Mathematical Understanding Research Articles

Development of Game-Based Mathematics Learning Media to Improve Mathematical Understanding Abilities

This research aims to develop mathematics learning media in the form of games. Apart from that, this research aims to determine the feasibility and find out whether the learning media being developed is appropriate and can improve students' understanding abilities in mathematics subjects. This type of research is development research with the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research subjects were class VII students at YP Sunan Dalem Gumeno Middle School. The research instruments used in this research were (1) Interview Guide (2) Validation Sheet (3) Student Response Questionnaire (4) Mathematical Understanding Ability Test Questions. The mathematics learning media in the form of games developed is expected to improve students' mathematical understanding abilities. The validation results from media experts and material experts respectively obtained an average of 4.4 and 4.2 with valid criteria. The validation results of the mathematical understanding ability test obtained an average score of 4.2 with valid criteria. The results of the student response questionnaire obtained an average practicality of 4.2 with practical criteria. The results of the mathematical understanding ability test were carried out using a t-test using the SPSS program and the results showed that the significant value was 0.000 < 0.05, meaning that students' mathematical understanding ability after using game learning media was better before using the game learning media, so it can be concluded that the learning media Games can improve students' mathematical understanding abilities and can be said to be effective. The results of this research show that learning media is said to be valid, practical, and effective. In other words, game-based mathematics learning media can improve students' mathematical understanding abilities.

MATHEMATICAL MODELS AND ALGORITHMS IN LOGISTICS: REAL- WORLD APPLICATIONS AND AI IMPACT

Have you ever pondered the importance of mathematics in the field of logistics? Have you also reflected on whether a solid understanding of mathematical principles is crucial for achieving success in a logistics profession? This article explores the intersection of mathematics and logistics, shedding light on the indispensable role mathematics plays within the industry. By exploring practical applications, it provides insights into the mathematical concepts integral to the daily activities of logistics professionals. Whether aspiring to enter the field or carrying out further studies in logistics, this article offers a foundational understanding of mathematics' importance in logistics. In addition, we have also shown a case in which technological development and artificial intelligence are applied, where we have employed logistic regression, k-nearest neighbors, and random forest classifiers on data collected from Amazon to analyze customer reviews. Our results demonstrate that logistic regression outperformed the others, achieving an accuracy rate of 86.75%. This result is suggestive of the importance of this technique in building customer relations, particularly in their use in decision-making methods.

Artificial intelligence-driven real-world battery diagnostics

Addressing real-world challenges in battery diagnostics, particularly under incomplete or inconsistent boundary conditions, has proven difficult with traditional methodologies such as first-principles and atomistic calculations. Despite advances in data assimilation techniques, the overwhelming volume and diversity of data, coupled with the lack of universally accepted models, underscore the limitations of these traditional approaches. Recently, deep learning has emerged as a highly effective tool in overcoming persistent issues in battery diagnostics by adeptly managing expansive design spaces and discerning intricate, multidimensional correlations. This approach resolves challenges previously deemed insurmountable, especially with lost, irregular, or noisy data through the design of specialized network architectures that adhere to physical invariants. However, gaps remain between academic advancements and their practical applications, including challenges in explainability and the computational costs associated with AI-driven solutions. Emerging technologies such as explainable artificial intelligence (XAI), AI for IT operations (AIOps), lifelong machine learning to mitigate catastrophic forgetting, and cloud-based digital twins open new opportunities for intelligent battery life-cycle assessment. In this perspective, we outline these challenges and opportunities, emphasizing the potential of innovative technologies to transform battery diagnostics, as demonstrated by our recent practice and the progress made in the field. This includes promising achievements in both academic and industry field demonstrations in modeling and forecasting the dynamics of multiphysics and multiscale battery systems. These systems feature inhomogeneous cascades of scales, informed by our physical, electrochemical, observational, empirical, and/or mathematical understanding of the battery system. Through data assimilation efforts, meticulous craftsmanship, and elaborate implementations—and by considering the wealth and spatio-temporal heterogeneity of available data—such AI-based intelligent learning philosophies have great potential to achieve better accuracy, faster training, and improved generalization.

