Tujuan penelitian ini adalah untuk mengetahui kontribusi aspek-aspek matematika pada sumur purbakala, sejarahnya, proses berpikir matematis dalam pembuatan sumur, dan proses pembelajaran matematika di sekolah. Hasil penelitian ini disajikan dalam bentuk kualitatif untuk mendeskripsikan tentang sejarah sumur purbakala. Bentuk bangunan sumur menggambarkan sebuah bangun datar seperti segitiga, segilima, persegi panjang, jajar genjang, trapesium, lingkaran, dan bangun ruang seperti balok dan tabung, yang merupakan aspek-aspek matematika pada materi geometri. Proses pembuatan sumur yang berbentuk lingkaran dapat dilakukan dengan segi-n yang didekati oleh limit n menuju tak hingga yang dilihat dari banyaknya batu bata pada susunan pertama dan banyaknya susunan pada pembuatan sumur. Hasil penelitian ini juga berkaitan dengan proses pembelajaran matematika di sekolah, seperti materi segitiga dan segiempat di SMP serta aturan sinus dan cosinus di SMA. Diharapkan hasil penelitian ini dapat dijadikan bahan ajar pada jenjang sekolah menengah ataupun referensi untuk penelitian lain di bidang budaya dan matematika. Ethnomathematics at the sumur purbakala Kaliwadas Village of Cirebon and relationship with mathematics learning in school AbstractThe purpose of this research is to know the mathematical aspects of sumur purbakala, its history, the process of mathematical thinking in the making of well, and the process of learning mathematics in school. The results of this research are presented in qualitative form to describe the history of the sumur purbakala. The shape of the building is constructed like a triangle, a pentagon, a rectangle, a parallelogram, a trapezoid, a circle, and a space-building like beams and tubes, which are the mathematical aspects of the material geometry. The process of making a well in the form of a circle can be done with the n-segments approximated by the boundary n to the not until seen from the number of bricks in the first order and the number of arrangements on the well-making. The results of this study are also related to the process of learning mathematics in schools, such as triangle and quadrilateral materials in junior high and the rules of sinus and cosine in high school. It is expected that the results of this study can be used as teaching materials at the level of the school and references to other research in the field of culture and mathematics.
This research motivated by the low of students' mathematical problem-solving ability and the utilization of learning media based on technology that was not maximum. Preparation of learning materials in the form of the interactive digital module was one of the ways can overcome that problem. The method that used in this research was RnD with the design model ADDIE that was analysis, development of implementation design and evaluation with the restrictions of not doing the implementation stage. The instrument of collecting data in this research was the form of validation and the form of practicalities of the user senior high school students that has to get the material of linear inequality absolute value. The data that was taken though with statistics descriptive way. The validation result of the digital module gets ratings in the amount of 83,33% from media expert and 85,57% from a material expert. This interactive digital module was decent to use and very practical with the average percentage for students' high cognitive ability 88,77%, medium 89,49%, and low 82,97%. Whereas the other user that was mathematics teacher give the percentage 84,78% so, according to them this digital module was very practical. ABSTRAK Penelitian ini dilatarbelakangi oleh rendahnya kemampuan pemecahan masalah matematis siswa dan pemanfaatan media pembelajaran berbasis teknologi yang belum maksimal. Salah satu cara yang dapat mengatasi masalah tersebut adalah dengan cara membuat bahan ajar berupa modul digital interaktif. Metode penelitian yang digunakan adalah RnD dengan model desain ADDIE yaitu analisis, desain, pengembangan, implementasi dan evaluasi dengan pembatasan tidak melakukan tahap implementasi. Instrumen pengumpulan data dalam penelitian ini adalah lembar validasi serta lembar praktikalitas pengguna siswa sekolah menengah atas yang telah mendapatkan materi pertidaksamaan nilai mutlak sebelumnya. Data yang telah diambil, diolah dengan cara statistika deksriptif. Hasil validasi modul digital mendapatkan dengan penilaian sebesar 83,33% dari ahli media dan 85,57% dari ahli materi. Hasil praktikalitas memperoleh rata-rata presentase untuk siswa berkemampuan kognitif tinggi 88,77%, sedang 89,49% dan rendah 82,97%. Sedangkan guru matematika memberikan presentase sebesar 84,78%.
