Mathematical Development Research Articles

Pengembangan Modul Ajar Matematika Berbasis Kurikulum Merdeka Pada Materi Aljabar

This research aims to (1) produce a mathematics teaching module for class VII algebra material based on the independent curriculum that can improve the process, learning outcomes and students' love for the mathematics subject of algebra material, (2) be able to make students interested in learning mathematics, and (3) increase enthusiasm for learning and mastering the subjects you like, especially mathematics. The development model used in this research is adapting the ADDIE model, with stages (1) analysis, (2) design, (3) development, (4) implementation, and (5) evaluation. The deployment stage was limited to the research location due to limited research time. The data analysis technique used is qualitative data analysis and quantitative data. From the research results, it is known that the development of an independent curriculum-based mathematics teaching module in class VII algebra material at SMP Ma'arif NU Darul Amin is valid and very good for improving learning outcomes. This is proven by the material expert validation results which obtained a score of 77.2%, including the feasible category, the media expert validation results obtained a score of 79.33%, including the appropriate category, the individual trial results obtained a score of 83.67%, including the very good category and the test results Trying a small group obtained a score of 87.33%, including the very good category

The methodology for adaptive modeling and forecasting nonlinear and nonstationary processes

The study is directed towards development of systemic methodology for modeling and forecasting nonlinear and nonstationary processes in economy, finances and other areas of human activities. There exist multiple problems that are to be solved with the data of such type practically in all areas of human activities: such as constructing adequate models including estimation and forecasting state of a system under investigation; technical, economic and medical diagnostics; automatic control in technologies; moving objects control; financial and other risk estimation and management; risk factor interaction; control and monitoring of microclimate in greenhouses and industrial enterprises; decision making support in business; dynamic strategic planning in production; providing stability for critical economic infrastructure etc. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as hie­rarchical architecture of the system, adaptive approach to model structure estimation, optimization of model parameter estimation procedures, functional completeness of the system providing for autonomous operation of the system, identification and taking into consideration of possible uncertainties available in the process of data processing and mathematical model development, application of appropriate sets of quality criteria that are guarantying high quality of intermediate and final results of data analysis. The possible uncertainties are inherent to data collecting, model constructing and forecasting procedures, and play the role of negative influence factors to the computational procedures of proposed information system. Reduction of their influence is favorable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the methodology developed proving the system functionality are provided.

Development and Cultivation of Mathematical Literacy: A Pedagogical Perspective

This study is dedicated to the formation and enhancement of mathematical literacy with a focus on pedagogical approaches. Mathematical literacy, a crucial skill in today's world, involves the ability to apply mathematical knowledge and skills in various contexts. The research aims to explore effective strategies for developing mathematical literacy among students, recognizing its importance in fostering critical thinking, problem-solving, and analytical skills. The pedagogical approach highlighted in this study centers on interactive teaching methods, incorporating real-life scenarios, and utilizing technology in mathematics education. By examining educational practices from various international contexts, the study identifies key factors that contribute to successful mathematical literacy development. These include a curriculum that integrates practical applications of mathematics, teacher training programs that emphasize innovative teaching methods, and the creation of a supportive learning environment that encourages exploration and inquiry. The findings indicate that enhancing mathematical literacy requires a comprehensive approach, combining effective teaching strategies, curriculum design, and continuous assessment to meet the diverse needs of learners. This research contributes to the field of mathematics education by providing insights into methods and practices that effectively nurture mathematical literacy in students, preparing them for the challenges of the 21st century.

Pengembangan Media Pembelajaran Matematika Articulate Storyline Terhadap Kemampuan Pemahaman Konsep Matematis Siswa di Kelas VIII-2 MTs Nurul Islam Indonesia Medan

This research aims to determine the validity, practicality, effectiveness and how the students' answers process in completing the conceptual understanding ability test of the developed Articulate Storyline. This type of research is ADDIE model development research. The subjects of this research were 15 students in class VIII-2. The research results showed that the validity of the media was 85% before revision and 98% after revision from material experts and 61.67% before revision and 98% after revision from media experts on very valid criteria. The practicality of the media has met practical criteria, based on teacher responses obtained at 100% and from student responses obtained at 92.36%. The effectiveness of the media has met the effective criteria in terms of classical student learning completeness reaching 86.67%, use of research time in accordance with the RPP, and student response of 91.67%. The N-Gain test result is 0.70 in the high category. For the student answer process on the ability test (pre-test) it was 38.89%, increasing to 46.67% on the final ability test (post-test). Increasing students' ability to understand mathematical concepts strengthens the development of Articulate Storyline mathematics learning media in the classroom learning process.