The Effect Of Adaptive Learning Experience (Adlx) On Mathematics Learning Outcomes Of High School Students In Grade Xi Based On Learning Motivation

This study aims to analyze the effect of the use of ADLX (Adaptive Learning Experience) on the mathematics learning outcomes of grade XI high school students by considering learning motivation. Using a quasi-experimental method with a non-equivalent control group design, this study involved several 11th grade high school students in X City who were divided into two groups: an experimental group using ADLX and a control group using conventional methods. The research instruments include mathematics learning outcome tests and learning motivation questionnaires validated by experts. The data were analyzed using the variance analysis technique (ANOVA) to test the hypothesis. The results showed significant differences in mathematics learning outcomes between the experimental and control groups, with the experimental group using ADLX showing better results. The data analysis also revealed that learning motivation interacted significantly with ADLX use, suggesting students with high learning motivation benefited more from ADLX use than students with low learning motivation. In general, students report that their learning motivation is influenced by the material's relevance to their daily lives and interactive and engaging teaching approaches. The use of ADLX, which involves hands-on experience and real-life examples, is considered effective in increasing understanding and motivation for learning math. This shows that the contextual learning approach is to improve students' understanding of mathematics. The conclusion of this study is that the use of ADLX can improve the mathematics learning outcomes of high school students in grade XI, especially for students with high learning motivation. These findings emphasize the importance of integrating adaptive technology in learning and the need for strategies to increase student learning motivation to achieve optimal learning outcomes.

Peran Orang Tua Dalam Mendukung Pembelajaran Matematika di Rumah Bagi Siswa Sekolah Dasar

This study aims to understand the critical role of parents in supporting children's mathematics learning at the elementary school level. In this context, the research employs a qualitative approach with a case study design to explore parental involvement in facilitating mathematics comprehension at home and collaboration with teachers. Data were collected through in-depth interviews, participatory observations, and document analysis of ten purposively selected families. The results indicate that effective communication between parents and teachers, as well as the support provided at home, plays a significant role in enhancing children's understanding and motivation in learning mathematics. Parents who are actively involved in their children's learning, both through direct interaction with teachers and by facilitating learning activities at home, are proven to help children overcome challenges in learning mathematics. The study also emphasizes the importance of consistent collaboration between home and school to create a supportive learning environment. The implications of this study suggest that active parental involvement and collaboration with teachers are crucial for achieving optimal mathematics learning outcomes.

The Effect Of Multy Reprecentacy Discourse Learning Assisted By Liveworksheet On Students' Mathematical Comprehension Ability

The discourse multy reprecentacy (DMR) model is one of the models that are able to improve students' mathematical understanding by collaborating in groups in class and using the Liveworksheet application. This study aims to determine the influence of students' mathematical knowledge after verifying the DMR model with the Liveworksheet application. This study uses a quantitative approach. Using a sample of grade VII students at SMPN 1 Cikeusik, class VIIA as an experimental class and VIIB as a control class were taken using a purposive sampling technique. The data collection techniques used in this study are observation and tests. This study uses statistical data analysis, but previously, a prerequisite test was carried out to conduct data analysis with parametric statistics using the polled variance formula. Based on the research, it can be concluded that the influence of the DMR model with the Liveworksheet application on the mathematical comprehension ability of junior high school students. Keywords: Multy Reprecentacy Discourse Model; Liveworksheet app; Understanding Mathematics

Factors Affecting Key Stage 3 Students’ Attitudes towards Mathematics in Fuvahmulah City, Maldives

