Mathematical Representation Research Articles

Indonesian Students’ Mathematical Representation Ability According To Learning Styles: Systematic Literature Review

The purpose of this research is to explain the outcomes of Indonesian students' mathematical representation ability according to learning styles. The learning styles are visual, auditory, and kinesthetic. A systematic literature review (SLR) is the research methodology employed in this study. This study used data from 18 papers about mathematical representation ability according to learning styles. Publications published in Indonesia between 2015 and 2023 that are indexed by Google Scholar, SINTA, or Scopus form the publishing data. According to the publication year, the media in which it was published, the research methods employed, the subject's educational background, the research location, and the research findings, the description of this study was reviewed. The most research on mathematical representation ability according to learning styles was found to have been published in 2023, according to SLR. The most prominent research media that published the most research were SINTA and Google Scholar. Qualitative methods dominated this study, with junior high school students serving as the majority of research subjects and the island of Java serving as the most prominent research location in Indonesia. Furthermore, it could be stated that one of the elements influencing mathematical representation ability is learning styles.

Recurrence quantification analysis of rs-fMRI data: A method to detect subtle changes in the TgF344-AD rat model

Background and objectiveAlzheimer's disease (AD) is one of the leading causes of dementia, affecting the world's population at a growing rate. The preclinical stage of AD lasts over a decade, hence understanding AD-related early neuropathological effects on brain function at this stage facilitates early detection of the disease. MethodsResting-state functional magnetic resonance imaging (rs-fMRI) has been a powerful tool for understanding brain function, and it has been widely used in AD research. In this study, we apply Recurrence Quantification Analysis (RQA) on rs-fMRI images of 4-months (4 m) and 6-months-old (6 m) TgF344-AD rats and WT littermates to identify changes related to the AD phenotype and aging. RQA has been focused on areas of the default mode-like network (DMLN) and was performed based on Recurrence Plots (RP). RP is a mathematical representation of any dynamical system that evolves over time as a set of its state recurrences. In this paper, RPs were extracted in order to identify the affected regions of the DMLN at very early stages of AD. ResultsUsing the RQA approach, we identified significant changes related to the AD phenotype at 4 m and/or 6 m in several areas of the rat DMLN including the BFB, Hippocampal fields CA1 and CA3, CG1, CG2, PrL, PtA, RSC, TeA, V1, V2. In addition, with age, brain activity of WT rats showed less predictability, while the AD rats presented reduced decline of predictability. ConclusionsThe results of this study demonstrate that RQA of rs-fMRI data is a potent approach that can detect subtle changes which might be missed by other methodologies due to the brain's non-linear dynamics. Moreover, this study provides helpful information about specific areas involved in AD pathology at very early stages of the disease in a very promising rat model of AD. Our results provide valuable information for the development of early detection methods and novel diagnosis tools for AD.

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.

An application of simultaneous stochastic optimisation on an open-pit copper mining complex with supply, recovery, and market uncertainties

ABSTRACT A mining complex is an integrated value chain that consists of multiple mines, stockpiles, processors, waste dumps, and tailing facilities, and where the in-situ materials mined are transformed into products sold to customers. Simultaneous stochastic optimisation provides a strategic mine planning framework that incorporates all components of a mining complex into a single mathematical representation, capitalising on the synergies between components while considering uncertainty. An application of this optimisation framework at a coper mining complex demonstrates that the incorporation of material supply, market demand, and processing recovery uncertainties into the modelling leads to production schedules that yield a higher NPV and metal recovery.

Eigenstructure assignment of constrained second-order linear systems: an optimised positively-invariant set control approach

Second-order systems constitute a mathematical model class used to represent a variety of physical processes to be controlled, such as vehicle damping systems, hydraulic pump flow, and robot manipulators. Due to the practical limitation inherent to physical systems (or their mathematical representation) and constraints on the input variables, the constrained control theory became an important research field. In this work, based on set-invariance theory, we propose an eigenstructure assignment optimisation using a state-feedback control law that guarantees the respect of state and control constraints for second-order systems. Positive invariance is the property of keeping the trajectory of the system states inside the set. This characteristic is incorporated into the analysis and design of the control law to ensure local stability and constraint fulfilment.