Optimizing mathematical proficiency: Integrating Cambridge and national curricula in mathematics education

As the primary education institution, ‘School X’ needs to plan a comprehensive and efficient curriculum. This comprehensive study critically evaluates the integration of the Cambridge and National Curricula, with a special emphasis on mathematics. Data collection techniques included interviews, observations, case studies, open questionnaires, and documentation. Open questionnaires conducted with teachers revealed their understanding of the integration of the Cambridge and National curricula. The methodology combines a detailed SWOT (Strengths, Weaknesses, Opportunities, Threats) analysis with a case study approach. Surveys of both teachers and parents at the school capture a wide range of perspectives on the effectiveness, challenges, and benefits of integrating these curricula in mathematics. The impact of this integration on student performance, teacher efficacy, and educational equity in mathematics is also explored. The study's results, focusing on improved curriculum management, dedicated teacher development in mathematics, and ongoing assessment of mathematical competencies. This provides a foundational framework for effective curriculum management in a globally adaptive educational environment, specifically focusing on mathematics.

An Explanation to the Concept of Actual Infinity and Potential Infinity through Set Theory and Calculus

The concept of infinity refers to either an unending process or a limitless quantity. Aristotle introduced two types of infinity: potential infinity and actual infinity. Potential infinity refers to a never-ending process, and actual infinity refers to a collection containing infinitely many elements. This paper presents a descriptive study of the concept of infinity and discusses its properties through set theory and calculus. Infinity plays a central role in the formation and development of mathematics, specifically in limit, derivative, and integral. Moreover, the similarities and differences between potential infinity and actual infinity are explained with the help of set theory and integral differential calculus. The relationship between mathematics and infinity is a vital one. Since infinity is an elusive and contradictory idea without mathematical tools, it is hard to understand it, and there is no other knowledge to explain and make it understandable. By the way, in the absence of infinity, mathematics will never survive. This paper provided some examples to show that without employing mathematics, solving problems involving infinity based on human intuitions or weak induction may provide inaccurate results or lead to contradictions. Therefore, this paper suggested that using mathematical tools is essential for solving problems involving infinity.

Numerical and Analytical Methods for Differential Equations and Systems

The theory and applications of differential equations have played an essential role both in the development of mathematics and in exploring new horizons in the applied sciences [...]

Tensor force impact on shell evolution in neutron-rich Si and Ni isotopes* *This study was supported by the Interdisciplinary Scientific and Educational School of Moscow University's "Fundamental and Applied Space Research." Sidorov S.V. expresses his gratitude for the support provided by the Foundation for the Development of Theoretical Physics and Mathematics "BASIS."

The influence of the tensor interaction of nucleons on the characteristics of neutron-rich silicon and nickel isotopes was studied in this work. Tensor forces are considered within the framework of the Hartree-Fock approach with the Skyrme interaction. The addition of a tensor component of interaction is shown to improve the description of the splittings between different single-particle states and decrease nucleon-nucleon pairing correlations in silicon and nickel nuclei. Special attention was directed toward the role of isovector tensor forces relevant to the interaction of like nucleons.

Uncertainties estimation in surveying measurands: application to volumes

Volume represents a measurand of great interest in civil engineering and construction works. The estimation of this measurand is a problem already solved by surveying engineering, but the quantification of its uncertainty has been overlooked. As a result, the inaccurate estimation of the volume can lead to significant deviations in the execution costs of earthworks. Moreover, it is not possible to comply with the internationally accepted requirements concerning the expression of measures with an indication of its uncertainty, i.e. the guidelines of the Bureau International des Poids et Mesures. In this context, this paper presents a methodology for the quantification of uncertainty in the surveying measurement of volumes, which is generally carried out through digital terrain models processed by computer-aided design or specific surveying software. Two methods for volume estimation are presented and the variance–covariance propagation laws are applied to each of them, leading to the computation of volume uncertainty from measures of position coordinates for which uncertainties are known. Then, the developed methods for uncertainty estimation are successfully tested in different scenarios. The conceptual and mathematical developments for the uncertainty quantification in the computation of volumes resulted in closed-form algorithms implemented in MATLAB that can be potentially incorporated into commercial surveying software.

