• The Mathematical Education
• /
• v.42 no.5
• /
• pp.697-706
• /
• 2003

In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

• Proceedings of the Korean Information Science Society Conference
• /
• 1998.10a
• /
• pp.630-632
• /
• 1998

본 논문에서는, Multi[le-Buffered a$\times$a Crossbar 수위치의 성능 분석 모형을 제안하고 스위치에 장착된 buffer 의 개수의 중가에 다른 성능 향상 추이를 분석하였다. buffered스위치 기법은 다수 데이터 패킷을 동시에 전송할 때 네트웍에서 발생되는 충돌문제를 효과적으로 해결할 수 있는 방법으로 널리 알려져있다. 제안된 성능 예측 모형은 스위치 입력 단에 유입되는 데이터 패킷이 buffered 스위치 내부에서 전송되는 유형을 확률적으로 분석하여 수립되었다. 모형의 수학적 복잡도 해결을 위하여 확률 식 유도 과정 등에 steady state 개념을 도입하였다. 제안한 모형은 스위치 크기 및 스위치에 장착된 buffer의 개수와 무관하게 buffered a$\times$a 크로스바 스위치의 성능 예측을 가능케 하고, 나아가서 이들로 구성된 다층 연결 망의 성능 분석에 확대 적용이 가능하다. 제안한 수학적 성능 분석 연구는 실효성 검증을 위하여 병행된 시뮬레이션 결과는 미세한 오차 범위 내에서 모형의 예측 데이터와 일치하는 결과를 보여 분석 모형의 타당성을 입증하였다. 또한, 분석 결과 스위치에 소수의 버퍼를 장착했을 때, throughput이 크게 증가하지만, 네 개 이상의 버퍼를 장착되는 버퍼의 개수가 네 개 정도일 경우 가격 대 성능비가 우수한 것으로 추론되었다.

• School Mathematics
• /
• v.13 no.1
• /
• pp.65-88
• /
• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.

• Communications of Mathematical Education
• /
• v.18 no.2 s.19
• /
• pp.341-358
• /
• 2004

본 연구에서는 영재교육 프로그램의 효과에 관한 실증적인 연구를 위해서 트레핑거의 자기 주도적 학습 모형과 렌줄리의 3부 심화학습모형을 이용하여, 제7차 초등수학 교육과정에서 다루어지고 있는 기본적인 개념뿐만 아니라, 영재교육과정과 관련된 주제들을 중심으로 초등 수학 영재아들의 자기 주도적 학습 능력 신장을 위한 프로그램을 자체 개발하여, 개발된 영재교육프로그램을 이수하기 전과 이수 후의 수학적 학습 태도에 차이가 있는지를 검증하기 위해서, 제주대학교 과학영재교육원 초등수학반 아동들을 대상으로 사전 ${\cdot}$ 사후 수학적 학습 태도를 분석하였다.

• School Mathematics
• /
• v.16 no.4
• /
• pp.677-690
• /
• 2014

The main goals of learning geometry include developing spatial ability and concepts on geometric objects based on understanding the attributes and relationships of them. While the instructions on geometric objects follow the concept development models, the ones on spatial ability are designed from the perspective of geometric transformation. However, there is a need for instructional materials to emphasizing the relationships among geometric concepts. This study hypothesizes that spatial ability stems from the intuitive understanding of geometric objects and the relational understanding on concepts, and it considers the isoperimetric problems as instructional materials to foster spatial ability.

• Journal of The Korean Association of Information Education
• /
• v.14 no.4
• /
• pp.537-545
• /
• 2010

The purpose of this paper is to develop mathematics learning contents for elementary school 3rd graders and to verify the educational effectiveness of contents developed. An ADDIE model was applied to develop mathematics learning contents based on storytelling for concept learning. After extracting 54 concepts from the mathematics curriculum, researchers designed strategies using concepts that were combined with context which is familiar to young students. Researchers implemented a survey and interview to students and teachers to verify the effectiveness of contents. As a result, the understanding, interest, concentration, and expectation of students toward the contents developed were very high, and teachers also mentioned that these contents could be very useful teaching materials for motivation.

• The Mathematical Education
• /
• v.61 no.1
• /
• pp.127-156
• /
• 2022

This study used the data of students from the 6th grade to the 3rd grade of middle schoolin the Korean Educational Longitudinal Study 2013 and classified them into subgroups with similar longitudinal changes in math academic achievement. In addition, the influence of longitudinal changes in the group's academic self-concept and teachers and parents academic support on the longitudinal changes in math academic achievement were analyzed, either directly or indirectly. As a result of the analysis, it was found that the academic self-concept of each group had a positive influence on the academic achievement in mathematics. In addition, the academic support of teachers and parents was found to have a positive influence on the academic achievement in mathematics through the mediating of the academic self-concept. In terms of direct and indirect influence on academic self-concept and math vertical scale scores, it was found that teachers' academic support had more influence than parents' academic support. The educational implications of these points were discussed.

• Journal of Educational Research in Mathematics
• /
• v.14 no.3
• /
• pp.239-266
• /
• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• Proceedings of the Korean Society of Computer Information Conference
• /
• 2011.01a
• /
• pp.159-162
• /
• 2011

이 연구는 인지기제를 활용한 문제기반학습이 학습자의 학업성취도와 수학적 태도에 미치는 효과를 분석하였다. 우선 초등학교 수학과 학습에서 학습자들의 인지과정을 안내할 수 있는 문제기반학습 설계를 위해 문제기반학습 모형에 란다(N. Landa)의 인지기제 교수학습설계이론을 적용하여 인지기제 활용 문제기반학습 모형을 도출하였다. 그리고 초등학교 수학과 4학년 2학기 4개 단원의 8차시를 추출하여 문제를 개발하고 서울시 소재 'ㅈ' 초등학교 4학년 학생들 중 동질집단으로 확인된 2개 학급에 이 모형을 적용하였다. 연구 결과 인지기제 활용 문제기반학습을 적용한 실험집단과 적용하지 않은 통제집단 간 학업성취도 효과에 있어서 통계적으로 유의한 차이가 있었다. 또한 수학적 태도와 관련해서는 하위영역 중 수학에 대한 자아개념과 수학에 대한 태도 영역에서는 유의한 차이가 있었으나 수학에 대한 학습습관 영역에서는 유의한 차이를 보이지 않았다. 특히 세부영역별로 자신감, 흥미, 우월감, 주의집중, 목적의식, 자율학습에 있어서 유의한 차이를 보였으며, 학습기술 적용과 성취동기에 대해서는 유의한 차이가 없었다.

• Journal of the Korean School Mathematics Society
• /
• v.19 no.3
• /
• pp.309-328
• /
• 2016

In this study we aimed to find out if a mathematics lesson with Jigsaw model can help to change such negative mathematical affective characteristic to a positive one. The results of the study were as in the following. First, the mathematics lessons applied Jigsaw model can help to inspire curiosity and motivation of students. During the lessons, communication among students was vitalized. Such communication inspired learner's curiosity and learning motivation. The expert group and home group activities in the Jigsaw model made the learner's question-answering activities more instantaneous and frequent. Second, the mathematics lessons applied Jigsaw model can help students to become aware of the value of mathematical concepts and formula.