Dynamic chaos unveiled: enhancing ship’s attitude time series prediction through spatiotemporal embedding and improved transformer model

Abstract During ship operations at sea, the vessel's attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship's attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a
Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.

KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL OLIMPIADE TINGKAT SMP

Mathematical representation abilities can be in the form of expressions, ideas or mathematical ideas, which originate from students' thoughts that emerge during learning in an effort to find mathematical solutions. There are three indicators of mathematical representation ability, namely verbal, pictorial and symbolic. The process of developing students' potential and thinking can be done by holding mathematics competitions or olympiads. The approach used in this research is qualitative with descriptive methods. Purposive sampling technique was used in this research to select samples with certain considerations. The aim of this research is to describe students' mathematical representation abilities in solving Olympiad questions. This research used a sample of 3 students each representing each high, medium and low representation ability group. Based on the results of research on visual representation abilities, some students already have high abilities, although there are some who are still medium or low. Meanwhile, in symbolic ability, there are many students whose abilities are high and only a few whose abilities are medium or low. For verbal representation, most students already have high abilities and only a few students have medium or low abilities

The hidden lessons in textbooks: Gender representation and stereotypes in European mathematics and language books

AbstractThis cross‐national European comparison examined gender representation and stereotypes in mathematics and language textbooks from Germany, Italy, Lithuania, the Netherlands and Romania. The results showed that female characters were numerically underrepresented. Female characters were also less often a main character or individually portrayed compared to male characters, but not proportionally to the overall lower number of female characters. Characters in occupational roles were less often female than male, whereas among characters with gender non‐conform characteristics, these were more often female than male in some textbooks. There was no sexual diversity among characters. The differences in gender representation are found within each country, but gender differences were smaller in more gender‐egalitarian countries. If textbooks are to offer the same learning benefits to both boys and girls, students should be equally represented in a diversity of roles and occupations.

Guest Editorial: Connecting Mathematical Representations from Algebra to Calculus

Guest Editorial: Connecting Mathematical Representations from Algebra to Calculus

Efektivitas Model Eliciting Activitis (Meas) Terhadap Kemampuan Representasi Matematis Siswa MTs

The purpose of this research is to describe and obtain data on the influence of Model-Eliciting Activities (MEAs) on the representational ability of MTs students. This type of research is an experimental study with control and experimental groups by observing the results of pretests and posttests. The research instrument is a mathematical representation ability test. The population of this research consists of all students at MTs Madrasah Miftahul Ulum II Punggur Kecil, with the sample being two eighth-grade classes selected purposively from the seven existing classes. Data analysis was conducted using a two-population mean difference test. The results of the study show that the mathematical representation ability of students who received Model-Eliciting Activities is better than that of students who received conventional teaching. The improvement in the mathematical representation ability of students who received Model-Eliciting Activities in both the upper and lower groups is statistically better than that of students who received conventional teaching.

REMEDIAL PRACTICES AND STUDENTS COMPETENCES IN MATHEMATICS IN PUBLIC SECONDARY SCHOOLS IN RWANDA A CASE OF GICUMBI DISTRICT

Background: Mathematics plays a crucial role in both vocational success (Jetter, 2017) and everyday life (Umameh, 2011), yet many students face challenges in mastering it. Globally, educational equity remains a priority, with persistent disparities in math education, especially among low-SES students (UNESCO, OECD). Tanzania and Rwanda are actively addressing these challenges to enhance educational outcomes. Materials and Methods: This descriptive survey study involved 171 participants from 32 secondary schools in Gicumbi District: 105 mathematics instructors, 50 subject leaders, 35 head teachers, and 110 students. Data collection employed random sampling, with Slovenes method used to select the study sample. SPSS version 21.0 facilitated analysis, encompassing descriptive statistics (frequency, percentage, mean, standard deviation) and inferential statistics (correlation, regression coefficients). Results and Discussions: Findings revealed strong consensus among respondents on the efficacy of modifying instructional methods (80.0%), using personalized learning materials (63.1%), integrating visual and auditory resources (60.0%), and creating tailored exercises (68.0%) to improve math competencies. Key indicators such as problem-solving (64.3%), method application (96.6%), reasoning (92.3%), and mathematical representation (92.3%) demonstrated significant improvements. Enhanced physical facilities also correlated positively with student outcomes, underscoring the role of supportive environments in fostering mathematical competence. Conclusion: The study emphasizes the effectiveness of adapting teaching methods and environments to enhance students math skills. Customized approaches, including personalized materials and multimedia integration, proved instrumental in improving competencies like problem-solving and reasoning. Statistical analyses consistently supported these findings, highlighting the importance of personalized and diversified teaching strategies in enhancing math education in Gicumbi, Rwanda.

