Basic Mathematical Concepts Research Articles

ОСОБЕННОСТИ ПРИМЕНЕНИЯ ПАКЕТА MAPLE В ШКОЛЬНОМ КУРСЕ МАТЕМАТИКИ

This article discusses the features of using the Maple package in a school math course. The school mathematics course consists of basic mathematical concepts, ideas and principles. The scientific nature of the course content and the abstract nature of the topics studied make this course difficult to study in the classroom. The current situation with the coronavirus pandemic has completely eliminated full-time education and made distance education more relevant. The share of independent work of students has increased significantly. This negatively affects the ability to read and understand very complex material. In this regard, the choice of the Maple package as a method of computer technology and its technological possibilities for the organization of independent work of students in school mathematics courses are justified. The authors of the article developed a technology of teaching using the Maple package for school mathematics courses on the basis of the South Kazakhstan State Pedagogical University. This teaching method is aimed at organizing the independent work of students in the study of school mathematics. Examples of the use of the Maple package to solve some problems in a school math course are presented. Taking into account the specifics of the tasks of teaching mathematics at school, the possibilities and advantages of the technology of organizing students' independent work with the help of the Maple package are considered in detail.

Reflections on the formation of mathematical imagination in preparing children for school

The article describes the system of work in the preparatory groups of preschool education. It has been shown that the formation of mathematical concepts is a key factor in raising children's worldview. This is not only to determine the level of knowledge of mathematics in the children of his group, but also to consider the importance of each educational activity in the whole system of work on the development of basic mathematical concepts in preschool children. Going to school is an important part of a child's life, as it changes the way he or she interacts with others. For the first time in a child's life, socially important learning activities take center stage. Unlike the usual free play activities, education is now mandatory and requires 4 serious attitudes from the first grader. As a leading form of educational activity, it reconstructs the daily life of the child: the agenda changes, the time for free play is reduced. It is also important for the child to have practical mental development in order to be educated in school, that is, to draw a pattern, to perform a descriptive task. Finally, special training involves teaching a child to read and form his or her understanding of the school's ability to adequately master the 1st grade curriculum material.

توقُّع الفائز في لُعبة نِيم

نظرية الألعاب تعرّف بأنها وسيلة من وسائل التحليل الرياضي لحالات تضارب المصالح، للوصول إلى أفضل الخيارات الممكنة لاتخاذ القرار في ظل الظروف المعطاة لأجل الحصول على النتائج المرغوبة. بالرغم من ارتباط نظرية الألعاب بالتسالي المعروفة كلعبة الداما، إكس أو، البوكر، إلا أنها تخوض في معضلات أكثر جدية تتعلق بعلم الاجتماع، والاقتصاد، والسياسة، بالإضافة إلى العلوم العسكرية، كما ويندرج تحت نظرية الألعاب عدة أنواع من الألعاب منها الألعاب التآلفية. يعطي هذا البحث للقارئ نظرة تفصيلية لإحدى أهم الألعاب التآلفية والتي تسمى لعبة (نيم)، قبل بدء اللعبة سنضع استراتيجية لتحديد الفائز مقدماً بمساعدة بعض المفاهيم الرياضية الأساسية مثل: الحد الأدنى المستبعد، أعداد غراندي، العدد XOR.

On the Okamoto-Uchiyama cryptosystem: (A brief essay on basic mathematics applied in cryptography)

The Okamoto-Uchiyama cryptosystem applies many consepts of basic abstract algebra, discrete mathematics and number theory. Many of these concepts are elementary and used in other branches of cryptography. However, those elementary concepts are not enough provided in the mathematics curriculla in under developed and developing countries despite the fact that in early stages teaching of those basic mathematics concepts, there is no need to provide sophiticated nor rigorous treatments beyond computations of integers.By exploring the basic mathematics applied in Okamoto-Uchiyama’s algorithm and its re-lated concepts, this exploration should make mathematics teachers, educators and instructors to be aware of the important teaching the basic abstract algebra, discrete mathematics and number theory as early as high school senior level or at the first year in colleges and universities.

