• Communications of Mathematical Education
• /
• v.25 no.3
• /
• pp.593-606
• /
• 2011

We carried out mathematics diagnostic tests for all first year engineering students at C University in Daejeon in 2008, covering precalculus and basic calculus. Then we divided into two classes such as regular and supplementary classes. The supplementary class students are lower 13% students. Then we gave extra classes for these students to support their basic and elementary calculus skills. As a result, these supplementary students received a meaningful accomplishment at the final exam. This paper analyzes the results and effects of various types of supplementary classes such as education by level, and proposes some strategies to enhance mathematics learning, particularly for under achieving first year engineering students.

• Communications of Mathematical Education
• /
• v.27 no.1
• /
• pp.19-37
• /
• 2013

In order to improve the problem-solving abilities and enhance the academic achievement of under achieving students for university basic mathematics, P-university has opened the basic mathematics and practice education courses. These education courses are operated as prerequisite subject of Calculus and we are progressing the class focused on presentation with variety learning materials by organizing level-based classes In this paper, we analyzed the acquired grade and the result of teaching assessment of 1,106 students registered in the 30 classes that the teaching portfolio of the basic mathematics and practice education courses were submitted to support 'Accreditation for Engineering Education of Korea'. In addition, we tried to find attention points and improved solutions on operating the level-based class of the basic mathematics and practice education courses based on the 'Continuous Quality Improvement Report' of teaching portfolio submitted by each professor who is in charge of this class.

• Journal of Educational Research in Mathematics
• /
• v.22 no.1
• /
• pp.23-38
• /
• 2012

The purpose of this paper is to describe the true meaning of smooth curve and to let people understand the smooth curve by way of velocity. It is true that it is not easy for us to perceive smooth curve because when there are no cups in the curve and the shape of the curve looks smooth, we often perceive it is smooth curve. However, even when the shape of curve looks smooth, it happens that it is not smooth curve. When the particle moves on the curve, depending on the velocity, it can be smooth curve or not. That is, even though the shape looks smooth, when the velocity is discontinuous or it is 0, it is not smooth curve. Therefore, this paper shows that it is important to understand and to teach smooth curve by way of velocity. In other words, when parameter of path for the smooth curve is taught in the calculus of high school, it needs to be understood by way of velocity. Finally, this paper tries to suggest that we need to shift our paradigm in teaching of smooth curve from fixed curve to dynamic curve.

• Journal of Educational Research in Mathematics
• /
• v.9 no.1
• /
• pp.217-228
• /
• 1999

The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. first, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.

• Korean Journal of Cognitive Science
• /
• v.4 no.2
• /
• pp.85-114
• /
• 1994

One of the major research topics in the area of the development of intelligent tutoring system(ITS)is the control of instructional mechanism consisting of lesson plans,curriculum plans,and discourse plans.This paper describes a method of building the lesson plans among these three instructional plans based on the case-based planning.It is more efficient to retrieve the lesson plan from the plan memoru than to generate it whenever an instructional goal is selected.The retrieved lesson plan may be modified to build more adaptive plan for the current goal.We have developed a lesson plan generator that has such capabilities as a component of an ITS for teching indefinite intergration.We also have devised a description language to represeint the generalized form for the given arithmetic expression as an instructional goal and a curriculum tree to represent the lesson units required to master the subject matter.The result of this research could be used either by a developer of the lesson plan generator in the other area of ITS or by human teacher as a curriculum in the actual class.

• Communications of Mathematical Education
• /
• v.34 no.1
• /
• pp.1-15
• /
• 2020

Today's healthcare, intelligent robots, smart home systems, and car sharing are already innovating with cutting-edge information and communication technologies such as Artificial Intelligence (AI), the Internet of Things, the Internet of Intelligent Things, and Big data. It is deeply affecting our lives. In the factory, robots have been working for humans more than several decades (FA, OA), AI doctors are also working in hospitals (Dr. Watson), AI speakers (Giga Genie) and AI assistants (Siri, Bixby, Google Assistant) are working to improve Natural Language Process. Now, in order to understand AI, knowledge of mathematics becomes essential, not a choice. Thus, mathematicians have been given a role in explaining such mathematics that make these things possible behind AI. Therefore, the authors wrote a textbook 'Basic Mathematics for Artificial Intelligence' by arranging the mathematics concepts and tools needed to understand AI and machine learning in one or two semesters, and organized lectures for undergraduate and graduate students of various majors to explore careers in artificial intelligence. In this paper, we share our experience of conducting this class with the full contents in http://matrix.skku.ac.kr/math4ai/.

• Journal of Educational Research in Mathematics
• /
• v.25 no.4
• /
• pp.717-754
• /
• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, which is very similar to the pattern of 'Conjectures and Refutations'(Lakatos, 1976). Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as humility and courage (Lampert, 1990), which is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.

• Communications of Mathematical Education
• /
• v.29 no.3
• /
• pp.423-439
• /
• 2015

This study examines the relationship between prior learning experience, the high school records, mathematics grade in the KSAT(Korean Scholastic Aptitude Test) and mathematics achievement, GPA(grade point average) of college freshmen. It analyses how much mathematics capacities in the time of high school affect mathematics achievement of college freshmen. This study surveyed 193 freshmen, attending in a college of science and engineering, taking the 'basic differential and integral calculus' lecture, which was opened for the first semester of 2014 in the A university. The data processing was fulfilled by means of technical statistics, correlation analysis, difference test, ANOVA, ex post facto test, and regression analysis. The outcomes of this survey are followings: Firstly, over 90 percent of college freshmen underwent prior learning of mathematics when they attended high school. Secondly, their perception of effectiveness for prior learning is founded to be meaningfully lower than their perception of its needfulness. Thirdly, while there is higher positive correlation between mathematics achievement and GPA in the college, there is little correlation between high school records and GPA in the college. Also, there is little correlation between mathematics grade in the KSAT and mathematics achievement in the college. Fourthly, the accomplishments in the high school(The high school records, mathematics grade in the KSAT) and the efforts, satisfaction, necessity, etc. for prior learning had little effect on academic achievement in college mathematics. Based on these results, this study makes some suggestions for developing academical achievement in college mathematics.

• Journal of Gifted/Talented Education
• /
• v.26 no.2
• /
• pp.405-421
• /
• 2016

The purpose of this study was to investigate students' perception of Advanced Placement Program. Participations of this study were 1144 students from 14 science high schools. The results showed as follows. First, students perceived positively regarding AP program and were willing to take AP courses because of interesting and challenging in academic area which is provided by AP courses. Secondly, many students would like to take AP courses in Differential and Integral Calculus 1, General Physics I, General Chemistry I and General Biology. Also, they would like to take AP courses in first term as a mandatory subjects. Third, responses perceived that AP courses were challenging, difficult, and of high quality. Finally, students perceived the benefit of AP courses in earing college credit. However, 35% of responses wished to receive an exemption for all AP courses. Also, they wished to have dual-major or participate in students exchange program as a benefit of AP program. Implications of the study were discussed in depth based on the results.

• The Mathematical Education
• /
• v.63 no.2
• /
• pp.123-138
• /
• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.