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The effect of PMRI assisted by augmented reality on circle for students’ problem-solving ability
Full text linkMathematical problem-solving ability among students remains low in conventional learning environments. The integration of Augmented Reality (AR) into the Indonesian Realistic Mathematics Education (PMRI) approach facilitates visualization of abstract concepts and promotes contextual learning. This study analyzes the effect of PMRI-based circle learning assisted by AR on students\u27 problem-solving abilities. A quantitative approach was employed using a One Group Pretest pretest-posttest design with 35 eleventh-grade students from SMA Srijaya Negara Palembang. Data were collected through a mathematical problem-solving test based on Polya\u27s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back, administered before and after the intervention. The Shapiro–Wilk test indicated that the data were normally distributed (pretest = 0.084; posttest = 0.309, both > 0.05). Paired sample t-test analysis revealed a pretest mean score of 19.37 and a posttest mean score of 66.51, with a mean difference of 47.14. The t-test result (t = -23.053, Sig. (2-tailed) < 0.001) indicated a significant difference between pretest and posttest scores. These findings demonstrate that the PMRI-based learning design assisted by AR is effective in improving students\u27 problem-solving abilities through contextual learning experiences and interactive visualization. The results suggest that integrating PMRI with Augmented Reality in circle learning represents an effective instructional innovation for enhancing students\u27 problem-solving abilities
Systematic Literature Review: Penalaran Adaptif Siswa dalam Pembelajaran Matematika
No full textThis study aims to examine trends in research methods used in articles related to students\u27 adaptive reasoning abilities in mathematics learning from 2015 to 2024 and to describe the improvement of students\u27 adaptive reasoning abilities. The method employed was a Systematic Literature Review (SLR) involving the identification, selection, evaluation, and data analysis of relevant articles. The reviewed articles were selected based on their relevance to students\u27 adaptive reasoning, were published between 2015 and 2024, were sourced from Google Scholar, focused on junior high to senior/vocational high school levels, and were indexed in Sinta 1 to 3. Irrelevant articles published before 2015, not obtained from Google Scholar, outside the specified education levels, or published in proceedings and journals below Sinta 3 were excluded. Students\u27 abilities increase by up to 82.7% with the use of Collaborative problem-solving-based tools and are very effective in improving students\u27 adaptive reasoning abilities. This study emphasizes the importance of implementing innovative and adaptive teaching methods while considering individual student factors to enhance adaptive reasoning abilities in mathematics learning. These findings are expected to serve as a reference for educators in designing more effective teaching strategies.Penelitian ini bertujuan untuk mengkaji tren metode penelitian yang digunakan pada artikel terkait kemampuan penalaran adaptif siswa dalam pembelajaran matematika dari tahun 2015 hingga 2024 serta mendeskripsikan peningkatan kemampuan penalaran adaptif siswa tersebut. Metode yang digunakan adalah Systematic Literature Review (SLR), dengan proses yang mencakup identifikasi, seleksi, evaluasi, dan analisis data dari artikel yang relevan. Penelitian dilakukan melalui Google Scholar dengan kriteria inklusi meliputi publikasi nasional dan internasional pada jenjang SMP hingga SMA/SMK dalam kurun waktu 2015-2024. Dari 207 data artikel google scholar yang diimpor, diperoleh sebanyak 18 artikel terpilih dari database Google Scholar berdasarkan kriteria inklusi dan eksklusi. Hasil penelitian menunjukkan bahwa metode kualitatif paling dominan digunakan (8 artikel), diikuti metode quasi-experimental design (4 artikel), kuantitatif (2 artikel), dan metode lainnya. Selain itu, peningkatan kemampuan penalaran adaptif siswa dipengaruhi oleh penggunaan model pembelajaran inovatif, perangkat berbasis kolaborasi, pendekatan etnomatematika, dan metode pembelajaran kontekstual seperti Realistic Mathematics Education (RME). Faktor individu seperti gaya belajar, self-efficacy, dan karakteristik lainnya juga berkontribusi signifikan. Peningkatan kemampuan siswa mencapai hingga 82,7% dengan perangkat berbasis Collaborative Problem Solving. Penelitian ini menegaskan pentingnya implementasi metode pembelajaran yang inovatif dan adaptif, serta mempertimbangkan faktor individual siswa untuk meningkatkan kemampuan penalaran adaptif dalam pembelajaran matematika. Temuan ini diharapkan menjadi rujukan bagi pendidik dalam merancang strategi pembelajaran yang lebih efektif
Developing PBL-based worksheets on sequences and series to enhance mathematical connection skills of senior high school students
