• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3284-3306
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• 2018

This study proposes a method to develop an authoring system(GeoMaTree) for diverse trees that constitute a virtual landscape. The GeoMaTree system enables the simple, intuitive production of an efficient structure, and supports real-time processing. The core of the proposed system is a procedural modeling based on a mathematical model and an application that supports digital content creation on diverse platforms. The procedural modeling allows users to control the complex pattern of branch propagation through an intuitive process. The application is a multi-resolution 3D model that supports appropriate optimization for a tree structure. The application and a compatible function, with commercial tools for supporting the creation of realistic synthetic images and virtual landscapes, are implemented, and the proposed system is applied to a variety of 3D image content.

• The Mathematical Education
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• v.47 no.2
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• pp.181-195
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• 2008

The purpose of this study was to investigate the understanding of basic knowledge of mathematics for $6^{th}$ grade students in elementary school by an essay test and provide instructional suggestions for teachers. A total of 132 students from 6 classes in 3 elementary schools were tested and analyzed in terms of the characteristics of correct answers and types of incorrect answers. The results showed that students had poor understanding of basic conceptual concepts and principles throughout six content areas of school mathematics curriculum, despite their good performance on mathematical skills. This study included implications to teaching and learning for each of the content areas.

• Research in Mathematical Education
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• v.14 no.4
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• pp.323-332
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• 2010

It is the development of a mathematics teachers' teaching knowledge that manifests a mathematics teacher's professional knowledge growth. It is becoming a direct and effective approach of conversion of mathematical knowledge into the knowledge of mathematics teaching. Through the investigation, the study revealed that the knowledge conversion process of mathematics teachers in middle school is restricted by three aspects including eight factors. From this point, the authors have structured the path and model on influencing factors of middle school Mathematics Teaching Knowledge Conversion (MPCK), and discuss the mechanism of the transformation process.

• The Mathematical Education
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• v.63 no.2
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• pp.319-334
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• 2024

The purpose of this study was to reveal the discursive constructs of AI-based mathematical objects by analyzing how concrete objects used in the optimization content of AI mathematics textbooks are transformed into discursive objects through naming and discursive operation. For this purpose, we extracted concrete objects used in the optimization contents of five high school AI mathematics textbooks and developed a framework for analyzing the discursive constructs and discursive operations of AI-based mathematical objects that can analyze discursive objects. The results of the study showed that there are a total of 15 concrete objects used in the loss function and gradient descent sections of the optimization content, and one concrete object that emerges as an abstract d-object through naming and discursive operation. The findings of this study are not only significant in that they flesh out the discursive construction of AI-based mathematical objects in terms of the written curriculum and provide practical suggestions for students to develop AI-based mathematical discourse in an exploratory way, but also provide implications for the development of effective discursive construction processes and curricula for AI-based mathematical objects.

• Research in Mathematical Education
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• v.16 no.1
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• pp.15-29
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• 2012

One of the important aims in mathematics education is to enhance mathematical thinking for students. And students posing questions is a vital process in mathematical thinking as it is part of the reasoning and communication of their learning. This paper investigates how students develop their mathematical thinking through working on tasks in fractions and posing their own questions after successfully solved the problems. The teaching was conducted in primary five classes and the results showed that students' reasoning is related to their analogy with what previously learned. Also, posing their problems after solving the problem not only helps students to understand the structure of the problem, it also helps students to explore on different routes in solving the problem and extend their learning content.

• The Mathematical Education
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• v.49 no.3
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• pp.313-328
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• 2010

Mathematical modeling has been observed in the way of a possibility to contribute in improving students' problem solving abilities. One of the important views of real life problem context could be described such as a useful ways to interpret the real life leading to children's abstraction process. The problem contexts for the grade 6 with mathematical modeling perspectives were developed by reviewing the current 7th National Mathematics Curriculum of Korea. Those include the 5 content areas such as number & operation, geometry, measurement, probability & statistics, and pattern & problem solving. One of problem contexts, "Space", specially designed for pattern & problem solving area, was applied to the grade 6 students and analyzed in detail to understand student's mathematical modeling progress.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.959-971
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• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• East Asian mathematical journal
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• v.23 no.3
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• pp.303-312
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• 2007

In this paper we extract the content of homework that leads the students to independent learners, based on the study of krutetski on individual differences and consider the specific activities related with this and the extent of task performances.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.371-382
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• 2002

경계를 통해서 유출되는 에너지 양을 측정하는 전체열용량 (total heat energy content)은 짧은 시간 극한에서 점근식 을 갖는데 그 계수 $\beta$$_{n}$은 기하학적 양에 의해서 국소적으로 계산 가능한 스펙트럼 불변량이다. 이 논문에서는 열용량 점근에 대하여 저자의 관심사 항을 중심으로 최근까지 연구되어진 바에 대하여 검토 및 정리해 보고자 한다.

• Research in Mathematical Education
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• v.16 no.1
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• pp.51-66
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• 2012

This study investigated the impact of entry level of mathematics subject knowledge on student teachers' mathematics pedagogical content knowledge development and performance in mathematics teaching practice. The sample consisted of 24 mathematics student teachers, 12 of whom passed A-Level mathematics and 12 of whom only passed O-level mathematics. They were all studying in a 4-year bachelor of education (Honours/Primary) programme; they were either majoring or minoring in mathematics. Results showed that student teachers' entry-level mathematics subject knowledge is not related to their mathematics pedagogical content knowledge development or their mathematics teaching performance. These findings may lead society to consider whether student teachers who have passed O-level mathematics are already eligible to be trained as professional primary mathematics teachers. As a consequence, this study raises the issues of how to develop student teachers' mathematics pedagogical content knowledge and whether we need to restructure our bachelor of education (Primary) programmes' curriculum in teacher professionalism.