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Some mathematics teachers in Indonesia still find it challenging to conduct a formative assessment in a class with many students. A problem emerges in how to facilitate an environment that uses the type of engaging discussion needed for formative assessment to be successful. Meanwhile, in mathematics learning, proceptual (process and conceptual) understanding is considered prominent for success in learning mathematics. This understanding could be enhanced by using an appropriate strategy of discussion, which could be managed along with conducting a formative assessment. Overcoming this challenge, promoting a connected classroom might be beneficial to facilitating formative evaluation in a large class. Therefore, this paper aims to develop a method for formatively assessing students’ mathematics understanding that mathematics teachers could use with a focus on proceptual understanding. Reviewing some literature on the topics of mathematics understanding, formative assessment, and connected classroom has established a framework to help teachers develop guidance for conducting formative assessment in proceptual understanding using a connected classroom. The framework based might be used to help mathematics teachers prepare formative assessments in a class with many students. An example of how to develop a guide to assess students' proceptual understanding of algebra is also provided in this paper. Keywords: proceptual understanding, formative assessment, connected classroom

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the examined studies were addressed in the learning areas of Analysis, Geometry, Algebra, Linear Algebra, Elementary Number Theory, Probability, Combinatorics, and MIX. Students in early grades tend more towards external and empirical proof schemes. On the other hand, the characteristics of the proof schemes become more sophisticated as the participants' profiles change to pre-service teachers or as they become more specializing in mathematics. Some results are as follows: the academic achievement levels, genders, and grade levels of the participants in the studies examined in this paper have indicated that they have similar traces with the schemes they use. In addition, it has been determined that new perspectives such as examining Harel and Sowder's classification with new lenses, revealing the overlooked roles of some dynamics in proof, or improving the framework provide an important research area in terms of revealing students' potentials.

The aim of this paper is to describe the views of mathematics teachers in Indonesia on the distance learning barriers during the early Covid-19 pandemic. Specifically, this paper investigates the barriers that teachers view as significant in distance learning and efforts taken to overcome the barriers during the early Covid-19 pandemic. This study employed a descriptive research design involving 415 mathematics teachers by snowball sampling to fill out an online questionnaire. This study shows that barriers related to pedagogical dimensions were perceived as significant in distance learning during the early Covid-19 pandemic. Moreover, this study reveals that most of the teachers did some efforts that can be done by the teachers themselves to overcome the barriers. Based on the findings, we argue that it is important to support teachers’ pedagogical competencies to conduct distance learning in order to face this current pandemic or any future crises that may potentially disrupt face-to-face learning.

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.

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.

Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are related. It is important that students understand how the property informs the written multiplication algorithm. Another component of successful use of the standard multiplication algorithm is extended number facts and the paper also explores students’ ability to understand and generate them. One purpose of the study was to investigate the extent to which students used the standard multiplication algorithm and if their use of it is supported by an understanding of the underpinning components of the array, partitioning, the distributive property, and extended number facts. That is, we seek to learn if students have a conceptual understanding of the multiplication algorithm and its underpinning mathematics that would enable them to transfer their knowledge to a range of contexts, or if they have procedurally learned mathematics. In this qualitative study, data were generated from the administration of a Multiplicative Thinking Quiz with a sample of 36 primary aged students. Data were analyzed manually and reported using descriptive statistics. The main implications of the study are that the connections among the multiplicative array, place value partitioning, base ten property of place value, distributive property of multiplication, and extended number facts need to be made explicit for children in terms of how they inform the use of the written algorithm for multiplication.

Di dalam paper ini dikonstruksikan operator linear-2 terbatas dari X2 ke Y , dengan X ruang bernorma-2 non-Archimedean dan ruang bernorma non-Archimedean. Di dalam paper ini ditunjukan bahwa himpunan semua operator linear-2 terbatas dari X2 to Y , ditulis B(X2, Y) merupakan ruang bernorma non-Archimedean. Selanjutnya, ditunjukan bahwa B(X2, Y), apabila Y ruang Banach non-Archimedean. [In this paper we construct bounded 2-linear operators from X2 to Y, where X is non-Archimedean 2-normed spaces and is a non-Archimedean-normed space. We prove that the set of all bounded 2-linear operators from X2 to Y , denoted by B(X2, Y) is a non-Archimedean normed spaces. Furthermore, we show that B(X2, Y) is a non-Archimedean Banach normed space, whenever Y is a non-Archimedean Banach space.]

Abstrak Penelitian ini bertujuan untuk mengetahui Pengaruh Model Pembelajaran Problem Based Learning Terhadap Pemahaman Matematis Ditinjau Dari Kemampuan Awal Matematika. Desain penelitian ini menggunakan pendekatan kuantitatif dan teknik analisis Anova dua jalur. Sampel penelitian berjumlah 32 orang untuk kelas eksperimen dan 31 orang untuk kelas kontrol di SMK Negeri 1 Pandeglang, dengan menggunakan metode quasi eksperimen. Penelitian ini menggunakan desain pretest dan postest sehingga dapat dilihat perbedaan peningkatan pemahaman matematis dari kelas eksperimen dan kelas kontrol. Hasil penelitian menunjukkan bahwa pemahaman matematis siswa yang mendapatkan pembelajaran PBL lebih tinggi dari siswa yang mendapatkan pembelajaran ekspositori. Berdasarkan uji hipotesis diperoleh sig. 0,027 < 0,05 maka H0 ditolak , maka dapat disimpulkan peningkatan pemahaman matematis siswa yang mendapat model pembelajaran PBL lebih tinggi dari siswa yang mendapat pembelajaran ekspositori. Hasil uji Anova dua jalur faktor pembelajaran dan KAM menimbulkan adanya interaksi dengan sig.0,004 < 0,05 . Hal ini berarti interaksi yang sangat signifikan antara model pembelajaran dan KAM terhadap pemahaman matematis. Dari hasil uji-t untuk KAM tinggi diperoleh sig. 0,00 < 0,05 maka H0 ditolak dan untuk KAM rendah diperoleh sig. 0,647 > 0,05 maka H0 diterima. Dengan demikian pembelajaran matematika dengan model PBL dapat dijadikan suatu alternatif untuk meningkatkan pemahaman matematis siswa. Kata kunci: problem based learning, pemahaman matematis, kemampuan awal matematika Abstract The purpose of this paper is to determine the effect of Problem Based Learning Model on Mathematical Understanding viewed from Early Mathematics Ability (EMA). The writer used quantitative analysis method and two-way anova analysis. This paper use primary data, 32 people from experimental class and 31 people from control class in SMK negeri 1 Pandeglang was taken as a interviewees for our research sample using the quasi-experimental method. This study used a pretest and post-test design therefore it can be seen the differences in the increase of mathematical understanding ability from experimental class and control class. The result of this study indicate that students who had PBL learning have higher mathematical understanding ability than students who had expository learning. Based on the hypothesis test sig. 0.027 0.05 H0 is accepted. Therefore we can conclude that learning mathematics using the PBL model can become an alternative way to improve students mathematical understanding ability. Keywords: problem based learning, mathematical understanding, early mathematics ability.