Mathematics can foster students’ capacity in reasoning and nurturing their critical thinking abilities. In turn, attitude emerges as a pivotal factor influencing students’ mathematical performance. The National Assessment of Learning Outcomes (NALO) has revealed a concerning decline in mathematics proficiency among Grade 7 students within this atoll over successive years. Scholarly investigations have underscored the significance of a positive attitude towards the subject in augmenting learning outcomes. Guided by the ABC model of attitude, this study sought to discern the factors shaping students’ perspectives towards mathematics, the specific challenges hindering them from realising their full potential, and the proposed reforms in pedagogical and environmental dimensions to enhance mathematical proficiency. Employing purposive sampling, a qualitative case-study approach, and semi-structured interviews, data was collected from eight students in Key Stage 3. The findings indicate that students’ outlook on the subject is influenced by a confluence of positive and negative emotions. Factors such as teachers’ attitude, pedagogical methodologies, insufficient parental support, and deficiencies in foundational mathematical understanding during primary schooling emerged as prominent impediments to students’ mathematical achievement. Additionally, students expressed a desire for a conducive and differentiated learning milieu to bolster their grasp of mathematical concepts.

Investigating prospective teachers’ skills of predicting and identifying significant student reasoning instances and deciding how to respond to those instances

ABSTRACT The importance of constructing mathematical arguments and critiquing the reasoning of others has been emphasized as a key component for deep mathematical understanding. As a result, acknowledging proof as an essential tool to comprehend mathematics at all grade levels has been suggested by many researchers as well as reform initiatives. To do so, both teachers and prospective teachers should be able to predict how students reason mathematically, identify significant student reasoning instances and decide how to respond productively to those instances. The participants consisted of eleven prospective teachers who enrolled in a teacher education program at a public university in Turkey. All participants enrolled in a two-credit mathematics education course about teaching reasoning and proving in the middle grades taught by the author. The results of this study demonstrated that the participating prospective teachers were able to predict student reasoning productively. However, the results regarding to the participants’ levels of identifying significant student reasoning instances were less successful. This study also documented that majority of the participants listed guiding questions. Although the elective course was not structured toward promoting participants’ noticing skills, all these results could suggest that the course might have influenced the participants’ prediction, identifying, and responding skills.

Pengembangan Media Pembelajaran Intelligent Math Snake (IMS) untuk Meningkatkan Kemampuan Pemahaman Matematis Siswa

This study aims to design a snakes and ladders game media and determine the feasibility and effectiveness of Intelligent Math Snake (IMS) learning media to improve students' mathematical understanding skills, especially on flat-sided space building material. This research uses development research or Research and Development (R&D) with the ADDIE development model. The sample in this study were students of class VIII-H MTs Negeri 7 Kuningan in the 2023/2024 school year. The data analysis technique used in this study used the Paired Sample T Test, N-Gain test, and questionnaire processing. From the results of the study, it was found that the Intelligent Math Snake (IMS) learning media developed was feasible to use in learning based on the verification results of media experts and material experts. The Intelligent Math Snake (IMS) learning media developed effectively improves students' mathematical understanding skills. This can be seen from the average student mathematical understanding test scores after using Intelligent Math Snake (IMS) learning media higher than before. The development of Intelligent Math Snake (IMS) learning media received good responses from students. This can be seen from the survey results of student response questionnaires to the Intelligent Math Snake (IMS) learning media

Mathematical Concept Representations in the Early Years of School: Analyzing Student’s Errors

In this paper we analyze students’ mathematics errors in the early years of Brazilian school. To achieve this goal, we developed a questionnaire with eight math problems that included basic operations. This instrument was distributed to 76 third-grade students in three different classes from three different schools. To comprehend what caused the errors, we analyzed each question. To perform these analyzes we used the following categories: Errors due to language difficulties; Errors due to difficulties in obtaining spatial information; Errors due to incorrect associations or rigidity of thinking; Errors due to the application of irrelevant rules or strategies; Errors due to deficient mastery of prerequisite skills, facts, and concepts; Incorrect reproduction of the task; Error of counting; Errors in the assemblage of the arithmetic operations; Errors in the summing up with values bigger than ten; and Specific errors of subtraction. We believe that using errors as motivation could improve students' understanding of mathematics. We seek to help teachers (and researchers) identify most of the mistakes made by students in order to recognize them in their classrooms. The results indicated that some of the students' most common errors are in line with what the literature points out, that is, difficulty in translating the problem into mathematical language; difficulties in using the operations algorithms and difficulties in understanding what the problem is asking.