Teacher Qualification Characteristics and Secondary School Students’ Mathematics Achievement: A Quantitative Study

Many Grade 12 Caribbean Secondary Education Certificate (CSEC) Mathematics examination registrants are consistently underperforming due to their inability to grasp basic mathematical concepts (Caribbean Examinations Council, 2006-2016). The purpose of this research was to examine the relation and association between five Teacher Qualification Characteristics (TQCs) and students’ 2016 CSEC Mathematics achievement at two secondary schools in the British Virgin Islands (BVI). A sample size of 113 participants were incorporated in this research (N=105 students and N=8 teachers). These teachers taught these students CSEC Mathematics during the year of examination, 2015-2016. The Spearman’s rho correlation revealed that there was a statistically significant positive relationship between teacher qualification, teacher certification, and teacher Mathematics teaching experience and students’ ordinal grades at [r=.416; p=.000 < ?=.001], [r=.235; p=.016 < ?=.05], and [r=.20; p=.041 < ?=.05] respectively. Similarly, the chi-square output showed a statistically significant association between teacher qualification, teacher certification, and teacher Mathematics teaching experience and students’ ordinal grades at [p=.000 < ? =.001], [p=.010< ? =.05], and [p=.003< ? =.05] respectively. On two occasions, the Bonferroni adjustment was used. For both tests, professional development and academic coaching were not statistically significant.

Laplace Transform, Application in Population Growth

Laplace transformation is an important chapter of Mathematical Analysis. It has wide applications in different fields of engineering and techniques besides basis sciences and mathematics. In this paper we will become acquainted with the basic concepts of operational mathematics, some properties of Laplace Transform and its application in demography. The purpose of this paper is to utilize the Laplace transformation to extract the logistic equation and to use the logistic equation in population projections.

Developing an Optimal Strategy for a Maximization Dice Game

Many dice games have been used to illustrate basic probability concepts in college mathematics and statistics classrooms (see, for example, [1, 5]). There has been growing interest in developing op...

Advances in Gaussian random field generation: a review

Gaussian (normal) distribution is a basic continuous probability distribution in statistics, it plays a substantial role in scientific and engineering problems that related to stochastic phenomena. This paper aims to review state-of-the-art of Gaussian random field generation methods, their applications in scientific and engineering issues of interest, and open-source software/packages for Gaussian random field generation. To this end, first, we briefly introduce basic mathematical concepts and theories in the Gaussian random field, then seven commonly used Gaussian random field generation methods are systematically presented. The basic idea, mathematical framework of each generation method are introduced in detail and comparisons of these methods are summarized. Then, representative applications of the Gaussian random field in various areas, especially of engineering interest in recent two decades, are reviewed. For readers’ convenience, four representative example codes are provided, and several relevant up-to-date open-source software and packages that freely available from the Internet are introduced.

Identifikasi Problematika Mahasiswa Calon Guru SD/MI dalam Menyelesaikan Masalah Matematika Dasar

Pentingnya keberadaan dan peran matematika dalam segala lini kehidupan menuntut untuk dipahami dan dikuasai dengan baik. Terlebih bagi guru atau calon guru sekolah dasar/madrasah ibtidaiyah yang akan menanamkan konsep matematika dasar pada para peserta didik. Penelitian ini dimaksudkan untuk mengidentifikasi permasalahan utama yang dihadapi oleh mahasiswa calon guru sekolah dasar/madrasah ibtidaiyah dalam menyelesaikan masalah matematika dasar. Penelitian ini merupakan penelitian deskriptif kualitatif dengan subjek penelitian mahasiswa Prodi PGMI IAIN Ponorogo. Hasil penelitian menunjukkan bahwa secara umum, terdapat dua problematika utama yang dihadapi mahasiswa calon guru sekolah dasar atau madrasah ibtidaiyah di IAIN Ponorogo. Pertama, masih rendahnya pemahaman terhadap konsep dasar matematika. Logika matematika merupakan materi dengan angka ketidakpahaman tertinggi dibandingkan materi lain. Ketidakpahaman konsep terjadi secara merata pada masing-masing kelompok mahasiswa, baik yang berasal dari MA, SMA, maupun SMK. Namun, angka ketidakpahaman konsep pada mahasiswa yang berasal dari SMK cenderung lebih tinggi. Kedua, terjadinya miskonsepsi. Miskonsepsi tertinggi terjadi pada materi bilangan dan operasi aljabar. Namun demikian, meskipun dalam jumlah terbatas, ditemukan juga miskonsepsi pada konsep matematika dasar lainnya. Miskonsepsi cenderung terjadi pada mahasiswa yang berasal dari SMA dan MA.

