Mathematical Symbols Research Articles

A Theoretical Scientific Programming Framework for Application of Linear Matrix Transformation in Plane Computer Graphics

Plane computer graphics are basic information carriers in many industrial scenarios, such as engineering simulation, automatic control, and software design. Plane computer graphics are generally a kind of digital signals guided by mathematical symbols, and each vertex of a plane computer graph forms a graph matrix. Therefore, linear matrix transformation serves as the most common algorithmic unit to realize various information processing operations. To improve ease of graph matrix computing in practical engineering scenarios, this paper proposes a theoretical scientific programming framework for application of linear matrix transformation in plane computer graphics. Firstly, theoretical basis of linear matrix transformation in homogeneous plane coordinates is displayed and analyzed. Then, the universal theorem about linear transformation of graph matrices is deduced, and corresponding proofs are also given. Finally, a case study is set up to demonstrate the main workflow of the proposed theoretical scientific programming framework. The simulative results reveal feasibility of the proposal.

Computational Thinking Process of Prospective Mathematics Teacher in Solving Diophantine Linear Equation Problems

<p style="text-align: justify;">Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT). However, many still find it challenging to solve this problem. The subjects in this study were twenty-one prospective mathematics teachers who took number theory courses, and then two research samples were selected using the purposive sampling technique. This study uses a qualitative descriptive method to describe the thinking process of prospective teachers in solving Diophantine linear equation problems. The results showed that the first subject's thought process was started by turning the problem into a mathematical symbol, looking for the Largest Common Factor (LCF) with the Euclidean algorithm, decomposition process, and evaluation. The second subject does not turn the problem into symbols and does not step back in the algorithm. The researcher found that teacher candidates who found solutions correctly in their thinking process solved mathematical problem used CT components, including reflective abstraction thinking, algorithmic thinking, decomposition, and evaluation. Further research is needed to develop the CT components from the findings of this study on other materials through learning with a CT approach.</p>

Automated Math Symbol Classification Using SVM

Handwritten character/symbol recognition is an important area of research in the present digital world. The solving of problems such as recognizing handwritten characters/symbols written in different styles can make the human job easier. Mathematical expression recognition using machines has become a subject of serious research. The main motivation for this work is both recognizing of the handwritten mathematical symbol, digits and characters which will be used for mathematical expression recognition. The system first identifies the contour in handwritten document segmentation and features extracted are given into SVM classifier for classification. GLCM and Zernike Moments are the two different feature extraction techniques used in this work. SVM with RBF kernel is used for classification. Zernike Moment features overperforms than GLCM. Zernike Moment achieves 97.89% accuracy and GLCM achieves 87.61% accuracy.

DESKRIPSI KEMAMPUAN KOMUNIKASI MATEMATIS SISWA DALAM PENYELESAIAN PERMASALAHAN PROGRAM LINIER

This study aims to describe the mathematical communication skills of high school students in class XI on linear program material. The research method used is descriptive research. The subjects in this study consisted of 5 students of class XI one of the public high schools in Karawang Regency which were determined using purposive sampling technique. The research data collection technique was obtained from a test instrument in the form of 3 validated description questions which contained 3 indicators of mathematical communication ability. The results of this study indicate that the mathematical communication ability of class XI high school students in Karawang Regency in understanding linear programming material is still very low. This can be seen from the average percentage of the three questions of mathematical communication skills is 48.3℅. In indicator 1, students have not been able to express mathematical ideas through writing, demonstrate and visually describe them. For indicator questions 2 students are able to understand, interpret, and evaluate mathematical ideas both in writing and in other visual forms, but there are still some errors. Meanwhile, on indicator questions 3 students have not been able to use terms, notations, mathematical symbols and their structures to present ideas, describe relationships with various situation models.