Pada umumnya teorema Morley diberlakukan pada segitiga, dalam tulisan ini akan dikembangkan ide teorema Morley untuk bangun datar dengan sisi yang lebih banyak (dalam hal ini segi empat) dan menentukan rumus panjang sisi segiempat Morley tersebut. Segiempat yang dibahas yakni persegi, persegi panjang, belah ketupat, layang-layang, dan trapesium sama kaki. Pembuktian dalam tulisan ini menggunakan cara yang lebih sederhana dengan konsep kesebangunan dan konsep trigonometri. Kata kunci: Teorema Morley, konsep kekongruenan, trigonometri. ABSTRACT Morley’s Theorem generally applies in triangle. This paper applied Morley’s Theorem in quadrilateral to determine the side lenght of Morley’s quadrilateral. Quadrilaterals discussed in this paper are square, rectangle rhombus, kite, and isoscelestrapezium. Simpler way is used to prove by applying congruence and trigonometric concepts. Keywords: Morley’s Theorem, congruence concept, trigonometry.

This paper aims to provide research trends in ethnomathematics from 2012 to 2022 using bibliometric analysis in the Google Scholar database. The sample consisted of 994 documents extracted from the Google Scholar database using the Publish or Perish (PoP) software, which was then analyzed and visualized using Ms.Excel and VoSViewer. The findings revealed an increase in the number of scholarly articles on ethnomathematics. It was discovered that there were five types of documents associated with ethnomathematics research, with journals dominating. The Journal of Physics: Conference Series was a prestigious conference series that included ethnomathematics publications. The visualization of ethnomathematics research trend resulted in four clusters: (1) ethnomathematics practice in the educational landscape, (2) ethnomathematics exploration in learning mathematics, (3) ethnomathematics related to learning materials, and (4) ethnomathematics domain in teaching approach and teaching materials. Cluster 4 provides opportunities for future ethnomathematics research. Researchers could use the findings of this study to identify the global trend of ethnomathematics research and recommend future research directions.

Paper ini mempelajari kontraksi θ-ϕ dan kontraksi tipe Kannan θ-ϕ serta beberapa teorema ketunggalan titik tetap pada ruang metrik parsial. Selanjutnya membandingkan Teorema serupa yang telah dikemukakan oleh peneliti sebelumnya dan membahas contoh sebagai ilustrasi dari teorema yang dibahas. [In this paper, we study the notions of θ-ϕ contraction and θ-ϕ Kannan Type contraction, and some fixed point theorem on partial metric spaces. The results presented in the paper study and consederation some previously results, we also give an example to illustrate our results.]

Teaching axiomatic representation of mathematical objects in all grades can and should be done. The paper analyzes students' understanding and how they perceive theorems using problem posing. We looked at how English-language learners create questions about four geometric theorems from a 9th-grade math textbook. The analysis looks at the question's distinctiveness, its elements' relationships, and sentence structure flaws. These lines, angle, and triangle theorems were chosen to exemplify problem scenarios when a theorem is conveyed in words but not explicitly symbolized. The difficulty of posing mathematically relevant problems stems from the required process of simultaneously changing the theorem language, home language, and formal mathematics language. In Van Hiele's methodology, the pupils' issues aren't classified as a formal or informal deduction. Questions either deduce from a formal system or emphasize theorems. Mastering the required representation registers can assist students in posing problems that reflect, at the very least, at the formal deduction level. The absence of symbolic representation increases the difficulty in posing original problems involving geometric theorems. As a result, how problems are made, especially how they are written, shows how well students understand math through problem-posing.

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.

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.

The level of quality reflective practice remains low among student teachers majoring in Mathematics education. This paper aims to identify the levels of reflective practice possessed by Mathematics education student teachers in a teacher training program at higher learning institutions in Namibia. The professional status requires that teachers become reflective practitioners to develop their effectiveness- a skill they can acquire during their training. A reflection framework was used to identify levels of reflective practices among Mathematics student teachers. This study is qualitative and employed a narrative inquiry approach to assess the effectiveness of reflective practice as experienced by student teachers. A total of ten third-year undergraduate students majoring in Mathematics Education participated in the study by generating reflective journals. The results show that student teachers have insufficient reflective skills which are limited to the first two levels of the reflection framework: technical reflection and reflection-in-and-on-action. This could be due to little guidance offered on developing reflective skills and its use by student teachers. This study's findings will be used to improve the rationality, social and educational practices among the student teachers.

Mathematical functioning in sub-Saharan Africa remains persistently weak in global terms. This limits the flourishing of young people and communities in the region. Moreover, affordable, effective ways to address the issue are not well established. This paper analyses outcomes from a blended learning ‘Mathematical Thinking and IT’ course, iteratively adapted for East African primary mathematics teacher educators. The course adopted theoretical approaches derived from the mathematics, teacher and technology education literatures. It aimed to address the problem of low mathematical functioning by equipping participants for their own work, and also for supporting local collaborative teacher development workshops. The reported study asked, ‘What are the affordances and constraints of the adapted course and the available technology for mathematics teacher educator development in this context?’A variety of qualitative tools were used to track the course’s impact on the ten mathematics teacher educator participants over six months, as they attempted to transfer course learning to their home professional context. The analysis adopted an ethnographic lens. Outcomes suggested participants with a broad mathematical and pedagogical capacity for change, including critical levels of reflection, made significant progress in their technological, mathematical and mathematics pedagogical expertise. However, teacher educators without such a threshold capacity appeared not able to re-envision practice. Free subject-specific software was appreciated by all participants, but not yet reliably accessible in these teacher educators’ institutional contexts. The reported study evidences the potential for affordable, sustainable, development of many mathematics teacher educators in this context, but further research is needed. Similar courses should take account of local technological and education constraints

Mathematics is a symbol of rationality and the highest intellectual achievements of human civilization. Mathematics has always been seen as abstract and formal knowledge. However, in the last few decades, the idea has emerged that mathematics is a knowledge that develops in human cultural activities. The concept of mathematics in culture is widely known as ethnomathematics. This paper aims to briefly describe the history, criticism, and challenges of ethnomathematics, the thoughts of ethnomathematics experts, and their influence in learning mathematics today. The development of ethnomathematics gave rise to a field of study covering aspects of anthropology and the history of mathematics, non-formal mathematics practice, traditional mathematics, and multicultural learning. Various research results indicate that ethnomathematics contributes to improving school mathematics. Although culture has an important role in learning mathematics, to integrate it requires comprehensive efforts to overcome various obstacles. Teachers need to improve competencies related to understanding local culture to maximize the transformation of ethnomathematics learning in the classroom.

