• The Mathematical Education
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• v.46 no.3
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• pp.245-261
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• 2007

This paper deals with the possible problems which may arise when students learn the names of elementary geometric figures in the languages of Korean, Chinese, English. The names of some simple geometric figures in these languages are analyzed, and a specially designed test was administered to some grade eight students from the three language groups to explore the possible influence of the characteristics of the languages on students' capability in identifying the figures, the way students define the figures, and students' understanding of the inclusive relationship among figures. It was found that the usage of the terms to describe geometric figures may indeed have affected students' understanding of the figures. The names of geometric figures borrowed from those of everyday life objects may cause students to fix on some attributes of the objects which may not be consistent with the definition of the figures. Even when the names of the geometric figures depict the features of the figures, the words used in the naming of the figures may still affect students' understanding of the inclusive relations. If there is discrepancy between the definition of a geometric figure and the features that the name depicts, it may affect students' understanding of the definition of the figure, and if there is inconsistency in the classification of figures, it may affect students' understanding of the inclusive relationship involving those figures. Some implications of the study are then discussed.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.565-586
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• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.183-203
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• 1999

In this study, we analysed the constituents of proof and examined into the reasons why the students have trouble in learning the proof, and proposed directions for improving the teaming and teaching of proof. Through the reviews of the related literatures and the analyses of textbooks, the constituents of proof in the level of middle grades in our country are divided into two major categories 'Constituents related to the construction of reasoning' and 'Constituents related to the meaning of proof. 'The former includes the inference rules(simplification, conjunction, modus ponens, and hypothetical syllogism), symbolization, distinguishing between definition and property, use of the appropriate diagrams, application of the basic principles, variety and completeness in checking, reading and using the basic components of geometric figures to prove, translating symbols into literary compositions, disproof using counter example, and proof of equations. The latter includes the inferences, implication, separation of assumption and conclusion, distinguishing implication from equivalence, a theorem has no exceptions, necessity for proof of obvious propositions, and generality of proof. The results from three types of examinations; analysis of the textbooks, interview, writing test, are summarized as following. The hypothetical syllogism that builds the main structure of proofs is not taught in middle grades explicitly, so students have more difficulty in understanding other types of syllogisms than the AAA type of categorical syllogisms. Most of students do not distinguish definition from property well, so they find difficulty in symbolizing, separating assumption from conclusion, or use of the appropriate diagrams. The basic symbols and principles are taught in the first year of the middle school and students use them in proving theorems after about one year. That could be a cause that the students do not allow the exact names of the principles and can not apply correct principles. Textbooks do not describe clearly about counter example, but they contain some problems to solve only by using counter examples. Students have thought that one counter example is sufficient to disprove a false proposition, but in fact, they do not prefer to use it. Textbooks contain some problems to prove equations, A=B. Proving those equations, however, students do not perceive that writing equation A=B, the conclusion of the proof, in the first line and deforming the both sides of it are incorrect. Furthermore, students prefer it to developing A to B. Most of constituents related to the meaning of proof are mentioned very simply or never in textbooks, so many students do not know them. Especially, they accept the result of experiments or measurements as proof and prefer them to logical proof stated in textbooks.

• MISULJARYO - National Museum of Korea Art Journal
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• v.96
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• pp.54-88
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• 2019