KEMAMPUAN NUMERASI PESERTA DIDIK MELALUI IMPLEMENTASI BLENDED LEARNING PADA MATERI BILANGAN PECAHAN

This study aims to describe the numeracy skills of students in the matter of fractional arithmetic. This research method is a type of combination research. The research subjects were 31 students of class VIIU1 SMP Muhammadiyah 4 Palembang, but three people were chosen as subjects to be interviewed. The data collection techniques in this study were questionnaires, tests, and interviews. The instrument in this study is the researcher and assisted by questionnaires, numeracy questions, and interview guidelines. The data analysis technique of this research is quantitative and qualitative with the stages of quantitative data analysis. The results showed that the response of students to blended learning was good. The numeracy ability of students after being given blended learning on fractional numbers is still low. This can be seen from the results of the written test which showed that there were only 2 students in the high category, 6 in the medium category, and 23 in the low category. Based on the results of written tests and interviews that have been analyzed based on indicators of numeracy skills, students are able to using various numbers or mathematical symbols related to basic mathematics and able to analyze information displayed in various forms (graphs, tables, charts, diagrams). This can be seen in students who are able to use mathematical concepts and procedures on fractional number material. Most of the students are not able interpret the results of the analysis to predict and make decisions, because students are not used to reinterpreting the results of calculations into the context of the problem

Student teachers’ common content knowledge for solving routine fraction tasks

This study focuses on the knowledge base that Swedish elementary student teachers demonstrate in their solutions for six routine fraction tasks. The paper investigates the student teachers’ common content knowledge of fractions and discusses the implications of the findings. Fraction knowledge that student teachers bring to teacher education has been rarely investigated in the Swedish context. Thus, this study broadens the international view in the field and gives an opportunity to see some worldwide similarities as well as national challenges in student teachers’ fraction knowledge. The findings in this study reveal uncertainty and wide differences between the student teachers when solving fraction tasks that they were already familiar with; two of the 59 participants solved correctly all tasks, whereas some of them gave only one or not any correct answer. Moreover, the data indicate general limitations in the participants’ basic knowledge in mathematics. For example, many of them make errors in using mathematical symbol writing and different representation forms, and they do not recognize unreasonable answers and incorrect statements. Some participants also seemed to guess at an algorithm to use when they did not remember or understand the correct solution method.

Handwritten Mathematical Expression Recognition via Attention Aggregation Based Bi-directional Mutual Learning

Handwritten mathematical expression recognition aims to automatically generate LaTeX sequences from given images. Currently, attention-based encoder-decoder models are widely used in this task. They typically generate target sequences in a left-to-right (L2R) manner, leaving the right-to-left (R2L) contexts unexploited. In this paper, we propose an Attention aggregation based Bi-directional Mutual learning Network (ABM) which consists of one shared encoder and two parallel inverse decoders (L2R and R2L). The two decoders are enhanced via mutual distillation, which involves one-to-one knowledge transfer at each training step, making full use of the complementary information from two inverse directions. Moreover, in order to deal with mathematical symbols in diverse scales, an Attention Aggregation Module (AAM) is proposed to effectively integrate multi-scale coverage attentions. Notably, in the inference phase, given that the model already learns knowledge from two inverse directions, we only use the L2R branch for inference, keeping the original parameter size and inference speed. Extensive experiments demonstrate that our proposed approach achieves the recognition accuracy of 56.85 % on CROHME 2014, 52.92 % on CROHME 2016, and 53.96 % on CROHME 2019 without data augmentation and model ensembling, substantially outperforming the state-of-the-art methods. The source code is available in https://github.com/XH-B/ABM.