Full text linkThis study was driven by students’ low mathematical connection ability in learning Sequences and Series, a skill essential for understanding relationships among mathematical concepts. The purpose of this research was to develop a Problem-Based Learning (PBL)-based student worksheet designed to improve students’ mathematical connection ability and to examine its validity and practicality. A development research approach was applied using the 4-D model—Define, Design, Develop, and Disseminate. The participants were tenth-grade students selected through purposive sampling. Data were collected using validation instruments, practicality questionnaires, interviews, and classroom observations. The validation process evaluated face, content, and construct validity. The developed worksheet demonstrated strong validity, with average scores of 89.29% for face validity, 89.29% for content validity, and 86.79% for construct validity. The overall validity score of 88.45% fell into the “very valid” category, indicating the product’s suitability for field implementation. The practicality assessment, focusing on design, clarity of material presentation, and ease of use, produced an average score of 83.27%, classified as “practical.” These findings suggest that the PBL-based worksheet is both valid and practical, offering potential as an effective instructional tool to support students in developing mathematical connection ability, particularly in topics related to Sequences and Series
Kemampuan Berpikir Kritis Siswa SMP dalam Menyelesaikan Masalah Geometri
No full textThis study aims to describe the critical thinking skills of junior high school (SMP) students in solving geometry problems. A descriptive qualitative approach was used, involving six eighth-grade students selected through purposive sampling. The subjects consisted of two students from each category of mathematical ability: high ( & ), medium ( & ), and low ( & ). The six students were selected based on their performance in the written test and their verbal communication skills, as observed during the pre-research phase, to ensure a more accurate representation of the population. Data were collected through written tests consisting of two essay questions and semi-structured interview guidelines developed based on Facione’s critical thinking indicators: interpretation, analysis, evaluation, and inference. The research data collected were written test results and interviews, which were then analyzed based on critical thinking indicators. The results showed that interpretation was the indicator most easily achieved by all subjects, analysis was optimally achieved only by students with high mathematical ability, while evaluation and inference were the most difficult indicators to fulfill. The study concludes that students’ critical thinking skills in solving geometry problems are generally low, primarily because of insufficient mastery of the underlying material.Penelitian ini bertujuan untuk mendeskripsikan kemampuan berpikir kritis siswa Sekolah Menengah Pertama (SMP) dalam menyelesaikan masalah geometri. Pendekatan yang digunakan adalah kualitatif deskriptif dengan subjek enam siswa kelas VIII yang dipilih secara purposive sampling, terdiri dari dua siswa pada masing-masing kategori kemampuan matematis tinggi (T1 & T2), sedang (S1 & S2), dan rendah (R1 & R2). Instrumen pengumpulan data dilakukan dengan tes tertulis dan pedoman wawancara yang disusun berdasarkan indikator berpikir kritis menurut Facione, yaitu interpretasi, analisis, evaluasi, dan inferensi. Hasil penelitian menunjukkan bahwa interpretasi merupakan indikator yang paling mudah dicapai oleh seluruh subjek, analisis hanya dicapai secara optimal oleh siswa berkemampuan tinggi, sedangkan evaluasi dan inferensi menjadi indikator yang paling sulit dipenuhi. Dapat disimpulkan bahwa kemampuan berpikir kritis siswa dalam menyelesaikan masalah geometri masih tergolong rendah hal itu disebabkan oleh kurangnya penguasaan konsep materi
Bahasa Inggris
No full textThe "realistic" concept in Realistic Mathematics Education (RME) is often confined to everyday contexts. In contrast, for aerospace engineering students, realistic mathematics should reflect the mathematical applications in their academic and future professional environments. This study aimed to design and evaluate instructional activities grounded in RME principles, integrating mathematics mobile applications to support conceptual understanding and reasoning. Using a design research approach, the study involved a questionnaire distributed to alums and third-year students, followed by two implementation cycles with first-year aerospace engineering students. The focus was on integral strategies in calculus, utilizing Photomath to bridge informal and formal mathematical reasoning. Results indicate that students engaged actively with the applications and demonstrated improved reasoning skills, particularly in inductive and imitative reasoning. This study highlights the potential of contextualized digital tools in supporting realistic mathematics learning in higher education. It suggests directions for aligning university-level mathematics with its practical applications in other disciplines, such as aerospace engineering
Students\u27 Learning Obstacles in SPLDV Materials Related to Computational Thinking Skills