Mathematics is an essential field of science applied in nearly all areas of knowledge and individuals’ daily lives. Therefore, understanding students’ attitudes towards it and affecting their mathematics performance is an essential step for appropriate intervention to make the subject enjoyable. This paper aims to give a comprehensive picture of students’ attitudes towards mathematics and factors that affect their attitude and achievement. To achieve this objective, purposive and random sampling techniques were used. A questionnaire measuring students’ attitudes and their achievement in the subject was distributed to sample students in secondary schools. Data were collected using a questionnaire that was validated, pilot tested, and its reliability was determined. The data were analyzed using descriptive statistics. Students were asked to respond to a 5-point Likert scale questionnaire that includes factors that affect the teaching practice, teachers’ attribution, classroom climate, and students’ concern as a contributing factor for their attitude towards mathematics. Besides, five free-response questions were also included to get an in-depth view of students towards mathematics. Results indicated that students have an almost positive attitude towards mathematics. Factors contributing to poor performance include lack of practice, language deficiency, societal influence, comprehensive content of the subject, lack of background on the course, development of examination in mathematics, absence of tutorial, the need for more recreation, and lack of confidence. Students’ attitude towards mathematics has determined students’ achievement directly as well as the perspective of students, and their achievements are interdependent.

Developing primary school students’ interest in and getting them motivated to learn mathematics has been a perennial focus of educators. The use of comics for classroom instruction is an area gaining more attention from educators. In this paper, we review some existing education literature on the impact of comics on students’ cognitive and affective learning needs. We also propose a TSCT (Theme, Storyline, Character, Text) framework for educators to design instructional material using comics for mathematics instruction in the primary mathematics classroom. With the TSCT framework, we demonstrate the design of one comics mathematics lesson on the topic of Fraction.

Jenis penelitian yang dilaksanakan dalam artikel ini adalah adalah deskriptif yang bertujuan untuk memberikan gambaran tentang kemampuan awal bernalar matematika mahasiswa, khususnya Universitas Negeri Medan, pada mata kuliah matematika diskrit. Subjek pada penelitian ini adalah mahasiswa semester IV pada program studi pendidikan matematika tahun akademik 2016/2017 yang berjumlah 45 orang. Pengumpulan data pada penelitian ini dilakukan dengan cara memberikan pretest kepada mahasiswa dengan waktu 15 menit dan wawancara. Wawancara dilakukan dengan tujuan mendapatkan informasi mengenai bagaimana mahasiswa menyelesaikan permasalah yang disajikan. Hasil dari pretest dan wawancara dijadikan bahan untuk menjawab masalah utama pada penelitian ini. Dalam hal ini, temuan penelitian mengemukakan bahwa kemampuan awal mahasiswa pada umumnya belum dapat membantu mereka memecahkan masalah-masalah graf bahkan sebagian mahasiswa tidak dapat menyelesaikan pertanyaan-pertanyaan yang disajikan. Dalam meyelesaikan permasalahan yang diberikan, beberapa mahasiswa cenderung melakukan metode trial and error, sedangkan yang lainnya menggunakan penjabaran penjabaran dengan kata-kata ataupun gambar. Kata kunci: analisis kemampuan awal, kemampuan bernalar (reasoning skills), graf, matematika diskrit. ABSTRACT This paper attempts to descibe descriptively towards a study which is conducted to provide an overview about college students’ initial reasoning skills, especially Universitas Negeri Medan, at Discrete Mathematics course. The implementation of this study involves 45 fourth-semester students of mathematics education program as the research subject. The data was collected by giving fifteen-minute pretest and conducting interview with the students. The interview aimed to acquire the information about how the students deal with the problems. The results of pretest and interview were laterly used to answer the main question of this study. In this case, the findings of this study show that the students’ initial understanding is not adequate to solve the problems about graph and some students leave the worksheet with no answer. In order to deal with the problems, students come up with trial and error method and others attempt to solve the problems with word description and pictures. Keywords: initial understanding analysis, reasoning skills, graph, discrete mathematics.

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with technological tools, describing and communicating information and ideas, developing ideas, and understanding improvement. This research describes students’ visual thinking ability to solve integral problems. The approach used in this study was descriptive qualitative. The subjects in this study were three students from the Department of Mathematics Education at the State Islamic Institute of Tulungagung. The data were collected by using tests and interviews. The steps to analyze the data were categorization, reduction, exposure, interpretation, and conclusion. Based on the analysis of students’ visual thinking skills in solving integral problems, there were three levels of visual thinking: semi-local visual, local visual, and global visual. At the semi-local visual level, students could only understand algebraically, and they have not shown it graphically at all. Meanwhile, at the local visual level, they have already understood geometry as an alternative language and been able graphically represented problems or concepts, even though it was not perfectly done yet. While on a global visual level, they could perfectly visualize visual thinking indicators, understand algebra and geometry as alternative languages for problem-solving, extract specific information from diagrams, graph problems, and use them to solve problems perfectly.

