Mathematical Symbols Research Articles

Deep transformer-based architecture for the recognition of mathematical equations from real-world math problems

Identifying mathematical equations from real-world math problems presents a unique and challenging task within the field of Natural Language Processing (NLP). It has a wide range of applications in various areas, such as academics, digital content design, and the development of automatic or interactive learning systems. However, the accurate understanding of these equations still needs to be enhanced due to the intrinsic complexity of mathematical symbols and various structural formats. Additionally, the unique syntax, diverse symbols, and complex structure of mathematical equations present significant obstacles that traditional NLP methods and Optical Character Recognition (OCR) systems need help to overcome. In this research, we utilize deep transformer architecture to recognize mathematical equations, and we have utilized our novel dataset with 3433 distinct observations. This dataset, which we have collected to include a diverse range of mathematical equations, is used to predict six (z=x+y, z=x−y, z=xy, z=x/y, y=x! and y=x) basic mathematical equations. We applied different transformer-based architectures, such as BERT, ELECTRA, XLNet, RoBERTa, and DistilBERT, and BERT performs best with 99.80% accuracy. To the best of our knowledge, this is the first NLP work in any language where we recognize the equation from the mathematical text.

Effect of Interactive E-Book to Measure Mathematical Representations on Optics in High School

This study aims to measure the effect of using interactive e-books in enhancing students' mathematical representation skills on optics material in high school. Mathematical representation involves students' ability to use mathematical symbols, graphs, and formulas to solve physics problems, particularly in the concept of optics, which is often considered abstract. The research method used was a quasi-experiment with a pretest-posttest control group design. The sample consisted of two classes: an experimental class using interactive e-books as learning media and a control class using conventional methods. The results showed an improvement in mathematical representation skills in both classes, with the n-gain value of the experimental class being 0.604 and the control class being 0.557, both in the medium category. However, the experimental class demonstrated a more significant improvement compared to the control class, indicating that interactive e-books are more effective in helping students deeply understand optical concepts. The interactive features in the e-book, such as simulations and animations, provided a more engaging learning experience and helped students visualize abstract concepts. In conclusion, the use of interactive e-books has a positive impact on improving students' mathematical representation skills and can be considered an effective alternative learning medium, especially for science subjects that require better visualization and conceptual understanding.

Implementation of Discovery Learning Model with Window Shopping Approach to Improve Mathematical Communication Ability of High School Students

The low ability of students' mathematical communication in learning mathematics, especially in expressing mathematical situations or problems in the form of pictures, diagrams, language or mathematical symbols, or mathematical models makes students less active in learning and their learning motivation decreases. This study aims to determine the achievement of students' mathematical communication skills through the discovery learning model with a window shopping approach. The method in this study is a quasi-experimental research type consisting of 2 classes, namely the experimental class that uses the discovery learning model with the window shopping approach and the control class that uses ordinary learning at school with a total of 70 students from class XI SMA in one of the public high schools in Bandung. The research test instrument was in the form of a test that would be analyzed using SPSS 21 to compare learning outcomes between the experimental class and the control class. The result of the study was that the achievement of the students' mathematical communication skills in the experimental class was better than that of the control class at a significance level of 0.05 where the average communication ability of the experimental class was 81.74 and that of the control class was 77.31. The effectiveness of learning in the experimental class showed that it was more active in group discussions as indicated by the interaction and creativity of students in presenting learning material in each group, and almost 85% of students enjoyed learning using the discovery learning model with the window shopping approach.

Analysis of students' mathematical communication skills in terms of learning styles

The purpose of this research is to obtain a description of the mathematical communication skills in terms of the learning styles of Grade XI TKR 3 students at SMK Negeri 1 Tanara for the 2023-2024 academic year. This research is qualitative in nature. Six subjects were selected, representing each learning style, from Grade XI TKR 3 students at SMK Negeri 1 Tanara, Tanara District, Serang Regency. The data collection techniques used were observation, interviews, documentation, and tests based on the indicators of mathematical communication skills, namely: (1) the ability to express mathematical symbols through everyday events, (2) the ability to determine the solution set by relating real objects to mathematical ideas, (3) the ability to explain mathematical problems related to elimination, (4) the ability to analyze mathematical problems related to substitution, and (5) the ability to evaluate mathematical thinking and strategies used in problems according to the observed object. The results showed that (1) subjects with a visual learning style have good mathematical concept comprehension on indicators 1, 2, 3, 4, and 5; (2) subjects with an auditory learning style have good mathematical communication on indicators 1, 2, and 5, but performed poorly on indicators 3 and 4; and (3) subjects with a kinesthetic learning style have good mathematical communication skills on indicators 1 and 2, but performed poorly on indicators 3, 4, and 5.

