• Education of Primary School Mathematics
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• v.26 no.4
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• pp.349-368
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• 2023

The purpose of this study is to explore ways for students to connect conceptual and procedural knowledge in mathematical modeling lessons. Accordingly, we selected the greatest common divisor among the learning contents in which elementary school students have difficulties connecting conceptual and procedural knowledge. A mathematical modeling lesson was designed and implemented to solve problems related to the greatest common divisor while connecting conceptual and procedural knowledge. As a result of the analysis, it was found that the mathematical modeling lesson had positive effects on students solving problems by connecting conceptual and procedural knowledge. In addition, through actual class application, a teaching and learning plan was derived to meaningfully connect conceptual and procedural knowledge in mathematical modeling lessons.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.499-521
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• 2013

This paper analyzed the relationship between middle school students' belief about understanding with regard to mathematical concepts, procedures, and applications of the procedures. In order to gain our purpose, the academic achievement results of midterm examination of 139 middle school students and the surveys about their beliefs about understanding, mathematical concepts, and mathematical procedures were collected. And the cross analysis and the frequency analysis of SPSS were conducted. The research results showed that students' belief about understanding are irrelevant to their academic achievements. And the percentage of the students who believe that they understand was almost the same with the percentage of the students who understand the procedures. But there were differences between the percentage of the students who believe that they understand and the percentage of the students who understand the concepts. Through these, it is conformed. Students' belief about understanding does not mean they understand mathematical concepts. They just can solve mathematical problems through mechanical procedures.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.109-120
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• 2004

This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.517-534
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• 2012

As observing the learning of middle school mathematics students for three years, I examined the relationship between students' procedural knowledge and their conceptual knowledge as they develop those knowledges in the rational number domain. In particular, I explored the implications of an unbalanced development in a student's conceptual knowledge and procedural knowledge by considering two conditions: (a) the case of a student who has relatively strong conceptual knowledge and weak procedural knowledge, and (b) the case of a student who has relatively weak conceptual knowledge and strong procedural knowledge. Results suggest that conceptual knowledge and procedural knowledge are most productive when they develop in a balanced fashion (i.e., closely iterative or simultaneously), which calls into question the assumption that one has primacy over the other.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.4
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• pp.773-778
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• 2020

In this paper, we analyzed the effects of musical stimuli on humans in performing mathematical tasks through EEG measurements. The musical stimuli were divided into preferred music and non-preferred music, and mathematical tasks were divided into memorization task and procedure task. The data measured in the EEG experiments was divided into frequency bands of Theta, SMR, and Mid-beta because of the concentration. In our results, preferred music causes more positive emotional response than no music and non-preferred music regardless of the type of mathematical task.

• School Mathematics
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• v.19 no.4
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• pp.639-661
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• 2017

The purpose of this study is to investigate the relationship between the distance function average speed and the speed function. Particularly, in this study, we investigate the process of constructing the speed function in the distance function (irrational function, exponential function) which is difficult to weaken the argument in the denominator. In this process, students showed various anxieties and expressions about the procedural knowledge that they constructed first. In particular, if student B can not explain all the knowledge he already knows in this process, he showed his reflection on the process of calculating the differential coefficient. This study adds an understanding of the calculation method of students in differential coefficient learning. In addition, it is meaningful that the students who construct procedural knowledge at the time of calculating the differential coefficient have thought about how to provide opportunities to reflect on the procedure they constructed.

• Communications of Mathematical Education
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• v.15
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• pp.71-76
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• 2003

학생들의 분수 나눗셈에 대한 이해는 개념적 이해를 바탕으로 수행되어야 함에도 불구하고 분수 나눗셈은 많은 학생들이 기계적인 절차적 지식으로 획득할 가능성이 높은 내용이다. 이것은 학생들이 학교에서 분수 나눗셈을 학습할 때에 일상생활에서의 경험과 선행 학습과의 연결이 잘 이루어지지 못하고 있는 것에 큰 원인이 있다고 본다. 본 연구에서는 학생들의 분수 나눗셈의 개념적 이해를 돕기 위하여 경험적 지식과의 연결 관계를 활용한 교수 방안을 실험 교수를 통해 조사하였다. 결과로서 번분수를 활용한 수업은 분수 나눗셈의 표준 알고리즘이 수행되는 이유를 알 수 있게 하는데 도움이 되나 여러 가지 절차적 지식이 뒷받침되어야 하며 분수 막대를 직접 잘라 보는 활동을 통한 수업은 분수 나눗셈에서의 나머지를 이해하는데 효과가 있다는 것을 알았다. 결론적으로, 학생들의 경험과 학교에서 이미 학습한 분수 나눗셈들의 관련 지식들을 적절히 연결하도록 한다면 수학적 연결을 통해 분수 나눗셈의 개념적 이해를 이끌 수 있다.

• Communications of Mathematical Education
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• v.3
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• pp.141-167
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• 1997

• ICROS
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• v.18 no.2
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• pp.33-38
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• 2012

"시스템 식별(system identification)"이란 신호처리(signal processing)의 한 분야로서, 제어분야에서는, 제어시스템 설계 시 요구되는 제어대상 플랜트(plant)의 수학적 모델을 실제 시스템의 입력과 출력데이터를 활용하여 얻기 위한 필요한 체계적인 절차들을 제공해준다. 본 기법은 물리적 또는 화학적 기초원리(first principles)로부터 시스템 모델을 얻기가 어렵거나 매우 복잡한 경우에 주로 쓰이고 있으며, 이때 따라 산업현장에서도 점차 그 역할이 중요해지고 있다. 제어의 다른 분야와 유사하게 이 분야 또한 매우 수학적이어서 제어로봇시스템 학회지의 이번 호부터 총 4회에 걸쳐서 이 분야의 가장 근본적이며 실제적인 이론과 적용방법 들을 간단한 예제와 함께 다룰 계획이다. 첫 번째 순서로서 이번 호에서는 시스템 식별분야에 대한 빠른 이해를 위해 단순한 정적 그리고 동적인 시스템 예제에 대하여 최소자승법(least squares method)을 통한 시스템 파라미터 추정기법을 설명하며, 시스템 식별기법의 종류 그리고 시스템 식별 수행 시 반드시 거쳐야 단계와 절차를 소개한다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.457-459
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• 2000

객체지향 방법론은 캡슐화(encapsulation), 상속(inherit), 다형성(polymorphism)과 같은 개념을 이용하기 때문에 기존의 절차적 방법론과는 다른 척도가 필요하다. 본 논문에서 제안하는 척도는 객체지향 시스템의 개발 절차 가운데 분석 단계에서 추출할 수 있는 정보만을 사용하여, 클래스가 객체지향 개념에 따라 잘 구성되었는지를 측량하게 된다. 이를 위하여 본 논문에서는 클래스의 품질을 측량하기 위한 척도로 협력의 복잡도와 인터페이스 복잡도를 제안한다. 협력의 복잡도는 클래스가 잠재적으로 얼마나 복잡할 수 있는지를 측량하기 위한 것으로서 클래스가 가지는 책임의 개수를 조사하여 정의된다. 인터페이스 복잡도는 클래스와 협력 관계에 있는 다른 클래스들의 인터페이스를 조사하여 정의된다. 제안된 척도는 기존의 척도들이 가지고 있는 문제점을 해결하기 위하여 이해하기 쉬운 수학적 명세를 용하였으며, 제안된 척도에 대한 수학적 증명과 사례 연구를 통한 검증을 하였다.