Studi ini bertujuan untuk mendeskripsikan algoritma berhitung pada transaksi jual-beli yang dilakukan Blijh (penjual sayur tradisional) dalam masyarakat Madura di Kabupaten Probolinggo, Indonesia. Studi ini merupakan studi kualitatif dengan pendekatan studi kasus. Data dikumpulkan dengan teknik observasi dan wawancara. Sumber data adalah 8 orang Blijh yang tinggal di Kecamatan Paiton, Kabupaten Probolinggo, Indonesia. Analisis data dilakukan dengan menggunakan model Miles Huberman, dengan tahapan analisis meliputi reduksi data, penyajia datam dan penyimpulan. Data yang diperoleh berupa data kualitatif yang menggambarkan beberapa algoritma berhitung yang terdiri dari penjumlahan, pengu­rangan, perkalian dan pembagian. Adapun dalam artikel ini akan fokus pada algoritma penjumlahan dan pengurangan. Hasil studi menunjukkan bahwa (1) algoritma berhitung penjumlahan dan pengurangan yang dilakukan oleh Blijh berbeda dengan algoritma yang diajarkan di sekolah; (2) dalam melakukan operasi penjumlahan dan pengurangan, cara yang berbeda yang digunakan oleh Blijh yaitu dengan menggenapkan bilangan pertama ke bilangan puluhan diatasnya, berbeda dengan cara yang diajarkan di sekolah, dimana cara yang digunakan yaitu cara bersusun panjang dan bersusun pendek. Hasil penelitian ini diharapkan dapat memberikan inspirasi dan alternatif dalam pembelajaran berhitung di kelas. Kata kunci: algoritma berhitung, Blijh, operasi bilangan, pendekatan pembelajaran Blijh’s arithmetic algorithm on Madurese society in Probolinggo Regency: An alternative approach in learning number operation Abstract The aim of this study was to describe arithmetic algorithm on transaction em­ployed by Blijh (traditional vegetables seller) in Madurese community at Probolinggo regency, Indonesia. The study was a qualitative approach by means of case study. The data were gathered through observation and interviews. The partisipants of this study were 8 Blijh living in Paiton, Probolinggo regency, Indonesia. The data were analyzed using Miles Huberman model, with analysis step consisting of data reduction, data display, and conclusion. The results of this study obtained some arithmatics algorithm of addition, subtraction, multipication, and division. This paper, however, will only focus on addition and subtraction algorithm. The data reveals that (1) arithmatic algorithm of addition and substraction which used by Blijh was different from the one taught at school; (2) In performing addition and substraction operations, the different method which used by Blijh namely replace the first number to tens above it, while the method that taught at school was using long and short-stacke method. The results of this study could be used as one of teaching and learning approach to develop numerical and mental calculation skills.

[English]: This paper describes how to develop a valid and reliable instrument for geometric creative thinking test based on the information processing taxonomy model. Using this model, geometry test can be classified in the level of creative thinking based on the information processing process of the mathematical knowledge they already have to solve problems according to the criteria at each hierarchical level. The development of the test instrument refers to Beyers (2011). A quantitative method was used to validate instruments through experts validation and instrument validation. The results showed that there was five geometry test that can be used to describe the student's creative thinking process at a different hierarchical level based on the information processing taxonomy. The results of this study can be a reference for teachers and other researchers to design mathematical test by paying attention to the hierarchical level of student's thinking abilities so that students with different abilities can solve problems which refer to their abilities. Keywords: Creative thinking,Geometry, Information processing taxonomy, Test design [Bahasa]: Artikel ini memaparkan tentang bagaimana menghasilkan instrumen yang valid dan reliabel untuk kemampuan berpikir kreatif geometris berdasarkan model taksonomi pemrosesan informasi. Dengan menggunakan model ini, soal geometri dapat diklasifikasikan dalam tingkatan berpikir kreatif siswa berdasarkan proses pengolahan informasi dari pengetahuan matematika yang telah mereka miliki untuk menyelesaikan masalah sesuai batas kriteria pada setiap tingkatannya. Pengembangan instrumen tes mengikuti langkah Beyers (2011). Metode kuantitatif digunakan untuk memvalidasi instrumen soal yang melalui tahap validasi ahli dan validasi instrumen. Hasil penelitian menunjukkan bahwa terdapat lima butir soal geometri yang dapat digunakan untuk mendeskripsikan proses berpikir kreatif siswa pada tingkatan hierarki yang berbeda berdasarkan model taksonomi pemrosesan informasi. Hasil penelitian ini dapat menjadi rujukan untuk guru maupun para peneliti lain untuk menyusun soal matematika dengan memperhatikan tingkatan hierarki kemampuan berpikir siswa agar siswa dengan berbagai kemampuan yang berbeda dapat mengerjakan soal sesuai dengan kemampuan yang mereka miliki. Kata kunci: Berpikir kreatif, Geometri, Taksonomi pemrosesan informasi, Desain tes

Dalam tulisan ini, didefinisikan subsemiring fuzzy dan menyelidiki sifat yang terkait. Selain itu, diperkenalkan konsep subsemiring yang diinduksi dari level subset. Akhirnya, karakteristik subsemiring fuzzy diperoleh. [In this paper, we define the notion of fuzzy subsemiring and investigate the related properties. Moreover, we introduce the idea of a subsemiring induced from the level subset. Finally, a characterization of a fuzzy subsemiring is obtained.]

Coronavirus 2019 (COVID-19), yang kasusnya dimulai di Cina, dalam kurun waktu dua bulan telah menyebar dengan cepat ke lebih dari 114 negara dan territorial. Pemahaman tentang dinamika penularan Covid-19 sangat penting untuk menentukan kebijakan dan strategi dalam pengobatan dan pengendalian penyebaran penyakit ini. Dalam makalah ini, disusun model matematika yang menggambarkan dinamika penularan penyakit menggunakan model matematika deterministik dengan menggunakan data penyebaran COVID-19 di Jakarta, Indonesia dari 3 Maret 2020, hingga 10 April 2020. Model berbentuk Sistem persamaan diferensial yang selanjutnya dilakukan analisis matematika dan simulasi numerik. Hasil simulasi menunjukkan bahwa tanpa intervensi, angka reproduksi penyebaran Covid-19 di Provisi Jakarta sekitar 1,658 dan jika Pembatasan Sosial Berskala Besar (PSBB) diimplementasikan, maka angka reproduksinya turun menjadi 1,40. Lebih lanjut, epidemi diperkirakan akan berakhir sekitar akhir November 2020 dengan kasus puncak pada pertengahan Juni 2020 dengan jumlah orang yang dikonfirmasi positif terinfeksi mencapai sekitar 9.000 jiwa. Dari hasil pemodelan ini, disimpulkan bahwa untuk meminimalkan penularan penyakit, perlu menerapkan kebijakan dan kontrol yang lebih ketat. [Coronavirus disease 2019 (COVID-19) which was initiated in China, has spread rapidly in more than 114 countries and territories over the last two months. An understanding of the dynamics of Covid-19 transmission is very important to determine policies and strategies in the treatment and control of the spread of this disease. In this paper, we formulated a mathematical model that describes the transmission dynamics of the disease using a deterministic mathematical model and the model is validated against data from Jakarta, Indonesia from March 3, 2020, to April 10, 2020. Mathematical analysis and numerical simulations are presented. We found that without intervention, the reproduction number is around 1.658 and the reproduction number declines to 1.40 if large scale social distancing is implemented. Furthermore, the end time of epidemic is predicted to be around the end of November 2020 with peak cases around mid-June 2020 and the number of confirmed infected individuals is around 9,000. To minimize the transmission of the diseases, it is necessary to enforce strict policies and controls.]

