• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권2호
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• pp.151-170
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• 2009

This study reports a research which was conducted on how frequently and where the students use the unit circle method while dealing with trigonometric functions in solving the trigonometry questions. Moreover, the reasons behind the choice of the methods, which could be the unit circle method, the ratio method, or the use of trigonometric identities, are also investigated to get an insight about their understanding. In this study, the relationship between the students' choices of methods in solving questions is examined in terms of instrumental or relational understanding. This is a multi-method research which involves a range of research strategies. The research techniques used in this study are test, verbal protocol (think aloud), and interview. The test has been applied to ten tenth grade students of a public school to get students' solution processes on the paper. Later on, verbal protocol has been performed with three students of these ten who were of the upper, middle and lower sets in terms of their performance in the test. The aim was to get much deeper data on the students' thinking and reasoning. Finally, interview questions have been asked both these three students and other three from the initial ten students to question the reasons behind their answers to the trigonometry questions. Findings in general suggest that students voluntarily choose to learn instrumentally whose reasons include teachers' and students' preference for the easier option and the anxiety resulting from the external exam pressure.

• 한국학교수학회논문집
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• 제7권2호
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• pp.81-97
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• 2004

본 논문은 그래픽 계산기를 활용한 이산수학의 ‘행렬과 그래프’개념의 이해과정에 관한 연구이다. 본 연구의 목적을 위해 우리는 TI-92 계산기를 활용하여 ‘행렬과 그래프’ 개념을 학습해 가는 두 명의 중학생을 조사하였다. 이 과정에서 우리는 켐코더나 녹음기를 활용하여 질적자료를 수집하였으며 이 자료들을 테크놀로지에 관한 학생들의 태도, 용어의 의미 이해, 행렬 연산의 이해 과정, 수학적 의사소통 등으로 범주화하였다. 이로부터 우리는 다음과 같은 결론을 얻었다. 첫째, 학생들은 그래픽 계산기를 활용하여 행렬의 의미와 역할을 그들 스스로 탐구하였으며 계산기는 이 과정에서 훌륭한 학습동반자 역할을 수행하였다. 둘째, 탐구과정에서 학생들이 오류를 범했을 때 그래픽 계산기가 에러메시지를 곧바로 출력함으로써 학생들의 자기주도적 학습을 가능하게 하였다. 셋째, 계산기는 교사와 학생들간, 혹은 학생들 사이의 수학적 의사소통을 강화시키는 역할을 하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권1호
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• pp.49-66
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• 2008

In this paper we present a cognitive developmental analysis of the arithmetic mean concept. This analysis leads us to a hierarchical classification at different levels of understanding of the responses of 227 students to a questionnaire which combines open-ended and multiple-choice questions. The SOLO theoretical framework is used for this analysis and we find five levels of students' responses. These responses confirm different types of difficulties encountered by students regarding their conceptualization of the arithmetic mean. Also we have observed that there are no significant differences between secondary school and university students' responses.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권2호
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• pp.95-114
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• 2012

This study examines the use of ill-structured problem to help the 4th graders' problem solving and reasoning. It appears that children with good understanding of problem situation tend to accept the situation as itself rather than just as texts and produce various results with extraction of meaningful variables from situation. In addition, children with better understanding of problem situation show AR (algorithmic reasoning) and CR (creative reasoning) while children with poor understanding of problem situation show just AR (algorithmic reasoning) on their reasoning type.

• East Asian mathematical journal
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• 제39권2호
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• pp.119-139
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• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권1호
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• pp.51-65
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• 2010

Open-ended problems can foster deeper understanding of mathematical ideas, generating creative thinking and communication in students. High-order thinking tasks such as open-ended problems involve more ambiguity and higher level of personal risks for students than they are normally exposed to in routine problems. To explore the classroom-based factors that could support or inhibit such higher-order processes, this paper also describes two cases of Singapore primary school teachers who have successfully or unsuccessfully implemented an open-ended problem in their mathematics lessons.

• East Asian mathematical journal
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• 제27권4호
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• 한국수학교육학회지시리즈A:수학교육
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• 제60권1호
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• pp.111-131
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• 2021

이 연구는 수학 교사들이 교과서 등으로 구현되는 교육과정을 어떻게 이해하여 활용하고자 의도하는가를 탐색하고자 한다. 이를 위해서, 교사들이 교과서 내용을 수업에 적용하는 의도와 목적을 파악하기 위한 설문검사 문항을 개발하였으며 25명의 교사들이 검사에 참여하였다. 자료 분석 결과로, 첫째, 연구 참여 교사들은 대체로 교과서의 내용을 그대로 수업에 활용하려는 경향을 드러낸다. 둘째, 교과서의 문제를 수정하거나 보완을 시도하는 경우에 그 결과물이 학생들의 수학적 사고 능력을 촉진하는 과제의 특성을 포함하는 단계에는 이르지 못하는 것으로 보인다. 셋째, 대체로 교사들은 학생의 수학적 역량을 개발을 목적으로 두기보다는 평가 준거로서 교과서를 활용하고자 의도하였다. 수학 교사들은 수업 실행에 있어서 교과서의 내용을 해석하여 능동적으로 수업에 활용하기 보다는 교과서 내용을 그대로 수용하여 충실히 따르고자 의도하는 것으로 나타났다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권1호
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• pp.13-22
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• 2009

School children in Brunei Darussalam, as elsewhere, learn how to apply a lot of algorithms and formulas in mathematics. These include methods of finding the lowest common multiple and highest common multiple of numbers and methods of factorizing quadratics. Investigations and experience have shown that both able and less able students learn to do these mechanically and unimaginatively and in a way that is reliable when answering examination questions. Most of them do not, however, learn these algorithms and methods so as to develop a deeper insight of what they learn and thereby perform even more effectively in examinations. Yet it is possible to teach these and other methods for understanding in ways that are enjoyable and enable students to use them effectively and with flair.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제20권1호
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• pp.31-38
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• 2016

WHAT we teach, and HOW students experience it, are the primary factors that shape students' understanding and beliefs of what mathematics is all about. Further, students pick up their sense of mathematics from their experience with it. We have seen the results of the approach to "break the subject into pieces and make students master it bit by bit. As an alternative, we strive to create a teaching environment in which students are DOING mathematics and thereby engender selected aspects of "mathematical culture" in the classroom. The vehicle for doing this is the so-called Japanese Open-ended approach to teaching mathematics. We will discuss three aspects of the open-ended approach - process open, end product open, formulating problems open - and the associated approach to assessing learning.