Defining and measuring quality in students’ mathematical writing: a systematic literature review

AbstractMathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.

Challenges Encountered by BSEd-Mathematics Students in the Implementation of Hybrid Learning in Gordon College

The study examines the challenges faced by Bachelor in Secondary Education Major in Mathematics students at Gordon College in implementing hybrid learning for the academic year 2022-2023. The research involved 73 students, primarily in their first year, and found that online students face difficulties with math symbol encoding, connectivity, time management, and financial constraints. Onsite students face learning gaps, commuting and access issues, and require additional financial support. The study found no significant difference in challenges based on profile-variables in online mode, but differences exist based on year level and municipality. Recommendations include enhanced technical support, online tool training, time and stress management programs, financial assistance for low-income students, and improved accessibility in onsite mode.

ANALYSIS OF MATHEMATICAL NUMERACY SKILLS ON LINE AND ANGLE MATERIAL IN CLASS VII IN TERMS OF EXTROVERTED INTROVERTED AND AMBIVERT PERSONALITIES

This research aims to analyze the mathematical numeracy abilities of class VII students with introverted, extroverted and ambivert personalities at SMP Negeri 2 Semarang. The method used was descriptive qualitative with research subjects consisting of 34 students, one student was selected from each personality category based on a questionnaire with 70 question items. The results of the questionnaire showed AAE (introvert), LPA (extrovert), and JRA (ambivert) students as research subjects. Mathematical numeracy ability tests and interviews were carried out to test the validity of the test results through technical triangulation. Indicators of mathematical numeracy abilities include the use of mathematical numbers and symbols, analysis of information in the form of tables, graphs and charts, as well as interpretation of analysis results for decision making. The results showed that introvert and ambivert students met all indicators of numeracy ability, while extrovert students did not. Introvert students can solve problems well, extrovert students tend to be in a hurry and lack details, while ambivert students show quite good results but there are still some answers that are less detailed. This research concludes that mathematical numeracy abilities vary based on student personality.

Research on the Use Power Point (PPT) in Junior High School Mathematics Classroom Teaching

Since PowerPoint (hereinafter referred to as PPT) is of great significance to mathematics teaching, more and more attention has been paid to how to use PPT effectively in junior high school mathematics classroom teaching. This paper uses the method of theoretical analysis, through the analysis of the characteristics of PPT, the current teaching situation and the problems existing in students' mathematics learning, combined with the various requirements of the Mathematics Curriculum Standards for Compulsory Education (2022 Edition) (hereinafter referred to as The Standards) for junior high school mathematics teaching, puts forward four strategies for using PPT in junior high school mathematics classroom teaching. Through analysis, we can know that PPT is characterized by its powerful presentation function, dynamic presentation effect, lacks of procedural presentation, multiple ways of emphasis, and strong inclusiveness. The current problem of students in mathematics learning is students do not have a firm grasp of basic knowledge and have an inaccurate understanding of many concepts, students' ability to analyze and solve mathematical problems is weak, and they cannot accurately understand the conditions and requirements of the problems, students lack enthusiasm for learning mathematics, and students have improper learning methods and lack the habit of writing on time. The current situation of mathematics classroom teaching is teachers pay too much attention to the teaching of problem-solving methods and calculations and neglect the inspiration and training of problem-solving ideas, teachers' teaching resources are obsolete, and the use of information technology in teaching is inadequate, teachers' teaching methods are rigid and lack diversity and innovation, and the interaction between teachers and students is mostly ineffective and the overall participation of students is low. The standard puts forward specific requirements for the teaching of number and algebra, graphics and geometry, statistics and probability in junior high school. Therefore, through the above analysis, we give the following suggestions: 1. Making full use of the multiple emphasis effect of PPT to highlight different mathematical symbols; 2. Skillfully using the dynamic presentation function of PPT to make the process of mathematical knowledge formation dynamic; 3. Expanding the scope of use of PPT and give full play to the value of PPT in all aspects of teaching; 4. Integrating and collocating a variety of technologies reasonably, and use PPT in a variety of ways to teach mathematics. These strategies can be used for reference by junior high school mathematics teachers in practical teaching.