[Bahasa]: Artikel ini membahas kepraktisan dan keefektifan perangkat pembelajaran matematika sekolah menengah kejuruan (SMK) berbasis teori van Hiele dan berorientasi pada penalaran spasial. Perangkat pembelajaran berupa rencana pelaksanaan pembelajaran (RPP) dan lembar kegiatan siswa (LKS). Pengembangan perangkat pembelajaran dalam penelitian ini menggunakan model pengembangan ADDIE. Instrumen pengumpulan data terdiri dari lembar observasi keterlaksanaaan pembelajaran, lembar penilaian kepraktisan dari guru dan siswa, dan tes penalaran spasial. Subjek uji coba perangkat pembelajaran adalah 106 siswa dari tiga kelas di SMKN 2 Ngawi. Hasil penelitian menunjukkan bahwa perangkat pembelajaran matematika SMK menggunakan teori van Hiele berorientasi pada penalaran spasial praktis. Hal ini dapat dilihat dari respon guru dan siswa yang menyatakan bahwa perangkat dapat digunakan dalam pembelajaran di kelas. Selain itu, perangkat yang dikembangkan juga efektif dilihat dari persentase ketuntasan kemampuan penalaran spasial siswa mencapai 82% setelah menggunakan perangkat pembejalaran yang dikembangkan. Perangkat ini dapat menunjang kemampuan penalaran siswa karena menyediakan ilustrasi gambar dan bidang kartesius untuk memfasilitasi siswa berpikir spasial. Kata kunci: Perangkat Pembelajaran; van Hiele; Penalaran Spasial [English]: This paper discusses the practicality and effectiveness of mathematics instructional package for vocational school based on van Hiele theory and oriented to spatial reasoning. The learning package was developed using ADDIE’s model. The research instruments consisted of observation sheet, practicality assessment sheets from teachers and students, and spatial reasoning test. The tryout involved 106 students from three classes in SMKN 2 Ngawi. The result of research showed that instructional package of vocational school based on van Hiele theory is practical to use as can be seen from the teacher's and students’ responses. The instructional package was also considered to be effective because 82% of students passed the spatial reasoning test. The package provided figures illustration and Cartesian model that could support students’ spatial thinking. Keywords: Instructional Package; van Hiele; Spatial Reasoning

Tujuan dari penelitian ini adalah memperkenalkan konsep interior fuzzy subgrup (interior subgroup) dalam grup dan menyelidiki beberapa sifat yang terkait. [The aim of this paper is to introduce the notion of fuzzy interior subgroup (interior subgroup) in a group and investigate some related properties.]

The aim of the study reported upon in this paper is to explore the potential of the use of mobile technology for supporting math trail program. An explorative study was conducted in the city of Semarang in Indonesia involving 30 students of SMPN 10 Semarang. The study consisted of an introduction session, a math trail activity supported by the use of mobile phone app, and a debriefing session. Data were gathered by means of participatory observation, students' work, and interviews. Findings indicate that math trail programs supported by the use of mobile phones have promoted the engagement of students in mathematical activities. The use of mobile technology has the potential to support the program. Mobile app has been able to play a role in guiding students in math trail activities with features offered, such as: navigation features, help buttons, and direct feedback.

Pada umumnya teorema Napoleon diberlakukan pada segitiga. Dalam tulisan ini dibahas teorema Napoleon pada segienam, yaitu segienam yang memiliki tiga pasang sisi sejajar dan sama panjang dengan kasus segienam beraturan yang dibangun mengarah ke luar. Pembuktian pada teorema Napoleon ini dengan menggunakan konsep kesebangunan dan konsep trigonometri. Kata kunci: Teorema Napoleon, konsep kekongruenan, trigonometri. ABSTRACT Napoleon’s Theorem generally applies in triangle. This paper applied Napoleon’s Theorem in hexagons that have three pairs of parallel sides in same length and regular hexagons that are built outward. Provided proofs use the congruence and trigonometric concepts. Keywords: Napoleon’s Theorem, congruency concept, trigonometry.

ABSTRAK Kecemasan matematika adalah salah satu faktor yang mempengaruhi prestasi belajar matematika. Faktor tersebut dapat dipengaruhi oleh beberapa hal, baik berkaitan dengan faktor internal maupun faktor eksternal peserta didik. Dalam tulisan ini akan membahas tentang apa itu kecemasan matematika, indikator kecemasan matematika, dampak serta cara mengatasinya. Berdasarkan beberapa penelitian tentang kecemasan matematika, terlihat bahwa kecemasan matematika sangat berpengaruh negatif terhadap hasil belajar/prestasi belajar maupun berpengaruh terhadap kemampuan matematis peserta didik. Sebagai seorang guru atau calon guru juga harus mengurangi kecemasan matematika sehingga dapat mengurangi kecemasan matematika yang dimiliki oleh siswa. Sehingga pada saat memberikan pengajaran tidak terjadi kesalahan dalam penyampaian serta dapat mengurangi kecemasan matematika siswa. Seorang guru / pengajar harus mengerti tentang bagaimana indikator kecemasan matematika siswa, sehingga dapat mengatasi kecemasan matematika yang terjadi pada siswa. Kata kunci: kecemasan matematika. ABSTRACT Math anxiety is one of the factors that affect mathematics achievement. These factors can be influenced by several things, both with regard to internal factors and external factors learners. In this paper will discuss what it is about math anxiety, math anxiety indicators, impacts, and how to overcome them. Based on several studies of math anxiety, math anxiety appears that negatively affect the results of the teaching / learning achievement and influence to the mathematical abilities of learners. As a teacher or prospective teacher should also reduce math anxiety so as to reduce math anxiety owned by students. So that when giving instruction error does not occur in the delivery and may reduce students' mathematical anxiety. A teacher/tutors should understand how math anxiety indicator of students, so as to overcome math anxiety that occurs in students.at home. Keywords: math anxiety.

