Mathematical Concepts Research Articles

HOW ARE STUDENTS' CREATIVE REASONING ABILITIES IN SOLVING STRAIGHT-LINE EQUATION PROBLEMS?

Creative 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.

비형식적 통계적 추리 교수·학습에서의 행위자-네트워크 분석

This study started from a critical awareness of the ontological position of technology in mathematics teaching and learning. Based on the perspective of Actor-Network Theory(ANT), we consider teaching and learning as a network and focus on the agency that emerges from the combination of human actors and non-human actors. The results of research with comparing data sets tasks based on the concepts of distribution and sample with elementary school students in grades 5 showed that the key actors were teachers and students, technology such as graphs, diagrams, TinkerPlots, and the concepts of distribution and sample. Through the translation of these actors, it was possible to confirm how the network is constructed. Bar graphs interessement students through the length or color of the bars, dot plots interessement through an environment for drawing various diagrams, and TinkerPlots interessement through utilizing different functions. Non-human actors have changed students from focusing only on a single data to considering various aspects of distribution. In addition, students form a concept image of distribution and make a inference using representative values and distribution. This means that mathematical concepts are expanded and distributed among various actors in the mathematics teaching and learning network.

Revitalizing Math Education: Unveiling the Impact of Holistic Mathematics Education Based “Sistem Among” in Elementary Classrooms

This research examines the impact of the Holistic Mathematics Education (HME) model based on the Among system on the mathematical concept understanding of third grade students at SD Negeri 21 Pulau Punjung. This model holds significant relevance to the current paradigm of liberating learning. In the era of modern education, there is a strong emphasis on learning approaches that promote independence, creativity, and critical thinking among students. The implementation of this model has shown an increase in mathematical concept understanding, as evidenced by statistical analysis (significance level 0.001). Based on the analysis results, it can be proven that the HME model based on the "among" system has a positive impact on the mathematical concept understanding of third-grade students at SDN 21 Pulau Punjung. The success of this method in enhancing mathematical concept understanding underscores the urgency to integrate more innovative and inclusive approaches in the mathematics curriculum, especially at the elementary level, as liberating education focuses not only on academic knowledge but also on the development of students' competencies and character. This study provides empirical evidence of the importance of adopting a more holistic and interactive educational model in elementary schools. Consequently, these findings support a transition towards more responsive, participatory, and future-ready learning methods.

Task Selection and Implementation: An Account of Mathematics Teachers’ Values

Students achieve the goals of learning mathematics through carefully chosen, organized, and implemented tasks. This study examined teachers' arguments as reflections of their values regarding task selection and implementation. Specifically, it aimed to explore teachers' values in selecting mathematical tasks and how they carried out these tasks. Valsiner's Zone theory was employed as a theoretical framework to guide the research from a sociocultural perspective. To fulfil the research objectives, various qualitative data were collected and analyzed through instrumental case studies, primarily consisting of value clarification interviews and observations. Narratives from the interviews and observations were analyzed using the constant comparison method. The findings revealed that teachers have had distinct approaches when it comes to selecting and implementing mathematical tasks. One of the teachers in the study prioritized conceptual comprehension and emphasized the interconnectedness of mathematical concepts over procedural fluency. Conversely, another teacher focused on student engagement, participation, and practical application of mathematics, promoting active discussions, group work, and critical thinking among students. Therefore, the study underscored the significance of teachers clarifying their values to effectively teach mathematics and enhance student comprehension within the Ethiopian educational framework.