CLUSTERING-BASED OBJECTS STATE DIAGNOSTICS IN CONDITIONS OF FUZZY SOURCE DATA

У The problem of distribution of a set of objects, the state of which is determined by a set of controlled parameters, into a set of subsets of objects maximally homogeneous in their properties is considered. Relevance of the problem and important advantage of the clustering procedure: when its implementing it is possible to reduce the initial difficult problem of high dimensionality objects analysing to the solution of a number of simpler problems of lower dimensionality. This circumstance acquires additional attractiveness and importance if the initial data of the problem contain uncertainty, for example, are vaguely defined. Research object is the procedure of partitioning a set of objects into clusters under conditions of uncertainty. In this regard, the purpose of the study is to develop a method for solving the problem of clustering in conditions where the initial data on objects controlled parametersthe values contain uncertainty. The method of solving the problem is based on clustering procedure mathematical model development, containing analytical expressions for the criterion of its effectiveness, written in the form of a twice fractionally quadratic function. The impossibility of mathematical programming problem direct solution initiated the development of a heuristic algorithm for its solution. As a result, an iterative method was obtained and applied to solve the clustering problem under conditions of fuzzy initial data. The developed computational procedure is based on a reasonable system of rules for performing operations on fuzzy numbers. The situations when the belonging functions of problem fuzzy parameters are defined on infinite or compact media are considered. The developed system of rules allows to correctly perform operations in the metric of fuzzy defined states between clustering objects. The proposed method is easily generalised to the case when the uncertainty of the initial data is hierarchical.

Verification of uncertainty estimates of autonomous field measurements of marine reflectance using simultaneous observations

The primary ocean color product is the spectrum of remote sensing reflectance RRS that allows the quantification of in-water optically significant constituents and all ocean color applications. The determination of its uncertainties is thus key to the creation of comprehensive uncertainty budgets for all derived ocean color products. The assessment of satellite RRS uncertainties has largely relied on corresponding field measurements but this process is solid only if these field measurements are in turn fully characterized. Uncertainty budgets have therefore been defined and reported for the radiometric measurements collected in the framework of the Ocean Color component of the Aerosol Robotic Network (AERONET-OC). The contemporaneous deployment of two autonomous systems for 5.5 years on the Acqua Alta Oceanographic Tower (AAOT) located in the northern Adriatic Sea led to the collection of 4,449 pairs of coincident observations (collected with a time difference lower than 10 min) distributed over 659 days of data acquisitions that can be used to verify reported uncertainty values. The comparison of matched pairs showed a good agreement for RRS (with differences of typically 2%–3% between 412 and 560 nm), as well as for the aerosol optical thickness τa (3%–6%). Differences between data from the two systems appear generally consistent with their stated uncertainties, indicating that they are metrologically compatible and that uncertainties reported for AERONET-OC data are usually trustworthy (with possible exceptions depending on the level of error correlation between measurements from the two systems). Using uncertainty cone diagrams, this result holds across the range of uncertainty values with few exceptions. Independent uncertainty estimates associated with non-systematic error contributions were obtained using a collocation framework allowing for error correlation between measurements from the two systems. The resulting uncertainties appeared comparable with the reported values for τa and RRS. The related mathematical development also showed that the centered root-mean-square difference between data collected by two systems is a conservative estimate of the uncertainty associated with these data (excluding systematic contributions) if these data show a good agreement (expressed by a slope of method II regression close to 1) and if their uncertainties can be assumed similar with errors moderately correlated (typically lower than 0.5).

