ANALYSIS ON FUNDAMENTAL ALGEBRAIC CONCEPTS AND INFORMATION SECURITY SYSTEM

Cryptography plays a key role to protect the data from unauthorized access. Nowadays various cryptographic algorithms are used. It is not meant of information technology to secure proposed work main target to achieve these tasks and goals. In research study related to any field of science is based on some basic definitions and understandings of some previous results. Therefore we introduce the basic definitions of Algebra and information security system in this chapter which is important to understand the dissertation of the coming chapters. This chapter is further divided into sections which explain the various concepts comprehensively.

The contribution of online mathematics games to algebra understanding in Grade 8

This study explores how online mathematics games contribute to Grade 8 learners’ understanding of basic principles and more sophisticated aspects of algebra. This project documents the trajectory of a purposive sample of 30 Grade 8 learners doing mathematics and one mathematics educator. The study is premised on the argument that learners with the guidance of the teacher can grasp algebraic concepts better and learn to manipulate these imaginatively and independently, by integrating new online mathematics games into standard classroom teaching of mathematics. The study was located within the interpretive qualitative research paradigm and used a case study approach. Data were collected by means of (1) lesson observations, (2) questionnaires and (3) semi-structured interviews. The data collected were analysed through the lens of the sociocultural theory, social constructivism and the activity theory. This study supports the view, set out in the literature reviewed, that the way in which resources are utilised can substantially improve the teaching and learning of algebraic concepts. Teachers should encourage learners to venture into the world of online mathematics games to learn algebra because they help learners to be creative, look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish structured forms of cooperation. The teacher’s role is to show and guide the learners how to use online mathematics games to solve mathematics problems. This study’s main recommendation, among others, is a revision of the curriculum to integrate online mathematics games into all subjects in classrooms at all levels.

Links Between HX-Groups and Hypergroups

The concept of an [Formula: see text]-group is an upgrade of the concept of a group, in which a new operation is defined on the family of non-empty subsets of a group. If this new support set together with the new operation is a group, then we call it an [Formula: see text]-group. On the other hand, a hyperoperation is a mapping having the same codomain as the operation of an [Formula: see text]-group, i.e., the family of non-empty subsets of the initial set, but a different domain — the set itself. This could be (and was indeed) a source of confusion, which is clarified in this paper. Moreover, [Formula: see text]-groups naturally lead to constructions of hypergroups. The links between these two algebraic concepts are presented, with the aim of reviving the old notion of an [Formula: see text]-group in the current research on algebraic hyperstructures. One of such existing links and one newly established link are also discussed.

Analysis of Students' Mathematical Literacy Ability in Algebraic Concepts Based on Trends in International Mathematics and Science Study (TIMSS) Problems

This research uses descriptive qualitative. The aim is to examine students' mathematical literacy abilities and types of errors made by students of MTs Mathla’ul Anwar Kedondong in solving algebraic concept questions that were first accessed from TIMSS. The subjects of this study were all students of class VIII-A MTs Mathla’ul Anwar Kedondong, which had 30 students. The data was collected using tests and interviews. All student answers in the analysis of mathematical errors are based on empathy for students' mathematical literacy abilities, namely aspects of knowledge, application, and communication. Furthermore, for further analysis of the students 'mathematical errors, 2 students with the lowest scores were selected, representing the mathematical errors of all students based on the four aspects of the students' mathematical literacy abilities for interviews. The data analysis technique is by reducing data, presenting data, and drawing conclusions. The results of the analysis of the data collected, the mathematical literacy ability of students included in the medium category with an average score of 62.38 scores on a scale of 100. Based on the analysis of the mathematical literacy scheme capability mentioned, students can request solutions according to their needs and sufficient good at solving problems on the criminal aspect. However, judging from the mathematical mistakes made by students, students who made mistakes did not review the answers in solving the problems. This causes the problem solving is not correct.

