• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권3호
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• pp.235-250
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• 2009

Researchers at Truman State University in Missouri, located in the heartland of the United States, have been using materials adapted from the English translations of the sixth national primary mathematics curriculum from Korea for professional development and assessment with groups of Missouri teachers for the purpose of enhancing teachers' understanding of the fundamentals of mathematics since 2002 [gecKo Mathematics (2008). Korean Mathematics in American Classrooms. Edited by J. Grow-Maienza. Adapted from Korean Mathematics (2001). Kirksville, MO: Truman State University. http://kmath.truman.edu/]. A professional development initiative for 50 teachers conducted in Missouri this past year is reported here. Significant gains in teacher understanding of fundamental mathematics concepts and pedagogy necessary for student achievement in primary mathematics were found as a result of the initiative.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.55-74
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• 2014

This study examined the potential teaching strategies of prospective elementary teachers and their perceptions of the procedural/conceptual nature of examples. Fifty-four prospective teachers participated in this study, engaging in two-phase tasks. Analysis of data indicated that: (a) Overall, the participants' perceptions were geared toward putting emphasis on conceptual understanding rather than procedural understanding; but (b) Generally, procedure-oriented strategies were more frequently incorporated in participants' potential teaching plans. This implied that participants' preconceived ideas regarding math examples were not always reliable indicators of their potential teaching strategies. Implications and suggestions for mathematics teacher preparation are discussed.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권1호
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• pp.31-41
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• 2003

Representation has been main topic in teaching and learning mathematics for a long time. Moreover, teachers' deficiency of representation about fraction results in teaching algorithms without conceptual understanding. So, this paper was conducted to investigate and analysize the elementary preservice mathematics teachers' representation about fraction. 38 elementary preservice mathematics teachers participated in this study. This study results showed that, the only model of a fraction that was familiar to the preservice teachers was the part of whole one. And research showed that, they solved the problems about fraction well using algorithms but seldom express the sentence which illustrates the meaning of the operation by a fraction. Specially, the division aspect of a fraction was not familiar nor readily accepted. It menas that preservice teachers are used to using algorithms without a conceptual understanding of the meaning of the operation by a fraction. This results give us some implications. Most of all, teaching programs in preservice mathematics teachers education have to devise to form a network among the concepts in relation to fraction. And we must emphasize how to teach and what to teach in preservice mathematics teachers education course. Finally, we have to invent the various materials which can be used to educate both preservice teachers and elementary school students. If we want to improve the mathematical ability of students, we will concentrate preservice teachers education.

• 한국지구과학회지
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• 제40권5호
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• pp.538-547
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• 2019

본 연구는 현직 및 예비 지구과학교사의 H-R도와 별의 진화에 대한 개념 이해 상태를 알아보기 위해 개념 지위 분석틀을 활용하여 수행하였다. 이해 가능성 영역에서 현직교사의 비과학적 용어 사용이 다수 발견되었고, 그래프작성에서 낮은 과학적 탐구 능력과 개념에 대한 비과학적 비유가 발견되어 교수 과정에서 잘못된 개념 전달의 가능성이 확인되었다. 예비교사는 중등교육과정 연계 문항에서 다수의 오류를 보였으며, 이와 관련하여 학교 현장에 적용이 더 잘 될 수 있도록 예비교사 교육 과정의 개선이 필요하겠다. 개연성 영역에서, 두 집단 모두 별의 진화가 갖는 우주론적 의미를 이해하고 있었으나, 예비교사의 별의 실제기작에 대한 설명이 구체적이지 않았다. 유용성 영역에서, 현직교사는 지구과학의 학문적 특성을 반영한 교육적 고민을 하고 있었고, 지식을 현실 문제해결에 활용, 적용하려는 경향이 높았다. 반면, 예비교사는 높은 무응답률을 보여 H-R도와 별의 진화를 실용적 개념으로 파악하지 않는 것으로 확인되었다. 결과적으로, 두 집단 모두에서 H-R도와 별의 진화에 대한 비과학적 개념이 다수 발견되어 교사 교육 및 교수 학습 계획 수립 시 주의가 필요함을 확인할 수 있었다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.1-29
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• 2014

When taught the precise definition of ${\pi}$, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that ${\pi}$ has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant nor formally proves that it is a constant. In this study, we aim to investigate prospective teachers' conceptual understanding of ${\pi}$, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of ${\pi}$, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제3권1호
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• pp.1-36
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• 1999