Analisis Kemampuan Numerasi Mahasiswa Calon Guru Matematika

Preservice mathematics teachers will eventually become mathematics teachers and teach mathematics in schools to students. Therefore, it is important to assess the numeracy skills of preservice mathematics teachers to develop their numeracy skills, which will positively impact students once they start teaching in schools. This study aims to describe the numeracy skills of preservice mathematics teachers about numeracy, including how well they can explore mathematical concepts in problems related to numeracy. This study is a qualitative descriptive. The subjects of this study are 28 mathematics education students from the University of Mataram. The instruments used in this study are questionnaires and tasks containing numeracy problems using the Sasak cultural context. Data analysis employs descriptive qualitative analysis, which includes data transcription, categorization, data presentation, description of the numeracy skills of teacher candidates, and conclusion. The results show that, in general, students have not been able to distinguish between numeracy and mathematics. Additionally, students still face difficulties in designing numeracy-oriented learning, especially using the socio-cultural context

Analysis of Ability to Understand Mathematical Concepts Class Students XI in Geometric Transformation Materials

The low ability of students to understand mathematical concepts is proven by the majority of students not being able to reformulate the solution to the problem given. This research aims to describe students' ability to understand mathematical concepts for each indicator so that it is known which indicators students experience problems with. The method used in this research is descriptive qualitative. The instruments in this research are test and interview instruments. The research subjects were 26 students of class XI Science 1 SMAN 5 Sukabumi City. Data were analyzed using data reduction, data presentation, and drawing conclusions. In data reduction, researchers summarize the data and classify the data. Based on the results of data analysis, it was concluded that students with high and medium abilities had excellent concept understanding abilities in restating a concept, classifying objects according to the concept, and presenting concepts in various forms of mathematical representation. while students with low abilities are in the good category. Highly capable students are able to restate the concepts they have learned and apply concepts or problem solving algorithms very well. Meanwhile, students with medium and low ability are in the sufficient category. In linking various concepts, high, medium and low ability students have quite good ability to understand mathematical concepts.

Research trends on learning mathematics with the CPA (Concrete-Pictorial-Abstract) approach

Learning mathematics with the CPA approach has been practiced in Singapore and proven its effectiveness. However, there needs to be a synthesis of previous studies to find research gaps for future research. This article is a preliminary-research for information on the CPA approach and its modifications to mathematical abilities and attitudes. This article is a Systematic Literature Review (SLR) of 39 studies published from 2010 to April 2023 using the Publish or Perish application with the Scopus database. This article aims to find out: (1) Description of mathematics education research trends using the CPA approach in terms of publication year, author, country, level of education, and mathematics content. (2) Application of the CPA approach to the type of mathematical ability and attitude of students. The results showed that research outside the elementary school level needs further investigation. Abstract mathematical concepts require a CPA approach. The CPA approach has a positive effect on students with or without learning disabilities or at risk of failure. Results and suggestions for future research on this topic are provided.

FEATURES OF USING VBA IN TEACHING ACTUARIAL MATHEMATICS

The article is devoted to the analysis of practice of application of specific computational techniques within MS Excel, including VBA, for teaching selected topics in actuarial mathematics. Formulation of the problem. With the evolution of financial and actuarial models towards complexity and reliance on machine learning and data science, there is a growing demand for modern mathematicians, particularly actuaries, to acquire new skills and knowledge. This demand is being driven by new fintech trends in banking and insurance, such as smart payments, real-time credit risk assessment, automated reputation management, customer analytics, fraud detection and cryptocurrency trading. As a result, the training of future actuaries must meet high standards to ensure they are equipped to handle the sophisticated mathematical calculations required by insurance companies and other financial institutions. Materials and methods. To yield results, both theoretical methods, which involve analyzing books and publications, in particular in professional journals in the domains of finance and actuarial mathematics, and empirical methods, entailing the observation of the educational process aimed at training prospective actuaries, are employed in this study. Results. A study aimed at tackling the challenges encountered in teaching actuarial mathematics topics, such as life expectancy and mortality tables, revealed that incorporating a balanced blend of theoretical concepts and hands-on applications, coupled with illustrating mathematical models through real-world examples and reinforcing diverse computational techniques, constitutes a cornerstone of successful training for aspiring actuaries. Leveraging a versatile and user-friendly tool like VBA (Visual Basic for Applications) integrated into MS Excel enables educators to customize examples and assignments to match the intricacy and emphasis of their syllabus, thereby offering students a more targeted learning journey. Conclusions. The teaching of mathematical disciplines, especially financial and actuarial mathematics, in academic programmes for future actuaries requires the adaptation of traditional methods and approaches. In particular, the integration of VBA is key to teaching specific actuarial mathematics concepts, which aims to equip students with the necessary practical competencies. VBA facilitates interactive learning by enabling students to manipulate variables and observe changes in calculations in real time, which improves their understanding of actuarial concepts. VBA also allows you to automate repetitive tasks involving complex mathematical calculations, which saves time and reduces errors. Therefore, its use is recommended when teaching topics involving tabular data, especially life expectancy.

