BERPIKIR MATEMATIS RIGOR: KONTRIBUSI PADA PENGEMBANGAN PENGETAHUAN METAKOGNITIF-SELF ASSESSMENT MAHASISWA

This study aims to analyze students' rigorous mathematical thinking from three levels of cognitive function structures associated with their contribution to self-assessment metacognitive knowledge in Real Number System lectures. This research is qualitative research with a type of case study. The research subjects were three students of the Mathematics Education Study Program who contracted the Real Number. System course selecting research subjects based on test results identifies students into three rigorous mathematical thinking cognitive function structure levels. This study's results indicate that rigorous mathematical thinking contributes to students' self-assessment metacognitive knowledge. The quality of review of students who have a rigorous mathematical thinking level can lead to thoroughness, intellectual perseverance, critical investigation, and truth-seeking in solving problems appropriately, structurally, and systematically into a direct experience in the learning process is described as metacognitive. Students at the level of abstract relational thinking can assess their own abilities very well, learn independently, and choose with certainty how to solve problems by placing the right method. Qualitative thinking level students focus more on symbols or symbols and represent their knowledge through visualization. He prefers that the type of evaluation problem solving is not in the form of long, detailed sentences but instead immediately transforms the sentences into clear mathematical symbols

Penerapan RealQu pada Sistem Bilangan Real dalam Pembelajaran di Masa Pandemi Covid-19

The purpose of this study was to analyze the application of the RealQu, which is a mobile learning media that contains real number system material that will support online lectures during the Covid-19 pandemic. The research method used is descriptive analysis. The research subjects were 20 students who had taken the real analysis. The data collection technique was carried out by analyzing student answers and conducting interviews with the interview guidelines. The results showed that students were more assisted and facilitated by the RealQu learning media which contained the real number system theorems. This is indicated by an increase in the value and results of the analysis by the stages of solving the questions which also increased after the use of RealQu. During the interview, students also stated that Realqu helped them remember all the theorems and how they were used in problem-solving.

Continuity in Intuitionism

The chapter features, first, a critical presentation of Brouwer’s intuitionistic doctrines concerning logic, the real numbers, and continuity in the real number system, including his Principle for Numbers and Continuity Theorem. This is followed by a parallel examination of Hermann Weyl’s quasi-intuitionistic views on logic, continuity, and the real number system, views inspired by (but grossly misrepresenting) ideas of Brouwer. The whole business wraps up with an attempt to place Brouwer’s and Weyl’s efforts within the trajectory of informed thinking, during the late 19th and early 20th centuries, on the subjects of continua, magnitudes, and quantities.

Basis Existence of Internal n-Graph Space

Graph of real valued continuous function with special addition and multiplication has already proven that is isomorphic to real number system. Furthermore, the graph of continous real valued function forms a field. The aim of this research was to generalize such concept to its n-tuple Cartesian Product and to prove that interchange of basis still able to be executed. The result of this research is n-tuple Cartesian Product of graph function forms a vector space over and interchange of basis still able to be executed

Hyperreal Numbers for Infinite Divergent Series

Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent series in a more comprehensive and tractable way.