Analisis Kemampuan Komunikasi Matematis Ditinjau dari Gaya Kognitif pada Siswa SMP-IT Yarsi Mataram

This study aims to analyze the mathematical communication ability that is reviewed from the cognitive style on SMP-IT students of Yarsi in academic year 2021/2022. This study used descriptive method. The sample chosen by using nonprobability sampling technique with purposive sampling type, and the VIII Al-Farabi class is chosen as the sample. The subject selection technique in this research is based on the result of Group Embedded Figures Test (GEFT) consisted of 4 students. The instrument used is the essay test to acquire the data of students’ mathematic communication ability, while the Group Embedded Figures Test (GEFT) is used to determine the cognitive style and the interview from the students. From the research result, it is concluded that: (a) Students with Field Independent (FI) cognitive style have a good mathematic communication. The students in this stage are able to write and explain the mathematic idea logically and systematically, state the mathematical problem into drawing or table clearly and precisely, and also able to use the mathematical terms and symbols correctly. (b) Students with Field Dependent (FD) have the mathematic communication that is said to be not quite enough. The students in this stage are incapable to write and explain the mathematic idea logically and systematically, state the mathematical problem into drawing or table precisely and accurately, and also unable to use the mathematic terms and symbols correctly.

ANALYSIS OF THE DIFFICULTIES OF CLASS X STUDENTS OF SMKN 4 PALANGKA RAYA IN SOLVING TRIGONOMETRY PROBLEMS

This research was motivated by the low scores obtained by students in the trigonometry material for the area of ​​triangles in class X GP of SMK Negeri 4 Palangka Raya. In the 2019/2020 school year, only 48% of the 34 students achieved the school's Minimum Completeness Criteria, which is 65. The purpose of this study is to describe the difficulties experienced by students in solving math problems on trigonometry material and the factors that students experience difficulties. This research is a qualitative descriptive study. The results showed that the difficulties experienced by students in solving trigonometry problems were: (a) Difficulties in counting were difficulties in performing number operations. The factor that causes students to be less careful. (b) Difficulty in transferring knowledge, namely determining the formula and sine value. The reason is that students do not understand the material being taught so they cannot distinguish the formula used in determining the area of ​​a triangle according to what is known in the problem. (c) Difficulty in understanding mathematical language, namely understanding mathematical symbols correctly. The reason is that students are less careful in writing down the numbers that match the existing mathematical symbols. (d) Difficulty in visual perception, namely making and understanding sketches or drawings based on existing problems. The reason is that students do not understand how to change what is asked in the question of the shape of a triangular image and vice versa.

Editorial Policy

Editorial Policy

Editorial Policy

Editorial Policy

Introduction: The Idiosyncratic Nature of Renaissance Mathematics

Introduction: The Idiosyncratic Nature of Renaissance Mathematics

CONNECTING THE MASTERY LEVEL IN TRANSLATING VERBAL STATEMENTS TO MATHEMATICAL SYMBOLS WITH VOCABULARY ENHANCEMENT

Translation from words to symbols is undeniably one of the solution processes in solving word problems that can be considered critical (Bardillion, Jr. 2004) cited by Dela Cruz, et.al (2014). Failure to translate the verbal statement to mathematical symbols can lead to incorrect solution. This study aimed at giving remedy to the least mastered competency in translating verbal phrases to mathematical symbols and improving the academic performance of the Grade 7 students at Tabuk City National High School, Tabuk City Division, School Year 2017-2018 using the Strategic Intervention Material developed by Ms. Apple Jean G. Yecyec (n.d.). This study focused on the fifteen (15) identified students having a score of 1-5 on a given formative test. A teacher-made pretest and posttest was utilized. The participants had a ?Very Low? performance on the pre-test at 24.65% level of mastery with regards to translating verbal phrases to mathematical symbols. Results showed there was a significant difference between the pretest and posttest of the participants. It implies that the strategic intervention material by Yecyec on translating verbal phrase to mathematical symbols is effective in improving the mastery level on the least learning competency. Thus, the Strategic Intervention Material (SIM) by Yecyec on translating verbal phrases to mathematical symbols is strongly recommended for dissemination and utilization.

