Mathematical Concepts Research Articles

An infrared and visible image fusion using knowledge measures for intuitionistic fuzzy sets and Swin Transformer

The objectives of infrared and visible image fusion are to generate a single image that includes significant objects and rich texture information. However, the current deep-learning methods ignore uncertainty in the decision-making process during the fusion phase. To address this issue, we propose a novel infrared and visible image fusion method using a Swin Transformer and knowledge measures of intuitionistic fuzzy sets (IFSs) named SWKIF-Fusion. This model employs a Swin Transformer-based pre-trained module for feature extraction, which is the most effective module for modeling long-range dependencies. The fusion process of SWKIF-Fusion integrates the proposed knowledge measure of IFSs. IFSs inherently possess a high capability to handle uncertainty, and the knowledge measure of IFSs provides uncertainty quantification. This integration in the fusion phase mitigates the uncertainty in the decision-making process. This fusion of IFSs, knowledge measures, and the Swin Transformer-based deep learning model enhances the overall performance, as demonstrated through experiments on the TNO, Roadscene, OTCBVS, M3FD, and MSRS datasets. This study also fills the gap in developing knowledge measures for IFSs by proposing novel general construction methods. It presents a theoretically sound framework for knowledge measures of IFSs using well-established mathematical concepts such as t-norms, t-conorms, automorphisms, and aggregation operators.

Ethnomathematics Exploration of Multiplying and Measuring Activities on The Dome of The Great Mosque of Baitul Hakim Madiun City

Ethnomathematics is a study that explains the relationship between culture and mathematics. Ethnomathematics is applied as a means to motivate, stimulate, overcome saturation, and give a new feel to mathematical learning. One of the cultures that can be studied with ethnomathematics is the mosque. This study aims to learn mathematical concepts and explore ethnomathematics in the building of the Grand Mosque of Baitul Hakim Kota Madiun, the explored building, namely the dome of the mosque. This qualitative research uses an ethnographic approach with data retrieval using observation, interview, and documentation techniques. The research was conducted at the Grand Mosque of Baitul Hakim City of Madiun with 3 subjects being mosque administrators (secretariat admin, takmir, and marbot). The results of the research were obtained from mathematical concepts and ethnomathematics activities at the Grand Mosque of Baitul Hakim. The mathematical concept obtained is the geometric concept related to the flat construction of isosceles triangles, isosceles trapezoids, ellipses, and limas space structures. The ethnomathematics activity obtained is the activity of measuring and enumerating. Therefore, it can be concluded that there is ethnomathematic activity and there are mathematical concepts in the Grand Mosque of Baitul Hakim Kota Madiun that can be used as a learning resource by educators.

Relationship Between Parents’ Involvement with Students’ Interest and Achievements in Mathematics Learning

Parental involvement has been recognized as a crucial factor in shaping a child's educational outcomes across various subjects, including mathematics. When parents actively participate in their child's education by showing interest, discussing mathematical concepts, and assisting with homework, students are more likely to develop a deeper interest in mathematics. This engagement fosters a positive attitude towards learning the subject and can lead to improved grades and overall academic success. Mathematics has been defined as the study of assumptions and applications and is one of the compulsory subjects in Sijil Pelajaran Malaysia (SPM). The students need to achieve at least a passing grade, since most tertiary educational institutions in Malaysia, especially the public have very strict requirements for enrollment, not to forget the stiff competition. The main purpose of this research is to study how parents’ involvement influences students’ interests, as well as their self-perceptions, and consequently how these elements may affect their achievements in Mathematics. 186 Form Four students from SMK Bandar Baru Bangi were selected as the respondents. A quantitative method, using a questionnaire was opted as instrument for data collection. The collected data was analyzed using the IBM Statistical Package of Social Science (SPSS). The findings showed that majority of parents can provide the essential educational tools for children, such as geometry sets, scientific calculator etc. Most students prefer their parents to engage more in their learning process. There is a statistically positive significant relationship between parents' involvement and students’ achievements, which proves the important roles of parents in improving the interest of their children towards learning. In a nutshell, based on the evaluations done by the students, this study may indirectly assist the parents to identify the ideas and the initiatives that they may take in improving their children’s performances.

