This study aims to identify the potential learning opportunities provided by ancient china’s geometric diagram introduced by Liu Hui into student task in learning Pythagorean theorem. We investigate the role of the history-based task, from Nine Chapter, in supporting students’ mathematics literacy and geometrical reasoning. Design research was chosen as a method to reach the purpose. Our discussion is limited only from a part of one phase, namely pilot experiment, from three main phases of design research. This research was conducted at three different Junior High schools in Indonesia. The instructional activities were designed based on history-based problem-solving. The analysis was focused on students’ learning process, and specifically, the results of their visual reasoning and mathematical literacy. The result indicated that the use of figures or diagrams, with written information act as a support for performing algebraic calculations for students who are unfamiliar using symbol or algebraic operation. In this way, by using geometric manipulation, a new figure is arrived at on which the solution can now be read easier. Furthermore, by using history-based context, students got more opportunities to improve their performance in mathematics literacy by formulating various contextual mathematics problem, sourced from history, into mathematical form.
This study aims to develop a social arithmetic learning design by integrating Islamic economic principles. Using various Islamic financial products as a context in mathematical tasks, we propose a hypothetical learning trajectory (HLT) to support the students' Islamic financial literacy (IFL) skills. We chose design research as the method to achieve the goal. However, we limit the discussion to a part of one phase, namely pilot experiments, of the three main phases of design research. This study involves six students at Islamic junior high school. The design consists of several activities that require students to solve mathematics-based Islamic financial literacy tasks. These tasks contain IFL knowledge, including money and shariah transaction, planning and managing finance using shariah product, risk, and reward of shariah finance product, and a landscape of shariah finance. We develop an instructional design by adapting the process domain of the OECD financial literacy by adjusting based on the principles of Islamic economics. In general, the stages of learning activities are identifying Islamic financial information, analyzing information in an Islamic financial context, and applying Islamic financial knowledge and understanding. At each of these stages, students are faced with problems that focus on each process domain. The results show that this design can bring out some fundamental mathematical capabilities and support the students' IFL. Furthermore, by infusing Islamic financial literacy in mathematics education, we get an opportunity to create a caring young generation on the development of Indonesian Islamic economics.
In this article, we explore how History of the Pythagorean theorem, especially from ancient China, as a source of inspiration for learning design. Based on historical examples and problem solving from the history of mathematics, we try to arrange instructional tasks for seventh-grade secondary education students and how its role in supporting students’ understanding of Pythagorean theorem. We focus on explaining the preliminary studies or the first phase of the three main phases in design research. The basic idea of instructional design is to introduce historical geometric diagrams and solve the right triangle problem in the manner of Liu Hui (3rd century CE). The purpose of introducing geometric diagrams is to connect students’ symbolic algebraic thinking with visual thinking about geometric shapes especially in the case of right triangles. In this study, we also conducted interviews and debrief sessions with teachers and tested the student’s history-based tasks to several students for initial investigation in the matter of developing the Hypothetical Learning Trajectory. Results of this study show that teachers have a positive response toward the history-based instructional task developed. On the other hand, we find the resolution of Right Triangles problems with diagrams by the students involving three steps: translation, transformation, and diagrammatic reasoning.
Sarana pendukung dalam proses pembelajaran submateri nilai rasio sudut istimewa trigonometri adalah media pembelajaran, mengajak siswa bermain sambil belajar merupakan upaya menciptakan situasi belajar yang menyenangkan, hidup, dan santai dalam proses belajar siswa. Tujuan dari penelitian ini yaitu untuk mendeskripsikan proses dan hasil pengembangan media pembelajaran permainan “Karjo Suwatri” (Kartu Jodoh Sudut Istimewa Trigonometri). Jenis Penelitian ini adalah penelitian pengembangan dengan model pengembangan Dick dan Carry. Subjek ujicoba pada penelitian pengembangan media berupa “Karjo Suwatri” adalah siswa SMK Kemala Bhayangkari 1 waru dan siswa SMK Informatika Sumber Ilmu Tulangan. Penelitian dilakukan pada tahun ajaran 2018/2019 Semester Gasal. Tahapan pengembangan dalam penelitian ini yaitu Analysis, Design, Development, Implementation, dan Evaluation. Penilaian dari validator diperoleh rata-rata skor total yaitu 3,55 atau termasuk dalam kategori valid. Penilaian dari observer menunjukkan persentase aktivitas siswa adalah 85% tercapai atau termasuk dalam kategori praktis. Persentase respon siswa adalah 86,5% atau termasuk dalam kategori sangat positif serta 86,67% siswa memperoleh nilai tuntas atau 39 dari 45 subjek mendapatkan nilai 70. Berdasarkan hasil penelitian tersebut media pembelajaran permainan “Karjo Suwatri” dapat dikatakan valid, praktis dan efektif.