Electronic Pocket Book of Algebra Concepts for Basic Chemistry Learning Stoichiometry Focus Subject

Mathematical abilities are very important in building students' abilities in all aspects. Mathematical abilities are needed not only as numeracy skills but the ability to use mathematical logic in solving problems. Mathematical concepts are needed even for other scientific fields. This algebra concept electronic pocket book was created to help students during basic chemistry learning. The focus of the material chosen in basic chemistry learning is stoichiometry that applies algebraic concepts. This pocket book is useful for streamlining basic chemistry learning, especially on stoichiometry materials that use algebraic concepts in their operations. This algebra concept electronic pocket book has been tested on stoichiometric material. This book was tested on first semester students for basic chemistry courses.The test results on the first semester students showed a significance value of less than 0.05, which indicates that there was a difference in the average between group A and group B

Pengembangan Video Pembelajaran Pengantar Struktur Aljabar

The development of instructional videos for an introductory course on algebraic structures aims to improve student understanding with different learning methods. Students produce videos containing algebraic structure material, they have mastered the concept correctly. Through the preparation of making instructional videos, students are motivated to increase their knowledge regarding algebraic structure material. The method used in this research is development research that describes student learning outcomes in mastering the concept of algebraic structures. The results showed that students who could explain the algebraic structure material in the video well showed a good understanding of algebraic material. In making videos, students are motivated to present interesting work and also the concept of correct algebraic structures. Students learn from various reading sources to present the correct algebraic concepts in the form of learning videos. The content of the learning videos contains concepts and practice questions. The conclusion that can be obtained in this study is that the development of instructional videos carried out by students can help students understand the algebraic structure material, because it contains cooperative learning methods.

How specific can language as resource become for the teaching of algebraic concepts?

Classroom research into mathematics and language has studied issues of context specificity such as cultures of explanation or the impact of language policies on practice. More recently, researchers in the domain have started to study issues of content specificity aimed at performing language-responsive mathematics teaching for the learning of precise mathematical content. Progress in the conceptualization of language as resource for mathematics teaching and learning makes it necessary to strengthen the discussion of the contexts of culture and interaction along with the linguistic demands given by the specificity of the mathematical content at play. In this paper, I introduce a sociocultural framing for a mathematical-linguistic view of grammar as resource with the focus on explicitness in communication. I then report developmental work with two teachers on their teaching of algebraic concepts, and address the question of how to learn to communicate explicit meanings for these concepts in classroom mathematical talk. The structuring principle adopted for this work was to critically distinguish and choose or produce instances of teacher talk that overtly communicated conceptual meaning within the algebra of equations. I conclude with preliminary evidence of the effectiveness of the work with the teachers.

ANALYSIS OF STUDENTS MATHEMATICAL CONNECTION ERRORS IN TRIGONOMETRIC IDENTITY PROBLEM SOLVING

The trigonometric identity is essential in learning Mathematics because it requires students to think critically, logically, systematically, and thoroughly. Solving trigonometric identity problems requires students to relate conceptual knowledge or procedural knowledge, which then used in questions. This study involved grade X students of senior high school, which were examined to find out the types of mathematical connections errors and causes of the errors. Before task-based interviews were conducted, 36 students were first given a test. Based on several considerations, seven students ( three males and four females) were selected to undergo a task-based interview. This research employed a qualitative research method with a case study design. The results of the analysis indicate that the errors in connecting to conceptual knowledge are most commonly the mistake of connecting the algebraic concept. On the other hand, 86.11% of students experienced errors in connecting to procedural knowledge. This error happened when the students worked on problems with trigonometric identities, which they had rarely encountered in exercises. Errors in mathematical connections in trigonometric identity are caused by the lack of understanding of the algebraic arithmetic operation, emphasis on the concept, and strategic knowledge. It shows that students need a variety of problems to be able to master various forms of trigonometric identities. This research's result also reinforces the critical role of algebraic concepts as prior knowledge in studying trigonometric identity.