Kemampuan mahasiswa dalam melakukan pembuktian matematis tidak sama bergantung dari kategori kognitifnya. Salah satu metode pembuktian matematika adalah induksi matematika yang memerlukan pemahaman konsep secara sistematis. Tujuan penelitian adalah untuk mengetahui kemampuan pembuktian matematis mahasiswa yang memiliki kategori kognitif tinggi dan rendah menggunakan induksi matematika. Subjek penelitian ini adalah empat orang mahasiswa tingkat tiga Program Studi Pendidikan Matematika dengan klasifikasi dua orang mahasiswa memiliki kemampuan kognitif tinggi dan dua mahasiswa berkemampuan rendah. Instrumen penelitian yang digunakan adalah lembar tes materi induksi matematika dan pedoman wawancara. Penelitian ini merupakan penelitian deskriptif yang mendeskripsikan kemampuan pembuktian matematis mahasiswa dalam menyelesaikan soal terkait induksi matematika disesuaikan dengan kemampuan kognitif tinggi dan rendah. Hasil penelitian menunjukkan bahwa mahasiswa dengan kategori kognitif tinggi mampu menyelesaikan setiap langkah pembuktian secara benar namun belum sistematis, sedangkan yang berkemampuan kognitif rendah tidak memahami alur pembuktian pada langkah induksi, kekeliruan memahami sifat distributif, dan ketidakteraturan menghubungkan setiap langkah pembuktian. Melalui artikel ini, peneliti berharap dapat menganalisis perlakuan yang tepat pada mahasiswa saat mengajar berbagai materi matematika yang menggunakan prasyarat induksi matematika. Kata kunci: pembuktian matematis, induksi matematika, kemampuan kognitif. ABSTRACT The students’ ability to perform mathematical proof is different depending on their cognitive category. One of mathematical proofing is mathematical induction which requires concepts understanding systematically. The purpose of this research is to know the ability of mathematical proof using mathematical induction of high and low cognitive category students. The subjects of this study are four third graders of Mathematics Education Study Program. Two students have high cognitive ability and the others have low cognitive ability. The mathematical induction material test sheet and interview guideline are used as research instruments. This is a descriptive research which describes the mathematical proof ability of students in solving problems related to mathematical induction adjusted with high and low cognitive ability. The results show that students with high cognitive category are able to complete each step of proof correctly but not systematically. At the same time, the students with low cognitive ability are not understand the proof steps at the induction step, the misunderstood the distributive property, and the irregularity connect the proof steps. The researcher expects to analyze the appropriate treatment to the students while teaching mathematical materials using mathematical induction prerequisites. Keywords: mathematical proof, mathematical induction, cognitive ability.
This study analyzes some hard skills (problem-solving abilities, level of logical thinking, and geometric thinking) and soft skills (students' self-concept and mathematical habits of mind) mathematics education students explicitly in the first year. The research method used is descriptive quantitative. From the population of all mathematics education students in the first year, one group of students was selected as a random sample using analysis techniques, data presentation, and conclusion drawing. Based on the research results, mathematics education students' overall ability in the first year is already good. Students were mastering five reasoning on the test of logical thinking (TOLT). It means they have solved problems with reasoning associated with proportional or ratio, control variables, probability, correlation and combinatorics. Most students have reached the level of thinking geometry at the analysis stage; that is, students have already understood the properties of concepts or geometry based on informal analysis of parts and component attributes. However, students do not have good soft skills. Even though they have a strong habit of mind, students' selfconcept is quite sufficient.
Keraton comes from the ancient Javanese language, namely the word keratuan showing place information, namely to reside in the king or the residence of the king. The king as head of government resides in the palace which is made the centre of the kingdom and all political, economic, social and cultural activities. High-ranking royal officials and nobles also lived in the vicinity. Because almost all community activities are centred around the palace, it develops into a city. The Keraton Kanoman was built in 1588 M by prince Muhamad Badarudin Kertawijaya who held the title Sultan Anom I. He set up his Keraton at the house of Prince Cakrabuana when he had just arrived at the tegal Alang-Alang called Witana. Titimangsa year the founding of the Keraton Kanoman is written in an image at the entrance of the Keraton Kanoman Jinem, which describes the sun means one, wayang Darma Kusuma which means five, the earth means one, and an animal which means zero. The Candrasangkala shows the numbers in 1510 Saka or 1588 M. So the Keraton Kanoman was founded in 1510 Saka or 1588 M. This study aims to reveal fractal geometry in the Keraton Kanoman complex which is seen in aspects of fractal dimensions of the building form. Fractal dimension analysis uses the boxcounting method to determine the level of roughness of buildings in the Keraton Kanoman complex by sketching several scales. This research method is ethnography and the type of research is qualitative descriptive. The data collection technique is done by interview, observation and documentation. The results showed that the shape of the building from the Lawang seblawong, Balai manguntur, and gapura Barat had fractal dimension depth with a fairly high level of roughness. Consequently, the details of the structure are classified as high.
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