• Communications of Mathematical Education
• /
• v.23 no.4
• /
• pp.1023-1041
• /
• 2009

The importance of the mathematical education on the ICT environment has been increased as the educational environment has been changed in 21st century. In Korea, many researches on ICT tools have appeared over the last 10 years. But most of researches are depending on the foreign tools, that was one major obstacle on adapting them in our mathematics curriculum. But we found the new open source tool which is called Sage-Math can be in effective solution to resolve those problems. Now we produce what we have done in linear algebra with this Sage-Math and mobile modules.

• Communications of Mathematical Education
• /
• v.30 no.3
• /
• pp.281-294
• /
• 2016

This study deals with the content that was developed by the authors and the utilization of the 'Interactive Engineering Math Laboratory (IEmath Lab).' IEmath Lab provides online review lectures as well as a wide range of examples and exercises from the curriculum of engineering mathematics courses. The lectures come with pre-coded Python-based SageMath cells through which students can run and modify the code directly from this free laboratory. IEmath Lab is accessible via mobile devices so that the students can use it anywhere, anytime for maximum learning effectiveness and achievement. IEmath Lab would be an ideal tool for the effective learning and teaching of engineering mathematics, which combines theory and practice.

• Communications of Mathematical Education
• /
• v.27 no.2
• /
• pp.121-134
• /
• 2013

Linear Algebra are arguably the most popular math subjects in colleges. We believe that students' learning and understanding of linear algebra can be improved substantially if we incorporate the latest advanced information technologies in our teaching. We found that the open source mathematics program 'Sage' (http://sagemath.org) can be a good candidate to achieve our goal of improving students' interest and learning of linear algebra. In particular, we developed a simple mobile content which is available for Sage commands on common cell phones in 2009. In this paper, we introduce the mobile Sage which contains many Sage functions on a smart-phone and the mobile linear algebra content model(lecture notes, and video lectures, problem solving, and CAS tools) and it will be useful to students for self-directed learning in college mathematics education.

• Communications of Mathematical Education
• /
• v.22 no.4
• /
• pp.533-543
• /
• 2008

Recently, many advanced countries have used original ICT tools in their educational courses. But Korea didn't have any effective origin ICT tools in our mathematical education, compared with other countries which have developed various tools, for examples, Web-Mathematica and HP Calculator. Although we have the advanced IT environment, the educational environments in mathematics using ICT seems to be not promising. In this paper, we suggest a new mathematics education tools in ICT and the internet environments in Korea, and a teaching and studyingmodel for the teachers, students and classrooms. It is based on the Sage-Math and RPG. Sage-Math which is the software based on the web and RPG(Random Problem Generator) will give a good answer for the future of Korean mathematics ICT education.

• Communications of Mathematical Education
• /
• v.27 no.1
• /
• pp.1-17
• /
• 2013

This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

• Communications of Mathematical Education
• /
• v.29 no.1
• /
• pp.19-33
• /
• 2015

Recently in major industrial areas, there has been a rapidly increasing demand for 'Computational Thinking', which is integrated with a computer's ability to think as a human world. Developed countries in the last 20 years naturally have been improving students' computational thinking as a way to solve math problems with CAS in the areas of mathematical reasoning, problem solving and communication. Also, textbooks reflected in the 2009 curriculum contain the applications of various CAS tools and focus on the improvement of 'Computational Thinking'. In this paper, we analyze the cases of mathematics education based on 'Computational Thinking' and discuss the mathematical content that uses the CAS tools including Sage for improving 'Computational Thinking'. Also, we show examples of programs based on 'Computational Thinking' for teaching Calculus in university.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.467-482
• /
• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Journal for History of Mathematics
• /
• v.32 no.6
• /
• pp.271-279
• /
• 2019

Pierre-Simon de Laplace(1749-1827) is considered one of the most influential scientists in history. He was known to his contemporaries as the Newton of France, and a scientific sage valued for his magisterial syntheses of scientific works through the 18th century. Laplace was a determined mathematician, astronomer, writer, philosopher, and educator. In this paper, we take a survey of his achievements in the areas of astronomy and mathematical statistics, along with his scientific philosophy, the universal determinism.

• Journal of Science Education
• /
• v.43 no.1
• /
• pp.17-42
• /
• 2019

This study, as an attempt to integrate mathematics and information for convergence education, was conducted to develop teaching-learning materials on mathematics education combined with coding education, which has recently been emphasized. We chose the subject of digital signature for coding education, and used SageMath as a coding program. In this study, we overview mathematics used in the elliptic curve digital signature algorithm, one of the many methods for digital signature, and developed the teaching-learning materials on the algorithm for mathematics education integrated with information education based on coding. The elliptic curve digital signature algorithm utilized in transactions of Bitcoin, which many people recently are interested in, is a good example, showing students that mathematics is applied to problem-solving in the real world and provides an optimal environment for implementation by coding. Accordingly, we expect that a class on algorithm will provide a specific teaching-learning program to achieve the goal of integrated mathematics education. By comprehensively considering the opinions of mathematicians, mathematics teachers and mathematics education experts, we expect that the teaching-learning program will be realized as a meaningful class in science high schools, high school's math clubs, and 'number theory' class in colleges.

• Communications of Mathematical Education
• /
• v.31 no.3
• /
• pp.241-255
• /
• 2017

The 4th industrial revolution is coming. In order to prepare for the new learning environment with it, we may need digital mathematics textbooks that fully utilize all possible technologies. So various attempts have been made in elementary and middle school mathematics education. However, despite the importance of higher mathematics, we haven't seen a best possible math digital textbooks yet in Korea. In this paper, we introduce our new model of interactive math digital textbook about Linear Algebra/ Calculus/ Differential Equations/ Statistics/ Engineering Math. Especially, this manuscript focuses on our experience of using digital contents and interactive labs for developing a new model for linear algebra digital textbook. We introduce our works on linear algebra digital textbooks which include pdf e-book, web contents, video clips of lectures, interactive lab. Using this linear algebra digital textbook, students can freely use any mobile devices to access diverse learning materials, lessons, and hands-on exercises without any limitations. Also, times saved in the computation, coding, and typing process can be used to have more discussions for deeper understanding of mathematical concepts. This type of linear algebra digital textbook, which contains all interactive free cyber-lab with codes and all lectures for each sections, can be considered as a new model for the next generation of math digital textbook.