some results on the radical theory of rings can be implemented in another branch or structure. In radical theory, it is interesting to bring some radical classes into graded versions. In this chance, we implement a qualitative method to conduct the research to bring the Brown-McCoy radical class to the restricted graded Brown-McCoy radical class as research objective. We start from some known facts on the Brown-McCoy radical class and furthermore, let G be a group, we explain the Brown-McCoy radical restricted with respect to the group G. The result of this paper, we describe the Brown-McCoy radical in restricted graded version and it is denoted by G^G. Furthermore, we also give the fact by explaining G^G (A)=(〖G(A))〗_G, for any ring A, as the final outcome of this paper.