• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권3호
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• pp.201-225
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• 2022

This paper details case study vignettes that focus on enhancing the teaching and learning of geometry and measurement in the elementary grades with attention to pedagogical practices for teaching through problem solving with rigor and centering equitable teaching practices. Rigor is a matter of equity and opportunity (Dana Center, 2019). Rigor matters for each and every student and yet research indicates historically disadvantaged and underserved groups have more of an opportunity gap when it comes to rigorous mathematics instruction (NCTM, 2020). Along with providing a conceptual framework that focuses on the importance of equitable instruction, our study unpacks ways teachers can leverage their deep understanding of geometry and measurement learning trajectories to amplify the mathematics through rigorous problems using multiple approaches including learning by doing, challenged-based and mathematical modeling instruction. Through these vignettes, we provide examples of tasks taught through rigorous problem solving approaches that support conceptual teaching and learning of geometry and measurement. Specifically, each of the three vignettes presented includes a task that was implemented in an elementary classroom and a vertically articulated task that engaged teachers in a professional learning workshop. By beginning with elementary tasks to more sophisticated concepts in higher grades, we demonstrate how vertically articulating a deeper understanding of the learning trajectory in geometric thinking can add to the rigor of the mathematics.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.101-123
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• 1998

The purpose of this study is to construct the "open" instructional model that might be used properly in mathematics classroom. In this study, the core philosophy of "openness" in mathematics instruction is looked upon as the transference itself from pursuing simply strengthening the function of instruction such as effectiveness in the management of educational environment into the understanding of the nature of mathematics learning and the pursuing of true effectiveness in mathematics learning. It means, in other words, this study is going to accept the "openness" as functional readiness to open all the possibility among the conditions of educational environment for the purpose of realizing maximum learning effectiveness. With considering these concepts, this study regards open mathematics education as simply one section among the spectrum of mathematics education, thus could be included in the category of mathematics education. The model for open instruction in mathematics classroom, constructed in this study, has the following virtues: This model (1) suggests integrated view of open mathematics instruction that could adjust the individual and sporadic views recently constructed about open mathematics instruction; (2) could suggest structural approach for the construction of open mathematics instruction program; (3) could be used in other way as a method for evaluation open mathematics instruction program.thematics instruction program.

• 대한수학교육학회지:수학교육학연구
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• 제26권1호
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• pp.79-101
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• 2016

등호에 대한 이해는 대수적 사고 발달에 핵심이 되는 바, 본 연구에서는 우리나라 초등학교 2~6학년 학생 695명의 등호 이해가 어느 정도인지 살펴보았다. 연구 결과 전반적으로 정답 반응이 오답 반응에 비하여 높게 드러났으나, 정답 반응 가운데 등호의 관계적 관점이 아닌 계산에 치중하는 등호의 연산적 관점 또한 적지 않게 발견할 수 있었다. 또한 표준 문맥 이외의 등식 문맥에서 등식 구조를 판단하거나 등식을 해결하는데 어려움을 겪고 있으며, 등호 개념에 관한 불안전한 이해를 가지고 있다는 것도 확인할 수 있었다. 본 연구를 통하여 우리나라 초등학교 학생들의 등호 이해의 실태를 파악하고 앞으로의 지도 방향에 대한 시사점을 모색할 수 있을 것이라 기대한다.

• 한국학교수학회논문집
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• 제5권1호
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• pp.111-122
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• 2002

The purpose of this study was to examine high school second graders' understanding of the basic nature of logarithm, the major type of error they made about logarithmic function and the cause of such an error, and to seek ways to instruct it better. For that purpose, three research questions were posed: 1. Investigate how much high school students in their second year comprehend the nature of logarithm. 2. Analyze what type of error they make about logarithmic function. 3. Analyze the cause of their error according to the selected error models and how it could be taught more efficiently. The findings of this study were as below: First, the natural science students had a better understanding of the basic nature of logarithm than the academic students. What produced the widest gap between the two groups' understanding was applying the nature of logarithm to the given problems, and what caused the smallest gap was the definition of logarithm and the condition of base. Second, the academic students had a poorer understanding of the basic nature of logarithmic function graph and of applying the nature of logarithm to the given problems. Third, the natural science students didn't comprehend well the basic nature of logarithmic function graph, the nature of characteristics and mantissa. Fourth, for all the students from academic and natural science courses, the most common errors were caused by the poor understanding of theorem or nature of the ［E4] model. Fifth, the academic students made more frequent errors due to the unfamiliar signs of the ［El］ model, the imperfect understanding of theorem or nature of the ［E4］ model, and the technical part of the ［E6］ model. Sixth, the natural science students made more frequent errors because of the improper problem interpretation of the ［E2］ model and the logically improper inference of the ［E3］ model.