ABSTRAK Ada beberapa faktor yang mempengaruhi siswa dalam belajar, antara lain prestasi dan minat. Oleh karena itu guru harus dapat mengembangkan prestasi dan minat siswa untuk belajar matematika. Pembelajaran Kolaboratif Berbasis Masalah dapat menjadi salah satu cara yang bisa digunakan untuk meningkatkan prestasi dan minat siswa. Pembelajaran kolaboratif berbasis masalah merupakan gabungan antara Pembelajaran Berbasis Masalah yang dilaksanakan secara kolaboratif. Berawal dengan menggunakan masalah dalam kehidupan sehari-hari, pembelajaran kolaboratif berbasis masalah ini dimulai dengan (1) Formulate; (2) Share; (3) Listen; dan (4) Create. Tujuan utama dari karya tulisan ini ialah membahas mengenai prestasi belajar dan minat siswa dan bagamaina mengembangkannya melalui Pembelajaran Kolaboratif Berbasis Masalah. Kata kunci: pembelajaran kolaboratif berbasis masalah, minat. ABSTRACT There are something principal to push pupils to learn. two of these is interest. The teacher must be agent to develop the student’s interest and achievement to learn mathematics. Collaborative Problem Based Learning model can be optioned to improve the student’s interest and achievement. Collaborative Problem Based Learning is the combine of problem based learning approach which is done collaborativelly. Starting point with a problem in real world, Collaborative Problem Based Learning can do with structure: (1) Formulate individually; (2) Share; (3) Listen; (4) Create. The main purpose of this paper is to investigate about student’s interest and how to develop it through a collaborative problem based learning model Keywords: Interest, Achievement, Collaborative Problem Based Learning.

[Bahasa]: Penelitian ini bertujuan untuk mengungkap kecenderungan lintasan belajar mahasiswa dalam melakukan penelitian pendidikan matematika, khususnya dalam kemampuan mendesain, melaksanakan, dan mempublikasikan hasil penelitian, dengan menggunakan model pembelajaran berbasis riset. Metode yang digunakan adalah design research dengan 3 tahapan, yaitu preliminary design, teaching experiment, dan retrospective analysis. Penelitian ini mendeskripsikan bagaimana lintasan belajar yang dikembangkan memberikan kontribusi dalam menumbuhkan keterampilan meneliti pada 9 mahasiswa pendidikan matematika di STKIP Surya, dengan mendeskripsikan kegiatan dosen, mahasiswa, dan melihat hasil akhir pembelajaran, selama kurun waktu 5 bulan. Hasilnya, 2 orang mahasiswa mampu memenuhi semua indikator keterampilan meneliti sampai tahapan publikasi karya ilmiah dalam jurnal yang terindeks Google Scholar, 1 orang mahasiswa sampai tahapan penulisan hasil penelitian (skripsi), 2 orang mahasiswa sampai tahapan pembuatan proposal penelitian dan sudah diseminarkan, 3 orang mahasiswa sampai tahapan pembuatan proposal penelitian, dan 1 orang mahasiswa masih dalam tahapan mendesain suatu penelitian. Selain itu, penelitian ini juga memberikan gambaran faktor-faktor penyebab keberagaman hasil yang diperoleh mahasiswa selama proses pembelajaran. [English]: This study aims to reveal the tendency of students' learning trajectory in doing research in mathematics education, especially in the ability to design, implement, and publish the research result by using research-based learning model. The method used is design research with three phases, i.e., preliminary design, teaching experiment, and retrospective analysis. This study describes how the learning trajectory that was developed to contribute to enhancing the research skills of nine pre-service mathematics’ teacher at Surya College of Education with describing the activities of lecturer, students, and the final result of learning during five months. As a result, two students were able to meet all the indicators of research's skill until publishing a scientific paper in journals indexed by Google Scholar. One student was able to the stage of writing the research result (undergraduate thesis). Two students were able to the stage of making a research proposal and already seminar. Three students were able to the stage of making a research proposal. One student is still in the stage of research design. Besides, this study also illustrates the diversity of the factors that cause results obtained by students during the learning process.

[Bahasa]: Sejarah merupakan sumber pengetahuan. Sejarah memberikan informasi berharga terkait perkembangan di masa lampau yang mendukung kemajuan di masa sekarang. Dalam hal ini, sejarah matematika juga memberikan pengetahuan bagaimana konsep matematika berkembang. Sejarah matematika menjelaskan, sebagai contoh, bagaimana al-Khwarizmi mengembangkan metode kuadrat sempurna dalam menyelesaikan persamaan kuadrat. Melalui sejarah matematika, kerja keras para matematikawan dalam menemukan dan mengembangkan suatu konsep atau penyelesaian suatu permasalahan bisa menjadi kisah inspiratif. Pengetahuan yang diperoleh melalui sejarah matematika sangat bermanfaat untuk digunakan dalam pembelajaran. Tulisan ini mencoba menjawab kenapa dan bagaimana penerapan sejarah matematika dalam pembelajaran melalui kajian pustaka (library research). Referensi terkait berupa ebook, artikel jurnal online dan proceedings konferensi dianalisis dengan memfokuskan pada dua hal, yaitu: manfaat sejarah matematika dalam membangun sikap positif siswa terhadap matematika; dan cara menerapkan sejarah matematika dalam pembelajaran matematika di Indonesia. [English]: History is a source of insight. History gives valuable information regarding the development in the past which contributes to the advance nowadays. In this case, the history of mathematics (HoM) also provides knowledge on how mathematics concept developed. The history of mathematics explains, for example, how al-Khwarizmi developed one of the methods in solving a quadratic equation. In the history of mathematics, how mathematicians worked hard in inventing and developing a concept or a solution upon a mathematics problem can be inspired story. Insight from the history of mathematics can be very useful for learning mathematics. This paper tries to answer why and how the use of history of mathematics in mathematics learning through library research. References consist of e-books, online journal articles and conference proceedings are thoroughly analyzed focusing on two cases, i.e. how the history of mathematics builds positive attitude of students toward mathematics; and how it can be implemented in Indonesia mathematics classroom.

