• The Mathematical Education
• /
• v.53 no.2
• /
• pp.275-290
• /
• 2014

This study investigated the types of the 3D geometric thinking and spatial reasoning through the observation of the 2D representing activities for representing the 3D geometrical objects with preservice secondary mathematics teachers. For this purpose, the 43 sophomoric students in college of education were divided into 10 groups and observed their group task performance on the basis of the representation they used. Observed processes were all recorded and the participants were interviewed based on the task. As a result, the role of physical object that becoming the object of geometric thinking and spatial reasoning, and diverse strategies and phenomena of the process that representing the 3D geometric figures in 2D were discovered. Furthermore, these processes of representing were assumed to be influenced by experience and study practice of students, and various forms of representing process were also discovered in the process of small group activities.

• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.539-558
• /
• 2019

An ideal of a commutative ring is called a d-ideal if it contains the annihilator of the annihilator of each of its elements. Denote by DId(A) the lattice of d-ideals of a ring A. We prove that, as in the case of f-rings, DId(A) is an algebraic frame. Call a ring homomorphism "compatible" if it maps equally annihilated elements in its domain to equally annihilated elements in the codomain. Denote by $SdRng_c$ the category whose objects are rings in which the sum of two d-ideals is a d-ideal, and whose morphisms are compatible ring homomorphisms. We show that $DId:\;SdRng_c{\rightarrow}CohFrm$ is a functor (CohFrm is the category of coherent frames with coherent maps), and we construct a natural transformation $RId{\rightarrow}DId$, in a most natural way, where RId is the functor that sends a ring to its frame of radical ideals. We prove that a ring A is a Baer ring if and only if it belongs to the category $SdRng_c$ and DId(A) is isomorphic to the frame of ideals of the Boolean algebra of idempotents of A. We end by showing that the category $SdRng_c$ has finite products.

• Journal for History of Mathematics
• /
• v.26 no.2_3
• /
• pp.131-148
• /
• 2013

Euler's formula provides the topological characteristics of geometrical objects including polyhedra, and so an important mathematical concept. Descriptions on Euler's formula had been in the textbooks according to the 3rd through 7th National Mathematics Curriculum. However, they are gone after that. In this study, we focus on Euler characteristic and Euler's formula as an educational material for educations for the gifted or after-school educations. We first look at the mathematical history and the applications of Euler's formula and national curriculums to search for its mathematical and educational meaning. We further make a suggestion for a learning environment which provides a better education relying on search activities, not just depending on memorization, illuminated from the education of Euler's formula.

• Korean Journal of Construction Engineering and Management
• /
• v.7 no.1 s.29
• /
• pp.73-79
• /
• 2006

Even though graphical simulation is very useful for construction planning, the application of graphical simulation has a limitation in dealing with objects without fixed form like earthmoving process. In this case, the mathematical/statistical simulation about the productivity of the whole processes based on the numerical data of working time, waiting time and working capacity of using equipment becomes effective. The mathematical/statistical simulation is not fully utilized in the field of construction due to the difficulties of creating process models and securing trust the numerically expressed results of simulation. In this research, the output of discrete-event simulation programs which are the most common mathematical/statistical simulation tool for construction processes were analyzed for the purpose of earthmoving process visualization. The purpose of this research is to develop a graphical simulation system that can help the construction planner select most suitable equipment and construction methods through the visualize the numerical simulation results of the working time, the queuing time as well as the amount resources etc.

• Journal of the Korean School Mathematics Society
• /
• v.23 no.1
• /
• pp.1-23
• /
• 2020

The purpose of this study is to theorize the conceptualizations of educational interest focused on mathematics learning and to investigate the directions of increasing students' interest in mathematics. This study reconsiders the interest theory of Dewey, classification of situational interest and individual interest, and the experimental research of mathematical interest. The conceptions of educational interest on mathematics learning are as follows. First, mathematical interest refers to the total experiences that an individual feels the need to engage in mathematical objects. Second, making a distinction between situational interest and individual interest is effective in suggesting educational interventions in order to improve students' learning interest. Third, interest is characterized by affect, cognition, and value. According to the conceptions of educational interest on mathematics learning, this study suggests that we should develop or construct good mathematics tasks to increase students' interest in mathematics. Good mathematics tasks consider both students' understanding and students' affection and provide activity's goals or values to be noticed by students.

• Education of Primary School Mathematics
• /
• v.14 no.1
• /
• pp.1-12
• /
• 2011

This paper provides an outline of mathematics education based on the classroom ecology. Ecology is the subject that concentrates on the relations of human and environment. As mathematics education consists of many factors, it is natural that mathematics education should be interest in the perspective of ecology. This paper examines the meaning of ecology and classroom ecology of mathematics education in the perspective of ecology. And it provides the directions of ecological mathematics education. In special, I set the frame of mathematics classroom in the perspective of ecology. The ecological structure divides microsystem(teacher, student, content), mesosysten(relations of microsystems), exosystem(school), and macrosystem(the objects of mathematics education). Lastly, I suggest the ways of mathematical learning and research of classroom ecology in mathematics education. For we should focus the improvement of students' mathematical ability, we must search for the various teaching and learning methods and the ares of research in the perspective of ecology classroom. Therefore, we should be interested in the classroom environments as well as teaching methods, contents based on the ecology classroom in mathematics education.