RME Educational Game Based on Android Mobile to Increase Students’ Mathematical Understanding Ability

This research aims to: 1) create an RME educational game based on Android about integers called Story Math Game as an edutainment medium for 1st grade elementary school students that contains stories about basic concepts of counting (addition and subtraction), practice questions, and learning evaluations (with various varying levels of difficulty) with the characteristic of using real problems; 2) assess whether the game is suitable for learning mathematics; and 3) describe the increase in students' mathematical understanding abilities who have used RME educational games in learning. This research is research and development (R&D) with a 4D development model. There are four stages: define, design, develop, and disseminate. Data analysis techniques include expert assessment (feasibility test and media quality test) and development testing (one-group pretestposttest design experiment). The feasibility of the RME educational game was evaluated by media and materials experts. The research results showed that 1) educational games reached a feasibility level of 75.00% with good criteria from media experts and 82.32% with good criteria from material experts, 2) the media was tested publicly by 100 parents of students, and the test results The public obtained application quality results of 83.20% with good criteria, and 3) development testing resulted in an increase in the mathematical understanding abilities of 1 st grade elementary school students. Based on the results of the data obtained, it appears that the RME educational game is suitable for use as a mathematics learning medium and can increase the students’ mathematical understanding abilities in 1 st grade elementary school.

Uniqueness, regularity, continuity, and stability of solutions of integral equations in irregular domains

This study explores the uniqueness, regularity, continuity, and stability of solutions to integral equations related to elliptical boundary value problems in irregular domains. Traditional methods usually consider soft boundaries, but this work extends these results to include domains with rough boundaries. By employing Sobolev spaces, especially fractional Sobolev spaces, we develop a comprehensive theoretical framework. Under appropriate conditions, the studied integral equation has a unique solution in fractional Sobolev spaces, maintaining the regularity properties of the input function. Two new theorems are introduced to strengthen the findings. The first theorem establishes that solutions are continuous with respect to perturbations in the input data. This means small changes in the input do not cause significant deviations in the solution, ensuring robustness in practical applications. The second theorem demonstrates the stability of the solutions when the domain geometry undergoes small changes. This stability is crucial for real-world scenarios where the exact shapes of domains may not be perfectly known or may vary slightly. These results significantly improve the mathematical understanding of boundary value problems in non-smooth domains. The proposed extended framework allows for more generalized applications, addressing challenges in various fields of physics and engineering. The ability to handle irregular domains with rough boundaries opens up new possibilities for modeling and solving complex problems where traditional soft boundary assumptions are not valid. This research provides a robust basis for future studies and applications, highlighting the importance of considering fractional Sobolev spaces in the analysis of integral equations.

Pengembangan Media Pembelajaran Komik Matematika (KOMKA) untuk Meningkatkan Kemampuan Numerasi Siswa Sekolah Dasar

This study aims to determine the validity and effectiveness of the mathematical comic learning medium (KOMKA) to improve the numeration ability of elementary school students especially on area & volume measurement materials. This type of research is Research and Development. The development model used is the ADDIE model developed by Dick and Carey, which has five stages: Analysis, Design, Development, Implementation, and Evaluate. The population in this development research is all students of SDN 2 Padarek in the 2023/2024 academic year. The sampling technique used in this development research is simple random sampling. The data analysis technique used in this study is a descriptive analysis technique to describe whether the digital comics developed by the study are valid and effective for use in class learning. Research results show that the KOMKA learning medium is valid for use in learning activities, derived from the validity results of media experts and material experts. The KOMKA learning medium is effective in improving students' numeration skills. This can be seen from the average test results of students' mathematical understanding ability after the application of the KOMKA learning medium was higher than before.