The case of four classrooms analyzed in this study point to many commonalities in the challenges of reforming mathematics teaching in Korea and the U. S. In both national contexts we have seen the need fur a clear distinction between implementing new student-centered social practices in the classroom, and providing significant new loaming opportunities for students. In particular, there is an important need to distinguish between attending to the social practices of the classroom and attending to students conceptual development within those social practices. In both countries, teachers in the less successful student-centered classes tended to abdicate responsibility fur sense making to the students. They were more inclined to attend to the literal statements of their students without analyzing their conceptual understanding (Episodes KA5 and UP 2). This is easy to do when the rhetoric of reform emphasizes student-centered social practices without sufficient attention to psychological correlates of those social practices. The more successful teachers tended to monitor the understanding of the students and to take proactive measures to ensure the development of that understanding (Episodes KO5 and UN3). This suggests the usefulness of constructivism as a model (or successful student-centered instruction. As Simon(1995) observed, constructivist teachers envision a hypothetical learning trajectory that constitutes their plan and expectation for students learning from the particular if the trajectory is being followed. If not, the teacher adjusts or supplements the task to obtain a more satisfactory result, or reconsider her or his assumptions concerning the hypothetical learning trajectory. In this way, the teacher acts proactively to try to ensure that students are progressing in their understanding in particular ways. Thus the more successful student-centered teacher of this study can be seen as constructivist in their orientation to student conceptual development, in comparison to the less successful student-centered teachers. It is encumbant on the authors of reform in Korea and the U. S. to make sure that reform is not trivialized, or evaluated only on the surface of classroom practices. The commonalities of the two reform endeavores suggest that Korea and the U. S. have much to share with each other in the challenges of reforming mathematics teaching for the new millennium.

• 한국과학교육학회지
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• 제22권5호
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• pp.1044-1070
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• 2002

Initial science teacher education in Hong Kong is provided by the Post-graduate Diploma in Education Programme (PGDE) for both pre-service and in-service secondary school teachers. This programme includes a balanced treatment of subject curriculum and teaching in science, general pedagogical knowledge and skills, educational psychology and school administration. The science courses in this programme also have some units that equip science teachers with the knowledge and skills that are essential for teaching a science curriculum that emphasises conceptual change and understanding of the nature and methods of science. This emphasis is illustrated by two studies: (1) Developing a conceptual change model of instruction in Biology teachers, and (2) Constructing understanding of the nature and methods of science.

• 대한수학교육학회지:수학교육학연구
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• 제10권1호
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• pp.103-113
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• 2000

A case study was conducted to investigate the understandings of the subject matter knowledge and pedagogical content knowledge held by 63 elementary preservice teachers in dealing with the division by a fraction. The study results showed that, in terms of the subject matter knowledge, the preservice teachers did not have a conceptual understanding of the division by a fraction and, in terms of the pedagogical content knowledge, they depended heavily on algorithms without a conceptual understanding of the meaning of the division by a fraction.

• 대한수학교육학회지:수학교육학연구
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• 제17권2호
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• pp.147-162
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• 2007

본 논문은 교수를 위한 중학교 수학교사들의 수학적 지식을 조사한 저자의 학위논문의 일부분으로써, 19명의 한국 및 중국 중학교 수학교사들의 분수 나눗셈(division by fractions)에 대한 개념적 실생활 모델을 조사, 분석하였다. 분수 나눗셈에 대한 이론적 배경을 제공함과 동시에, 실제 현장 교사들이 가지고 있는 분수 나눗셈에 대한 개념적 이해를 조사, 분석함으로써 분수 나눗셈을 효과적으로 가르치기 위한 교사 지식의 구체적 예들을 제공하고 있다. 본 연구에서는, 연구에 참가한 교사들 대부분이 분수 나눗셈을 "역수 곱하기(invert and multiply)"와 같은 전통적 알고리즘에 기초하여 이해하고 있었으며, 분수 나눗셈의 의미를 실생활 모델로 나타내는 교수과제를 성공적으로 수행한 교사는 단 두 명에 뿐이었다. 이러한 현상은 그 교사들 대부분이 가지고 있는 범자연수 나눗셈 모델이 분할 모델 (partitive model)로 제한되어 있기 때문이었다. 하지만, 또 다른 흥미로운 연구 결과는, 교사가 분할모델 만을 가지고 있더라도, 그 모델의 개념적 구조(conceptual structure)를 깊이 이해하고 있을 때는, 그 기본적 개념 구조를 변형하여 분수 나눗셈의 실생활 모델을 응용해 내는 사고의 융통성을 보였다. 본 논문에서는 이러한 교사들의 성공적 사례뿐만 아니라, 주어진 교수 과제를 수행하는데 실패한 교사들의 인터뷰결과들도 분석, 해석하여 제공하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권2호
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• pp.127-141
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• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.