Kalamatika (E-Journal)
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STUDENTS' DIFFICULTIES IN LEARNING THE CONCEPT OF CURVED-SIDED SPACES: A LITERATURE REVIEW
No full textThis study aims to identify and review several articles discussing students' learning difficulties in understanding material related to curved-sided geometric shapes in elementary schools. The research method employed is a literature study, in which data is collected from various scientific journals relevant to students' learning difficulties in comprehending curved-sided spaces. The findings indicate that students face multiple challenges, including difficulties in understanding basic concepts, remembering formulas, and applying appropriate problem-solving strategies. Common errors include procedural mistakes, difficulties in transforming information, and improper use of mathematical symbols. Factors contributing to these difficulties include a lack of interest in mathematics, the abstract nature of mathematical concepts, and insufficient practice in applying the concepts learned. This research is expected to serve as a recommendation for teachers and education practitioners to improve teaching methods and provide more intensive exercises to help students better understand the concepts related to curved-sided spaces
META-ANALYSIS OF CONSTRUCTIVISM’S APPROACHES TO STUDENTS’ MATHEMATICAL ABILITY
No full textThis study examined the effectiveness of the constructivist approach in enhancing students' mathematical abilities through meta-analysis. Data were gathered from 20 journal publications implementing constructivist teaching strategies in mathematics instruction for Indonesian primary and high school students. Cohen's criteria were applied to assess effect sizes on students' mathematical abilities. The findings indicated that 15 studies (75%) demonstrated small effect sizes (0.0–0.20), suggesting a limited influence on students' mathematical skills. However, all studies showed higher average scores between pretests and posttests, highlighting the potential benefits of the approach. The remaining five studies (25%) reported moderate effect sizes (0.51–1.00), indicating a more substantial positive impact of constructivist methods on students' mathematical aptitude
CHALLENGES IN DEVELOPING JUNIOR HIGH SCHOOL STUDENTS' COMPUTATIONAL THINKING SKILLS IN MATHEMATICS THROUGH PROBLEM-BASED LEARNING
No full textThis research aims to analyze students' computational thinking abilities in mathematics learning through problem-based learning. A qualitative approach with a case study design was employed. The research was conducted at SMP Negeri 1 Cibinong, Bogor Regency, West Java. The subjects were three ninth-grade students who had studied material on exponents and roots, selected based on the teacher's recommendations. Data were collected through computational thinking tests and interviews. Based on the analysis, it was found that students, despite their teachers implementing problem-based learning, still lacked strong computational thinking skills. The suboptimal implementation of PBL and the students' unfamiliarity with problem-solving contributed to their difficulty in effectively applying computational thinking skills. In conclusion, the use of problem-based learning in mathematics, particularly in the topics of exponents and roots, has not yet enabled students to fully develop computational thinking skills
ETHNOMATHEMATICS EXPLORATION IN THE TRADITIONAL ART OF RANDAI MINANGKABAU
No full textMathematics is a scientific field that delves into numbers, measurements, and formulas. When mathematical concepts intertwine with culture, it forms what is known as ethnomathematics. Integrating mathematics with cultural elements can significantly enhance the learning experience. This research aims to identify and elucidate mathematical elements in the traditional Minangkabau art form of Randai. The methodology employed in this study is qualitative descriptive, utilizing a library research approach. No field studies were conducted; the research relied solely on a literature review. The data utilized comprises documents derived from studies of Randai art and other written references relevant to the research problem. The researcher serves as the primary instrument, indispensable to this study. Data collection methods include documentation and an extensive literature review. The findings reveal that traditional Minangkabau randai art encompasses not only artistic expression but also philosophical insights, cultural values, and mathematical elements, known as ethnomathematics. Ethnomathematics manifests in Randai art through its form, spatial dimensions, and musical instruments
UNDERSTANDING COMMON ERRORS IN LINEAR EQUATIONS SYSTEMS AMONG EIGHT GRADE STUDENTS
No full textThis research employs a qualitative descriptive method. The average student score in the first semester final summative assessments indicates that the minimal completion criteria have been met; however, a review of the list of incorrect responses shows that many of the errors are related to two-variable linear equation systems. Additionally, it is common for students to struggle with converting a mathematical model from the problem. The purpose of this study is to describe the errors made by students in solving problems related to two-variable linear systems and to analyze the factors contributing to these errors. We used data analysis of student responses in this study because it allows us to observe the students' thought processes and ensures the accuracy of the information. According to the study's findings, students' errors in answering the questions stemmed from their inability to grasp relevant concepts. One possible solution is for students who struggle with conceptual understanding to focus more on mastering the material, practice answering questions frequently to become accustomed to various question types, and ultimately enhance their comprehension of mathematical concepts