• 대한수학교육학회지:학교수학
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• 제17권3호
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• pp.447-467
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• 2015

본 연구의 목적은 도(degree)와 라디안을 호의 측도로 해석하는 것이 라디안과 각의 측정에 대한 개념적 이해에 어떠한 영향을 미치는지 살펴보는 것이다. 이에 호의 길이를 이용한 각의 측도에 대한 내용지식을 26명의 예비중등교사를 대상으로 조사하였으며, 그 결과를 반영하여 두 명의 중학생들을 대상으로 실험을 진행하였다. 예비교사들과 두 중학생의 반응을 분석한 결과, 도(degree)의 개념을 호의 측도로 해석한 경험이 라디안의 이해에 긍정적인 영향을 미쳤으며, 호의 측도로 각의 측도를 파악하는 과정이 '선형 측정'에 대한 개념적 이해를 가능하게 하였다. 또한 각에 관한 다양한 문제에서 원의 맥락과 호의 등분 전략이 효과적인 문제해결전략으로 작용하였으며, 각과 호의 측도 사이의 관계를 탐구할 수 있는 직접적인 조작활동을 제공하는 것이 각의 측정 개념에 대한 이해에 도움을 줄 수 있다는 것을 확인하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권1호
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• pp.75-96
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• 2006

The purpose of this study was to analyze how elementary pre-service teachers learned the pedagogical content knowledge of mathematics and to understand the challenges and difficulties that they experienced in the course of student teaching. A qualitative case study provided an in-depth description of the whole three weeks of student teaching process. Four pre-service teachers and two mentor teachers participated in this study. Multiple data collection techniques were used; classroom observations, in-depth interviews, document analysis, and researcher's field notes. The results of this study showed how pre-service teachers learn PCK of mathematics in designing mathematics lessons, understanding mathematics learners and delivering mathematics lessons and what are the difficulties and challenges they experienced. Finally this study discussed about some suggestions to pre-service program and future research.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권1호
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• pp.15-40
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• 2005

This study basically investigates the meaning and properties of performance task applicable to mathematics classroom and it finds out how to run effectively performance task activities included in the present mathematics textbooks. To accomplish this, this study deals with twelves kinds of mathematics textbooks for ninth graders and is proceeded on the basis of textbook analysis and teacher interview. Considering a situation that in future mathematics textbook would be developed, according to the analytic results of this study, common understanding of performance task and qualified performance task are needed, a variety of tasks classified by differentiated level are needed. In addition, each task should be dealt with the contents related to curious and interesting real-life situations. Furthermore, fairness of checking and recording should be established and teachers' positive attitudes to applying performance tasks to math class are needed.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권2호
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• pp.141-158
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• 2011

In recent years, an increasing number of viewpoints hold that students should be engaged in a learning environment where understanding and knowledge transfer take place. This study introduces Mathematics Created by You (MCY)-mentoring program, which allows students to construct artefacts that are required to learn. This program is online-based and so can be shared by several people and mathematics leaning takes place through interactions within this carefully designed environment. Also, MCY intends to provide students a series of sequential activities related to creative play, creative learning and creative inquiry based on a Constructive and interactive environment. Furthermore, a creative activity- constructing a creative product using building blocks- was presented as an example. Finally, we investigate the pedagogical implications and suggest directions for the further development.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제6권2호
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• pp.135-143
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• 2002

This study was executed in M elementary school for a week, T elementary school for a week, N high school for a week, and S high school for a week in 2000. There were mathematics teacher interviews, mathematics classroom observations, and student interviews in each school. We can draw the conclusion from this study as follows. Firstly, the teaching of mathematics in both elementary and high school was very good in the standard of mathematical concepts, procedures, and connection. Secondly, it is very good in the standard of mathematics as problem solving, reasoning, and communication. Thirdly, it is not so good in the standard of promoting mathematical disposition. Fourthly, it is good in elementary schools, but not in high schools regarding the standard of assessing students' understanding of mathematics. Fifthly, it is very good in elementary schools, but not so good in high schools regarding the standard of learning environments.

• 대한수학교육학회지:수학교육학연구
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• 제12권4호
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• pp.523-542
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• 2002

The matter of understanding mathematical concepts in learning mathematics is one of the most important issues in mathematics education. There have been so many studies about it but the more practical study has been asked. When we Think using intuitional models such as examples, figures of speech, situations and activities, it is supposed that the major elements of cognitive mechanism are prototypes, analogies, metaphors and metonymies. In this paper, we tried to examine Rosch's prototype theory, the studies about analogies in congnitive psychology, Lakoff and Johnson's metaphor theory from the viewpoint of teaching mathematics, and then tried to analyze examples, analogies, analogical transfers, metaphorical expressions, metonymies in middle school mathematics text books used in Korea now.