THE BRAILLE SYSTEM: THE WRITING AND READING SYSTEM THAT BRINGS INDEPENDENCE TO THE BLIND PERSON

The braille System is the most adopted writing and reading process in relief worldwide and includes the writing of the alphabet and of mathematical, chemical, phonetic, computer, and musical symbols. This text aims to explain what the braille System is and its importance for the independence of the blind person. In addition to demonstrating the appropriate distance between the points and proving that writing on the conventional slate is the best resource for correct writing in braille, the main objective of the research is to emphasize the importance of using the braille System and to value the conventional slate as a braille writing instrument. From the reading of theoretical texts and writings performed using both slates, the result is even more evident that writing on the conventional slate meets the tactile reading of the blind person, who uses the pad of the index finger to feel the braille dots.<p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/edu_01/0941/a.php" alt="Hit counter" /></p>

A Study of Symbolic Analysis of Electrical Circuits on the Example of a Radio Frequency Filter

The year 2022 marks the 175th anniversary of Kirchhoff's theorem on finding a symbolic expression of the current of an electric circuit branch from its contour determinant in the form of a fraction with a denominator and numerator. The first part of Kirchhoff's theorem concerning finding the contour determinant (fraction denominator) marked the beginning of graph theory, while the second part of the theorem on finding the numerator of a fraction remains unused to date. A symbolic circuit analysis calculation of transient processes in the radio frequency filter is carried out at the operator's stepwise and harmonic influences. The computer-aided calculation program developed by the authors is based on the modified Kirchhoff rule for finding the symbolic expression of the current of a branch of an electrical circuit from its contour determinant and it can be useful for researchers, engineers and students of mathematical and technical specialties. The program console is written in the Delphi package and opens in the Windows environment under the name "TINS" and it has an intuitive interface. The expressions for the branch currents can be copied without modification to the Maple computer algebra package, and to the Mathcad package – with the replacement of mathematical symbols. The reliability of the calculations was checked by initial and final conditions by comparing the Laplace transform table with the originals found by the “invlaplace” operation built into the Mathcad package. The presented computer program and calculation methodology allow you to quickly understand certain sections of mathematics and radio electronics and easily choose another object as a study. Computer-aided calculation of electromagnetic processes in radio engineering devices using the "TINS" program reduces the analysis time by obtaining results in symbolic form.

Translation Failure from Verbal to Symbolic Representations on Contextual Mathematics Problems: Female vs Male

Representation translation is the ability to change one form of representation to another. This research aims to describe the failure of the translation of verbal to symbolic representations in solving contextual problems in male and female students. The research partisipant were eight students of class VII an Islamic public school at Gresik. The data collection technique is through task-based interviews. The data on the translation of verbal to symbolic representations were analyzed by unpacking the source, preliminary coordinator, constructing the target, and determining equivalence. The results showed that at the stage of unpacking the source, both male and female students experienced the same failure, namely not understanding more complex contextual problems. In the preliminary coordinator stage, male students failed to understand the requested symbolic representation, understand the meaning of mathematical symbols, and determine keywords, while female students only failed due to their mistakes in the previous stage. In the constructing the target stage, male students failed to construct a symbolic representation of the plans made and translate into mathematical symbols, while female students failed to translate verbal words into mathematical symbols and mathematical operations. At the determining equivalence stage, male and female students have not been able to do it.