Treynor Ratio merupakan model pioner inovatif ukuran kinerja saham yang dikemukakan Jack Treynor pada tahun 1965 yang terdiri atas 3 (tiga) komponen, yaitu return saham, return bebas risiko, dan beta saham. Banyak penelitian mendekati return bebas risiko dengan suku bunga termasuk saat mengukur kinerja saham syariah, sedangkan suku bunga dilarang dalam konsep keuangan islam. Tulisan ini membahas variabel alternatif untuk mendekati return bebas risiko selain dengan suku bunga (BI-Rate), yaitu dengan 4 (empat) pendekatan, yaitu: menghilangkan suku bunga, mengganti dengan zakat rate, mengganti dengan inflasi, dan mengganti dengan gross domestic produc (GDP) pada model Treynor Ratio yang diimplementasikan pada pasar modal syariah di Indonesia periode Januari 2011-Juli 2018. Hasil yang diperoleh adalah terdapat kesesuaian yang sangat tinggi hasil pengukuran model Treynor Ratio dengan suku bunga dengan keempat model lainnya. Namun, model-model tersebut tidak menjamin bahwa saham yang memilki kinerja terbaik pada saat ini akan memilki kinerja terbaik dimasa yang akan datang atau sebaliknya. Dilihat dari kedekatan hasil pengukuran kinerjanya, kelima model Treynor Ratio tersebut dapat dikelompokan jadi 2 (dua), yaitu model dengan suku bunga, model dengan inflasi, dan model dengan GDP sebagai kelompok pertama, sedangkan model tanpa suku bunga dan model dengan zakat-rate sebagai kelompok kedua. [Treynor Ratio is an innovative pioneer model the size of stock performance proposed by Jack Treynor in 1965 which consists of 3 (three) components, namely stock returns, risk free returns, and stock beta. Many studies approach risk-free returns with interest rates, including when measuring the performance of Islamic stocks, while interest rates are prohibited in the concept of Islamic finance. This paper discusses alternative variables to approach risk-free returns other than interest rates (BI-Rate), namely with 4 (four) approaches, namely: eliminating interest rates, changing zakat rates, changing inflation, and substituting gross domestic products (GDP) in the Treynor Ratio model that is implemented in the Islamic capital market in Indonesia for the period January 2011 - July 2018. The results obtained are very high conformity in the measurement results of the Treynor Ratio model with interest rates with the other four models. However, these models do not guarantee that stocks that have the best performance at this time will have the best performance in the future or vice versa. Judging from the closeness of the results of performance measurement, the five Treynor Ratio models can be grouped into 2 (two), namely models with interest rates, models with inflation, and models with GDP as the first group, while models without interest rates and models with zakat-rate as second group.]

Dalam makalah ini, akan diperkenalkan notasi image (pre-image) di bawah homomorfisma grup, dan akan dibuktikan image (pre-image) interior subgrup fuzzy (interior subgrup) di bawah homomorfisma grup selalu interior subgrup fuzzy (interior subgrup). [In this paper, we will introduce the image (pre-image) under the group homomorphism, and we will prove the image (pre-image) of the interior of the fuzzy subgroup (the interior of the subgroup) under the group homomorphism is always the interior of the fuzzy subgroup (the interior of the subgroup).]

Abstract: The need for variations in learning resources for students of SMK Diponegoro Tumpang and the development of 2 stcentury technology are the basis of this development research. The purpose of this paper is to describe the development of valid, practical and effective learning media for combinatoric material. This development uses the ADDIE model. The test subjects in the development of learning media consisted of expert validators, practitioner validators, observers, 5 students of class XII as group trials, and 22 students of class XII KPR as field trials. The instruments used were learning media, lesson plans, observation sheets, student response questionnaires, and teacher response questionnaires. The results of the development state that learning media are valid, practical, and very effective. Abstrak: Kebutuhan variasi sumber belajar bagi siswa SMK Diponegoro Tumpang dan perkembangan teknologi abad 21 merupakan dasar dari penelitian pengembangan ini. Tujuan penulisan ini adalah mendeskripsikan pengembangan media pembelajaran materi kombinatorika yang valid, praktis, dan efektif. Pengembangan ini menggunakan model ADDIE. Subjek uji coba dalam pengembangan media pembelajaran ini terdiri dari validator ahli, validator praktisi, observer, 5 siswa kelas XII sebagai uji coba kelompok, dan 22 siswa kelas XII KPR sebagai uji coba lapangan. Instrumen yang digunakan adalah media pembelajaran, RPP, lembar observasi, angket respon siswa, dan angket respon guru. Hasil pengembangan menyatakan bahwa media pembelajaran valid, praktis, dan sangat efektif.

Makalah ini membahas tentang model matematika dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Dengan mengacu pada model pertumbuhan ekonomi endogen pada suatu negara, dengan fungsi output berbentuk fungsi Cobb-Douglas akan diturunkan model matematika yang mendeskripsikan dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Selanjutnya, akan dikonstruksikan pula fungsi ongkos yang berhubungan dengan model matematika yang telah diturunkan. Mengingat model matematika tersebut masih dalam bentuk sistem persamaan nonlinear, maka diperlukan proses linearisasi untuk menghasilkan model matematika yang linear sehingga memudahkan untuk dianalisis maupun diaplikasikan. [This paper discusses the mathematical model of the impact of climate change on the macroeconomic conditions of a country. By referring to an endogenous economic growth model in a country, with the output function in the form of a Cobb-Douglas function, a mathematical model will be described that describes the effects of climate change on the macroeconomic conditions of a country. Furthermore, it will also construct cost functions related to mathematical models that have been derived. Considering that the mathematical model is still in the form of a nonlinear equation system, a linearisation process is needed to produce a linear mathematical model that makes it easy to analyze and apply.]

Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan. [The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]

Ebola is a deadly disease caused by a virus and is spread through direct contact with blood or body fluids such as urine, feces, breast milk, saliva and semen. In this case, direct contact means that the blood or body fluids of patients were directly touching the nose, eyes, mouth, or a wound someone open. In this paper examined two mathematical models SIRD (Susceptibles-Infected-Recovery-Deaths) the spread of the Ebola virus in the human population. Both the mathematical model SIRD on the spread of the Ebola virus is a model by Abdon A. and Emile F. D. G. and research development model. This study was conducted to determine the point of disease-free equilibrium and endemic equilibrium point and stability analysis of the dots, knowing the value of the basic reproduction number (R0) and a simulation model using Matlab software version 6.1.0.450. From the analysis of the two models, obtained the same point for disease-free equilibrium point with the stability of different points and different points for endemic equilibrium point with the stability of both the same point and the same value to the value of the basic reproduction number (R0). After simulating the model using Matlab software version 6.1.0.450, it can be seen changes in the behavior of the population at any time.