Geometric Modelling of a Family of 3-point Quaternary Subdivision Schemes Rζ

Computer-aided geometric design combines mathematical concepts and computing skills that smooth curves through subdivision schemes. Subdivision schemes perform smoothing by turning the control polygon into a limit curve under a refinement rule, a prime example of which is improving the signal-to-noise ratio in modern devices. Because of the importance and location of subdivision schemes, mathematicians use them in CAD, computer graphics and advanced simulation methods. In this research, a family of 3-point Quaternary approximating subdivision scheme $R_{\zeta}$ is presented with its properties and analysis, including necessary conditions for convergence, Laurent polynomial, degree of the generation and polynomial reproduction, continuity analysis, Hölder regularity, and limit stencils. The visual performance of the proposed scheme is also presented to highlight the importance of this research and to validate the scheme.

Developing LEGAMAT on Geometric Distribution: A Teaching Tools for Understanding Mathematics Concept

<p class="06ContentAbstract">The traditional approach to teaching geometric distributions, which focuses on proving theorems, makes it difficult for students to apply the concept in everyday life. Moreover, the content delivered by the teacher is challenging for students to understand. Therefore, developing learning media to increase student interest and understanding of the concept was necessary. In response to these challenges, the researchers developed 'Lempar Gelang Matematika (LEGAMAT)', a set of teaching tools for geometric distributions, accompanied by a student worksheet. Consequently, this study aimed to produce valid and practical teaching tools. This study employed a design research method with two stages: the preliminary stage (preparation and design stage of teaching tools and Student Worksheet) and the formative evaluation stage (evaluation and revision stage). The participants of this research were nine pre-service teachers. The data were collected by walkthrough, observation, and interview. The collected data was analyzed qualitatively. Based on the results of expert judgments and trials at the one-to-one stage, it was found that the set of LEGAMAT teaching tools was valid in media appearance aspects, easiness aspects, aesthetic aspects, and usage requirements aspects. It is practical to be used by students based on the observation in the small group stage. The researchers suggested that further studies continue until the field test stage to determine the effectiveness of the teaching tools. Additionally, they recommended developing other teaching tools related to geometric distribution topics.</p><p class="06ContentAbstract"> </p><p class="06ContentAbstract"><span lang="EN-GB">Proses pembelajaran distribusi geometri, yang biasanya terbatas pada pembuktian teorema, membuat siswa sulit ketika konsep tersebut diterapkan dalam kehidupan sehari-hari. Selain itu, materi yang disampaikan oleh guru sulit untuk dipahami oleh siswa. Oleh karena itu, diperlukan pengembangan media pembelajaran untuk menambah minat belajar serta membantu siswa memahami materi pembelajaran tersebut. Berdasarkan hal tersebut, peneliti mengembangkan media pembelajaran berupa Alat Peraga yaitu <em>Lempar Gelang Matematika</em> (LEGAMAT) dengan Lembar Kerja Peserta Didik. Adapun tujuan dari penelitian ini adalah untuk menghasilkan alat peraga yang valid dan praktis. Metode yang digunakan dalam penelitian ini adalah <em>Design Research</em> tipe <em>Development Study</em> yang terdiri dari dua tahap yaitu tahap pendahuluan (tahap persiapan dan perancangan alat peraga dan Lembar Kerja Peserta Didik) dan tahap evaluasi formatif (tahap evaluasi dan revisi). Adapun subjek dari penelitian ini adalah 9 orang mahasiswa calon guru. Pengumpulan data dilakukan dengan cara <em>walkthrough</em>, observasi, dan wawancara. Data yang terkumpul dianalisis secara kualitatif. Berdasarkan hasil expert judgement dan uji coba tahap one-to-one diperoleh hasil bahwa seperangkat ajar LEGAMAT valid baik isi, konstruk, dan bahasa. Seperangkat alat ini praktis digunakan oleh mahasiswa calon guru berdasarkan observasi pada tahap kelompok kecil. Peneliti menyarankan agar peneliti selanjutnya melanjutkan penelitian hingga tahap <em>field test</em>, sehingga dapat mengetahui keefektifan perangkat pengajaran dalam proses pembelajaran. Peneliti juga menyarankan untuk mengembangkan perangkat pengajaran lain yang berkaitan dengan topik sebaran geometri.</span></p>

