• The Mathematical Education
• /
• v.60 no.2
• /
• pp.159-172
• /
• 2021

The purpose of this study is to compare and analyze the effects of physical manipulative and exploratory geometry software on the spatial sense for 5^th grade elementary school students in learning nets. For this purpose, ton experimental group used Geofix, an operational learning tool, and the experimental group used Cabri 3D, an exploratory geometry software to learn the nets of solids. The comparison group was learned by worksheet only without any manipulative or software. Spatial sense tests were conducted before and after to determine the level, and eye tracking were used to analyze the strategies of students in solving nets problems. As a result, it was confirmed that the using Geofix group was the most effective for the spatial sense, and Cabri 3D could also be a good tool for learning the nets of solids. In addition, after learning the nets of solids, the analytical strategy, which was the most effective strategy for students' solving strategies, increased. In the process of solving spatial tasks such as the spatial sense tasks, eye tracking technology become a very useful tool for exploring students' strategies, so it is expected that objective and useful data will be collected through more active use in the future.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.4
• /
• pp.344-350
• /
• 2001

In this paper, we are focused on the analysis of acyclic schedule for the determination of the opti-mal cycle time and minimization of work in process. Especially, this paper deals with the product ratio-driven cyclic scheduling problem in FMS with different products and ratio using the TPN(Time Petri Nets)un-folding.

• Journal of Educational Research in Mathematics
• /
• v.15 no.4
• /
• pp.489-504
• /
• 2005

In this paper, we design a environment in computers and mathematics education. For this purpose, we study two different points of view about relations between computers and mathematics education. As theoretical background, we also study constructionism and microworld. Next, we introduce functionization as a basic principle for computers and mathematics education. The concept of functionization focuses on the variation of mathematical objects, and it is a basic concept of both mathematics and computer science. We consider the concept of functionization as a paradigm for the research and practice of the computers and mathematics education. We also present the concept of functionization as a principle for designing a computer environment. Finally, we use the concept of functionization to integrate two famous microworlds, LOGO and DGS by introducing such objects as tiles and folding nets. Combining LOGO and DGS, we design a new microworld that can be used under the internet environment. We present tiles and folding nets to introduce how the concept of functionization is used to design a new microworld and to integrate two microworids.

• The Mathematical Education
• /
• v.45 no.2 s.113
• /
• pp.165-176
• /
• 2006

In this paper, we consider changes of algebra strands around the world. And we suggest needs of designing new computer environment where we make and manipulate geometric recursive patterns. For this purpose, we first consider relations among symbols, meanings and patterns. And we also consider Logo environment and characterize algebraic features. Then we introduce L-system which is considered as action letters and subgroup of turtle group. There are needs to be improved since there exists some ambiguity between sign and action. Based on needs of improving the previous L-system, we suggest new commands in JavaMAL microworld. So we design a microworld for recursive patterns and consider meanings of letters in new environments. Finally, we consider the method to integrate L-system and other existing microworlds, such as Logo and DGS. Specially, combining Logo and DGS, we consider the movement of such tiles and folding nets by L-system commands. And we discuss possible benefits in this environment.

• Journal of Educational Research in Mathematics
• /
• v.16 no.4
• /
• pp.367-386
• /
• 2006

There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.