Analisis Kesulitan Belajar Mahasiswa Pendidikan Guru Sekolah Dasar Pada Mata Kuliah Konsep Dasar Matematika Di Universitas Jambi

Abstract. The purpose of this study is to find out the difficulties of any difficulties experienced by students and what factors influence it. The procedure of this study uses a qualitative approach, the place of research in Elementary School Teacher Education FKIP Jambi University. The study population was 261 students. The sample of this study 15% with random sampling technique. Data was taken through observation, tests, questionnaires and interviews. Data analysis is done by studying, arranging, synthesizing, looking for patterns and finding what is systematically meaningful. The results of the study only 20% of students reached KKM 75 / B + passed the test because: (1) students had difficulty understanding basic geometry concepts (2) students had difficulty in using the formula (3) routine students in understanding the connectedness of each build and 4 ) Difficult students solve questions that are mixed with application stories that require analysis. While the factors that influence it are (1) the basic ability of students to mathematics is still low (2) learning motivation is still low (3) low learning readiness (4) the availability of books / references that are minimal (5) lack of trying to solve complicated / reasoning questions . Conclusion of Research, that students have difficulty learning in geometry material, and the determining factor is the lack of readiness and seriousness of students in solving these difficulties.
 
 Keywords: Analysis, Learning Difficulties, Basic Concepts of Mathematics

Measuring Effectiveness of Mobile Application in Learning Basic Mathematical Concepts Using Sign Language

Technology plays an important role in our society, especially in the field of education. It is quite regrettable that people, particularly the deaf, still face a lot of challenges in acquiring an education. Their learning methods are different as compared to hearing people. They use Sign Language (SL) rather than natural language to communicate and learn. They are required to put a lot of effort into learning different concepts using conventional pedagogies. Therefore, there is a dire need for some assistive technology to improve their learn-ability and understandability. In the present study, 192 deaf participants aged 5–10 years were sampled from two special child institutes. The objective of the present study was to determine the effectiveness of a mobile interface through a developed mobile application for learning basic mathematical concepts using Pakistan Sign Language (PSL). The present study bridges the gap between the technology-based method and conventional teaching methods, which are used for teaching mathematical concepts using PSL. The participants were divided into two groups, that is, one group learned through conventional methods (flash cards and board) and the other group through the developed mobile application. The difference in the performance of both the groups was evaluated by conducting quizzes. The quiz results were analyzed by the Z-test and ANOVA. The findings revealed that the Experimental Group (EG) participants, who were instructed by our mobile application showed higher proficiency in the quizzes as compared to the Control Group (CG). EG participants performed better than CG by 12% in the quizzes. A gender based difference was also observed for the quiz scores. Male participants in category C (word problem learning) performed 2.7% better than females in the EG and 2.5% better in the CG. Moreover, a significant difference was also observed in the time taken by participants in both groups to complete the quizzes. CG participants took 20 min longer than EG participants to complete the quizzes. The results of the ANOVA showed that the quiz scores were directly affected by the mode of teaching used for participants in both groups.

KAJIAN KEMAMPUAN LITERASI KUANTITATIF SISWA SMA 8 KOTA BENGKULU

Quantitative literacy is the ability and confidence in using basic mathematical concepts and calculating operations needed for problem solving, decision making of economic problems and their applications in everyday life. Mastery of basic mathematics is an absolute requirement for achieving good quantitative literacy skills. The aim of this activity was to improve mathematical literacy skills of the students at SMA 8 Bengkulu City. The activities were begun by giving pre-tests to students, preparing of modules, presenting the materials of the modules in classroom, practicing through LKS and post-tests. Several techniques, methods and approaches in number counting operations have been presented in this activity. This activity has provided an increase in quantitative literacy skills in class XI IIS-1 SMA 8 Kota Bengkulu. Even so, the improvement of students' abilities can be said to be less optimal because there are still some questions that cannot be answered by almost all students. Therefore, cooperation and involvement of all parties is needed to improve students' quantitative literacy skills and follow-up activities in an effort to strengthen quantitative literacy skills.