No full textIntegrating computational thinking into Programme for International Student Assessment (PISA) assessments presents a significant challenge for Indonesian students, particularly in mathematics education. Despite its crucial role in problem-solving, computational thinking has not been widely implemented by students due to the presence of learning obstacles. This study aims to identify the learning obstacles that junior high school students encounter in understanding systems of linear equations in two variables, specifically about their computational thinking abilities. A qualitative approach with a phenomenological method was employed. Research instruments included a computational thinking test and a semi-structured interview guide. Data were collected from 20 students at a junior high school in Wonosobo Regency, Indonesia. Data analysis consisted of three stages: reduction, display, and conclusion. The findings reveal that students experience three types of learning obstacles—epistemological, ontogenical, and didactical when engaging with systems of linear equations in two variables, indicating that these obstacles hinder the development of their mathematical computational thinking skills.The existence of computational thinking skills into PISA brings up new challenges for Indonesian students. This skill plays a significant role, yet students do not really implement it in problem solving due to learning obstacles. This is qualitative research implementing phenomenology. It aims at identifying students’ learning obstacles in junior high school regarding the computational thinking skill. Research instruments used were questions on computational thinking skills and interview guidelines. The data were taken from the test on 20 students in one of junior high schools in Regency of Wonosobo. Data reduction, data presentation, and data conclusion drawing were the data analysis techniques employed. The research results show that students underwent three types of learning obstacles in SPLDV materials related to computational thinking skills., which were epistemological, ontogenical, and didactical
Analisis Kesalahan Siswa dalam Menyelesaikan Soal Eksponen Menggunakan Prosedur Newman
No full textExponents constitute a fundamental concept essential for understanding advanced mathematical topics such as logarithms, geometric sequences, and compound interest. However, many students continue to experience difficulties in solving exponent-related problems. This qualitative descriptive study aims to analyze the types of errors made by tenth-grade students when solving exponent problems using Newman’s procedure and to investigate the factors contributing to these errors. The participants were 23 students from Madrasah Aliyah Negeri (MAN) Insan Cendekia Siak in the 2024/2025 academic year. Data were collected through written tests and interviews, then analyzed by organizing and categorizing students’ errors according to Newman’s five stages. The results show that 12% of students committed reading errors due to inaccuracies in interpreting the questions, while no comprehension errors were identified. Transformation errors were the most common (49%), primarily due to students’ difficulties in constructing appropriate mathematical models. Process skill errors accounted for 21%, primarily due to computational mistakes, and encoding errors represented 18%, arising from students’ inability to use the provided information effectively. These findings deepen the understanding of students’ patterns of error in exponent problems and imply the need for more targeted instructional strategies, especially those that strengthen mathematical modeling and procedural accuracy.Eksponen adalah konsep dasar untuk memahami topik-topik tingkat lanjut seperti logaritma, urutan geometris, dan bunga majemuk. Namun, banyak siswa yang masih kesulitan dalam menyelesaikan soal eksponen. Penelitian ini bertujuan untuk mendeskripsikan kesalahan siswa dalam menyelesaikan soal eksponen. Penelitian ini menggunakan metode kualitatif yang melibatkan 23 siswa kelas sepuluh MAN Insan Cendekia Siak tahun ajaran 2024/2025. Teknik pengumpulan data menggunakan tes tertulis dan wawancara. Analisis dilakukan dengan menggunakan pendekatan kualitatif deskriptif dengan mengorganisasikan dan mengelompokkan jenis kesalahan siswa sesuai dengan prosedur Newman. Hasil penelitian menunjukkan bahwa 12% siswa melakukan kesalahan membaca karena ketidaktepatan dalam menginterpretasikan pertanyaan. Tidak ada kesalahan pemahaman yang teridentifikasi. Kesalahan transformasi adalah yang paling umum (49%), terutama karena kesulitan siswa dalam membuat model matematika yang sesuai. Kesalahan keterampilan proses muncul pada 21% jawaban, yang diakibatkan oleh kesalahan komputasi. Kesalahan pengkodean terjadi pada 18% kasus, yang disebabkan oleh ketidakmampuan siswa untuk menggunakan informasi yang diberikan secara efektif. Temuan ini diharapkan dapat meningkatkan pemahaman tentang kesalahan siswa dan mendukung pengembangan strategi pembelajaran yang lebih efektif untuk meminimalkan kesalahan tersebut
Development of instruments of higher order thinking skills (HOTS) for phase D students
