Learning Of Discrete Mathematics Research Articles

Penerapan Project Based Learning Pada Mata Kuliah Matematika Diskrit Untuk Meningkatkan Kemampuan Pemecahan Masalah

Learning that focuses on students' problem-solving abilities is the focus of higher education. Students who are able to develop critical thinking skills in solving problems are a necessity along with changes in workforce capability needs in the informatics era. One of the mathematics lessons at the higher education unit level is discrete mathematics. The problem that arises in discrete mathematics learning is that learning outcomes and the percentage of students completing lectures are still relatively low. The aim of this research is to improve students' solving abilities through the application of the project based learning method. This research uses classroom action research methods. The application of the project based learning method in discrete mathematics courses with graph material can improve students' abilities in solving mathematical problems, this can be seen from the research results after corrective actions were taken in learning activities in Cycles I and II. Based on the research results, it shows that through project-based learning, third semester RB class students in the Informatics Engineering Education Program at Indraprasta University PGRI Jakarta have improved their ability to solve mathematical problems in terms of individual grades and classical completion.

A theoretical analysis of the validity of the Van Hiele levels of reasoning in graph theory

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of reasoning whose descriptors need to be validated according to the structure of this model. In this paper, the validity of these descriptors has been approached with a theoretical analysis that is organized by means of the so-called processes of reasoning, which are different mathematics abilities that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. The analysis gives support to the internal validity of the levels of reasoning in graph theory as the properties of the Van Hiele levels have been verified: fixed sequence, adjacency, distinction, and separation. Moreover, the external validity of the levels has been supported by providing evidence of their coherence with the levels of geometrical reasoning from which they originally emerge. The results thus point to the suitability of applying the Van Hiele model in the teaching and learning of graph theory.

Teaching and learning discrete mathematics

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes, topics, and mathematical practices that distinguish discrete mathematics. We then present potential benefits of focusing on discrete mathematics topics for mathematics education; in particular, we discuss the accessibility of topics in discrete mathematics, the connection to mathematical processes and affect, and the relevance of discrete mathematics in our current society. We also emphasize discrete mathematics from an international perspective, highlighting studies from the US, Italy, France, Chile, and Germany, which are across all school levels–primary, middle, and secondary school, and with some implications for post-secondary education. We particularly discuss discrete topics including number theory, combinatorics, iteration and recursion, graph theory, and discrete games and puzzles; we describe and situate these topics within literature. We also suggest the additional topics of game theory and the mathematics of fairness that we hope to see addressed in future studies.

Development of a Platform for STEM Teaching and Learning Resource Materials in the field of Discrete Mathematics

Past studies have found that there are constraints on teachers in developing teaching and learning (TnL) resources to implement STEM education in the classroom. Based on this issue, this research has developed a platform containing a variety of STEM TnL resource materials that focus on the field of Discrete Mathematics learning. This field of study is an area of learning in KSSM Mathematics for form four students. It encompasses three titles, namely Logical Reasoning, Operations on Sets, and Network in Graph Theory. Discrete Mathematics was the focus in the development of this platform as it is often considered difficult for students to understand. Additionally, as teachers find it challenging to find suitable learning materials to get students to be more interested. The wide range of TnL STEM source materials contained in this platform makes it easier for teachers to choose and apply them in TnL. The ADDIE model was used as the development model for this platform. This model is among the most systematic and effective development models, consisting of five phases, i.e. analysis, design, and development, implementation, and evaluation. The platform was developed using an interactive multimedia medium that makes learning fun for students.

The Relationship of Offline Learning with Discrete Mathematics Learning Interests After the Pandemic

This article aims to determine the relationship between offline learning and interest in learning discrete mathematics after the pandemic. The research method used is quantitative. The sampling technique in this study used purposive sampling. Data collection in this study used a questionnaire with a Likert scale of 1 to 5. The variables in this study consisted of variable X, namely offline learning and variable Y, namely interest in learning. Each variable consists of 4 indicators. The result of this research is that there is a relationship between offline learning and students' interest in learning in discrete mathematics courses of 0.801. So it can be said that the relationship between offline learning and learning interest is very strong. This is because in offline learning students can interact directly with the lecturer so that discrete mathematics material that has not been understood can be directly asked during learning. Offline learning can also encourage interest in learning so that students are more enthusiastic and enthusiastic about participating in discrete mathematics lectures.

Advanced Mathematic Thinking Ability Based on The Level of Student's Self-Trust in Learning Mathematic Discrete

<p class="BodyAbstract">Mathematical thinking and self-confidence are indispensable aspects of learning mathematics and are influential in solving mathematical problems. In higher education mathematics learning, advanced mathematical thinking skills are required (Advance Mathematical Thinking. Advanced mathematical thinking processes include: 1) mathematical representation, 2) mathematical abstraction, 3) connecting mathematical representation and abstraction, 4) creative thinking, and 5) mathematical proof. Discrete mathematics is one of the courses in mathematics education FKIP UNS. The problems in Discrete Mathematics courses are usually presented in the form of contextual problems. Students often experience difficulties in making mathematical expressions and mathematical abstractions from these contextual problems. In addition, students also experience difficulties in bookkeeping. Most students often prove by using examples of some real problems. Even though proof in mathematics can be obtained by deductive thinking processes or inductive thinking processes, the truth is that mathematics cannot only come from the general assumption of inductive thinking. Based on this, a qualitative descriptive study was carried out which aims to determine the advanced mathematical thinking skills based on the level of student self-confidence. Research with the research subjects of FKIP UNS Mathematics Education Students in Discrete Mathematics learning for the 2019/2020 school year gave general results that the student's ability in advanced mathematical thinking was strongly influenced by the level of student confidence in learning. The higher the student's self-confidence level, the better the student's advanced mathematical thinking ability, so that high self-confidence has a great chance of being successful in solving math problems.</p>