PENGARUH MINAT BELAJAR TERHADAP KEMAMPUAN PEMAHAMAN MATEMATIS PESERTA DIDIK SEKOLAH DASAR

This research was motivated by the low mathematical understanding abilities of elementary school students. The formulation of the problem in this research is: 1) Is there a positive correlation between learning interest scores and the acquisition of mathematical understanding abilities? 2) Does students' interest in learning have a positive effect on the acquisition of mathematical understanding abilities? The aim of this research is to determine the influence of interest in learning on students' mathematical understanding abilities. The research method used in this research is a quantitative method. The research instruments used were a learning interest questionnaire and a mathematical understanding ability test. Based on the results of data analysis and hypothesis testing using SPSS version 29.0 software, there is a significant positive correlation between learning interest scores and mathematical understanding ability scores, with a correlation coefficient value of 0.498, which means that it is 0.248 or 24.8% of students' mathematical understanding ability. determined by interest in learning. So it can be concluded that interest in learning has a positive effect on the mathematical understanding ability of elementary school students.

The Differences in Effectiveness of Learning Using Contextual Teaching and Learning (CTL) and The Missouri Mathematics Project (MMP) in Terms of Mathematics Learning Outcomes

This study aims to compare the effectiveness of learning using Contextual Teaching and Learning (CTL) and the Missouri Mathematics Project (MMP) in terms of students' mathematics learning outcomes. The research method employed was an experiment with a pretest-posttest non-equivalent comparison-group design. The research population consisted of seventh-grade students, with the sample being students from class VII A using the CTL learning model and class VII B using the MMP learning model. The independent variable in this study is the learning model, while the dependent variable is the mathematics learning outcomes. The instruments used were a learning outcome test and an observation sheet for the implementation of learning. The results of the study indicate that both learning models, CTL and MMP, are effective in improving students' mathematics learning outcomes. The Wilcoxon test analysis showed that the significance values for both models were less than 0.05, indicating their effectiveness. However, the Mann-Whitney test revealed no significant difference in effectiveness between the two learning models. These findings suggest that both CTL and MMP can be used as effective alternative teaching methods to enhance students' mathematics learning outcomes. This study contributes to the selection of appropriate teaching methods to improve understanding and learning outcomes in mathematics. It is recommended for future researchers to investigate other aspects such as cognitive, psychomotor, or affective domains, and for teachers to consider using CTL and MMP in their teaching activities.

High accuracy solutions for the Pochhammer–Chree equation in elastic media

This study investigates the nonlinear Pochhammer–Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims to derive precise analytical solutions and validate them using He’s variational iteration method (VIM). The Pochhammer–Chree equation’s relationship to other nonlinear evolution equations, such as the Korteweg-de Vries and nonlinear Schrödinger equations, underscores its significance in the field of nonlinear wave dynamics. The methodology employs the Khater III method for deriving analytical solutions, while He’s VIM serves as a numerical validation tool, ensuring the accuracy and stability of the obtained results. This dual approach not only yields novel solutions but also provides a robust framework for analyzing complex wave phenomena in elastic media. The findings of this study have significant implications for material science and engineering applications, offering new insights into the behavior of waves in elastic rods. By bridging the gap between theoretical models and practical applications, this research contributes to the advancement of both mathematical theory and physical understanding of nonlinear wave dynamics. Situated within the domain of applied mathematics, with a focus on nonlinear wave equations, this work exemplifies the interdisciplinary nature of contemporary research in mathematical physics. The results presented herein open new avenues for future investigations in related fields and highlight the potential for innovative applications in material science and engineering.

Teaching and learning fraction: A systematic literature review

Fractions are one of the materials that have an important role in mathematics learning both domestically and abroad. Therefore, several articles discussing fractions published in several journals can be found in several sources, both national and international. This article aims to provide an overview of learning fractions, especially in context, activities and learning outcomes based on relevant literature. Therefore, we are interested in conducting a Systematic Literature Review (SLR) of the 10 articles resulting from the Meta analysis (PRISMA) process. This research focuses on three aspects, namely: 1) Activities and contexts used in learning fraction material, 2) Learning outcomes related to the application of these activities and contexts and 3) Main findings in the research. Systematic literature review found that there were 10 contexts and activities implemented in learning fraction material. Apart from that, we also concluded that the holistic, interactive and contextual learning approach, namely PMRI, had a positive impact on students' understanding of fraction material. Providing meaningful and relevant experiences can increase student interest and build a strong foundation for further mathematical understanding. The results of this research can provide a summary of existing literature and literature to identify weaknesses or gaps for further investigation in future research related to the topic of fractions.