Integration of Ethnomathematics Teaching Materials in Mathematics Learning in Elementary School

Objective: This research serves as a preliminary study to outline the framework and projection of ethnomathematics studies, particularly concerning the integration of ethnomathematics into mathematics curriculum and the development of mathematics learning objectives using an ethnomathematical approach. Method: The research employs a Systematic Literature Review (SLR) methodology involving identifying, evaluating, and interpreting relevant literature on the research topic. Results: The findings reveal that the ethnomathematical approach effectively enhances students' understanding of mathematics. Students exhibit higher motivation and satisfaction with mathematics learning when connected to their local culture. Novelty: This research shows that the ethnomathematics approach facilitates the development of teachers' competencies in integrating cultural elements into mathematics education. Both teachers' recommendations and research findings support the inclusion of ethnomathematics in mathematics curricula both directly in developing learning tools and materials and in curriculum policies. Additionally, there is potential for technology applications to support ethnomathematics learning, enabling students to study mathematics independently. In conclusion, integrating ethnomathematics holds significant potential in improving students' mathematical understanding, connecting mathematics with local culture, and motivating students to learn mathematics more enjoyable and relevantly.

Impact of Kindergarten Teachers’ Scientific Processing Skills Training on Children’s Science and Mathematics Development

ABSTRACT The purpose of the study is to examine the impact of in-service education for early childhood teachers about scientific processing skills on young children’s (5–6 year-old) science and mathematics performance and teachers’ science teaching attitudes. A pretest-posttest with control group design was applied. From the treatment group nine teachers and 60 children (27 boys, 33 girls); and from the control group eight teachers and 95 children (56 boys, 39 girls) completed the study. After pretests, treatment group teachers received scientific processing skills training. For eight weeks treatment group teachers had applied eight experiments and eight illusion activities that were taught to them during the training. A mixed ANOVA indicated a significant effect of treatment on children’s TEMA-3 scores (mathematics performance) from pretest to posttest. A Mann – Whitney U test did not indicate any significant difference between treatment and control groups’ differences for C-PALLS+STEM (science knowledge) posttest minus pretest scores. Responses to a scale measuring teachers’ attitudes toward science teaching revealed that treatment teachers’ attitude toward science teaching increased significantly, whereas such an increase was not recorded in control group teachers. Qualitative data revealed that the training positively affected teachers’ perspectives on science and contributed to their conducting higher quality scientific activities in their classrooms.

A global heat flow topology for revealing the synergistic effects of heat transfer and thermal power conversion in large scale systems: Methodology and case study

In the processes of modeling, optimization, heat transfer analysis, and thermal power conversion analysis in large-scale complex systems, challenges are encountered regarding intricate design and optimization. In this paper, a global heat flow topology is proposed that reveals the synergistic effect of heat transfer and thermal power conversion in large-scale systems. The approach involves the construction of a heat flow topology, mathematical model development, analysis of specific parameters, and multi-objective optimization. It integrates various methods and tools, including heat flow topology, numerical simulation tool, entransy transfer analysis, global thermal resistances visualization, genetic algorithm (GA), and technique for order preference by similarity to ideal solution (TOPSIS). By using the LNG cold energy recovery and regasification process in floating storage and regasification units (FSRU) as a case study, the methodology provides a comprehensive understanding of the interactions and conversions between heat transfer and thermal power within the system. The results demonstrate that the optimal configuration achieves a maximum thermal efficiency of 21.73 % and a maximum cold recovery efficiency of 58.48 %. Additionally, the interaction between LNG pressure and seawater temperature exhibits limited synergistic impact on both LNG cold exergy efficiency and entransy transfer efficiency. Similarly, the combined influence of LNG pressure and evaporator temperature shows weak synergistic effects on parameters such as supply/demand ratio, thermal efficiency, and entransy transfer efficiency. The analysis of the global thermal resistance bubble chart reveals the significant impact of evaporator temperature and seawater temperature on the evaporator resistance, as well as the notable impact of LNG pressure on the condenser resistance.

МАТЕМАТИЧНА ПОЕЗIЯ ТРАГIЧНОЇ НЕСКIНЧЕННОСТI

The article, very briefly, tells about the life path and scientific achievements of the Indian mathematician Srinivasa Ramanujan Iyengar, who made a significant contribution to number theory, mathematical analysis and other areas of mathematics. With no formal training in mathematics, he taught himself the discipline, relying on limited resources and his own intuition. He formulated many theorems, made assumptions that were later proved by other mathematicians, and developed new research methods. His works had a significant impact on the development of mathematics in the 20th century.

Finding Your Mathematical Roots: Inclusion and Identity Development in Mathematics

Finding Your Mathematical Roots: Inclusion and Identity Development in Mathematics

The quest for psychological symmetry through figural goodness, randomness, and complexity: A selective review.

