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A didactical design for introducing the concepts in algebraic forms using the theory of praxeology Nadya Syifa Utami; Sufyani Prabawanto; Nanang Priatna
Beta: Jurnal Tadris Matematika Vol. 15 No. 1 (2022): Beta May
Publisher : Universitas Islam Negeri (UIN) Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20414/betajtm.v15i1.508

Abstract

[English]: This phenomenological study aims to thoroughly investigate the meaning of concepts in algebraic forms developed by students, both in the past learning process and in the didactical design implementation, as well as a teacher's instructional experiences as the basis for preparing a didactical design. Six seventh-grade students and a mathematics teacher participated in the study, comprising three phases: (1) analyzing students’ learning obstacles through a test and teacher’s interview, (2) preparing hypothetical learning trajectory (HLT) and didactical design based on the identification of the obstacles and in-depth interviews with the teacher, and (3) implementing the didactical design. This study revealed that students have a didactical obstacle because the teacher delivers formal definitions of algebraic form concepts followed by examples of problems. It results in epistemological obstacles, as students' understanding of the concepts is limited according to what the teacher explains. Furthermore, an HLT was developed that bridges students' arithmetic knowledge with algebra. The series of tasks were organized referring to the theory of praxeology by taking the daily-life context Let's Save. During the learning process, students use different representations, such as symbols and letters, to demonstrate the variable, reason for using a particular representation, and state the definition of a variable based on their work. The procedure was also applied to the remaining four concepts. Through the tasks, students can actively construct their conceptual understanding of the concepts in the algebraic forms. [Bahasa]: Penelitian fenomenologi ini bertujuan untuk mengkaji secara mendalam pemaknaan siswa terhadap konsep-konsep dalam bentuk aljabar, baik pada proses belajar sebelumnya maupun pada implementasi desain didaktis, serta pengalaman mengajar guru sebagai landasan dalam membuat desain didaktis. Enam siswa kelas 7 dan seorang guru matematika menjadi partisipan pada penelitian ini, yang terdiri dari tiga tahap, yaitu: (1) analisis hambatan belajar siswa melalui uji tes dan wawancara guru, (2) menyiapkan lintasan belajar hipotetik (HLT) siswa dan desain didaktis berdasarkan identifikasi hambatan belajar siswa dan wawancara mendalam dengan guru, dan (3) mengimplementasikan desain didaktis kepada siswa. Hasil penelitian ini menunjukkan bahwa siswa mengalami hambatan didaktis yang disebabkan oleh cara guru mengajar. Guru cenderung memberikan definisi formal pada konsep-konsep bentuk aljabar dilanjutkan dengan contoh-contoh soal. Hal ini mengakibatkan siswa mengalami hambatan yang bersifat epistemologis, dimana pengetahuan siswa terhadap konsep-konsep bentuk aljabar terbatas berdasarkan apa yang dijelaskan oleh guru. Kemudian, dirancang HLT yang menjembatani pengetahuan aritmatika siswa dengan aljabar. Rangkaian tugas disusun berdasarkan teori praxeology dengan mengambil konteks kehidupan sehari-hari bertema Ayo Menabung. Selama proses pembelajaran, siswa menggunakan berbagai macam representasi seperti simbol dan huruf, untuk menunjukkan variabel, mengemukakan alasan dari penggunaan representasi tertentu, dan mengungkapkan definisi variabel sesuai dengan hasil pekerjaannya. Hal ini juga berlaku pada keempat konsep lainnya. Melalui tugas yang diberikan, siswa dapat berpartisipasi aktif dalam membangun pengetahuan tentang konsep-konsep dalam bentuk aljabar.
Pembelajaran Bentuk-Bentuk Aljabar Berlandaskan pada Teori Situasi Didaktis pada Siswa Sekolah Menengah Atas di Yayasan Graha Asuh Jabal 165 Kabupaten Bandung Nadya Syifa Utami; Aswin; Ade Riastuti; Woro Anglia Banda Sutomo; Khairunnisa; Nurdiyah Kurniati; Putri Armania; Al Jupri
Jurnal Pengabdian kepada Masyarakat Indonesia (JPKMI) Vol. 3 No. 1 (2023): April : Jurnal Pengabdian Kepada Masyarakat Indonesia (JPKMI)
Publisher : Pusat Riset dan Inovasi Nasional

