• Journal of Educational Research in Mathematics
• /
• v.16 no.2
• /
• pp.95-113
• /
• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.3
• /
• pp.1015-1029
• /
• 2021

Modern technology offers many ways to enhance teaching and learning that in turn promote the development of tools for educational activities both inside and outside the classroom. Many educational programs using the augmented reality (AR) technology are being widely used to provide supplementary learning materials for students. This paper describes the potential and challenges of using GeoGebra AR in mathematical studies, whereby students can view 3D geometric objects for a better understanding of their structure, and verifies the feasibility of its use based on experimental results. The GeoGebra software can be used to draw geometric objects, and 3D geometric objects can be viewed using AR software or AR applications on mobile phones or computer tablets. These could provide some of the required materials for mathematical education at high schools or universities. The use of the GeoGebra application for education in Laos will be particularly discussed in this paper.

• Journal of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.41-49
• /
• 1993

• Journal of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.67-80
• /
• 2015

For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice category Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regular monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the category Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an object) here to be regular injective is being convex and present an example to show that the converse is not true, in general.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.2
• /
• pp.41-47
• /
• 2007

A fine segmentation algorithm is proposed for extracting objects in an image, which have both weak boundaries and highly non-convex shapes. The image has simple background colors or simple object colors. Two concepts, geometric attraction-driven flow (GADF) and edge-regions are combined to detect boundaries of objects in a sub-pixel resolution. The main strategy to segment the boundaries is to construct initial curves close to objects by using edge-regions and then to make a curve evolution in GADF. Since the initial curves are close to objects regardless of shapes, highly non-convex shapes are easily detected and dependence on initial curves in boundary-based segmentation algorithms is naturally removed. Weak boundaries are also detected because the orientation of GADF is obtained regardless of the strength of boundaries. For a fine segmentation, we additionally propose a local region competition algorithm to detect perceptible boundaries which are used for the extraction of objects without visual loss of detailed shapes. We have successfully accomplished the fine segmentation of objects from images taken in the studio and aphids from images of soybean leaves.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.367-379
• /
• 2015

The existence of mathematical objects was considered through diorism which was used in ancient Greece as conditions for the existence of the solution of the problem. Proposition I-22 of Euclid Elements has diorism for the existence of triangle. By discussing the diorism in Elements, ancient Greek mathematician proved the existence of defined object by postulates or theorems. Therefore, the existence of mathematical object is verifiability in the axiom system. From this perspective, construction is the main method to guarantee the existence in the Elements. Furthermore, we suggest some implications about the existence of mathematical objects in school mathematics.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.71-80
• /
• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.575-584
• /
• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.135-148
• /
• 1998

We propose the new controls constructed via the second or direct method of Liapunov to solve the collision avoidance control problems for moving objects and a robot arm in the plane. We also explicate the controlling effect by the simulations.

• Journal of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.409-425
• /
• 2024

The category of pairs is the category whose objects are maps between two based spaces and morphisms are pair-maps from one object to another object. To study the self-homotopy equivalences in the category of pairs, we use covariant functors from the category of pairs to the group category whose objects are groups and morphisms are group homomorphisms. We introduce specific subgroups of groups of self-pair homotopy equivalences and put these groups together into certain sequences. We investigate properties of these sequences, in particular, the exactness and split. We apply the results to two special functors, homotopy and homology functors and determine the suggested several subgroups of groups of self-pair homotopy equivalences.