Full text linkThis research aims to develop test instruments for Higher Order Thinking Skills (HOTS) that are validated, reliable, and possess excellent discrimination power, as well as appropriate levels of difficulty. These tools are intended to boost the advanced thinking abilities of students at phase D. According to the Organization for Economic Cooperation and Development (OECD) report on December 5, 2023, which analyzed the 2022 Program for International Student Assessment (PISA) scores in mathematics, including HOTS questions, there has been a notable worldwide decline. Specifically, Indonesia ranked 68th, with a math score of 379. The focus of this study is on developing HOTS test tools that address topics such as relations, functions, linear equations, and systems of two-variable linear equations, drawing from the AKM (Minimum Competency Assessment) and HOTS mathematics question books. The HOTS questions are designed to encompass cognitive levels C4 (analyzing), C5 (evaluating), and C6 (creating), following the revised Bloom\u27s Taxonomy by Krathwohl and Anderson. As highlighted by the Ministry of Education, Culture, Research, and Technology (2022), the development of HOTS questions must include elements such as (1) incorporating stimuli and (2) presenting new contexts within the material or question formulation. The questions are constructed in essay format, adhering to standards for validity and reliability, as well as optimal difficulty and discrimination levels. This study employs a development model comprising two phases: the preliminary phase, which involves analysis and design, followed by the formative evaluation phase, encompassing self-evaluation, expert review, one-on-one sessions, small group interactions, and field tests. The outcome of this study produced 17 valid questions with a reliability coefficient of 0.848; 14 questions exhibited strong discrimination power, and 3 demonstrated adequate discrimination power, with all 17 HOTS questions classified in the medium difficulty range
Design research on developing primary students’ conceptual understanding of area through visual-spatial activities
Full text linkThis study examines how primary students develop a conceptual understanding of composite shapes, a topic that many learners find challenging beyond the routine use of formulas. The research was motivated by the persistent issue that instruction in the area in elementary classrooms is often procedural and does not sufficiently foster reasoning about spatial structure, decomposition, and measurement. This study employed a Design Research approach in a sixth-grade classroom (n = 6 students) to iteratively develop and test a Hypothetical Learning Trajectory (HLT) for the learning area of composite shapes through visual-spatial and puzzle-based activities. Data were collected through a pre-test, two instructional activities (Activity 1 and Activity 2), classroom observations, and a post-test. Data were analyzed qualitatively through retrospective analysis aligned, with HLT, supported by descriptive coding of students’ strategies, triangulation of written work, and teacher field notes. Findings indicate that students shifted from purely visual recognition toward more analytical strategies, such as partitioning, conservation, transitivity, and additivity, which emerged during instruction. The results suggest that structured visual-spatial tasks grounded in a realistic context effectively bridge abstract area concepts and classroom practice, informing future instructional design in elementary geometry
Improving elementary school students\u27 mathematical problem-solving skills: The effectiveness of realistic mathematics education with problem-based learning
Full text linkMathematics education in Indonesian elementary schools faces significant challenges in developing students\u27 problem-solving skills, as evidenced by the 2022 PISA results, which showed that only 18% of Indonesian students achieved the minimum proficiency level, far below the OECD average. This study aims to evaluate the effectiveness of integrating the Realistic Mathematics Education (RME) approach with Problem-Based Learning (PBL) to enhance fourth-grade students\u27 mathematical problem-solving skills in Bekasi Regency. A quasi-experimental design with a nonequivalent control group was employed, involving 52 students selected through cluster random sampling. The experimental class received RME-based PBL instruction, while the control class received PBL instruction based on the scientific approach. Data were collected using a validated problem-solving essay test and analyzed using descriptive and inferential statistics, including independent-samples t-tests and normalized gain scores. The results demonstrated that the RME-PBL approach significantly improved students\u27 problem-solving skills across all measured aspects: problem identification, formulation, strategy application, and result explanation. Notably, 92% of students in the experimental class achieved good or very good categories, compared to only 22.22% in the control class. The normalized gain for the experimental class was 0.81 (high category), substantially higher than the control class\u27s 0.41 (moderate category). It is concluded that the RME-PBL approach is significantly more effective than the scientific-PBL approach in enhancing elementary students\u27 mathematical problem-solving abilities