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/jpkmi.v3i1.1217

Abstract

Algebra becomes an essential topic for all school mathematics topics. Nevertheless, many students still experience difficulties in learning algebra, one of them is senior high school students in Yayasan Graha Asuh Jabal 165, Kabupaten Bandung. Lack of effective learning activity in the class becomes the primary source for students’ difficulty. As an attempt to overcome this problem, the theory of didactic situation (TDS) could be adopted as a reference to implement the learning activity that possibly engages the students to be more active in the learning process. Therefore, this activity is held to help students in understanding the concept of algebraic forms with the learning based on the TDS. The method of this activity consisted of three stages, that was 1) the analysis of students’ difficulty in understanding the algebraic forms, 2) the learning implementation based on the TDS, and 3) the evaluation of students’ learning. The result shows that in the analysis stage, many students did not understand the concept of variables, coefficients, constants, equations, and algebraic operations. The next stage is learning implementation based on the TDS which comprises of the situation of action, formulation, validation, and institutionalization. The last one is evaluation where all students manage to understand the concept of algebraic forms and their application in daily life. This shows an improvement of their conceptual understanding in algebra.
ASSESSING STUDENTS' MATHEMATICAL PROBLEM-SOLVING ABILITY Sufyani Prabawanto; Nadya Syifa Utami; Aneu Pebrianti
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 12, No 2 (2023)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v12i2.7346

Abstract

Students' ability to solve mathematical problems is the most important part of learning mathematics. Therefore, assessing students' ability to solve mathematical problems is one of the tasks of mathematics teachers that must be done. This study aims to develop a test instrument to assess students' ability to solve mathematical problems. The research method used Systematic Literature Review (SLR) by analyzing primary sources from books and articles. Before developing an instrument to assess students' ability to solve mathematical problems, the variables involved in mathematical problem solving were first analyzed. Furthermore, there are four domains involved in the instrument development framework carried out. They are resources, heuristics, control, and belief system. Based on this study, it was found that: (1) the aspects correlated with mathematical problem solving are reasoning, decision making, critical thinking, and creative thinking; (2) the types of tasks related to mathematical problem solving can be viewed from the structure, the number of essential steps needed to reach the solution, its orientation, and its presentation.
An analysis of mathematics textbook of Indonesian curriculum based on functional thinking framework Nadya Syifa Utami; Sufyani Prabawanto; Jarnawi Afgani Dahlan
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 8 Issue 4 October 2023
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v8i4.1928

Abstract

Functional thinking (FT) is individual’s cognitive process to identify the relation between variables and is essential for students to learn algebra. However, not much studies addressing the examination of the contents of FT problems within school mathematics textbooks, particularly in Indonesian curriculum. This study aims to describe the mathematics problems presented in junior high school mathematics textbooks of the new Indonesian curriculum (Kurikulum Merdeka) based on the FT framework. To reach this aim, the student mathematics textbook published by The Ministry of Education, Culture, Research, and Technology (Kemdikbud) in 2022 was used to conduct the analysis. The textbooks used were seventh and eighth-grade mathematics textbooks. The data was collected by observing the textbook's contents in the algebra domain. The analysis was based on the framework of FT consisting of recursive patterns, covariance, and correspondence. The results show that the FT tasks appear in the learning of algebraic terms, modelling with algebra, and linear functions. Moreover, this study also found that tasks in each topic develop students’ FT at different stages. Tasks in algebraic terms fulfill all FT’s stages in hierarchical order, tasks in modelling with algebra focus on the correspondence stage, and tasks in linear functions include all FT stages but not in chronological order; that is, recursive patterns, correspondence, and then covariation. In conclusion, this study finds that algebraic problems provided by Indonesian textbooks already support students’ FT. Thus, designing more FT tasks and connecting each task to different algebra topics might help students develop their FT.