THIẾT KẾ TRÒ CHƠI HỌC TẬP GIÚP TRẺ MẦM NON LÀM QUEN BIỂU TƯỢNG TOÁN VỚI SỰ HỖ TRỢ CỦA PHẦN MỀM WORDWALL

Digital game-based learning is gradually becoming a trend in education, with certain positive impacts. Thanks to the game element, children's learning process becomes easier and more enjoyable. This study surveyed over 100 preschool teachers in Hue city, Thua Thien Hue province, to clarify the importance of applying technology software in designing educational games. Consequently, the process of designing and using educational games to help children become familiar with Math symbols is proposed based on Wordwall software. The proposed process received strong agreement from preschool teachers. To use Wordwall software-based games effectively in math familiarization activities, teachers need to be flexible and proactive in selecting games that are appropriate for the lesson’s objectives and content as well as the characteristics of preschool children. This study serves as a useful tool to support preschool teachers in designing educational games in general and educational games for familiarizing children with mathematical symbols in particular. Keywords: Educational games; Mathematical symbols; Wordwall; technology software; Thua Thien Hue

Application of SMOTE Method on Topic Based Question Classification Using Naïve Bayes Algorithm

In today's digital era, the utilization of technology in education is essential to support the learning process. This research discusses the classification of junior high school mathematics questions using the Naïve Bayes method. The use of an automated system in question classification helps reduce time and effort in grouping questions based on topics. The Naïve Bayes method was chosen because of its simplicity and ability to process data. The results showed that Naïve Bayes with SMOTE and Math symbols achieved 69% accuracy, while without SMOTE, the accuracy was lower. Cross-validation showed that the classification without symbols attained an accuracy of 89.35%, slightly superior to the classification using symbols, which was 88.79%. This result indicates that Naïve Bayes with SMOTE is more effective. Although the difference in accuracy with or without symbols is slight 0.56%, the performance is relatively equivalent, with an accuracy of 89%.

Logic and symbolism of switchable porous framework materials

Metal-organic frameworks (MOFs) are highly porous materials composed of organic linkers and inorganic nodes. A subset of MOFs can switch between at least two structures differing significantly in porosity, offering new opportunities for application technologies. However, network topology, micromechanics of building blocks and their hinges, particle size, defects, agglomeration etc., are convoluted into the responsiveness of the system. Many factors are a consequence of the material’s history, including synthesis, desolvation, and all subsequent handling steps, leading to a complex interplay of factors difficult to express clearly by ordinary language systems, chemical or mathematical symbols without loss of intuitive understanding. Here, we propose a symbolic language for the rationalization of switchability emphasizing the history-dependent responsivity of many dynamic frameworks and their stimuli-induced phase transitions. The system follows a bivalent logic inspired by Freges “Begriffsschrift”, providing a fundamental logic structure for the rationalization of statements and representation of logic gates.

Web-Based Math Braille Translator Using Indonesian Braille Symbols

According to estimates from the Indonesian Ministry of Health in 2017, at least 3,750,000 people in Indonesia have visual impairments. This significant number highlights the need for special attention to their educational needs, especially in mathematics. Educational media is essential to facilitate learning for visually impaired students and educators, as they often struggle with understanding math due to limited access to visual content. One solution is to use Mathematical Braille symbols, yet technology that translates these symbols into mathematical text is still limited. To address this, the author has developed a web-based Math Braille Translator application aimed at assisting visually impaired individuals and educators. This website translates mathematical Braille into notation by inputting Braille using the keys s, d, f, j, k, and l on the keyboard. The application is developed using the waterfall methodology and is based on the Indonesian Mathematical Braille Symbol Reference NOMOR 056/U/2000.