MATHEMATICAL MODELING IN THE SYSTEM OF ECONOMIC EDUCATION

An important component of the training of future economists is to increase their level of mathematical education. This involves understanding the essence of the basic concepts, ideas and methods that are studied in the course of higher mathematics, their interpretation in methods to solve professionally-oriented tasks. The article describes the role of higher mathematics as an important tool for effective work of an economist. The article considers the necessity of teaching students of economic specialties of higher educational establishments to mathematical modeling as a means of professional-oriented teaching of higher mathematics. The expediency of using applied problems, which demonstrate the necessity of introducing basic mathematical concepts, raises motivation and stimulates the study of discipline, promotes development of research skills of future specialists.

Creating an environment for the restoration of dignity to disadvantaged mathematics foundation classrooms

This article chronicles how aconducive environment creates arestoration of dignity to disadvantaged mathematics foundation learners. The variation theory was used to provide the sequential building blocks required to learn foundation mathematics to grade 1- 5 learners in a district in the Eastern Cape province of South Africa. A sample of 23 learners participated in this study. Structured worksheets covering mathematics content for grade 1-5 were prepared for the learners to practice after school in a homework club on their own, in rural settings in a study that followed qualitative methods. Results indicated how the creation of a supportive and caring environment developed the learners’ resilience, restored their dignity and increased their competence in understanding of basic mathematics concepts. The learners also developed good relationships with each other while they shared information and helped others to restore their dignity and led them ultimately to independence of acquiring other mathematical skills and ownership of the learning experiences. The intervention with the after school programme may serve as a suitable environment for the disadvantaged learners and restore their competence in understanding mathematics concepts while providing a platform for learners to share knowledge gained with the underprivileged ones.

Методы геоинформатики и нечеткой математики в анализе геофизических данных

В настоящей работе приведен обзор базовых математических понятий и конструкций, которые легли в основу методов геоинформатики, развиваемых научной школой академика А.Д. Гвишиани. Важно отметить, что в рамках указанной школы геоинформатика понимается более широко, чем изучение и применение географических информационных систем. Геоинформатика включает в себя исследования по созданию методов и алгоритмов, позволяющих автоматизировать решение задач в области наук о Земле на базе данных исходных наблюдений. Под решением понимается адекватное моделирование логики эксперта, осуществляющего анализ данных и принятие решений вручную. Именно системы наблюдений и регистрируемые данные о процессах, происходящих в недрах Земли и в околоземном пространстве, являются основой фундаментальных исследований как в области геоинформатики, так и других науках о Земле. Так, под руководством академика А.Д. Гвишиани была существенна развита система наблюдений магнитного поля Земли. Настоящая статья в большей мере посвящена математическому аппарату, используемому для анализа данных наблюдений с целью последующего выявления новых закономерностей в процессах Земли и околоземного пространства.

Improving Pre-Service Teachers’ Performance in the Teaching of Common Fraction Using Cuisenaire Rods

This research study was undertaken to assess the difficulties pre-service teachers face using Cuisenaire Rods in teaching Common Fractions and how often these concrete models are used in their mathematics lessons. The extent of pupils’ participation and understanding the basic concept of common fractions, the student-teachers’ preference of using Cuisenaire Rods as against the use of fractional rules in teaching common fractions formed the integral part of the research study. Action research design was used for this study. The design allows the researcher to obtain answers to the questions raised directly from the respondents. The target population was pre-service teachers of Berekum College of Education. Random sampling procedure was used to select 50 student-teachers and JHS2 pupils as sample for the study so as to enhance the validity and generalization of the result. Observation of student-teachers’ teaching practices, model teaching by the researcher, questionnaire, and interviews granted to pupils on the study of common fraction on the use of Cuisenaire Rods were among the research instruments used. Descriptive statistics in terms of frequencies with their percentages were also used in analyzing the data obtained from the questionnaire. The research findings revealed that the use of Cuisenaire Rods to teach Common Fractions stimulates motivates and arouses the interest of learners to participate fully in the teaching and learning process. This helps pupils to actively partake in learning basic concepts in mathematics whenever concrete models were used in the lesson presentation. The research findings strongly indicated that no matter how different the pre-service teachers are prepared; the competencies of teacher education in our contemporary world would much depend on student-teachers’ teaching methods and teaching practices that can bring real meaning into the lives of their pupils. It is recommended that the supply of mathematics syllabus into the Colleges of Education should be accompanied with adequate teaching and learning aids for pre-service teachers. This would allow them to receive sufficient pre-training in all aspects of the curriculum before becoming professional teachers DOI : 10.7176/JEP/10-9-01 Publication date :March 31 st 2019

