• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.89-104
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• 2010

In a rapidly changing and increasingly technological society. the use of technology should not be disregarded in issues of learning algebra. The use of technology in learning algebra raises many learning and pedagogical issues. In this article, previous research on the use of technology in learning algebra is synthesized on the basis of the four issues: conceptual understanding, skills, instrumental genesis, and transparency. Finally, suggestions for future research into technological pedagogical content knowledge (TPCK) are made.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• School Mathematics
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• v.12 no.3
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• pp.323-335
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• 2010

Linear algebra is not only applied comprehensively in the branches of mathematics such as algebra, analytics, and geometry but also utilized for finding solutions in various fields such as aeronautical engineering, electronics, biology, geology, mechanics and etc. Therefore, linear algebra should be easy and comfortable for not only mathematics majors but also for general students as well. However, most find it difficult to learn linear algebra. Why is it so? It is because many studying linear algebra fail to achieve a correct understanding or attain erroneous concepts through misleading knowledge they already have. Such cases cause learning disability and mistakes. This research suggests more effective method of teaching by analyzing difficulty and errors made in learning system of linear equations.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.89-110
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• 2009

This paper observed the effect of CAS calculator usage while studying algebra on the achievement of low-achievement students. Participants were composed of 70 low-achievement tenth grade students from a high school located in a metropolitan city. That had never used a mathematics educational calculator before. Target participants were divided into two groups: an experiment group that studied activity papers with the aid of a CAS calculator, and a control group that studied the same activity papers using only paper-and-pencil. The content of the activity papers for the two groups was the same, but the structure differed. Content consisted of numbers and operations, equations and inequalities(character and expressions), and functions. Students in the experiment group exhibited matacognition learning using a CAS calculator. The two groups completed mathematics achievement tests both before and after the activity papers. Therefore, ANCOVA analysis results showed that compared to the pretest, results of the experiment group improved considerably more than the control group.

• The KIPS Transactions:PartA
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• v.14A no.6
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• pp.383-390
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• 2007

This paper describes the e-learning system for science and engineering mathematics using computer algebra system and Bayesian inference network. The best feature of this system is using one of the most recent mathematical dynamic web content authoring model which is called client independent dynamic web content authoring model and using the Bayesian inference network for diagnosing student's learning. The authoring module using computer algebra system provides teacher-user with easy way to make dynamic mathematical web contents. The diagnosis module using Bayesian inference network helps students know the weaker parts of their learning, in this way our system determines appropriate next learning sequences in order to provide supplementary learning feedback.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.89-99
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• 2010

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. Vector theory and matrix theory constitute of main topics in linear algebra. In the present paper we consider the question which of the two topics is prior in teaching of linear algebra. We suggest that vector theory should be prior to matrix theory contrary to the historical order of them.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.121-134
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• 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
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• v.10
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• pp.505-517
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• 2000

수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.111-130
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• 2015

The purpose of the study was to investigate the differences between two groups of students according to information recognition styles such as visual learners and linguistic learners. Two instructional methods, algeblocks and factorization formula, were utilized to introduce the factorization. Four students were participated for the study, and two of them were visual learners and the other two were linguistic learners based on learning style test. Interviews and the diagnostic tests were implemented before the instructions which were lasted for 6 sessions. After the instructions all the participants were interviewed and the researchers also interviewed them 5 days later. The results of the study were the followings: 1. All the participants regardless of their learning style revealed that algeblocks were helpful in understanding the factorization. 2. Visual learners were more likely using algeblocks, while the linguistic learners were more enthusiastic and proficient in using formula to solve the problems. 3. Five days later, two types of learning style students revealed different tendencies. Visual learners mainly used algeblocks, and linguistic learners were not enthusiastic about using algeblocks and one of them did not use them at all. 4. Five days later, two visual learners could not remember the formula, but linguistic learners could remember the formula in somewhat different level.