Literature Study: Analysis of Literacy and Numeracy Abilities in High School Physics Learning

The aim of this research is to see and determine the growth of students' literacy and numeracy skills and abilities in physics material. Literacy and numeracy skills in solving physics learning problems refer to numbers and symbols used to make conceptual predictions in data analysis to draw conclusions. This research uses a literature study method with the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) technique. Based on the results of the analysis of 3 appropriate journals from a database of 200 journals reviewed, it can be concluded that increasing students' literacy and numeracy skills can improve student learning outcomes in effective physics learning, improve learning outcomes and develop and increase interest in physics and the level of students' literacy and numeracy abilities are at the secondary level, and there is a significant positive relationship between literacy and numeracy abilities and physics learning outcomes based on research findings. Students in the high ability category in numeracy literacy are able to state the meaning, use of numbers and basic mathematical symbols. Students with moderate abilities are less precise in using numbers and basic mathematical symbols, some are not able to obtain information, and not all are able to make decisions.

Numeracy literacy of junior high school students in implementing the Merdeka mathematics learning curriculum

Numeracy literacy skills play a crucial role in the Independent Learning Curriculum. Currently, students' literacy skills are geared towards more independent learning. With these skills, students can solve problems accurately and develop critical thinking towards their challenges. This study aims to evaluate students' abilities in numeracy literacy in the era of more independent learning. This study focuses on eighth-grade students at SMP Muhammadiyah 1 Probolinggo, consisting of 28 students who have followed the Independent Curriculum. This study uses a qualitative descriptive method, collecting data through written tests with five questions encompassing various aspects of numeracy literacy skills. Indicators for numeracy literacy skills include (1) Using numbers and mathematical symbols to solve everyday problems; (2) Analyzing information in various forms (graphs, tables, etc.; and (3) Interpreting analysis results to predict, formulate, and make decisions. Data were analyzed by calculating the average percentage for each indicator of numeracy literacy skills. The analysis results show that the numeracy literacy skills of junior high school students in the era of independent learning are still at a low level.

Apakah Discovery Learning dapat Meningkatkan Keterampilan Komunikasi Matematis Siswa?

To face the Information and Communication Technology (ICT) Era, students need to master 21st century skills. One of them is mathematical communication skills. It is very important for students to master mathematical communication skills because it will help them connect ideas and concepts with mathematical symbols. This research aims to improve mathematical communication skills through the discovery learning model. This research is classroom action research (PTK) which was carried out in three steps, namely pre-cycle, cycle 1, and cycle 2. The research data was collected through tests and observations. The data analysis techniques used include data reduction, data presentation, and concluding. The PTK results show that the discovery learning model can improve students' mathematical communication skills in geometric transformation material. This is proven by obtaining a percentage result of 85% in mathematical communication skills, the indicator of presenting mathematical information or ideas with other forms of representation, and the indicator of composing arguments in solving mathematical problems in the last cycle phase. Apart from that, there was an increase in indicators of analyzing and evaluating mathematical thinking in mathematical communication by 75%.

Semiotic Mathematics Representation Ability Based on Symbolic in Solving SPLSV Problems in Class VII Students

Mathematical semiotic representation is the ability to analyze and express mathematical ideas or notions of a phenomenon and everyday problem situations into the form of signs, images, symbols, and symbols that represent them and provide meaning and explanation to a package of verbal sign messages. The symbolic stage is the stage where students have understood the symbols and concepts and have ideas that are strongly influenced by language and logic skills and students are able to manipulate symbols or symbols of a particular object. The purpose of this study was to determine the representation of symbolic-based mathematical semiotics in seventh grade students of MTS Al Barokah Ajung Jember on SPLSV material using qualitative descriptive method. The instrument used by researchers in the form of written test questions consisting of two questions tailored to the symbolic representation that has two indicators that use mathematical symbols to solve problems and interpret mathematical symbols. From the results of research that has been done obtained the error of representation on indicators using mathematical symbols to solve the problem of 100% and error of representation on indicators interpreting mathematical symbols of 0%. Several studies have been carried out to explain the mistakes that students make in representation skills. This paper presents the ability of mathematical symbolic semiotic representation of students who are more specific in solving SPLSV problems that can be considered by teachers in designing learning about the ability of mathematical semiotic representation and information for observers of mathematics education.