ПРИКАЗНА МАТЕМАТИКА – РАЗНОВЪЗРАСТОВА ГРУПА

The topic of using interactive games for the formation of elementary mathematical concepts is gaining special relevance now that information technologies are widely distributed in the educational process. At the level of preschool education, interactive games become an assistant in the organization of pedagogical interaction. This report presents a mathematical story used in a diff erent age group – five and six year old children, in all educational cores of the educational direction “Mathematics“. The following objective is set: Use of fairy mathematics to form elementary mathematical concepts in the five-six-year-old child. Concepts: clarifying questions, directions, encouragement, self-assessment.

Pembelajaran Distribusi Gamma dalam Masalah Biomedis: Tinjauan pada Pengaruh Dosis Beracun pada Tikus

Purpose: The objective of this study is to examine the use of the Gamma function in the Gamma distribution and its application in analyzing the effect of toxic doses on rats. Methodology: The methodology employed in this study utilizes a non-standard Gamma distribution, with a continuous random variable X that has parameters α and β. The research methods employed in this study include a literature review and a case study. Findings: The results of the calculations indicated that the mean time to death for the rats was 50 weeks, with a standard deviation of 22.36 weeks. Significance: It was also found that the probability of rats surviving for more than 60 days was less than 60%. Based on these findings, the study offers recommendations for the teaching of mathematics, particularly in the context of understanding probability distributions and their applications in biological and toxicological contexts. This study underscores the significance of grasping the Gamma distribution in anticipating and interpreting data in the life sciences, as well as the capacity of mathematical concepts to be operationalized in genuine settings.

Improving Mathematical Understanding Ability Using Tournament Learning with the Help of Panta Media

Students' understanding of mathematical concepts is still relatively low, especially in data material. One of them is caused by the learning process which is still student-centered. So this research aims to find out how to increase student's ability to understand mathematical concepts using tournament-based learning with the help of panta media. This type of research is quasi-experimental with a nonequivalent control group research design. The population used was class V students in North Sumedang District with research samples from class V at SDN Sindang II as the experimental class and SDN Jatihurip as the control class. The instrument used is a test of the ability to understand mathematical concepts with description questions. The analysis technique in this research is the mean difference test (paired sample t-test and independent sample t-test) which has been tested for normality and homogeneity. To determine the increase in students' mathematical abilities, the N-Gain test was carried out. The two classes were given different treatments, namely the experimental class with tournament-based learning assisted by panta media and the control class with conventional learning. The increase in students' ability to understand mathematical concepts can be seen from the average N-Gain results in the experimental class of 0.6500 in the moderate improvement category and in the control class of 0.2591 which is classified as low improvement. The two classes have significant differences in their ability to understand mathematical concepts. It was concluded that tournament-based learning with the help of panta media can improve students' understanding of mathematical concepts.

EKSPLORASI ETNOMATEMATIKA PADA KERAJINAN CAPING DI DAERAH KABUBATEN KAMPAR

Mathematical concepts are often used in everyday life. The term that refers to mathematical concepts in cultural concepts is ethnomathematics. Ethnomathematics is a science used to understand how mathematics is adapted from a culture. This research discusses the exploration of ethnomathematics contained in the process of making Caping crafts in Kampar Regency. This research aims to explore the ethnomathematics concept found in Caping crafts in Kampar Regency. This type of research is qualitative with data collection obtained from observation, documentation and interviews related to Caping crafts in Kampar Regency. The results of the research show that: The mathematical concept that exists in the Caping making process is the geometry of flat shapes, namely equilateral triangles, circles and rectangles. The geometric shape of a space is a cone. Transformation geometry is reflection.

Mathematical Concepts and Cultural Values in Sonaf Tamkesi: Ethnomathematics Study in a Traditional Village on Timor Island

Mathematics is a universal science, and it is crucial for everyone to master it, both in terms of its applications and its cognitive patterns. The purpose of this research is to explore the concepts of mathematics and cultural values found in the artifacts of Sonaf Tamkesi Manufui. The study was conducted in the traditional village of Tamkesi, south Biboki District, North Central Timor Regency, in July 2023. The subjects of this study were three community leaders. The type of data collected for this research was primary data obtained through documentation and interviews between the researcher and the respondents. Data analysis was conducted through stages of domain analysis, taxonomy, componential analysis, and cultural themes. The research findings indicate that there are concepts of plane geometry in the artifacts such as trapeziums, rectangles, squares, rhombuses, triangles, circles, cylinders, hexagons, and cubes. Meanwhile, the cultural values of the artifacts in Sonaf Tamkesi are the roof symbolizes harmony, the door symbolizes greatness and respect for ancestors, the pillars symbolize vertical relations with ancestors, the betel-nut container symbolizes service, the clay pot symbolizes a gift from ancestors to the living, the hearth symbolizes balance, and harmony in achieving goals.