Identifying the use of artificial intelligence in math learning based on learning outcomes

In an era of rapidly developing technology, the need to simplify and improve the learning process of mathematics is increasingly urgent. One emerging solution is the utilization of Artificial Intelligence (AI) in mathematics education. AI provides learning content that is tailored to students' needs, creating a relevant and engaging learning experience. An understanding of AI and the ability to interact with technology is important, helping students face the challenges of the digital age. Understanding math concepts is the foundation for logical thinking, problem solving and critical thinking. Research shows that some students do not fully understand mathematical concepts. Therefore, this study aims to identify the impact of using AI in mathematics learning on student learning outcomes. The preliminary study data showed the prevalence of AI use in mathematics learning. The results show a very strong positive correlation between the use of AI and mathematics learning outcomes, where student learning activities observed during learning using AI (Artificial Intelligence) based on observation sheets include several indicators, with the following results: 1) Visual indicators of 88%, 2) Listening indicators of 84%, 3) Oral indicators of 72.5%, and 4) Mental indicators of 84.5%. The results showed that learning activities were in the high category with a percentage of 82.25%. This shows that during learning activities, there is a good stimulus for students.

ETHNOMATHEMATICS EXPLORATION IN THE TRADITIONAL ART OF RANDAI MINANGKABAU

Mathematics 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.

Pengaruh Sudut Terhadap Besar Resultan Gaya Vektor: Kajian Eksperimental Menggunakan Praktikum Cookbook Laboratory

Vectors are fundamental concepts in mathematics and physics that play a crucial role in various scientific and engineering applications. This study investigates the relationship between the angle and magnitude of the resultant force vector using the Cookbook Laboratory practical approach. The experiment involved combining two forces at different angles and measuring the resultant force. The results indicate a linear relationship between the angle and magnitude of the resultant force, suggesting that as the angle increases, the magnitude of the resultant force also increases. However, this finding contradicts the theoretical prediction of an inverse relationship. This discrepancy is attributed to experimental limitations, particularly parallax error, which may have affected the accuracy of the measurements. Further experiments are recommended to minimize parallax error and obtain more accurate results. A thorough understanding of vector concepts and measurement techniques is essential for comprehending the relationship between angle and resultant force magnitude. Keywords: Angle; Cookbook Laboratory; Resultant Force; Vector.