Development of Mathematics Learning Tools Based on Education for Sustainable Development (ESD) Using the Outdoor Learning Mathematics Method to Enhance Mathematical Connections in Junior High School

This research aims to develop mathematics learning tools based on Education for Sustainable Development (ESD) using the Outdoor Learning Mathematics method with the goal of enhancing mathematical connections of junior high school students in statistics. The research method employed is a mixed-methods approach combining qualitative and quantitative methods, both conducted through developmental research comprising planning, development, and evaluation stages. The sample for this research was two classes at SMPN 1 Tempeh with homogeneous mathematical abilities, where one class will be used as the experimental group and one class as the control group. Determining the research area using a purposive area sampling technique with the consideration that learning using the outdoor learning mathematics method with educational sustainable development (ESD) based learning tools has never been implemented at SMPN 1 Tempeh. The selection of eighth-grade classes is based on the consideration that statistics material is currently being taught in eighth grade, and eighth-grade students have not been subjects of research for similar studies before. The learning tools developed are designed in accordance with ESD principles and utilize outdoor mathematics learning approaches to enhance students’ understanding and skills in statistics. The results from Hypothesis Testing for Pretest indicate that a p-value of 0.648 is obtained, where this value > 0.05 means H0 is accepted and H1 is rejected. Therefore, it can be concluded that there is no difference in the mean between the control and experimental groups in the pretest. Whereas the result of Posttest Hypothesis Test indicate that a p-value of 0.028 is obtained, where this value < 0.05 means H0 is rejected and H1 is accepted. So the use of ESD-based mathematics learning tools with the Outdoor Learning Mathematics method is effective in improving students’ mathematical connections in statistics. The implication of this research underscores the importance of integrating mathematics education with sustainable development principles to reinforce students’ understanding and skills in mathematics while also fostering awareness of environmental and social issues.

Improving Concepts Understanding Of Class V Students With The Utilization Of Geogebra Learning Media

The purpose of this research is to create a learning media for the concept of geogebra to improve students' mathematical understanding of the material of spatial structure. The things tested in this study were validity, practicality, and effectiveness. This research method is RD with a 4-D model, namely defining, designing, developing and distributing. However, in this study only up to the development stage. Based on the research that has been done, the result is that the average score of media experts is 3.6, material experts are 3.6, which means the results are very good. Furthermore, the practicality score obtained from the teacher's response questionnaire is 89,93% and the student's is 78,67%. Furthermore, the results of the effectiveness of learning media get 90% of students who get complete learning using geogebra learning media.

Comparing Ninth-Grade Students’ Approaches to Trigonometric Ratio Problems Through Real-World and Symbolic Contexts

This study investigates the problem-solving strategies employed by ninth-grade students when addressing symbolic and real-world contextual problems involving trigonometric ratios. Conducted with 46 ninth-grade students from a Turkish public high school, this research employed a worksheet consisting of six problems aligned with the Turkish ninth-grade mathematics curriculum. Three of these problems were based on real-world contexts, while the other three were conventional symbolic problems. The findings indicate that students exhibited proficiency in identifying similarity ratios using side length ratios. Additionally, the results revealed that students were more adept at solving real-world mathematical scenarios compared to purely symbolic tasks. This study offers significant insights into the problem-solving strategies of ninth-grade students when confronted with trigonometric ratio problems. It underscores crucial implications for mathematics curricula and pedagogy, highlighting the importance of preparing ninth-grade students for success in their future academic and professional endeavors. The study emphasizes the necessity for a balanced approach in teaching, integrating both real-world and symbolic problem-solving tasks to enhance students’ mathematical understanding and application. By identifying the strengths and areas for improvement in students’ problem-solving strategies, this research contributes to the development of more effective educational practices that address the diverse needs of learners.