• School Mathematics
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• v.1 no.2
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• pp.555-569
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• 1999

The graph unit(chapter) is a good example of a topic in elementary school mathematics for which computer use can be incorporated as part of the instruction. Teaching graph can be facilitated by using the graphing utilities of computers, which make it possible to observe the property of many types of graphs. This study was concerned with utilizing an educational software Graphers as an instructional tool in teaching to help young students gain a better understanding of graph concepts. For this purpose, three types of instructional activities using Graphers were shown in the paper. Graphers is a data-gathering tool for creating pictorial data chosen from several data sets. They can represent their data on a table or with six types of graphs such as Pictograph, Bar Graph, Line Graph, Circle Graph, Grid Plot and Loops. They help students to select the graph(s) which are the most appropriate for the purpose of analyzing data while comparing various types of graphs. They also let them modify or change graphs, such as adding grid lines, changing the axis scale, or adding title and labels. Eventually, students have a chance to interpret graphs meaningfully and in their own way.

• Journal of Korean Elementary Science Education
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• v.33 no.1
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• pp.172-180
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• 2014

The first purpose of this study is to distinguish difficult chapters in 'Speed of objects' chapter and find the factors which give difficulty to the teachers and students. Also, it attempts to compare the students' assessment scores with the degree of difficulty in teaching and also with the degree of difficulty in learning. This report is expected to help science teachers develop their PCK(Pedagogical Content Knowledge) for teaching the chapter professionally. 15 teachers who had taught the 'Speed of Objects' chapter and their 386 students took part in the survey to acquire information about the difficulties in teaching and learning. 386 students also received a test to examine their understandings of the chapter. The results of this study are as follow; First, the degree of teachers' and students' difficulty is only affected by the contents, and the degree of onerousness felt by teachers is higher than that of students. Second, The topics caused higher difficulty to teachers were 'Understanding the meaning of motion(2nd lesson)', 'Understanding the meaning and unit of speed(5th lesson)', 'Changing unit of speed(6th lesson)', 'Drawing a distance-time graph(7th lesson)', and 'Understanding the relative motion(10th). The topics that led higher difficulty to students were the contents of 5th, 6th, and 7th lessons. Third, the 'Speed of Objects' chapter can be divided into 4 types of difficulty according to the degree of teaching and learning; 'Strong difficulty', 'Learning difficulty', 'Weak difficulty', and 'Teaching difficulty'. Last, students showed low achievement to the tasks that were related with 'Strong difficulty' and 'Teaching difficulty'.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.477-493
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• 2018

The six core competencies included in the mathematics curriculum Revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the creativity and convergence competency is very important for students' enhancing much higher mathematical thinking. Based on the creativity and convergence competency, this study selected the five elements of the creativity and convergence competency such as productive thinking element, creative thinking element, the element of solving problems in diverse ways, and mathematical connection element, non-mathematical connection element. And also this study selected the content(chapter) of the graph in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the five elements of the creativity and convergence competency were shown in each textbook.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1069-1105
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• 2001

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.