ОПТИМИЗАЦИЯ РАСПОЛОЖЕНИЯ РЕГИОНАЛЬНЫХ ЦЕНТРОВ ТЕХНИЧЕСКОГО ОБСЛУЖИВАНИЯ И РЕМОНТА СЕЛЬСКОХОЗЯЙСТВЕННОЙ ТЕХНИКИ

The results of studies on optimizing the location of regional centers for maintenance and repair of agricultural machinery are presented. An original technique is proposed, the implementation of which includes three stages. The number of regional centers for maintenance and repair of agricultural machinery in the region, taking into account the relevant basic dealer standards, depending on the number of agricultural machinery in the region under consideration, was determined at the first stage.The second stage included the division of the considered territorial area into subareas, using the theory of sets. The elements of set theory made it possible to establish a one-to-one correspondence between the area under consideration as a territorial subject and a certain set as a mathematical object with certain mathematical properties. The elements of set theory made it possible to establish a one-to-one correspondence between the area under consideration as a territorial subject and a certain set as a mathematical object with certain mathematical properties. The representation of an area, which is a territorial unit, as a set, defined as a mathematical object, made it possible to abstract and proceed to the study of its physical properties using mathematical symbols and criteria. he values of the effective time for each district center included in the subdomain under consideration were determined at the final stage, and the choice of one district center within each subdomain under consideration was carried out according to the smallest value of the effective time. The coefficient of availability of serviced equipment for a particular district center, in which it was supposed to design a center for maintenance and repair of agricultural equipment, was used in calculating the effective time. It was determined that the travel time of a service center specialist - 1.8 hours was established. The optimal distance for finding technical service objects from the main or additional service centers - no more than 63 km was established.

Math Accessibility for Blind People in Society Using Machine Learning

Math plays a crucial role in each and every sector belonging to human beings in society. Sometimes, it is very difficult to recognize math equations and symbols due to variation in writing, change in stroke, touching symbols, and many more. The blind people get very low success in math recognition as compared to character and digit recognition. It is needed to develop blind math application in which various math equations and symbols have to be recognized. The proposed system uses a machine learning approach to identify the various math equations and symbols by extracting various statistical and complex features with well-known classifier viz. support vector machine, neural network, and K-nearest neighbor. The math documents have to be scanned and recognized. Finally, a text to speech converter has been made to get the contents of math documents for blind people in society. The proposed system will be helpful for blind math applications and it will not affect the health of blind people in terms of stress on the eye to recognize so the health can be maintained and documents can be read.The implemented system can be used by blind people to read the math documents, digits on a bank check, calculate the valuation of currency, etc.

Analysis of Students' Mathematical Communication Skills In Terms of Self-Confidence

Mathematical communication skills are the ability to convey mathematical ideas or ideas orally or in writing, and to understand and accept other people's ideas or ideas carefully, analytically, critically, and evaluative to sharpen the understanding. The purpose of this study is to analyze students ' mathematical communication skills in terms of self-confidence. The study was conducted in SMP Negeri 3 Soe with the subject of research being VIII grade students as many as 22 students. This study uses the qualitative descriptive method. Data collection techniques in the form of tests, questionnaires, and interviews. The data analysis follows the miles and Huberman model. The results showed that students ' mathematical communication skills are seen from different levels of confidence. Students who have a high level of confidence can meet 4 indicators of mathematical communication skills, namely connecting real objects, images, and diagrams into mathematical ideas; able to present ideas in the form of images; able to use terms, mathematical symbols, and structures to present ideas, describe relationships and model making; able to understand, interpret and evaluate mathematical ideas. Students who have a moderate level of confidence can meet three indicators, namely connecting real objects, images, and diagrams into mathematical ideas; being able to present ideas in the form of images; able to use terms, mathematical symbols, and structures to present ideas, describe relationships and model making. Students with a low level of confidence are only able to meet one indicator, namely in using terms, mathematical symbols, and structures to present ideas, describe relationships, and model making.

Concurrent Validity of Proficiency in English Language on Mathematics Performance among Senior High School Students in Shama Senior High School

One source of evidence to validate assessment result is criterion-related evidence which states that two set scores on the same content should be able to be substituted. The study sought to determine how the students’ performance in mathematical symbols test and predict their performance on mathematical word problem. The descriptive design was used for the study. The stratified random sampling technique was used to select two classes each from General Science and General Art. Sample of 144 students were used in the study. Pearson Moment correlation was used to analyze the data. It was found that there is a significant low positive correlation between students’ performance in mathematical word problem and mathematics symbol problem due to gender and course of study. It was recommended that mathematics teachers need some professional development on how to help students understand the linguistic necessities of the subject (mathematics). This would be achieved as they go through in-service training.