• Journal for History of Mathematics
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• v.33 no.6
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• pp.327-343
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• 2020

This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

• School Mathematics
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• v.6 no.3
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• pp.267-281
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• 2004

The purpose of this study is to understand Preservice elementary teachers' knowledge about multiplication of fractions by focusing on their computation abilities, understanding of meanings, generating appropriate problem contexts and representations. A total of 115 preservice elementary teachers participated in the present study. The results of this study indicated that most of preservice elementary teachers have little difficulty in computing multiplication of fractions for right answers, but they have big difficulty in understanding meanings and generating appropriate problem contexts for multiplication of fractions when the multiplier is not an integer, called 'multiplier effect.' Likewise, the rate of appropriate representations surprisingly decreased for multiplication of fractions when the multiplier is not an integer. The findings also point out that an ability to make problem contexts is highly correlated with representations and meanings. This study implies that teacher education programs need to improve preservice elementary teachers' profound understanding of elementary mathematics in order to fundamentally improve the quality of teaching practices in classrooms.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.107-122
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• 2003

The present study aims at theoretically reviewing studies en the need of alignments among assessment, curriculum and instruction in order to implement the goals of mathematics education. This paper discusses about issues and models fer alignment between instruction and curriculum, and then mainly focuses on alignment of assessment with instruction and curriculum at two levels, classroom and large-scale assessment. It was pointed out that both many published standardized tests for large-scale assessment and classroom assessments failed to meet curricular goals and contents, and instructional methods. The findings imply that reform in mathematics education should not be driven by assessment, but be embedded in instructional practices.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.549-569
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• 2015

Reflecting on own beliefs about teaching and learning, developed during "the apprenticeship of observation", is a central task for pre-service years. This case study analysed a lesson observation course which could identify, challenge pre-service teachers' folk pedagogy about classroom communications and induce to change of beliefs about teaching and learning. Our analysis shows that targeting and refuting pre-service teachers' specific belief may be an effective strategy for teacher educators to foster new teaching practice.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• The Mathematical Education
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• v.61 no.4
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• pp.559-579
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• 2022

Research on lexicon and language provides insights into the interests, values and practices of a community where individuals use the language. The International Classroom Lexicon Project, in which ten countries participated, identified own country's mathematics teaching and learning lexicons by investigating mathematics classroom instruction from teachers' perspectives in a speaking-oriented community. This study, as an extension of the International Classroom Lexicon Project research, investigated pedagogical lexicons used in 「Mathematics and Education」 journals specialized for Korean professional mathematics teachers published by the Korean Society of Teachers of Mathematics. Using the text mining approach, we also traced how these pedegogical lexicons have changed quantitatively over the past 10 years with a diachronic perspective. As a results, several novel terms were found in the writing-oriented community, which were not identified in the speaking-oriented community. In addition, we could discover some pedagogical lexicons have increased statistically significantly and some lexicons appeared(increased) rapidly across years. This implies the teacher community's values and zeitgeist by reflecting these changes in the sociocultural, incidental and social changing (i.e., periodical change) contexts. This study has value as a first step in understanding zeitgeist for mathematics education in Korean mathematics teacher community according to changes of times over the past 10 years. Also, this study contributes to the methodological insights: the text mining technique provides a methodological contribution to researching changes in interests, values and zeitgeist according to these changes in the times.

• Education of Primary School Mathematics
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• v.8 no.2 s.16
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• pp.69-96
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• 2004

The purpose of this study is to understand teaching and learning mathematics in elementary school classroom by considering mathematics as a kind of social practices and mathematics classroom as a kind of community of practice. The research questions of this study are as followings: 1) Which kinds of lesson organization reveal? 2) Which kinds of social participation structure reveal? 3) Which processes of making meaning reveal? This study was based on ethnomethodology. It was executed participation observations, interviews and surveys with teacher and 5 graders to collect the data related to the social practices formed their classroom. The social practices of mathematics classroom was analyzed from three aspects such as lesson organization, social participation structure and making meaning. The results from which we analyzed the social practices of the mathematics classroom are as followings. From the aspect of lessons organization, the teacher had a lot of power and authorities in the classroom and used them to elicitate students' responses. From the aspect of social participation structure, five SPSs(social participation structures) which revealed in Jo(1997)'s economics classrooms, were shown in this mathematics classroom, but there were a difference to the situations or frequencies which the SPSs appeared. From the aspect of making meaning, it was common that meanings are formed by the explanation of the teacher, but the teacher didn't deliver the mathematical meanings directly. She tried to interact with students to arrive shared meanings.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.439-464
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• 2020

This study conducted a systematic review of mathematics teacher learning communities, especially the characteristics of teacher collaboration in community activities. Our review includes 14 research papers published in national academic journals indexed in KCI and 24 research papers in international academic journals indexed in SSCI from 2003 to 2019. Results show that the literature varied in research design, research topics, and patterns relating to teacher collaboration. While both international and national papers report teacher community activities concerning the organization, management, and participation, there were different levels of involvement, visions, and activities across the communities of practice. For example, research in national journals has presented teacher community as professional development while papers in international journals have focused on documenting teacher community becoming a reflective community of practice. This study contributes to understanding the interplay of context, conflicting epistemic culture, and professional agency in fostering collaboration in teacher communities. This paper also discusses relevant research methods to investigate mathematics teacher communities and insights into the policy and practice of mathematics teacher education.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.107-126
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• 2021