PATOGE geometry transformation board: A teaching aid to enhance junior high school students' conceptual understanding

Geometric transformation is a vital mathematics topic that should be learned at the junior high school level. Students often consider This material difficult because it is abstract and lacks concreteness. One effort to overcome this difficulty is by using teaching aids. This study aims to develop a geometric transformation board teaching aid to improve the conceptual understanding of 9th-grade junior high school students. This research employs a research and development method. The research sample consists of 17 9th-grade junior high school students. The results show that using the geometric transformation board teaching aid can enhance the conceptual understanding of 9th-grade students. The average student learning outcomes evidence this increase from 57.65 to 79.41. This study implies that PATOGE can effectively make abstract mathematical concepts more concrete and easier to understand.

Exploring the relationship between students' attitudes and fraction sense proficiency across lower secondary grades

Understanding fractions is a critical mathematical skill necessary for more advanced mathematical concepts and applications. However, many students struggle with fraction sense, which is the foundational understanding and flexible use of fractions. This study aims to explore the relationship between students' attitudes toward learning fractions and their proficiency in fraction sense in lower secondary grades. Using a descriptive-correlational design, data were collected from 296 students aged 13 to 15 using the Fraction Sense Test (FST) and the Attitudes Towards Learning Fractions Questionnaire (ATLF). The study found that students consistently struggled with fractional concepts, achieving low scores across all grades. Nevertheless, a significant, though diminishing, relationship was observed between positive attitudes towards fractions and fraction sense proficiency from Secondary One to Secondary Three. These findings suggest the need to integrate meaningful fraction learning approaches to maintain students' positive attitudes, thereby improving their overall mathematical competence.

THE EFFECTIVENESS OF MATHEMATICS LEARNING THROUGH A REALISTIC MATHEMATICS EDUCATION APPROACH IN ELEMENTARY SCHOOLS

The research aims to analyze the effectiveness of mathematics learning through the realistic mathematics education approach in learning the concept of counting integers in grade VI elementary school students. The research used a quasi-experiment with one pretest postets design. The research involved 32 grade VI students at SDN 205 Neglasari, Coblong District, Bandung City. The research instrument is in the form of a multiple-choice test that includes addition and subtraction of decimal numbers. Research shows that the RME approach is effective in producing a significant improvement in students' learning completeness in the addition and subtraction of decimal integers, as well as improving mathematical problem-solving, self-efficacy, reasoning, and mathematical literacy. RME encourages students to recognize the practical application of mathematical concepts through real-world contexts and cultural elements, as well as to cultivate creative and imaginative thinking skills so that they can be an important strategy in improving mathematics education in primary schools.

PENGGUNAAN MEDIA SOFTWARE GEOGEBRA UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA SMA

Mathematical representation ability is an important ability in understanding mathematical concepts as an effort to obtain clarity of meaning and understanding in solving problems. Technology-based learning media can simplify the learning process thereby helping students in representing mathematical problems. This research aims to determine the increase in students' mathematical representation abilities using Geogebra software. This research is quantitative research with a quasi-experimental type. The population is students of class XI MIPA at SMA Negeri 1 Lhoong Aceh Besar for the 2023/2024 academic year consisting of 2 classes totaling 60 people. There are 30 people in Class XI MIPA 1 as an experimental class with the Geogebra software learning media, and 30 people in XI MIPA 2 as a control class without the Geogebra program learning media. The data collection technique in this research is using Pretest and Posttest. Meanwhile, the data analysis techniques used in this research are descriptive statistical analysis and inferential statistical analysis. The results of the research showed that there was an increase in students' mathematical representation abilities who were taught using Geogebra software media in class XI MIPA students at SMA Negeri 1 Lhoong. Most students answered the questions according to indicators of mathematical representation ability in the form of visual, symbolic and verbal representations.

The Systematic Review of the Studies Conducted in Turkey on the Topic of Applying 3D Printing in Mathematics Education

3D printing technology is increasingly widely used in all areas of STEM education. Many researchers emphasize that 3D printing in the context of mathematics education unpacks students' mathematical and design thinking, as well as helps them develop spatial skills, and is a key tool for visualizing mathematical concepts, especially in calculus and geometry. However, when the relevant literature is examined, it is seen that there is no existing systematic review that comprehensively describes and synthesizes the findings in the literature on how 3D printers are applied in mathematics education in the context of studies conducted in Turkey. The purpose of this research is to make a systematic review of the studies conducted between 2015-2023 in Turkey on the topic of applying 3D printing in mathematics education. The results of this study show that qualitative research method is more preferred in the analyzed studies. The predominant dependent variable employed in these investigations is mathematics achievement, with the majority of participants being middle school students. The results of this systematic review indicated that applying 3D printing in mathematics instruction usually helps to improve students’ mathematical literacy, and mathematical skills in the context of studies conducted in Turkey.