Of the four interrelated concepts in the title, only symmetry has an exact mathematical definition. In mathematical development, symmetry is a graded variable-in marked contrast with the popular binary conception of symmetry in and out of the laboratory (i.e. an object is either symmetrical or nonsymmetrical). Because the notion does not have a direct graded perceptual counterpart (experimental participants are not asked about the amount of symmetry of an object), students of symmetry have taken various detours to characterize the perceptual effects of symmetry. Current approaches have been informed by information theory, mathematical group theory, randomness research, and complexity. Apart from reviewing the development of the main approaches, for the first time we calculated associations between figural goodness as measured in the Garner tradition and measures of algorithmic complexity and randomness developed in recent research. We offer novel ideas and analyses by way of integrating the various approaches.

Review of research on microteaching in mathematics teacher education: Promises and challenges

Microteaching has been viewed as a professional development tool that gives pre-service teachers the chance to strengthen their teaching skills. This paper presents an overview of the research on microteaching in mathematics teacher education, noting its prospects and challenges while also making recommendations for modifications to its application. A thorough analysis of 28 empirical papers on microteaching in mathematics teacher preparation that were published between 2000 and 12 May 2023, was conducted. Findings demonstrate that microteaching is an effective approach for enhancing pre-service teachers’ core mathematics teaching skills. It is suggested that microteaching, which begins in a laboratory setting with the development of essential teaching skills, should not end there; it should give trainee teachers an opportunity to learn and practice in a real classroom context. Microteaching activities require more time, more supervisors, and more resources to function at its maximum capacity. Technology has also demonstrated greater promise when it comes to enhancing microteaching’s position in facilitating the development of pre-service mathematics teachers’ instructional skills.

MENTORING NO DESENVOLVIMENTO PROFISSIONAL DE PROFESSORES DE MATEMÁTICA RELACIONADO AO PLANEJAMENTO DE AULAS, INTEGRANDO TECNOLOGIAS DIGITAIS

ABSTRACT: This paper refers to mentoring in the professional development of mathematics teachers concerning the planning of their classes with the integration of digital technologies. The research follows a qualitative approach and the context was a practice carried out with two mathematics teachers from primary public school. We had seven meetings, one a week and adapted practices because of COVID-19. The aim was to investigate how the mentoring strategy can influence mathematics teachers in planning their classes with integrated digital technologies. The results of this study showed that it was possible to understand that mentoring helped the teachers in planning classes with integrated technologies. Reflections and discussions contributed to understand the importance of class objectives and the need to get them involved with the planned activities. Furthermore, the teachers realized that they, before mentoring, did not discuss class topics with students, they only taught classes in a transmissive way.

О некоторых аспектах инженерного решения задачи о трисекции угла: история и новый алгоритм решения

The article is devoted to the history of the formulation and solution of the problem of trisection of an angle - dividing an angle into three equal parts using a compass and a ruler, which has a history of more than 2.5 thousand years. Traditionally, the origins of the problem were associated with the practical activities of masters and artisans of Ancient Greece, but it is known that with the help of simple practical techniques or small assumptions in the original formulation, the problem is completely solvable. It is shown that the problem of angle trisection is based not on practical interest, but on deeper grounds related to the worldview of the philosophers and mathematicians of Hellas and the historical course of development of mathematics. In particular, with the methodological work of representatives of the Pythagorean school, who created geometric algebra with objects in the form of lines, circles and tools for their construction - compasses and rulers. On the other hand, the engineering approach, the origins of which are also located in Ancient Greece, allowing in the solution process the use, in addition to compasses and rulers, notches, scales, additional curves and any drawing tool that creates a finite thickness of drawn lines, allows us to solve the problem of trisection of an angle. As an example of an engineering approach to the problem of trisection of an angle, the original solution of the author of the article is given, using a compass, a ruler and a drawing object having a finite thickness. The proposed algorithm makes it possible to mathematically solve the problem of trisection of an angle with any accuracy. From a historical perspective, it is surprising that the tradition of formulating the search for a solution to the problem of trisection of an angle only with the help of a compass and a ruler, while rejecting numerous possibilities of the engineering approach, remained and was supported by all subsequent generations of mathematicians for 2.5 thousand years until the present day.