예비 수학교사들이 이산수학 학습에서 겪는 어려움 분석

This study aims to help improve teacher education by investigating and analyzing the causes and backgrounds of learning difficulties experienced by pre-service mathematics teachers in discrete mathematics. To this end, we conducted a questionnaire and evaluation of them on discrete mathematics, and the data obtained were analyzed. As a result, first, pre-service mathematics teachers need to share their perceptions of the need for discrete mathematics education. Second, a review of the adequacy of the discrete mathematical content and its the credits are required. Third, The causes of their learning difficulties needs to be looked at from a different perspective than the learning factors. And two implications were obtained. One is necessary to study the systematicity and sequence of content elements of discrete mathematics in the aspect of its continuity of curriculum of secondary school and university. The other is required consideration for adjusting the ratio of discrete mathematics to secondary teachers’ employment examination.

MODEL SEM-PLS TERBAIK UNTUK EVALUASI PEMBELAJARAN MATEMATIKA DISKRIT DENGAN LMS

Research on the use of Structural Equation Modelling-Partial Least Square (PLS-SEM) related to Learning Management System LMS has developed very rapidly. However, in these studies, it was not explained how to choose the best model used to evaluate the relationship among latent variables in the model. This study aims to select the best SEM-PLS model related to evaluating the use of LMS in Discrete Mathematics learning based on the criteria of Q2, AIC, AICu, AICc, BIC, HQ, and HQc. Data obtained from a survey of 109 3rd semester students who took Discrete Mathematics courses at STMIK IKMI Cirebon using 5 latent variables. The Main Model is formed based on all research latent variables and evaluated by stages 1) PLS-Algorithm, 2) Bootstrapping and 3) Blindfolding. Based on the Main Model, 16 alternative models are created with the same manifest variables as the Main Model. The best model is determined based on the highest Q2 value, and the least AIC, AICu, AICc, BIC, HQ and HQc values. The results of the study show that the Main Model is better based on the Q2 value compared to other models in this study. Different results are obtained if the AIC, AICu, AICc, BIC, HQ and HQc criteria are used, where Model C2 and B2 are the best models based on these criteria

PEMANFAATAN LEARNING MANAGEMENT SYSTEM DALAM PROSES PEMBELAJARAN MATEMATIKA DISKRIT

This paper presents the results related to the influence of Mathematics Ability variables and Application-Computer Self-Efficacy (ACSE) students on the Quality of Learning Outcomes in the process of learning Discrete Mathematics by utilizing LMS as a support system. The research method used is Classroom Action Research (CAR), using a quantitative approach. Respondents were third semester students of the Informatics Engineering study program STMIK IKMI Cirebon. The research data were obtained from observations, questionnaires, databases of grades of Calculus and Linear Algebra courses, and recapitulation of student learning outcomes for one semester in Discrete Mathematics lectures. Data analysis was performed using the Dummy Regression method. Based on data analysis, it was found that Mathematical Ability and Application-Computer Self-Efficacy (ACSE) of students had a positive effect on the quality of the results of Discrete Mathematics learning using LMS as a support system.

Applications of CAS in the Teaching and Learning of Discrete Mathematics

In this paper our experience in application of CAS Maple for modelling and solving counting problems as well as for solving recurrence equations is represented. Some procedures for calculating combinations with repetition and variations with repetition in case of authorized number on appearance of elements are given. The result is a list of the allowed number of appearances of the element in the polynomial involved in the generating function. Some conclusions have been visualized. The represented approaches correspond to the Curriculum of the Bachelor Degree Program in Applied Mathematics and Informatics at TU-Sofia and are based on methodological principles and the educational tradition in our country.

Developing of mLearning for Discrete Mathematics Based on Android Platform

In this paper, we present Discrete Mathematics Learning system based on Android operating system. The objective of this system is to advice student to learn discrete mathematics more convenient on mobile platform. The design approaches and functional components of this system were described and this application was developed on Knowledge. In this project, it was divided the result by the research purposes into 2 parts: developing the Mobile application for students and testing and evaluating the system. Black box technique was used to evaluate application performances and Questionnaires were applied to measure user satisfaction with system usability by experts and students.

Teaching Formal Methods and Discrete Mathematics

Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help during the development cycle is essential but we think that education of computer scientists and software engineers is also an important challenge to take up. Indeed, we believe that formal methods courses do not appear sufficiently early in compter science curricula and thus are not widely used and perceived as a valid professional skill. In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop- ment within FoCaLiZe. We also believe that this could considerably benefit the learning of discrete mathematics.