Upaya Meningkatkan Pemahaman Konsep Matematika Siswa Melalui Penerapan Model CORE di MA NW Putra Narmada Tahun Pelajaran 2023/2024

This study was conducted as an effort to enhance students' understanding of mathematical concepts through the application of the CORE (Connecting, Organizing, Reflecting, Extending) model at MA NW Putra Narmada, West Lombok Regency. This research is a Classroom Action Research (CAR) carried out in two cycles with stages of planning, implementation, observation, and reflection. The subjects of this research are 34 students from the 10th grade at MA NW Putra Narmada. The research instruments used are observation sheets and test sheets. The data collection techniques employed are testing and observation. The data analysis techniques used are both quantitative and qualitative data analysis. The results of this study indicate an improvement in the understanding of mathematical concepts among the 10th grade students of MA NW Putra Narmada after applying the CORE learning model. Test results show an increase in students' understanding of mathematical concepts in cycle I to 57% with a sufficient category, while in cycle II, it increased to 95.00% with an excellent category. Observation results show 68% in cycle I with a good category and 96.00% in cycle II with an excellent category.

PENINGKATAN PEMAHAMAN PENJUMLAHAN DENGAN TEKNIK MENYIMPAN MENGGUNAKAN ALAT PERAGA DI KELAS II SD NEGERI 218/LIMBUR BARU

ABSTRACT The research problem is the lack of understanding of the material for calculating sequential additions. The aim of this research is to improve understanding of compound addition material by storing techniques through the use of number value racks. Class II students at SD Negeri 218 Limbur who have mild intellectual disabilities will benefit from a better understanding of the concept of multilevel addition operations. This type of research is called Classroom Action Research (PTK). This research was carried out in two cycles, each cycle being carried out in three meetings. Each cycle has four interrelated phases: observation, reflection, action implementation, planning phase, and reflection. The research subjects were four students of SD Negeri 218 Limbur class II. Data was collected through test and observation methods. Quantitative analysis was carried out on the data, and a table was presented showing student learning outcomes. Based on the results of research conducted in cycle I and cycle II, the results of data analysis and reflection show that cycle I research has not met the expected indicators of success, namely better understanding of mathematical concepts because it shows learning outcomes and students' abilities in understanding and carrying out sequential addition operations. using the saving technique, then the average result in cycle II was 62.5%. By using the saving technique, students were able to understand the concept of sequential addition, which not only achieved the desired goal but also improved. This shows that the use of the number value rack display tool can improve students' understanding of the addition material using storing techniques. Keywords : stacked addition, rack of number values.

Alternative ways to initiate students’ intuition, and hence internalization, of why zero factorial is equal to one

Zero factorial, defined to be one, is often counterintuitive to students but nonetheless an interesting concept to convey in a classroom environment. The challenge is to delineate the concept in a simple and effective way through the practice of justification, a familiar concept in mathematics and science education. In this regard two algebraic and one statistical justification using the squeeze theorem are presented. To assess the effectiveness of the justifications, a student survey was conducted at a comprehensive university incorporating the analysis of the pre- and post-presentation statements. They clearly present that the justifications are useful in giving credence to zero factorial equals one. Overall, the result from the online survey supports that the students preferred Justification 1. The justifications provide instructors alternative ways to initiate exploration of students’ intuitive set up of comprehending unobvious facts like zero factorial equals one. For a range of learners with their varied abilities to perform various mental activities most closely associated with learning and problem-solving, the justifications as simple alternative methods offer the potential to raise the current level of cognitive skills to inspire differentiated paths of learning. These are evident from survey results noting the role of statistical thinking and techniques.