ANALYSIS OF HIGH SCHOOL STUDENT'S KNOWLEDGE OF RECOGNIZING EUCLIDEAN ELEMENTS
No full textEuclid's Elements is a work written by an ancient Greek mathematician named Euclid in the 3rd century BC. It is one of history's most famous and influential mathematical works, serving as a significant basis for studying geometry and number theory for centuries. This research aims to describe Euclid's Elements and determine the extent of high school students' knowledge about Euclid and his work and their level of understanding in solving mathematical problems. This qualitative research utilizes case study methods and literature reviews. Data were collected through problem-solving exercises and interviews. Thematic data analysis was conducted to elucidate Euclid's Elements and students' level of knowledge. The case study involved presenting mathematics problems and interviewing five high school students, using assessment instruments incorporating problem-solving and open interviews. The findings reveal that many students lack familiarity with the elements of Euclid's Elements but demonstrate proficiency in solving mathematical problems related to it
English
No full textCreative reasoning is a person's ability to solve mathematical problems in a manner of thinking that deviates from the norm, yet remains logical and grounded in a strong mathematical foundation. While crucial for students, many have not yet attained proficiency in creative reasoning, necessitating comprehensive research on the subject. This study aims to elucidate students' creative reasoning abilities in tackling straight-line equation problems, focusing on indicators such as creativity, plausibility, and anchoring. Employing a qualitative approach with a case study design, the research involved three students from Madrasah Tsanawiyah who had studied straight-line equations. The primary instrument was the researcher, supported by a creative reasoning ability description test and interviews. Data collection utilized triangulation techniques, encompassing tests and interviews. Analysis of the research findings entailed describing students' creative mathematical reasoning abilities for each creative reasoning indicator in straight-line equation material. Results indicated that while students could provide correct and reasonable arguments in solving mathematical problems, they struggled to devise alternative methods and employ strategies based on mathematical concepts. Consequently, they only met the plausibility criterion, falling short in creativity and anchoring. Thus, it can be concluded that students have not yet achieved creative reasoning proficiency in solving straight-line equation problems.Penalaran kreatif adalah kemampuan seseorang dalam memecahkan masalah matematika dengan cara berpikir yang berbeda dari biasanya, namun proses penalarannya masuk akal dan mempunyai landasan matematika yang kuat. Penalaran kreatif merupakan hal yang penting untuk dimiliki siswa, namun banyak siswa yang masih belum mencapai penalaran kreatif, sehingga diperlukan penelitian yang mendalam mengenai penalaran kreatif. Penelitian ini bertujuan untuk mendeskripsikan kemampuan penalaran kreatif siswa dalam menyelesaikan permasalahan persamaan garis lurus yang meliputi indikator penalaran kreatif yaitu creativity, plausibility, dan anchoring. Metode penelitian yang digunakan adalah pendekatan kualitatif dengan desain studi kasus. Subyek penelitian ini adalah tiga orang siswa Madrasah Tsanawiyah yang pernah mempelajari persamaan garis lurus. Instrumen utama penelitian ini adalah peneliti dan instrumen pendukung yang digunakan adalah tes deskripsi kemampuan penalaran kreatif dan wawancara. Hasil penelitian menunjukkan bahwa siswa dapat memberikan argumen yang benar dan masuk akal dalam menyelesaikan masalah matematika tetapi belum mampu menghasilkan metode yang berbeda dan tidak dapat menggunakan strategi berdasarkan konsep matematika. Artinya siswa hanya memenuhi indikator masuk akal dan belum memenuhi indikator kreativitas dan penjangkaran pada indikator penalaran kreatif, sehingga dapat disimpulkan bahwa siswa belum mencapai penalaran kreatif dalam menyelesaikan masalah persamaan garis lurus
ANALYSING INTEGER DIVISION KNOWLEDGE AND SKILLS IN PROSPECTIVE PRIMARY TEACHERS
No full textThis study aims to investigate prospective primary (MI) teachers’ knowledge of the sign of the division result of integers, their skills in illustrating the division model of integers, and their ability to perform integer division operations. This study comprehensively describes prospective MI teachers' work on integer division problems through a descriptive qualitative research approach. Data were collected using a test. The participants were considered to have received instruction on integer division material, thus preparing them to become teachers who understand the concept of integer division. They demonstrated the correct knowledge regarding the sign of the division result of integers. They illustrated the division models of integers in four categories: (1) unable to illustrate the division models of integers, (2) illustrating integer division models incorrectly, (3) illustrating integer division models correctly but without demonstrating their understanding, and (4) illustrating integer division models correctly and understandably. The skills of the MI teachers in performing integer division included using downward division by separating integer signs correctly, using downward division by attaching integer signs correctly, using downward division by attaching integer signs incorrectly, and not