This paper discusses the basic concepts and some of semicontinuous function, begins by introducing the concept of upper limit and lower limit.

Dislocated quasi metric spaces is spaces with distance function that only satisfies two conditions from four conditions of distance function in metric spaces. Every metric spaces is dislocated quasi metric spaces, but the convers not satifies, so the characters that satisfies in metric spaces may not satisfies in dislocated quasi metric spaces. This paper is to recite fixed point theorems without continuity of any mapping in dislocated quasi metric spaces, also gives an example using the theorems that has recited

According to the National Science Education Standards, teachers should emphasize students’ interests, needs, experiences, inquiry, collaboration and understanding in their classrooms. One of the characteristics of inquiry is using scaffolding. Because of the benefits, it is important to investigate the effect of scaffolding on achievement in mathematics. Based on some relevant previous studies, scaffolding can be used to support better achievement in mathematics. In scaffolding, teacher’s guidance decreases gradually and student’s autonomy increases gradually. By giving guidance, teacher revises student’s misconceptions; while by giving autonomy, teacher supports student’s motivation in learning. Minimizing misconceptions and maximizing motivation can lead students to better achievement in mathematics. Many studies in this paper emphasize the importance of teachers' contribution in giving scaffolding to their students. Further research should be conducted to investigate the role of other people surrounding the students, such as parent and peer, in supporting effective scaffolding. Keywords: scaffolding, achievement in mathematics, misconceptions, motivation

Polio (Poliomielitis) is an infectious disease caused by the polio virus. This disease attacks the entire body (including the muscles and nerves) and can lead to muscle weakness that is permanent, paralysis or death. This paper will discuss on the influence of vaccination against polio disease spread in the human population that settled in the form of mathematical modeling.

One of the mathematics learning purposes is using reasoning in patterns and properties, mathematical manipulation in making generalization, compiling evidence, or explaining mathematical ideas and statements. Mathematical learning based on behaviorism has been seen as less successful in instilling character of mathematics reasoning. Therefore, it is necessary to find alternative learning not only teaching but instilling character of mathematical reasoning. This paper offers constructivist in mathematics learning, which is one of the ways to involve the use of inductive-deductive thinking. Activities that involve students learning to use the inductive-deductive mindset needs to be designed and implemented by teachers. Using inductive thinking can be conditioned, especially in the process of understanding a concept or generalization. Deductive thought patterns can be conditioned to improve mathematical reasoning, for example, in the proofing. The mindset of inductive and deductive mathematical reasoning is difficult to separate in the mathematical reasoning therefore it is regarded involving the use of inductive-deductive thinking.

In this paper geometric algebra and its aplication in the theory of classical electrodynamic will be studied. Geometric algebra provide many simplification and new insight in the theoretical formulation and physical aplication of theory. In this work has been studied aplication of geometric algebra in classical electrodynamics especially Maxwell’s equations. Maxwell’s equations was formulated in one compact equation ÑF=J. The various equation parts are easily identified by their grades.

In this paper the observability of continuous descriptor system of the form Ex(t)= Ax(t) Bu(t), x(0)=x0 will be studied, where E,A, and B are constant matrices that may be singular and u(t) is piecewise continuous function which is differentiated (m-1) times, where m is the degree of nilpotency system. Two definitions about observability of descriptor systems along with their characterizations given by Dai and Yip will be both discussed, then further the relationship and comparison between these characterizations will be presented.

Since the signed memorandum of understanding between BAPEPAM with Dewan Syariah Nasional-Majelis Ulama Indonesia (DSN-MUI) on the principle of Islamic capital market in 2003, the Islamic capital market in Indonesia has developed significantly. In each investment, including Islamic capital market investment, there are 2 (two) fundamental things that always accompany it, the return and risks. This paper discusses the analysis of return and risk of sharia stocks that always go in Jakarta Islamic Index (JII) after the global crisis in 2008, risk analysis tools using Value at risk (VaR) approach to model the Generalized Autoregressive Conditional Heteroscedastic (GARCH), then proceed with the analysis of the typology to determine the characteristics of these stocks. The results that shares sharia can be grouped into 4 (four) : 6 (six) shares entering the low return and low risk (TLKM, UNVR, SMGR, AALI, ELSA, and SGRO), 3 (three ) shares into group of low-return but high risk (INCO, ANTM, and TINS), 3 (three) shares enter the group of low risk but high return (PTBA, LSIP, and KLBF), and 4 (four) shares enter the group high return but high risk (ITMG, ASII, INTP, and BMTR).

Permasalahan sistem persamaan linear banyak dijumpai dalam persoalan ilmu pengetahuan dan teknologi, seperti pada penyelesaian numerik persamaan diferensial biasa, diferensial parsial, analisis jaringan dan sebagainya. Ukuran yang besar dan bilangan yang terlibat dalam matriks seringkali menjadi kendala dalam menyelesaikan secara analitik. Penyelesaian secara numerik adalah salah satu alternatif yang dapat dilakukan. Dalam mengembangkan kearah numerik, algoritma dibangun dengan konsep aljabar, agar mampu digunakan dalam menyelesaikan sistem persamaan linear secara umum. Dalam paper ini dibahas bagaimana mengkonstruksi algoritma dari bentuk aljabar linier ke perhitungan numerik.

In this Paper introduced a coring from tensor product of bialgebra. An algebra with compatible coalgebrastructure are known as bialgebra. For any bialgebra B we can obtained tensor product between B anditself. Defined a right and left B -action on the tensor product of bialgebra B such that we have tensorproduct of B and itself is a bimodule over B. In this note we expect that the tensor product B anditself becomes a B -coring with comultiplication and counit.Keywords : action, algebra, coalgebra, coring.

AbstrakPenelitian mengenai penyebaran HFMD pertama dilakukan menggunakan model SIR. Pada model ini,populasi individu yang sebenarnya telah terinfeksi tetapi belum menunjukkan gejala-gejala penyakit tidakdijelaskan. Dalam paper ini akan dibahas mengenai pembentukan model matematika dari penyebaranpenyakit HFMD menggunakan model SEIRS. Adanya penambahan kelas populasi E (Exposed) untukmelengkapi kekurangan pada model sebelumnya. Berdasarkan model, diperoleh titik ekuilibrium bebaspenyakit dan endemik. HFMD tidak akan mewabah jika R0 1. Selanjutnya dilakukan simulasimenggunakan MAPLE 13.