• 한국수학교육학회지시리즈A:수학교육
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• 제42권1호
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• pp.11-18
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• 2003

One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권1호
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• 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.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제26권4호
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• pp.219-236
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• 2023

본 연구는 분수의 곱셈과 나눗셈에서 예비교사의 수학적 이해와 문제 만들기 사이의 관련성을 탐색하였다. 이를 위해여 41명의 예비교사들을 대상으로 분수의 곱셈과 나눗셈에 대한 시각적 표현과 문제 만들기 과제를 수행하고 수학적 이해 정도와 문제 만들기 능력을 측정하였으며, 수학적 이해 정도와 문제 만들기 능력 사이의 관련성을 교차분석을 통해 알아보았다. 그 결과, 예비교사들의 대부분은 분수의 곱셈과 나눗셈의 개념적 이해를 나타냈으며, 다섯 가지 유형의 어려움이 나타났다. 문제 만들기에서는 대부분의 예비교사들이 풀 수 있는 수학 문제를 만들지 못했으며 이 과정에서 네 가지 유형의 어려움이 나타났다. 또한 교차분석 결과, 수학적 이해 정도는 문제 만들기 능력과 연관이 있었다. 이러한 결과를 바탕으로 예비교사의 수학적 이해와 문제 만들기에 대한 시사점을 제시하였다.

• East Asian mathematical journal
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• 제29권2호
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• 한국수학사학회지
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• 제34권6호
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• 대한수학교육학회지:수학교육학연구
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• 제13권2호
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• pp.123-141
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• 2003

본 연구는 Freudenthal의 언어 수준을 토대로 중학생들의 수학적 언어의 이해 수준과 사용수준을 조사하였다. 본 연구에서 개발한 기하 개념에 대한 언어 이해 검사는 신뢰도와 타당도를 가진 것이었으며, 이 검사를 통해 학생들이 수학적 언어를 이해하는 것에 수준의 위계가 있음이 밝혀졌다. 학생들이 수학 개념을 설명하면서 사용하는 언어의 수준은 수학적 언어를 이해하는 수준과 상관이 없었으며. 과제에 따라 정답에 기여하는 언어 사용 수준이 달랐다. 마지막으로 중학생들이 이해하기에 쉬운 언어는 수학적 대상에 이름을 붙인 지표를 일상언어의 관계로 설명되는 3 수준이었으며 이것은 언어 이해 수준, 언어 사용 수준과 상관이 없었다. 본 구의 결과를 토대로 교사는 학생들의 이해 수준과 사용 수준이 다르다는 점을 염두에 두고 그에 맞게 수학 학습 지도를 해야 할 것이며, 수학적 언어를 자신 있게 사용 할 수 있는 의사소통의 과제를 제시해야 할 것이다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권1호
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• pp.97-104
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• 2006

The purpose of this study is to extract some suggestions in developing the elementary students' abilities to solve the fundamental mathematical problems by analyzing the degree of the correlation between the fundamental mathematical capability and the reading capability of the elementary 3th graders. In order to achieve this goal, this article analyzed the correlation between the fundamental mathematical capability and the reading capability on the basis of the studying result about the diagnostic evaluation conducted on 20,556 elementary 3th graders by the KICE as a national level basic scholastic achievement evaluation. The coefficient of correlation between the fundamental mathematical capability and the reading capability was .621. As such, it shows that the reading capability plays an important role in solving the fundamental mathematical problems. Particularly, the coefficient of correlation between the corollary arguments and the problem solving ability and the reading capability was the highest among the sub-capabilities of fundamental mathematical capability. In addition, judging from the result that the coefficient of correlation between the practical understanding capability and the solving capability of the fundamental mathematical problems was .528, it informs that the practical understanding capability takes an' important part in developing the fundamental mathematical capability of the elementary students. The results of this study support the hypothesis that the understanding capability plays the very important role in solving the fundamental mathematical problems. In particular, the results suggest that it is necessary that the pupils should be simultaneously supported not only by the capability of the mathematical basis, but also by the reading capability, especially the practical understanding capability about the problems, in order to develop the capability to solve the fundamental mathematical problems.

• 한국초등수학교육학회지
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• 제13권2호
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• pp.247-268
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• 2009

본 연구는 주어진 문장제의 이해에 초점을 두고 그 문제를 구성하고 있는 수학적 구성요소에 대한 이해 및 그 요소들 사이의 구조를 바탕으로 수학학습 성취도가 높은 학습자 군이 보이는 문장제 이해의 특징을 살펴보고, 일반 학생들의 문장제 이해를 돕는 지도 방안을 구안하는데 연구 목적이 있다. 이 연구 목적을 위하여 수학교과서 및 수학익힘책 총 24권에 제시되어 있는 문장제를 수학적 구성요소에 의거 수학적 구조를 유형화하고, 3학년 1개 학급의 수학학습 성취도가 높은 학생을 대상으로 그들이 보여주는 문장제의 수학적 구조 파악의 특징을 살펴보았으며, 이를 문장제의 수학적 구조 파악을 강조하는 일반적인 지도 방안 구안에 적용하였다. 연구 결과는 첫째, 문장제는 문장제를 구성하고 있는 수학적 구성요소가 이루고 있는 구조를 총 9가지 유형으로 분류할 수 있다. 둘째, 수학학습 성취도가 높은 학습자는 문장제를 이해할 때, 4가지의 특징을 보였다. 셋째, 문장제의 수학적 구조 파악을 강조하는 지도 방안을 4가지 도출해 내어 수정 보완하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제4권1호
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• pp.1-22
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• 2000

The purpose of this study was to investigate the effects of using graphing calculators on students' understanding of the linear and quadratic function concepts. The populators of this study are tenth graders at high school in Seoul, one class for the treatment group and another class for the comparison group, and experiment period is 14 weeks including two weeks for school regular exams.Function tests used in the study was proposed which described a conceptual knowledge of functions in terms of the following components: a) Conceptual understanding, b) Interpreting a function in terms of a verbal experission, c) Translating between different representations of functions, and d) Mathematical modeling a real-world situation using functions. Even though the group test means of the individual components of conceptual understanding, interpreting, translating, mathematical modeling did not differ significantly, there is evidence that the two groups differed in their performance on conceptual understanding. It was shown that students learned algebra using graphing calculators view graphs more globally. The attitude survey assessed students' attitudes and perceptions about the value of mathematics, the usefulness of graphs in mathematics, mathematical confidence, mathematics anxiety, and their feelings about calculators. The overall t-test was not statistically significant, but the students in the treatment group showed significantly different levels of anxiety toward mathematics.