• The Mathematical Education
• /
• v.24 no.2
• /
• pp.74-104
• /
• 1986

This study aims at investigating the correlation between such variables as a child's family circumstance and personality and that of the child's mathematical ability. For the objects of the study five hundreds and sixteen students (male 273, female 243) were andomly selected from the fifth grade primary school students in the city of Seoul. For the tool of measure the investigation of Korean family circumstances with particular characteristics, the personality test by Chong Pom Mo and Kim Ho Kwon, and the intelligence test by Lee Sang Ro, Chin Whal Kyo and Pyon Chang Jin were employed. For the statistical analysis S. A. S. C., the statistical analysis package of KAIST was employed. The resutis of the test can be summarized as follows. The correlation between the variable of family Circumstance and that of mathematical alility 1) In case of the significance level 0.05 the education of the childs mother and the order of the child's birth have much to do with the perception speed. In case of the significance level 0.1 it makes some difference in the child's perception spead whether the clild's mother has a job or not. 2) In case of the significance level 0.05 the education of the child's father and mother, the father's job and the type of habitation have influence on the child's perception of space. 3) In case of the significance level 0.05 the education of the child's father and mother, the father's job, the order of the child's birth, the type of habitation, their religion, and their cultural, and economic standard have influence on the child's ability of inference. 4) In case of the significance level 0.05 the education of the child's father and mother, the father's job, the type of habitation, their religion and their cultural and economic standard have influence on the child's ability of calculation. 5) In case of the significance level 0.05 any variable of the child's family circumstance has nothing to do with the child's memory. In case of the significance level 0, 1 the type of family and the type of habitation have effect on the child's memory. 6) In case of the significance level 0.05 the education of the child's parents, the jobs of the parents, the type of habtation, their religion, and their cultural and economic standard have influence on the child's linguistic notion. The correlation between the variable of the child's personality and that of the child's mathematical ability 1) In regard to the priority of the variables influencing the child's perception speed, the child's discretion comes first in order, and then sociability and impulsiveness of the child. 2) The child's discretion has effect on the child's space perception. 3) The child's discretion has effect on the child's ability of inference. 4) In regard to the child's ability of calculation the child's discretion comes first in order, and then impulsiveness and sociability of the child. 5) The child's discretion has effect on memory. 6) The child's discretion has effect on the child's linguistic notion.

• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.353-366
• /
• 2014

Recently, the widespread usage of 3D-Printing has grown rapidly in popularity and development of a high level technology for 3D-Printing has become more necessary. Given these circumstances, effectively using mathematical knowledge is required. So, we have developed free web tools for 3D-Printing with Sage, for mathematical 3D modeling and have utilized them in college education, and everybody may access and utilize online anywhere at any time. In this paper, we introduce the development of our innovative 3D-Printing environment based on Calculus, Linear Algebra, which form the basis for mathematical modeling, and various 3D objects representing mathematical concept. By this process, our tools show the potential of solving real world problems using what students learn in university mathematics courses.

• 제어로봇시스템학회:학술대회논문집
• /
• 2004.08a
• /
• pp.1424-1429
• /
• 2004

In this paper a mathematical framework for deriving acceleration bounds from given joint torque limits of multiple cooperating robots are described. Especially when the different frictional contacts for every contact are assumed and the torque limits are given in 2-norm sense, we show that the resultant geometrical configuration for the acceleration is composed of corresponding parts of ellipsoids. Since the frictional forces at the contacts are proportional to the normal squeezing forces, the key points of the work includes how to determine internal forces exerted by each robot in order not to cause slip at the contacts while the object is carried by external forces. A set of examples composed of two robot systems are shown with point-contact-with-friction model and insufficient or proper degree of freedom robots.

• 제어로봇시스템학회:학술대회논문집
• /
• 2004.08a
• /
• pp.1993-1998
• /
• 2004

This paper proposes a new framework for control system design, called the data-based control approach or data space approach, in which the input and output data of a dynamical system is directly and solely used to analyze or design a control system without the employment of any mathematical models like transfer functions, state space equations, and kernel representations. Since, in this approach, most of the analysis and design processes are carried out in the domain of the data space, we introduce some notions of geometrical objects, e.g., the openloop and closed-loop data spaces, which serve as the system representations in the data space. In addition, we establish a relationship between the open-loop and closed-loop data spaces that the closed-loop data space is contained in the open-loop data space as one of its subspaces. By using this relationship, we can derive the data-based stabilization condition for a linear time-invariant discrete-time system, which leads to a linear matrix inequality with a rank constraint.