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 Influence of Mathematical Beliefs on The Mathematical Representation Ability of Students in Class VII

The Influence of Mathematical Beliefs on The Mathematical Representation Ability of Students in Class VII

MATHEMATICAL REPRESENTATION ABILITY OF HIGH SCHOOL STUDENTS IN SOLVING PROBABILITY MATERIAL PROBLEMS BASED ON HONEY MUMFORD LEARNING STYLE

This study aims to describe the mathematical representation ability of grade XII high school students in solving permutation subsubject probability material problems based on Honey Mumford's learning style. This type of research is qualitative research with a descriptive method. The data collection techniques used were Honey Mumford's learning style questionnaire, mathematical representation ability test, and interview. The source of data in this research is grade XII students of science 5 MAN 2 Pamekasan for the 2023/2024 school year. The subjects selected were 2 students who each had a theorist learning style and an activist learning style based on questionnaires and considerations with mathematics teachers. The data analysis techniques used are data reduction, data presentation, and conclusion drawn. The results of the study show that students with a theorist learning style can meet all indicators in the aspect of representation, both visual, symbolic, and verbal representation. Meanwhile, students with activist learning styles have not been able to meet the indicators in the aspect of visual representation but can meet all indicators in the aspect of symbolic representation and verbal representation.

Elementary students' argumentative and explanatory mathematical writing about fractions

AbstractMathematical writing (MW) is an important yet underutilized form of mathematics discourse. Given the lack of attention to MW, there are few resources to support the implementation and assessment of MW. This study responds to the lack of resources by describing a MW unit focused on fractions that was implemented during a summer school program to support rising fourth grade students with explanatory and argumentative writing. Findings from the study revealed that students used different forms of reasoning about fractions to compose their mathematical argument and explanation. We also identified five categories that captured how students communicated a mathematical argument and explanation: writing organization, precise mathematical vocabulary, mathematics content, mathematical representation, and characteristics specific to a mathematical argument/explanation. The five categories led to the development of an analytic rubric for argumentative and explanatory writing.

Teachers’ practice of mathematical representation, and its relationship to the preschooler’s utilization of it in expressing mathematical ideas

هدفت الدراسة إلى الكشف عن العلاقة بين مستوى ممارسة المعلمات لعملية التمثيل الرياضي وتوظيف طفل ما قبل المدرسة له في التعبير عن الأفكار الرياضية. اتّبعت الدراسة المنهج الوصفي الارتباطي، واشتملت الأدوات على بطاقتي ملاحظة مغلقة لكل من المعلمة والطفل. تم اختيار العينة بطريقة قصدية، وتكونت من (15) معلمة في مرحلة ما قبل المدرسة، يعملن في مدارس رياض الأطفال التي تطبق برنامج رياضيات خلال البرنامج اليومي في مدينة الأحساء و(120) طفل من الأطفال في فصولهن، وتم معالجة البيانات إحصائيًا باستخدام البرنامج (SPSS)، خلصت النتائج إلى وجود علاقة ارتباطية موجبة دالة إحصائيًا بين درجات ممارسات المعلمات للتمثيل الرياضي وتوظيف الطفل له في التعبير عن الأفكار الرياضية، كما أظهرت أنّ مستوى ممارسات المعلمات لعملية التمثيل الرياضي جاء بمستوى منخفض، ومستوى توظيف الطفل لعملية التمثيل الرياضي في التعبير عن أفكاره الرياضية جاء بمستوى منخفض. وفي ضوء النتائج توصي الدراسة بتوفير برامج تطوير مهني لمعلمات الطفولة المبكرة تتضمن طرق استخدام التمثيلات الرياضية في تقديم وشرح مفاهيم الرياضيات، وتوفير الوقت الكافي والأنشطة الملائمة نمائيًا لجميع الأطفال للانخراط في أنشطة الرياضيات عامةً والتمثيل الرياضي خاصة.