ANALISIS KEMAMPUAN SISWA KELAS XI DALAM MENYELESAIKAN SOAL LITERASI NUMERASI MATERI TURUNAN

Numeracy literacy entails the knowledge and skills to utilize various numbers and symbols associated with basic mathematics to solve problems in everyday life and analyze information presented in different symbols, subsequently using the results of this analysis to make decisions. In 2018, based on the PISA results released by the OECD, Indonesia's numeracy literacy level was ranked 74th out of 79 countries, indicating that Indonesia's numeracy literacy level is still very low. This study aims to determine and describe the numeracy literacy skills of eleventh-grade students in solving numeracy literacy problems on derivative material at SMA N 1 Sedayu in the academic year 2023/2024. The subjects in this study were 22 eleventh-grade students. The method used in this research is descriptive qualitative. Data collection techniques used were numeracy literacy ability tests and interviews. The numeracy literacy indicator in this research consists of 3 components, namely: (1) identifying and explaining mathematical concepts; (2) designing and applying mathematical concepts; (3) interpreting calculation results. The instrument in this research consists of 3 items of Numeracy Literacy material on Derivatives. The research results showed that 77% of students were in the low category, 14% of students were in the medium category, and 9% were in the high category, thus it can be concluded that in general, students' ability to solve numeracy literacy problems is still low.

Ethnomathematics in Intermediate Phase: Reflections on the Morabaraba Game as Indigenous Mathematical knowledge

Mathematics education remains a worrisome issue in the South African education system. This dilemma presents itself in the underperformance of learners in Intermediate Phase mathematics. In an effort to address this challenge and develop alternative approaches to the teaching of mathematics, a university-based project was initiated. As part of the project, this article reflects on the experiences of five project members who observed the implementation of Morabaraba, which is an Indigenous game, rich in mathematical relevance. This qualitative case study explored how mathematics teachers implemented the Morabaraba game to teach Intermediate Phase mathematics content. The method used to capture the data entailed reflections of the team that were derived from the observation of mathematics lessons in the Intermediate Phase. From these observations the researchers found that teachers invented their own rules when integrating mathematical concepts; they reinvented the game to cater for the complexity of mathematical content and experienced challenges in the playing of the game. We conclude that the Morabaraba game can be implemented, with practical adjustments, to comply with the objectives of the mathematics concept. The recommendation is that ethnomathematical games be employed as a teaching strategy as they are found to encourage active learning. Future research endeavours include exploring how ethnomathematical games can be sustained for future use.

PENGARUH PENDEKATAN CONTEXTUAL TEACHING AND LEARNING TERHADAP KEMAMPUAN PEMAHAMAN KONSEP MATEMATIS SISWA

Understanding concepts is one of the goals of mathematics learning. Understanding mathematical concepts is not just knowing a concept, but being able to re-express the concepts studied in a form that is easier to understand and being able to apply them in problem solving. Students' ability to understand mathematical concepts will be formed systematically if students can construct their mathematical knowledge and connect it to contextual problems. One effort that can be made to improve students’ ability to understand mathematical concepts is to apply the Contextual Teaching and Learning approach. This research aims to determine the effect of the Contextual Teaching and Learning approach on students' ability to understand mathematical concepts. This research is a quasi-experimental research. This research was carried out at SMP Negeri 1 Pangkalan Susu. The sample selection technique used in this research is purposive sampling technique. The population of this study were all class VII students. The samples in this study were 2 classes, namely class VII-4 which was used as the experimental class and class VII-5 which was used as the control class. The results of this research show that there is an influence of the Contextual Teaching and Learning approach on students' ability to understand mathematical concepts.

English learners learn from worked example comparison in algebra

Comparison is an important mechanism for learning in general, and comparing two worked examples has garnered support over the last 15 years as an effective tool for learning algebra in mainstream classrooms. This study was aimed at improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to effective mathematics learning in an ESOL (English to Speakers of Other Languages) context. It investigated a novel instructional approach to help English Learners (ELs) develop better understanding in mathematical reasoning, problem solving, and literacy skills (listening, reading, writing, and speaking). Findings suggest that MLS-WEPs not only enhanced ELs’ ability to solve algebra problems, but it also improved their written explanation skills and enabled them to transfer such skills to different mathematical concepts. Moreover, when controlling for ELs’ prior knowledge, the effectiveness of the MLS-WEPs intervention for performing and explaining calculations did not vary by their English proficiency.

