• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권1호
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• pp.81-91
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• 2011

The aim of this study was to explore the grade 1-3 students' geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 1-3. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele's model merely level 0 (Visualization) across textbooks for grades 1-3.

• East Asian mathematical journal
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• 제26권4호
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• pp.487-507
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• 2010

We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.

• East Asian mathematical journal
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• 제31권2호
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• pp.167-188
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• 2015

Formula for the area of a trapezoid is an educational material that can handle algebraic and geometric perspectives simultaneously. In this note, we will make up the expression equivalent algebraically to the formula for the area of a trapezoid, and deal with the conversion of a geometric point of view, in algebraic terms of translating and interpreting the expression geometrically. As a result, the geometric conversion model, the first algebraic model, the second algebraic model are obtained. Therefore, this problem is a good material to understand the advantages and disadvantages of the algebraic and geometric perspectives and to improve the mathematical insight through complementary activity. In addition, these activities can be used as material for enrichment and gifted education, because it helps cultivate a rich perspective on diverse and creative thinking and mathematical concepts.

• 대한수학교육학회지:학교수학
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• 제9권2호
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• pp.313-326
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• 2007

최근 대수 교육과정에서 패턴들을 표현하면서 일반적인 규칙을 인식하고 설명하는 것이 하나의 대안으로 제시되고 강조되고 있다. 우리나라 역시 제 7 차 교육과정에서 '규칙성과 함수' 영역과 관련하여 초등학교 과정에서 다양한 형태의 패턴활동을 지도하고 있다. 그러나 최근 패턴활동을 통한 학습에 대한 연구에서 학생들의 어려움과 문제점이 지적되고 있다. 이 글에서는 우리나라 초등학교 교육과정에 많이 도입되고 있는 시각적 패턴의 탐구 활동을 통한 일반화 과정을 중심으로 하여, 시각적 패턴의 일반화 과정에서의 다양한 접근과 학생들의 사고전략, 기호화 상태를 고찰한다. 그리고 시각적 패턴의 일반화, 기호화의 어려움을 논의하고 시각적 패턴의 탐구 활동 학습을 위한 몇 가지 제안을 하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권1호
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• pp.83-98
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• 2015

By analysing the examination papers for geometry, we classified the errors occured in the proofs for geometric problems into 5 main types - logical invalidity, lack of inferential ability or knowledge, ambiguity on communication, incorrect description, and misunderstanding the question - and each types were classified into 2 or 5 subtypes. Based on the types of errors, answers of each problem was analysed in detail. The errors were classified, causes were described, and teaching plans to prevent the error were suggested case by case. To improve the students' ability to express the proof of geometric problems, followings are needed on school education. First, proof learning should be customized for each types of errors in school mathematics. Second, logical thinking process must be emphasized in the class of mathematics. Third, to prevent and correct the errors found in the proofs for geometric problems, further research on the types of such errors are needed.

• 한국실내디자인학회논문집
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• 제23권4호
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• pp.129-139
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• 2014

The objective of this research is to suggest new geometric possibilities in digital architecture by investigating the characteristics of hybridization in digital geometry. The research begins with theoretical background research such as defining hybridization, investigating hybrid thinking, and studying the theory of digital geometry, along with the four conceptual characteristics of hybridization that could be drawn, such as temporality, liquidity, complexity, and connectivity. Based on these characteristics, the generative method of hybrid digital geometric languages such as Blob, Particle, Morph, Loft, and Boolean was analyzed with case research in contemporary digital architecture. As a result, diverse hybrid geometric keywords were extracted; these keywords suggest potential meanings of hybridization such as accidentality, mobility, diversity, and identity. Different elements represent the "mobility" in time by the force and wave, and they are "accidentally" combined in gradual change. The united species in "diverse" characters are seamlessly connected and emerge as a new "identity." The research maximizes the generative possibilities in digital geometry and provides a theoretical basis to apply the digital hybrid methods to architectural design by suggesting the potential meanings and possibilities in hybridization.

• 대한수학교육학회지:학교수학
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• 제15권4호
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• pp.957-973
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• 2013

본 연구에서는 중학교 3학년 수학영재 학생들이 비유클리드 쌍곡원반모형에서 정삼각형 테셀레이션을 구성하는 활동을 하면서 나타나는 사고과정을 분석하였다. 역동적 기하환경인 poincare disk. gsp 파일에서 테셀레이션을 구성하기 위해 쌍곡평면에서 도형과 변환에 대한 학습을 하였다. 쌍곡선분의 특징을 탐구하고 도형인 정삼각형의 작도와 반전 변환을 학습 한 후 작도 과정을 반복한 후 쌍곡평면에서 테셀레이션이 가능하게 되는 조건을 탐구하는 과제를 해결하였다. 학생들은 이러한 과제를 해결하며 다양한 전략적 사고과정이 나타났고, 비유클리드 기하체계를 인지하는 경험을 할 수 있었다.

• 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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• 제8권2호
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• pp.565-586
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• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• 한국학교수학회논문집
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• 제16권3호
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• pp.539-560
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• 2013

본 연구의 목적은 고등학교 수학영재 학생들이 GrafEq를 활용한 디자인 활동을 하는 과정에서 나타나는 사고의 특성 알아보고자 함이다. 사전조사를 통해 GrafEq를 사용해 본 경험이 없고, 디자인 활동에 필요한 부등식의 영역을 학습한 과학 고등학교 학생 8명을 선발하여, 2인 1조로 4개의 팀으로 나누어 각각 6차시에 걸쳐 실험을 실시하였다. 연구 결과, 논리적 사고 및 수학적 추상화, 직관적 구조적 통찰, 유연한 사고, 발산적 사고 및 독창성, 패턴의 일반화 및 귀납적 추론과 같은 특성들이 나타났으며, 이를 통해 GrafEq에서의 디자인 활동은 학생들에게 다양한 사고를 자극함으로써 학생들의 인지적인 발달을 촉진시키는데 효과적임을 알 수 있었다.