• 인문언어
• /
• 제2권2호
• /
• pp.301-319
• /
• 2002

In a recent paper, I have proposed an analysis concerning propositions and 'that'-clauses as a solution to Kripke's puzzle and other similar puzzles, which I now call 'the Indefinite Description Analysis of Belief Ascription Sentences.' I have listed some of the major advantages of this analysis besides its merit as a solution to the puzzles: it is amenable to the direct-reference theory of proper names; it does not nevertheless need to introduce Russellian (singular) propositions or any other new entities. David Lewis has constructed an interesting argument to refute this analysis. His argument seems to show that my analysis has an unwelcome consequence: if someone believes any proposition, then he or she should, ipso facto, believe any necessary (mathematical or logical) proposition (such as the proposition that 1 succeeds 0). In this paper, I argue that Lewis's argument does not pose a real threat to my analysis. All his argument shows is that we should not accept the assumption called 'the equivalence thesis': if two sentences are equivalent, then they express the same proposition. I argue that this thesis is already in trouble for independent reasons. Especially, I argue that if we accept the equivalence thesis then, even without my analysis, we can derive a sentence like 'Fred believes that 1 succeeds 0 and snow is white' from a sentence like 'Fred believes that snow is white.' The consequence mentioned above is not worse than this consequence.

• 대한수학교육학회지:수학교육학연구
• /
• 제16권4호
• /
• pp.345-366
• /
• 2006

본 연구에서는 3차원 공간도형의 학습에 유용한 동적 기하 소프트웨어인 Cabri3D 프로그램을 논의의 대상으로 하여 이를 공학적도구의 교육적 활용이라는 관점에서 수학 문제해결지도에 바람직하게 사용하는 방안에 대하여 살펴보았다. 예비수학교사들을 대상으로 학교수학에의 Cabri3D프로그램 활용에 관한 탐구 수업을 진행한 후, 중등수학의 지도에서 문제해결력 신장을 위해 이 프로그램이 효과적으로 활용될 수 있는 구체적인 사례들을 수집하였다. 폴리아가 제시하는 문제해결의 각 단계에 Cabri3D가 보조도구로서 유용한 역할을 할 수 있는 문제 사례와 그 활용방법을 예시하면서 현장의 수학교사들이 공학적 도구를 수학교육에 활용하는 방법에 대한 바람직한 관점을 갖게 하는데 도움을 주고자 하였다.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제19권1호
• /
• pp.19-41
• /
• 2015

Previous studies indicated that students tended to hold less satisfactory beliefs about the discipline of mathematics, beliefs about themselves as learners of mathematics, and beliefs about mathematics teaching and learning. However, only a few studies had developed curricular interventions to change students' beliefs. This study aimed to examine the effect of a problem-solving curriculum (i.e., Mathematical Problem Solving for Everyone, MProSE) on Singaporean Grade 7 students' beliefs about mathematical problem solving (MPS). Four classes (n =142) were engaged in ten lessons with each comprising four stages: understand the problem, devise a plan, carry out the plan, and look back. Heuristics and metacognitive control were emphasized during students' problem solving activities. Results indicated that the MProSE curriculum enabled some students to develop more satisfactory beliefs about MPS. Further path analysis showed that students' attitudes towards the MProSE curriculum are important predictors for their beliefs.

• 대한수학교육학회지:학교수학
• /
• 제6권4호
• /
• pp.313-324
• /
• 2004

수학교육은 이제 국민대중교육, 교양교육으로서의 수학교육의 이념을 재발견하여 수학교육의 본래의 모습을 회복해야 할 시점에 와 있다. 오늘날 우리가 학교에서 가르치는 수학 지식은 어떤 성격의 지식이며 우리는 그러한 지식을 가르침으로써 인간을 어떤 상태로 만들려고 하는가\ulcorner 본고에서는 수학교육 사상의 뿌리를 탐색해 봄으로서 수학이라는 지식을 배우는 요한 목적은 실용성을 넘어 수학이라는 지식을 통하여 인간과 만물 이면에 있는 현상의 세계를 지배하는 실재를 깨달아 가도록 하는 인간교육의 구현에 있음을 밝히고, 그러한 이념을 오늘날 국민교육으로서의 수학교육이 우선적으로 지향해야 할 방향으로 제시하였다.

• 한국수학교육학회지시리즈C:초등수학교육
• /
• 제5권2호
• /
• pp.71-94
• /
• 2001

The purposes of this study were to design small group collaborative learning models for developing the creativity and to analyze the effects on applying the models in mathematics teaching and loaming. The meaning of open education in mathematics learning, the relation of creativity and inquiry learning, the relation of small group collaborative learning and creativity, and the relation of assessment and creativity were reviewed. And to investigate the relation small group collaborative learning and creativity, we developed three types of small group collaborative learning model- inquiry model, situation model, tradition model, and then conducted in elementary school and middle school. As a conclusion, this study suggested; (1) Small group collaborative learning can be conducted when the teacher understands the small group collaborative learning practice in the mathematics classroom and have desirable belief about mathematics instruction. (2) Students' mathematical anxiety can be reduced and students' involvement in mathematics learning can be facilitated, when mathematical tasks are provided through inquiry model and situation model. (3) Students' mathematical creativity can be enhanced when the teacher make classroom culture that students' thinking is valued and teacher's authority is reduced. (4) To develop students' mathematical creativity, the interaction between students in small group should be encouraged, and assessment of creativity development should be conduced systematically and continuously.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제42권2호
• /
• pp.229-245
• /
• 2003