Control-Lab-in-a-Box: Bridging the Gap between Control Theory and Engineering Practice

Traditional control engineering teaching methods heavily rely on abstract mathematical concepts, often leaving students puzzled about real-world applications. Common simulation tools, such as MATLAB and Simulink provide a good visual demonstration but don't necessarily bridge the gap between theory and application. The proposed ‘lab-in-a-box’ approach offers a tangible method for students to connect control theory with a practical control engineering experience. The literature has observed a shift towards such portable labs, given the advancements in compact computing devices such as Raspberry Pi and Arduino boards in electronics and control teaching. The primary goal of these labs is to deliver an authentic engineering experience with essential hardware. Evaluation of this method, through the student module evaluation questionnaire (MEQ), revealed a significant increase in student satisfaction after its introduction. While the results are promising, challenges remain, such as the initial set-up of the kits. However, the ‘lab-in-a-box’ is found to be a valuable tool in control engineering education, bridging the gap between theoretical and practical understanding. An on-going development includes updating of the kits to match future engineering challenges and needs, e.g., electrification and autonomy of vehicles.

APPLICATION OF THE QUANTUM LEARNING MODEL ASSISTED BY GEOGEBRA TO SUPPORT STUDENT’S CONCEPT UNDERSTANDING ABILITY

Understanding concepts is very important in learning mathematics because the material in mathematics learning is interconnected between one material and another. To provide understanding of concepts, student-centered learning is needed. One student-centered learning model is the quantum learning model assisted by geogebra to visualize the material provided with the aim of supporting students' understanding of concepts. The aim of this research is to describe students' ability to understand mathematical concepts after applying the geogebra-assisted quantum learning model to cube and block material. This type of research is descriptive quantitative with a posttest only research design. The subjects in this research were students in class VIII.3 of SMP Ikhlasiyah Palembang. Data collection techniques use tests of ability to understand mathematical concepts and observation of teacher and student activities to see the application of the quantum learning model. The test results show that students' ability to understand mathematical concepts is in the good category with an average score of 80.02 which is measured based on indicators of understanding mathematical concepts and from observing teacher and student activities with an average teacher activity score of 93.05%. and 94.38% of student activity shows that the application of the quantum learning model is implemented very well in the learning process.

Exploring the Golden Ratio in Nature by Using a STEAM Approach: A Diagnostic and Quasi-Experimental Study at a Senior University

This research addresses the social exclusion of elderly citizens in terms of lifelong education via an interdisciplinary STEAM (science, technology, engineering, arts, and mathematics) approach. Technological literacy among older people is a critical factor in social exclusion. This study seeks to provide senior citizens with competencies in scientific, artistic, mathematical, and technological domains by enhancing scientific and technological literacy. The research developed a series of non-formal education sessions on the golden ratio using a STEAM educational approach. A quantitative methodology approach was carried out by using a diagnostic survey of the participants’ conceptions and a subsequent quasi-experimental study to evaluate the impact of the intervention. This study, conducted with 37 senior citizens (n = 37), found positive results aligning with the existing literature on the potential of the STEAM approach. The STEAM approach proved to be engaging for seniors, offering a holistic and interdisciplinary educational experience. Despite the limited availability of science educational programs for seniors and the scarcity of studies on lifelong learning using the STEAM approach, this research highlights the need for such initiatives, especially given the growing senior population. Applying STEAM education shows promise in enhancing scientific literacy and motivation among adult learners. By integrating mathematical concepts, such as the golden ratio, with practical applications in arts and natural sciences, STEAM education can provide a rich, motivating, and accessible learning experience, promoting active and healthy ageing through lifelong learning. Further research and development in this area could maximise educational benefits for the senior population.