The analysis of students’ answers in solving ratio and proportion problems

The ratio and proportion is one of the basic concepts in mathematics. This concept is not only used to solve problems in mathematics but also in other disciplines and in daily lives. So, students should be have proficiency in solving ratio and proportion problems. During solving ratio and proportion problems, among students may have difference answers. Based on the students’ answer and prediction of didactical situation, lesson plan and anticipation of didactical situation would be done by teacher. The purpose of this study was to analyze the various answers of students as well as to see the mistakes made by students in solving ratio and proportion problems. The method used in this study was a descriptive qualitative. The subject were ten students of junior high school in South Tangerang, Indonesia. Written tests related to ratio and proportion problems would be done by the subject and to be continued with depth interviewing. The result of this study are that almost students apply formula although without understand why the formula be used and the concept of ratio and proportion. These results can be used as a reference in implementing the learning of the ratio and proportion.

CAI and conventional method for retention of mathematics: an experimental study

An experimental study was conducted to compare the effectiveness of Computer Assisted Instruction (CAI) and Conventional Method (CM) for retention of Mathematics in Higher Education. Instructional and measuring tools were developed for five units of Matrix Algebra, two units of Calculus & five units of Numerical Analysis. Pilot study was also conducted to examine reliability and validity of tools. Ninety undergraduates participated in final investigational study. Pre-test – Post-test Equivalent – Groups research design was used. SPSS v.16 was used for data analysis. Findings supported efficiency of CAI for retention of basic mathematical concepts. Administrators should encourage faculty members to develop Computer Assisted Instructional Material (CAIM) for retention of basic Concepts of Mathematics in Higher Studies.

Realistic Mathematics Education (RME) Provides Great Benefits for Students in Indonesia

Mathematics as a part of basic science is considered very difficult, especially for students from elementary school to high school. To facilitate the process of learning mathematics has been developed many new learning methods by experts in mathematics education, one of them is realistic mathematics education. Realistic mathematics education is one of therenewed learning methods on basic mathematical concepts that related to the context, illustrations, and based on everyday life situations. Besides realistic mathematics education motivated students to be more active and creative in solving mathematical problems according to real conditions, it also more emphasize cooperative and communicative learning so that students are more interested in learning mathematics. This encourages the government to include realistic mathematics education in the curriculum of basic education and also through the provision of training and education for teachers. It is expected that the education system that accommodates Realistic Mathematic Education can increase the interesting of students' learning

Effectiveness of Keyword Mnemonic Strategies to Increase the Math Vocabulary of Slow Learner Students

The slow learner characteristics that students have affect their ability to understand specific concepts / information such as understanding the basic concepts of mathematics. This has a negative impact on the failure of students’ vocabulary to slow learning. This study aims to determine the mnemonic keyword strategies in increasing vocabulary acquisition and retention of mathematical vocabulary in students with the slow learner. Mnemonic keywords strategy strategies are strategies that differ between information that will be used for students with information that students already know. Information that has been used by students as a keyword that helps students remember the new information they teach. The study design was a multiple-baseline design on subjects in three slow-learning junior high school students with 12-15 years of income. The intervention given to the subject is in the form of vocabulary prospects with mnemonic keyword strategies. The data chase technique uses a vocabulary assessment with a reliability of 0.849α which measures vocabulary acquisition and vocabulary retention. The research data was determined by determining the results of each research subject and using the Wilcoxon t test statistical analysis. Descriptive results show that the vocabulary of students’ vocabulary and retention of slow mathematical vocabulary can be improved through a mnemonic word intervention strategy. Meanwhile, the results of the analysis show that the mnemonic keyword strategy is effective in increasing the acquisition of vocabulary and the retention of students’ vocabulary with the slow learner. The implication is that this research can be the basis for developing more complex slow student mathematics.