Lexicon is closely related to human thinking. In particular, a classroom lexicon results from objectifying the teaching-learning activity in classrooms, allowing humans to recognize and explore the activities and phenomena in classrooms explicitly. Therefore, using the lexicon and clarifying what the words mean is to enhance the understanding of teaching activities. The International Classroom Lexicon Project investigates and identifies each country's mathematics classroom lexicon, where ten countries participated. The purpose of this current study is to compare the differences in perceptions between teachers and pre-service teachers about the Korean classroom lexicon previously investigated as a part of the international collaborative project. By comparing the responses of 147 teachers and 127 pre-service teachers, the degree of familiarity with pedagogical terms and the frequency of occurrence or usage in classrooms were compared and analyzed to understand the recognition of pre-service teachers' pedagogical terms. Finally, we also discuss reflections on Korean mathematics teaching practices in Korea.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2017.04a
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• pp.161-161
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• 2017

스마트 시설환경의 제어 요소는 난방기, 창 개폐, 수분/양액 밸브 개폐, 환풍기, 제습기 등 직접적으로 시설환경의 조절에 관여하는 인자와 정보 교환을 위한 통신, 사용자 인터페이스 등 간접적으로 제어에 관련된 요소들이 복합적으로 존재한다. PID 제어와 같이 하는 수학적 논리를 바탕으로 한 제어와 전문 관리자의 지식을 기반으로 한 비선형 학습 모델에 의한 제어 등이 공존할 수 있다. 이러한 다양한 요소들을 복합적으로 연동시키기 위해선 기존의 시퀀스 기반 제어 방식에는 한계가 있을 수 있다. 관행의 방식과 같이 시계열 상에서 획득한 충분한 데이터를 이용하여 제어의 양과 시점을 결정하는 방식은 예외 상황에 충분히 대처하기 어려운 단점이 있을 수 있다. 이러한 예외 상황은 자연적인 조건의 변화에 따라 불가피하게 발생하는 경우와 시스템의 오류에 기인하는 경우로 나뉠 수 있다. 본 연구에서는 실시간으로 변하는 시설환경 내의 다양한 환경요소를 실시간으로 분석하고 상응하는 제어를 수행하여 수학적이며 예측 가능한 논리에 의해 준비된 제어시스템을 보완할 방법을 연구하였다. 과거의 고성능 컴퓨팅(HPC; High Performance Computing)은 다수의 컴퓨터를 고속 네트워크로 연동하여 집적적으로 연산능력을 향상시킨 기술로 비용과 규모의 측면에서 많은 투자를 필요로 하는 첨단 고급 기술이었다. 핸드폰과 모바일 장비의 발달로 인해 소형 마이크로프로세서가 발달하여 근래 2 Ghz의 클럭 속도에 이르는 어플리케이션 프로세서(AP: Application Processor)가 등장하기도 하였다. 상대적으로 낮은 성능에도 불구하고 저전력 소모와 플랫폼의 소형화를 장점으로 한 AP를 시설환경의 실시간 제어에 응용하기 위한 방안을 연구하였다. CPU의 클럭, 메모리의 양, 코어의 수량을 다음과 같이 달리한 3가지 시스템을 비교하여 AP를 이용한 마이크로 클러스터링 기술의 성능을 비교하였다.1) 1.5 Ghz, 8 Processors, 32 Cores, 1GByte/Processor, 32Bit Linux(ARMv71). 2) 2.0 Ghz, 4 Processors, 32 Cores, 2GByte/Processor, 32Bit Linux(ARMv71). 3) 1.5 Ghz, 8 Processors, 32 Cores, 2GByte/Processor, 64Bit Linux(Arch64). 병렬 컴퓨팅을 위한 개발 라이브러리로 MPICH(www.mpich.org)와 Open-MP(www.openmp.org)를 이용하였다. 2,500,000,000에 이르는 정수 중 소수를 구하는 연산에 소요된 시간은 1)17초, 2)13초, 3)3초 이었으며, $12800{\times}12800$ 크기의 행렬에 대한 2차원 FFT 연산 소요시간은 각각 1)10초, 2)8초, 3)2초 이었다. 3번 경우는 클럭속도가 3Gh에 이르는 상용 데스크탑의 연산 속도보다 빠르다고 평가할 수 있다. 라이브러리의 따른 결과는 근사적으로 동일하였다. 선행 연구에서 획득한 3차원 계측 데이터를 1초 단위로 3차원 선형 보간법을 수행한 경우 코어의 수를 4개 이하로 한 경우 근소한 차이로 동일한 결과를 보였으나, 코어의 수를 8개 이상으로 한 경우 앞선 결과와 유사한 경향을 보였다. 현장 보급 가능성, 구축비용 및 전력 소모 등을 종합적으로 고려한 AP 활용 마이크로 클러스터링 기술을 지속적으로 연구할 것이다.