Penelitian deskriptif kualitatif ini bertujuan untuk mendeskripsikan hasil analisis kesalahan siswa SMK dalam menyelesaikan soal matematika materi sistem persamaan linier tiga variabel. Penelitian ini dilakukan di SMK Persatuan 1 Tulangan pada tahun ajaran 2019/2020 di kelas X-Tata Busana. Subjek dipilih berdasarkan banyaknya kesalahan yang dilakukan dalam menyelesaikan soal. Adapun teknik pengumpulan data dalam penelitian ini menggunakan metode tes dan wawancara. Tes dilakukan kepada semua siswa di kelas X-Tata Busana. Dari hasil tes soal diambil subjek yang memiliki kesalahan terbanyak. Selanjutnya subjek yang terpilih diwawancara. Hasil tes dan wawancara dianalisis dengan menggunakan analisis kesalahan Newman yaitu kesalahan membaca, kesalahan memahami, kesalahan mentransformasi, kesalahan dalam keterampilan proses dan kesalahan pada jawaban akhir. Berdasarkan penelitian dengan menggunakan analisis Newman dapat disimpulkan bahwa siswa melakukan kesalahan membaca dengan bentuk kesalahan tidak dapat membaca kata-kata penting yang ada dalam soal, siswa melakukan kesalahan memahami dengan bentuk kesalahan tidak dapat menuliskan yang diketahui dan ditanyakan dan menuliskan tetapi salah, siswa melakukan kesalahan mentransformasi dengan bentuk kesalahan tidak dapat membuat model matematika, siswa melakukan kesalahan keterampilan proses dengan bentuk kesalahan tidak dapat menyelesaikan soal dan prosedur tidak sesuai, dan siswa melakukan kesalahan pada jawaban akhir dengan bentuk kesalahan menuliskan jawaban salah dan tidak menuliskan jawaban.
Abstrak Representasi matematis digunakan siswa ketika menghadapi soal matematika yang harus mereka selesaikan. Hal ini karena representasi matematis merupakan bentuk ungkapan ide yang ditampilkan siswa dalam bentuk yang beragam dalam situasi tertentu sebagai upaya menemukan solusi dari soal yang dihadapi. Rendahnya pemahaman siswa terhadap soal yang diberikan kemungkinan besar disebabkan oleh siswa yang tidak mampu menggunakan reprentasi matematis dengan benar. Penelitian ini merupakan penelitian deskriptif dengan pendekatan kualitatif yang bertujuan untuk mendeskripsikan representasi matematis siswa SMP, khususnya siswa berkemampuan tinggi dalam menyelesaikan soal matematika. Subjek penelitian ini merupakan salah satu siswa kelas VIII SMP 10 Nopember Sidoarjo yang dipilih berdasarkan tes kemampuan matematis. Hasil deskripsi data menunjukkan bahwa dalam menyelesaikan soal, siswa berkemampuan matematika tinggi cenderung menggunakan representasi visual untuk menyelesaikan masalah, membuat persamaan matematis atau ekspresi matematis, serta menjawab permasalahan dengan menggunakan kata-kata atau teks tertulis dengan hasil penyelesaian soal sebagian besar benar. Abstract Mathematical problems that they must solve. This is because mathematical representation is a form of expression of ideas displayed by students in various forms in certain situations in an effort to find solutions to the problems faced. The lack of students' understanding of the questions given is most likely due to students who are not able to use mathematical representation correctly. This research is a descriptive study with a qualitative approach that aims to describe the mathematical representation of junior high school students, especially students with high ability in solving math problems. The subject of this research is one of the eighth grade students of SMP 10 November Sidoarjo selected based on a mathematical ability test. The results of the data description show that in solving problems, students with high mathematical abilities tend to use visual representations, make mathematical equations or mathematical expressions, and answer problems by using written words or text with the results of solving problems mostly correct.
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