In this paper, we present a review of research perspectives and investigations in collegiate mathematics education from the four decades of development in the journal published by Korea Society of Mathematical Education. Research of mathematics education at the tertiary level, which had been a minor area in mathematics education, has made a significant development in the last decade in Europe md U.S.A. In this context, international journals for research in mathematics education were selected to comparatively examine and identify research trends and tasks in collegiate mathematics education. Based on the analysis of domestic at international journals, we present recommendations for further the development of Korean collegiate mathematics education research. First it is necessary to diversify the topics of educational research. Korean research of mathematics education at the tertiary level has been limited to the issues of curriculum developments, teacher education and computer technology. It is necessary to pursue more various topics such as conceptual development mathematical attitude and belief gender, socio-cultural aspect of teaching and teaming mathematics. Second, it is necessary to apply research methods for systematic investigations. It is important to note that international research of mathematics education introduces variety of research methods such as observation, interview, and survey in order to develop grounded theory of mathematics education. We end with pedagogical implications of the analyses presented and general conclusions concerning the perspectives for the future in collegiate mathematics education.

• 한국학교수학회논문집
• /
• 제9권2호
• /
• pp.141-161
• /
• 2006

Freudenthal의 '현실주의 수학교육'(realistic mathematics education)에 따르면, 학교수학은 경험적이고 실제적인 맥락에서 출발하여 교사의 안내를 거치면서 재발명하는 경험을 제공해야 한다. 그러나 오늘날 학생들은 학교수학을 학습하는 과정에서 오히려 수학을 현실과 구분하는 경향이 있다. 본 연구는 실제적인 맥락 속에서 학교수학을 다루기 위한 노력으로, 맥락문제를 개발 적용하여 그 결과를 분석한 것이다. 맥락문제는 실생활과 관련된 상황만을 단편적으로 담는 것이 아니라, 장소와 이야기를 비롯하여 프로젝트, 주제, 스크램 등의 형태에서 계속해서 제시되며, 학교수학에서 다루는 다양한 수학적인 내용을 일정한 맥락과 함께 유기적으로 연결시키는 것이다. 본 연구는 일차적으로 우리나라 초등수학 교과서(4-가, 나)에 제시된 실생활 관련 문장제를 5가지 맥락문제의 유형(장소, 이야기, 프로젝트, 스크랩, 주제)으로 구분하여 검토해보았다. 다음으로 초등수학 교육과정에 맞추어 유형별 맥락 문제를 개발하고 이것을 실제수학 수업에 교수-학습 자료로 적용하였으며, 유형별 맥락문제가 초등학생의 수학적 신념 및 태도에 어떠한 변화를 가져오는지를 살펴보았다 또한 학업성취도에 따라 학생들이 선호하는 맥락문제의 유형과 그 이유에 대해 분석하였다.

• 한국수학교육학회지시리즈C:초등수학교육
• /
• 제4권2호
• /
• pp.105-110
• /
• 2000

This paper is discussing about the culture of mathematics classroom for problem solving. The mathematics classroom which we have to aim at is where every students make proper belief and attitude about mathematics, and also can express their own idea and make question freely. In that classroom, the students can meet with various problem solving methods and communicate with other students, and then elaborate their own method.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제42권3호
• /
• pp.387-402
• /
• 2003

Realistic Mathematics Education (RME) focuses on guided reinvention through which students explore experientially realistic context problems to develop informal problem solving strategies and solutions. This research applied this philosophy of RME to design a differential equation course at a university level. In particular, the course encouraged the students of the course to use numerical methods to solve differential equations. In this context, the purpose of this research was to describe the developmental process in which the students constructed and reinvented Euler algorithm in the class. For the purpose, this paper will present the didactical principle of RME and describe the process of developmental research to investigate the inferential process of students in solving the first order differential equation numerically. Finally, the qualitative analysis of the students' reasoning and use of symbols reveals how the students reinvent Euler algorithm under the didactical principle of guided reinvention. In this research, it has been found that the students developed deep understanding of Euler algorithm in the class. Moreover, it has been shown that the experience of doing mathematics in the course had a positive impact on students' mathematical belief and attitude. These findings imply that the didactical principle of RME can be applied to design university mathematical courses and in general, provide a perspective on how to reform mathematics curriculum at a university level.

• 한국지능시스템학회논문지
• /
• 제1권2호
• /
• pp.4-45
• /
• 1991

Measures of two types of uncertainty that coexist in the Dempster-Shafer theory are overivewed. A measure of one type of uncertainty, which expresses nonspecificity of evidential claims, is well justified on both intuitive and mathermatical grounds. Proposed measures of the other types of uncertainty, which attempt to capture conflicts among evidential claims, are shown to have some deficiencies. To alleviate these deficiencies, a new measure is proposed. This measure, which is called a measure of discord, is not only satisfactory on intuitive grounds, but has alos desirable mathematical properties. A measure of total uncertainty, which is defined as the sum of nonspecificity and discord, is also discussed. The paper focuses on conceptual issues. Mathematical properties of the measure of idscord are only stated ; their proofs are given in a companion paper.