explaining any methods for operating with integers. This study's results can serve as a basis for improving the learning process, curriculum, and training programs for prospective MI teachers.This study aims to investigate prospective primary (MI) teachers’ knowledge of the sign of the division result of integers, their skills in illustrating the division model of integers, and their ability to perform integer division operations. This study comprehensively describes prospective MI teachers' work on integer division problems through a descriptive qualitative research approach. Data were collected using a test. The participants were considered to have received instruction on integer division material, thus preparing them to become teachers who understand the concept of integer division. They demonstrated the correct knowledge regarding the sign of the division result of integers. They illustrated the division models of integers in four categories: (1) unable to illustrate the division models of integers, (2) illustrating integer division models incorrectly, (3) illustrating integer division models correctly but without demonstrating their understanding, and (4) illustrating integer division models correctly and understandably. The skills of the MI teachers in performing integer division included using downward division by separating integer signs correctly, using downward division by attaching integer signs correctly, using downward division by attaching integer signs incorrectly, and not explaining any methods for operating with integers. This study's results can serve as a basis for improving the learning process, curriculum, and training programs for prospective MI teachers
LEARNING OBSTACLES ANALYSIS ON MULTIPLICATION OF NATURAL NUMBERS IN ELEMENTARY SCHOOL
No full textThis research aims to find learning obstacles students experienced during natural number multiplication lessons in third-grade elementary school. Learning obstacles were obtained from the Respondent Ability Test (RAT) analysis on students who had studied the lessons on multiplication of natural numbers. The method used in this research is a qualitative descriptive method. The subjects were respondents who participated in RAT, namely 22 third-grade elementary school students in Bandung, Indonesia. Data collection techniques use tests, interviews, and documentation. Data analysis techniques include data collection, reduction, display, and conclusion. Learning obstacles found in natural number multiplication lessons are categorized into three types, namely ontogenic, epistemological, and didactical obstacles. Ontogenic obstacles occur when there is a gap in the students' thinking when analyzing concrete to abstract concepts. Epistemological obstacles may occur if students need help to apply the concepts they have learned in the context of story problems. Didactical obstacles happen when the learning carried out by teachers is only procedural, so students only memorize each multiplication result. Therefore, it is essential to analyze these learning obstacles and find the causes as a reference in finding solutions to design future learning tools that prevent these learning obstacles from happening.Penelitian ini bertujuan untuk mengetahui hambatan belajar yang dialami siswa pada pembelajaran perkalian bilangan asli di kelas 3 SD. Hambatan belajar diperoleh dari hasil analisis Tes Kemampuan Responden (TKR) pada siswa yang telah mempelajari pembelajaran perkalian bilangan asli. Metode yang digunakan dalam penelitian ini adalah metode deskriptif kualitatif. Subjek penelitian adalah responden yang mengikuti RAT, yaitu 22 siswa kelas 3 SD di Bandung, Indonesia. Teknik pengumpulan data menggunakan tes, wawancara, dan dokumentasi. Teknik analisis data meliputi pengumpulan data, reduksi, display, dan penarikan kesimpulan. Hambatan belajar yang ditemukan pada pembelajaran perkalian bilangan asli dikategorikan menjadi tiga jenis, yaitu hambatan ontogenik, epistemologis, dan didaktis. Hambatan ontogenik terjadi ketika terdapat kesenjangan dalam berpikir siswa ketika menganalisis konsep konkret ke abstrak. Hambatan epistemologis dapat terjadi ketika siswa membutuhkan bantuan untuk menerapkan konsep yang telah dipelajarinya dalam konteks soal cerita. Hambatan didaktis terjadi ketika pembelajaran yang dilakukan guru hanya bersifat prosedural, sehingga siswa hanya menghafal setiap hasil perkalian. Oleh karena itu, penting untuk menganalisis kendala pembelajaran tersebut dan mencari penyebabnya sebagai acuan dalam mencari solusi untuk merancang perangkat pembelajaran masa depan yang mencegah terjadinya kendala pembelajaran tersebut
STUDENTS' MATHEMATICAL CREATIVE THINKING SKILLS IN SOLVING PISA PROBLEMS: A CASE IN INDONESIA
No full textThis study analyzes students' creative thinking skills in solving PISA questions involving spatial and geometric content. A descriptive qualitative approach was used, selecting three groups of students based on mathematical ability: high, medium, and low. Data were collected through tests, interviews, and documentation. The test consisted of three PISA items designed to assess students' creative thinking indicators: fluency, flexibility, originality, and elaboration. The conclusions of this study show that students with high mathematical ability exhibit a high level of creative thinking, as evidenced by the fulfillment of all indicators: fluency, flexibility, elaboration, and originality. Students with moderate mathematical ability demonstrate limited or moderate creative thinking, fulfilling only the fluency and originality indicators, while elaboration and flexibility are not optimal. Students with low mathematical ability fulfill only the originality indicator, with low fluency and elaboration, and do not demonstrate flexibility