Kemampuan Komunikasi Matematis Siswa SMP ditinjau dari Gaya Belajar

Taking into account auditory, visual, and kinesthetic learning modalities, this research animed to evaluate students mathematical communication abilities on the subject of Two Variable Linear Equation Systems. This qualitative study surveyed six junior high school students from the city of Sukabumi. The tools used for this study were a written exam to evaluate mathematical communication abilities and a learning style questionnaire. Mathematical communication skills are the basis of the learning style questionnaire. These skills include the ability to draw connections between mathematical ideas and real word objects, images, and diagrams to explain mathematical concepts, situations, and relationships in writing and to express events or ideas using mathematical symbols or language. Communication abilities are excellent among students with low visual learning styles, as are those with high visual learning styles, according to the study’s findings. The communication abilities of pupils whose learning style is mostly auditory are good, while those whose learning style is predominantly visual are poor. The same holds true for students communication abilities, those who learn best via movement tend to have excellent ones, while those who learn best by sitting still tend to struggle. Knowing one’s own learning style is crucial for pupils to enhance their mathematics communication abilities

ANALISIS KEMAMPUAN REPRESENTASI MATEMATIS PESERTA DIDIK PADA MATERI TRANSLASI DI KELAS XI SMA NEGERI 2 KEPULAUAN TANIMBAR

This research aims to analyze students' mathematical representation abilities in translation material using the Indonesian Realistic Mathematics Education Approach in class XI, SMA Negeri 2, Tanimbar Islands. This research was carried out at SMA Negeri 2 in the in the Tanimbar Islands. In this research, a qualitative approach was used. This type of research is research that describes data in the form of words and describes phenomena or facts obtained in the research. The data collection techniques used were research documentation, written tests, and interviews. The data analysis techniques used are data collection, data reduction, data presentation, and data verification or drawing conclusions. The results of research on analyzing students' mathematical representation abilities using a realistic mathematics education approach show that students are able to represent mathematics in visual form by solving problems given by using visual representation indicators correctly, both in the form of tables and graphs, as well as the problem-solving process. Once completed, students are able to represent mathematical symbols by solving the problems given by using mathematical symbol representation indicators according to the concept of translation correctly. Likewise, the problem-solving process is resolved, and students are able to represent written text by simply determining the known information using written text indicators, but in the solving process, they are not able to complete it to get the final result.

Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Materi Trigonometri Ditinjau Dari Gaya Belajar

According to the OECD, the 2018 PISA results state that 71% of Indonesian students experience difficulties when faced with conditions that require them to solve problems by applying mathematical concepts, so they fail to achieve minimum competitive ability in mathematics. Based on the observations of researchers, there are MAN 1 Gresik students who have difficulty in solving trigonometric problems because they think that this material is too much memorizing formulas. This study used learning style questionnaires, test questions, and interviews to collect data in order to find out students' difficulties in solving trigonometry problems in terms of students' learning styles. The results obtained from this study include: 1) The difficulties of auditorial subjects are the inability to remember the steps of proving trigonometric identities; the basic concepts of trigonometric comparisons and the Pythagorean Theorem, unable to recognize mathematical angle symbols, less careful in calculating powers and calculating fractions, and the inability to draw conclusions. 2) The difficulties of kinesthetic subjects are the inability to remember the steps of proving trigonometric identities and the Pythagorean Theorem, the inability to recognize mathematical angle symbols, and less careful in calculating powers and calculating fractions; 3) The difficulties of visual subjects are the inability to remember the steps of proving trigonometric identities, the inability to recognize mathematical angle symbols, and the inability to draw conclusions.

Students’ reception of two alternative arrangements of mathematical symbols and words: Differences in focus and text navigation

To engage with specialized subject content, students must develop adequate reading skills. In mathematics, this includes to integrate information from different semiotic resources. This study elucidates how differences in the structural connections between mathematical symbols and written language in mathematics texts can affect the reading process. With the help of eye-tracking techniques, we investigated differences in focus and navigation when 15-year-olds read task texts in two distinct designs: a traditional design with written language presented in lines and all connections based on semantics; and a design including a graphic emphasizing links between symbols and explanations. While the graphic design was found to facilitate fast interpretation of the symbol–language connections, the traditional design seemed to encourage global reading, involving more text parts. When designing texts for mathematics learning, structural connections may be chosen to adapt texts to various student groups and purposes.