Sustaining Retentive Memory of Mathematics Concepts in Adolescents Utilising Game-Based Learning: A Case of Repeated Measures

Effective mathematics education is pivotal for students’ academic achievements and future career prospects. However, traditional teaching methods are often inadequate for helping students retain mathematical concepts, emphasizing the necessity for innovative approaches such as game-based learning. This research aimed to assess the efficacy of game-based learning in bolstering the retention of trigonometry concepts among senior secondary school students. Employing a mixed between and within measures ANOVA design, the study randomly assigned 60 students (aged 15-16 years, 31 males and 29 females) to either an experimental group (n=28) receiving game-based learning or a control group (n=32) receiving traditional instruction. Data, collected through the study’s tool (Mathematics Achievement Test [MAT]) at the pre-test, post-test, and retention test stages, underwent repeated measures ANOVA analysis. Results indicated significant effects of Group [F(1, 58) = 44.081, p<.001, ?²p=.432], Time [F(1.783, 103.4) = 16.561, p<.001, ?²p=.222], and Group by Time interaction [F(1.783, 103.4) = 18.125, p<.001, ?²p=.238]. The experimental group exhibited notably higher retention scores (Time 3 mean = 74.82) than the control group (Time 3 mean = 44.38). Importantly, gender, age, and location did not significantly moderate the effectiveness of the game-based approach. In conclusion, game-based learning effectively enhances and sustains students’ retention of trigonometry concepts, irrespective of demographic variables. This study furnishes empirical validation for integrating game-based learning into mathematics education, underscoring its potential to fortify conceptual retention, and offering actionable insights for educators and policymakers alike.

Development of Interactive Multimedia Based on ISpring Suite with Corrective Feedback to Improve Student’s Conceptual Understanding Ability

The ability to understand mathematical concepts are one of the abilities that must be achieved. Based on the results of the initial test, the conceptual understanding ability of class IX students at one of schools in Magelang are relatively low. The aim of this research was to produce iSpring Suite-based learning multimedia products with valid, practical and effective corrective feedback in improving students' concept understanding abilities. The research belongs to research and development using the Borg and Gall model. The results of the validity test were 88.44% by material experts in the "very valid" category, and 80.77% by multimedia experts in the "very valid" category. The results of the practicality test were based on the results of the student response questionnaire with an average score percentage of 90% in the "very practical" category, then based on the teacher response questionnaire with a percentage of 88% in the "very practical" category, and based on learning implementation questionnaire, the score was 93.33% with the "very good" category. The results of the test involving 32 students based on the N-Gain were 0.71 in the high improvement category, and the Wilcoxon test obtained Z = -4.941. So, interactive multimedia based on ISpring Suite with Corrective Feedback are valid, practical and effective to improve junior high school students' concept understanding skills in quadratic equation material.

Culturally Contextualized E-Module Based on Papua: Why Teachers and Students Need It for Teaching Linear Programming Material?

The use of e-modules in mathematics learning significantly aids both teachers and students in the teaching and learning process. However, the design of e-modules has not been extensively linked to the cultural context in which students live. Therefore, this study aims to explore and analyze the needs of teachers and students in developing culturally integrated e-modules, particularly those reflecting the culture of Papua, for high school students. The research design employed is phenomenological. Participants included Mathematics teachers for grades X, XI, and XII in Nduga Regency, Papua Highlands, and 64 high school students (42 male and 22 female). Data collected from observations and interviews were qualitatively analyzed using Miles-Huberman Interactive Analysis. Findings revealed that the high schools still use the 2013 curriculum, relying on standard textbooks as teaching materials. These textbooks pose problems for students as they are often uninteresting, use formal language, are difficult to understand due to abstract content, and are not contextualized to students' daily lives. Additionally, the reduction in face-to-face learning hours, due to the school's location in a conflict area, hampers effective teaching and learning processes. Another interesting finding is that high schools in Nduga Regency have not yet utilized technology in learning, despite having internet access. These findings imply the need for teaching materials integrated with technology and local culture to help students understand mathematics concepts and assist teachers in teaching both inside and outside the school.

Caracterización del conocimiento de estudiantes universitarios al relacionar una función con su función derivada desde un enfoque gráfico

This paper aims to show how university students relate a function with its derivative function in a task with a purely graphical approach. This task is part of a diagnostic test used in a broader investigation whose objective is to build the concept of derivative in university students with the help of the APOE theory, which provides mental structures required to understand a mathematical concept: action, process, object, and scheme. Initially the paper shows the details of the test and the analyzed task, then it shows the qualitative and quantitative analysis of the observed responses. In general, the results obtained show deficiencies in students when faced with graphic focus exercises. Likewise, the justifications observed in students show an inclination towards solving exercises from an algebraic aspect, thus leaving aside the graphics of the activity. We assume that future research may use these results as background for their works, and active teachers may encourage their students to resolve this type of conceptual items in the classrooms.