Matching concepts across HOL libraries

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert. In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types

Penerapan Model Pembelajaran Discovery Learning untuk Meningkatkan Pemahaman Konsep Matematis

The purpose of this study was to improve students' understanding of mathematical concepts on the competence of rational and irrational inequalities through the application of the discovery learning model. The research method used is quantitative method with discovery learning approach, the subject of this research is X TKJ class students of SMK Negeri 1 Tuhemberua. This research took place in two cycles, namely cycle I consisting of 3 meetings and cycle II consisting of 3 meetings. Data collection techniques in this study were observation and objective tests. The instruments used were observation sheets and objective test questions. Based on the results of the study, it was found that the implementation of mathematics learning with the application of the discovery learning model can improve the understanding of mathematical concepts of class X TKJ students of SMK Negeri 1 Tuhemberua on the competence of rational and irrational inequality of one variable. This is based on data obtained through the results of cycle I tests and cycle II tests, the average percentage of students' understanding of mathematical concepts has increased by 15.67%, namely in cycle I of 66.28% and increased to 77.81% in cycle II. The conclusion in this study is that the average percentage of students' understanding of mathematical concepts has increased in cycle I and increased again in cycle II. Based on the qualification guidelines in the percentage table presented in the discussion section, it is classified in the high category.   Keywords: discovery learning model, concept comprehension, high school mathemati

PENGARUH MODEL PEMBELAJARAN DISCOVERY LEARNING TERHADAP PEMAHAMAN KONSEP MATEMATIKA SISWA MATERI PECAHAN SENILAI KELAS IV SEKOLAH DASAR

This study aims to determine the effect of the discovery learning learning model on students' understanding of mathematical concepts in fractional material worth class IV of Elementary School 47 Cakranegara. This type of research is a Pre-Experimental Design type of One Group Pretest-Posttest Design. The population in this study were all students of class IV at State Elementary School 47 Cakranegara as many as 47 students, while the sample in this study were students of class IV B as an experimental class of 23 students. The instruments used were observation sheets of learning implementation and concept understanding tests. Data analysis begins with the normality test and continues with the homogeneity test, then the hypothesis is tested with the t-test using the Paired Sample T-test. The results of data analysis show that the value of t_count>t_table is 6.310 > 1.717 and the value of Sig. (2-tailed) 0.00 < 0.05. This shows that students' understanding of mathematical concepts using the discovery learning learning model is better than before using the discovery learning learning model, meaning that the discovery learning learning model influences students' understanding of mathematical concepts

PENGARUH MODEL PEMBELAJARAN DISCOVERY LEARNING TERHADAP PEMAHAMAN KONSEP MATEMATIKA SISWA MATERI PECAHAN SENILAI KELAS IV SEKOLAH DASAR

This study aims to determine the effect of the discovery learning learning model on students' understanding of mathematical concepts in fractional material worth class IV of Elementary School 47 Cakranegara. This type of research is a Pre-Experimental Design type of One Group Pretest-Posttest Design. The population in this study were all students of class IV at State Elementary School 47 Cakranegara as many as 47 students, while the sample in this study were students of class IV B as an experimental class of 23 students. The instruments used were observation sheets of learning implementation and concept understanding tests. Data analysis begins with the normality test and continues with the homogeneity test, then the hypothesis is tested with the t-test using the Paired Sample T-test. The results of data analysis show that the value of t_count>t_table is 6.310 > 1.717 and the value of Sig. (2-tailed) 0.00 < 0.05. This shows that students' understanding of mathematical concepts using the discovery learning learning model is better than before using the discovery learning learning model, meaning that the discovery learning learning model influences students' understanding of mathematical concepts

Penerapan Model Pembelajaran Discovery Learning Pada Materi Operasi Hitung Matriks

The learning process occurs naturally in student learning activities and understanding the concepts studied. Generally, the process of delivering mathematical concepts by teachers focuses more on conventional methods, with teachers dominating the learning process leading to a lack of student involvement. Students are passive in learning, making it difficult for them to understand and build mathematical concepts, and students only memorize concepts without understanding them. This causes students not to know how to form, use, and communicate with the material they will learn in everyday life. Therefore, active learning is needed, one of which is applying the discovery learning model. The Discovery learning model is a learning process in which students are not presented with lessons/teaching materials in their final form. However, students must carry out various activities to collect information, categorize, analyze, integrate, organize materials and make conclusions that lead to discovery. The concept of the material being studied. This study aims to determine how students' activities and responses to the discovery learning model on matrix arithmetic operations in Year 12. Data were obtained from observing student activities through assessment rubrics and response questionnaires. The results of this study indicate that the student's activity during the learning process is good, and the student's response to the discovery learning model on matrix arithmetic operations is positive

Rough Standard Neutrosophic Sets: An Application on Standard Neutrosophic Information Systems

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets

Penerapan Model Discovery Learning Berbantuan Geogebra Untuk Meningkatkan Pemahaman Konsep Matematika Pada Persamaan Garis Lurus di SMPN 2 Peukan

Penelitian ini bertujuan untuk memperoleh perangkat pembelajaran berbasis discovery learning berbantuan Geogebra yang efektif dalam meningkattkan kemampuan pemahaman konsep matematika siswa SMP. Kriteria efektif bersandar pada teori intervensi pembelajaran yang meliputi adanya peningkatan capaian hasil belajar setelah intervensi, adanya respon positif siswa dan guru terhadap perangkat pembelajaran yang dikembangkan, keterlibatan (engagement) siswa yang tinggi dalam pembelajaran, serta diperoleh lebih dari 75% siswa mencapai skor 75 dari skala 100 dalam tes pemahaman konsep matematika. Peningkatan pemahaman konsep matematika diselidiki melalui indeks gain ternormalisasi. Peningkatan pemahaman konsep matematika dideskripsikan dengan bersandar pada statistik deskriptik. Penelitian ini menghasilkan perangkat pembelajaran yang memiliki karakteristik efektif dalam meningkatkan pemahaman konsep matematika siswa SMP sehingga siap untuk disebarluaskan. Disarankan agar guru lebih diberi kesempatan untuk mengimplementasikan perangkat pembelajaran yang dikembangkan sesuai dengan tujuan pembelajaran matematika sehingga dapat di harapkan siswa memperoleh kemampuan pemahaman konsep yang lebih tinggi lagiThis study aims to obtain a Geogebra-assisted discovery learning-based learning tool that is effective in increasing the students' ability to understand mathematical concepts. Effective criteria rests on the theory of learning interventions which include an increase in learning outcomes after the intervention, a positive response from students and teachers to the learning tools developed, high student engagement in learning, and more than 75% of students achieving a score of 75 from a scale of 100 in a test of understanding mathematical concepts. Improved understanding of mathematical concepts is investigated through a normalized gain index. Improved understanding of mathematical concepts is described by relying on descriptive statistics. This research produces learning tools that have effective characteristics in improving junior high school students' understanding of mathematical concepts so that they are ready to be disseminated. It is recommended that teachers be given more opportunities to implement learning tools developed in accordance with the objectives of learning mathematics so that students can expect higher understanding of concept