Improving fake news detection on social networks through a novel machine learning approach

Recent years have seen an increase in societal information, such as commercial advertisements, celebrity information, political news, etc., due to the growth of online social networks. Some social media sites including Facebook, Instagram, and Twitter, were impacted by Fake News (FN) spread by their users. Nevertheless, some individuals propagate false information using words, images, and videos to increase their connections and reputation. The most current information is unreliable and misleads other members on an online social network. Because FN is circulated to encourage users to trust disinformation, it’s hard for detection algorithms to recognize false information according to uploaded material. In this research, we will provide an autonomous false news detection strategy called Grey Wolf optimized Adaptive Bidirectional Gated Recurrent Unit (GWO+ABi-GRU) that can identify FN on Twitter. The TF-IDF method translates textual material into a mathematical representation that accurately captures the value of terms and their context in the dataset. We improve the overall efficiency of the BiGRU by applying this GWO, which leads to increased accuracy when spotting false news. The experimental examination of real-world data shows that the proposed FN detection strategy GWO+ABi-GRU outperforms traditional approaches regarding recall, accuracy, F1 score, and precision. This enhanced performance proves essential in preventing the circulation of false news on social media, protecting the integrity of information sources, and mitigating the potential damage caused by false information.

Mathematical Representation of Peterson’s Rules for Fuzzy Peterson’s Syllogisms

Mathematical Representation of Peterson’s Rules for Fuzzy Peterson’s Syllogisms

Dynamic characteristic analysis and key parameter optimization of throttling orifice type air damping air spring

Abstract The unique hysteretic characteristic of rubber bellows and the nonlinear flow of internal airflow in the system results in the significant nonlinear dynamic characteristic of throttling orifice type air damping air springs (OADASs). To solve the problem of mathematical representation of dynamic characteristic and key parameters optimization of throttling OADAS, this paper comprehensively considers the hysteretic characteristic of rubber bellows under variable pressure, the nonlinear dynamic characteristic model and linear model of throttling OADAS are established based on the concepts of gas thermodynamics and fluid mechanics. The static and dynamic characteristic tests of the throttling OADAS are conducted, to verify the accuracy and effectiveness of the proposed model, and to reveal the influence laws of excitation amplitude, excitation frequency, and throttling orifice diameter on the quantitative characterization indexes. Finally, a complete throttling orifice diameter optimization method is proposed based on the eight-degree-of-freedom model of the entire vehicle. Optimization results illustrate that the RMS values of the vertical acceleration of the body and the vertical acceleration of the driver are decreased by 19.02% and 38.44%, respectively. Overall, the outcomes of this paper can provide the design idea and theoretical basis for air damping matching and active suspension control.

Mathematical Representation Ability of Middle School Students in the REMAP-TPS Learning Model and Student Activeness

Kemampuan representasi matematis siswa kelas VIII SMPN 1 Way Bungur masih rendah. Aktivitas belajar yang bervariasi antar siswa menimbulkan perbedaan kemampuan pada setiap siswa. Hal ini menyoroti perlunya revitalisasi pendekatan pengajaran dengan menggunakan model pembelajaran yang berpusat pada peserta didik, yang mendorong peningkatan aktivitas siswa dan pemahaman materi. Model pembelajaran REMAP-TPS hadir sebagai pendekatan inovatif yang melibatkan siswa secara dominan dalam proses pembelajaran dan membantu eksplorasi materi melalui penggunaan peta konsep. Penelitian ini bertujuan untuk menilai keefektifan model pembelajaran REMAP-TPS dalam meningkatkan kemampuan representasi siswa. Desain penelitian yang digunakan adalah quasi eksperimen Posttest-Only Control Group Design. Instrumen yang digunakan untuk mengukur kemampuan representasi matematis meliputi soal deskriptif terkait geometri sisi data dan angket untuk menilai aktivitas pembelajaran. Tes diberikan kepada siswa setelah proses pembelajaran selesai, dilanjutkan dengan analisis menggunakan ANOVA. Temuan penelitian menunjukkan bahwa model pembelajaran REMAP-TPS unggul dalam mengembangkan kemampuan representasi matematis siswa. Hal ini terlihat dari rata-rata nilai posttest kelompok eksperimen sebesar 79,56, melampaui rata-rata kelas kontrol sebesar 68,52.