The Album of Complete Views of Seas and Mountains comprises sixty real scenery landscape paintings depicting Geumgangsan Mountain, the Haegeumgang River, and the eight scenic views of Gwandong regions, as well as fifty-one pieces of writing. It is a rare example in terms of its size and painting style. The paintings in this album, which are densely packed with natural features, follow the painting style of the Southern School yet employ crude and unconventional elements. In them, stones on the mountains are depicted both geometrically and three-dimensionally. Since 1973, parts of this album have been published in some exhibition catalogues. The entire album was opened to the public at the special exhibition "Through the Eyes of Joseon Painters: Real Scenery Landscapes of Korea" held at the National Museum of Korea in 2019. The Album of Complete Views of Seas and Mountains was attributed to Kim Eung-hwan (1742-1789) due to the signature on the final leaf of the album and the seal reading "Bokheon(painter's penname)" on the currently missing album leaf of Chilbodae Peaks. However, there is a strong possibility that this signature and seal may have been added later. This paper intends to reexamine the creator of this album based on a variety of related factors. In order to understand the production background of Album of Complete Views of Seas and Mountains, I investigated the eighteenth-century tradition of drawing scenic spots while travelling in which scenery of was depicted during private travels or official excursions. Jeong Seon(1676-1759), Sim Sa-jeong(1707-1769), Kim Yun-gyeom(1711-1775), Choe Buk(1712-after 1786), and Kang Se-hwang(1713-1791) all went on a journey to Geumgangsan Mountain, the most famous travel destination in the late Joseon period, and created paintings of the mountain, including Album of Pungak Mountain in the Sinmyo Year(1711) by Jeong Seon. These painters presented their versions of the traditional scenic spots of Inner Geumgangsan and newly depicted vistas they discovered for themselves. To commemorate their private visits, they produced paintings for their fellow travelers or sponsors in an album format that could include several scenes. While the production of paintings of private travels to Geumgangsan Mountain increased, King Jeongjo(r. 1776-1800) ordered Kim Eung-hwan and Kim Hong-do, court painters at the Dohwaseo(Royal Bureau of Painting), to paint scenic spots in the nine counties of the Yeongdong region and around Geumgangsan Mountain. King Jeongjo selected these two as the painters for the official excursion taking into account their relationship, their administrative experience as regional officials, and their distinct painting styles. Starting in the reign of King Yeongjo(r. 1724-1776), Kim Eung-hwan and Kim Hong-do served as court painters at the Dohwaseo, maintained a close relationship as a senior and a junior and as colleagues, and served as chalbang(chief in large of post stations) in the Yeongnam region. While Kim Hong-do was proficient at applying soft and delicate brushstrokes, Kim Eung-hwan was skilled at depicting the beauty of robust and luxuriant landscapes. Both painters produced about 100 scenes of original drawings over fifty days of the official excursion. Based on these original drawings, they created around seventy album leaves or handscrolls. Their paintings enriched the tradition of depicting scenic spots, particularly Outer Inner Geumgang and the eight scenic views of Gwandong around Geumgangsan Mountain during private journeys in the eighteenth century. Moreover, they newly discovered places of scenic beauty in the Outer Geungang and Yeongdong regions, establishing them as new painting themes. The Album of Complete Views of Seas and Mountains consists of four volumes. The volumes I, II include twenty-nine paintings of Inner Geumgangsan; the volume III, seventeen scenes of Outer Geumgangsan; and the volume IV, fourteen images of Maritime Geumgangsan and the eight scenic views of Gwandong. These paintings produced on silk show crowded compositions, geometrical depictions of the stones and the mountains, and distinct presentation of the rocky peaks of Geumgangsan Mountain using white and grayish-blue pigments. This album reflects the Joseon painting style of the mid- and late eighteenth century, integrating influences from Jeong Seon, Kang Se-hwang, Sim Sa-jeong, Jeong Chung-yeop(1725-after 1800), and Kim Hong-do. In particular, some paintings in the album show similarities to Kim Hong-do's Album of Famous Mountains in Korea in terms of its compositions and painterly motifs. However, "Yeongrangho Lake," "Haesanjeong Pavilion," and "Wolsongjeong Pavilion" in Kim Eung-hwan's album differ from in the version by Kim Hong-do. Thus, Kim Eung-hwan was influenced by Kim Hong-do, but produced his own distinctive album. The Album of Complete Views of Seas and Mountains includes scenery of "Jaundam Pool," "Baegundae Peak," "Viewing Birobong Peak at Anmunjeom groove," and "Baekjeongbong Peak," all of which are not depicted in other albums. In his version, Kim Eung-hwan portrayed the characteristics of the natural features in each scenic spot in a detailed and refreshing manner. Moreover, he illustrated stones on the mountains using geometric shapes and added a sense of three-dimensionality using lines and planes. Based on the painting traditions of the Southern School, he established his own characteristics. He also turned natural features into triangular or rectangular chunks. All sixty paintings in this album appear rough and unconventional, but maintain their internal consistency. Each of the fifty-one writings included in the Album of Complete Views of Seas and Mountains is followed by a painting of a scenic spot. It explains the depicted landscape, thus helping viewers to understand and appreciate the painting. Intimately linked to each painting, the related text notes information on traveling from one scenic spot to the next, the origins of the place names, geographic features, and other related information. Such encyclopedic documentation began in the early nineteenth century and was common in painting albums of Geumgangsan Mountain in the mid- nineteenth century. The text following the painting of Baekhwaam Hermitage in the Album of Complete Views of Seas and Mountains documents the reconstruction of the Baekhwaam Hermitage in 1845, which provides crucial evidence for dating the text. Therefore, the owner of the Album of Complete Views of Seas and Mountains might have written the texts or asked someone else to transcribe them in the mid- or late nineteenth century. In this paper, I have inferred the producer of the Album of Complete Views of Seas and Mountains to be Kim Eung-hwan based on the painting style and the tradition of drawing scenic spots during official trips. Moreover, its affinity with the Handscroll of Pungak Mountain created by Kim Ha-jong(1793-after 1878) after 1865 is another decisive factor in attributing the album to Kim Eung-hwan. In contrast to the Album of Famous Mountains in Korea by Kim Hong-do, the Album of Complete Views of Seas and Mountains exerted only a minor influence on other painters. The Handscroll of Pungak Mountain by Kim Ha-jong is the sole example that employs the subject matter from the Album of Complete Views of Seas and Mountains and follows its painting style. In the Handscroll of Pungak Mountain, Kim Ha-jong demonstrated a painting style completely different from that in the Album of Seas and Mountains that he produced fifty years prior in 1816 for Yi Gwang-mun, the magistrate of Chuncheon. He emphasized the idea of "scholar thoughts" by following the compositions, painterly elements, and depictions of figures in the painting manual style from Kim Eung-hwan's Album of Complete Views of Seas and Mountains. Kim Ha-jong, a member of the Gaeseong Kim clan and the eldest grandson of Kim Eung-hwan, is presumed to have appreciated the paintings depicted in the nature of Album of Complete Views of Seas and Mountains, which had been passed down within the family, and newly transformed them. Furthermore, the contents and narrative styles of Yi Yu-won's writings attached to the paintings in the Handscroll of Pungak Mountain are similar to those of the fifty-one writings in Kim Eunghwan's album. This suggests a possible influence of the inscriptions in Kim Eung-hwan's album or the original texts from which these inscriptions were quoted upon the writings in Kim Ha-jong's handscroll. However, a closer examination will be needed to determine the order of the transcription of the writings. The Album of Complete View of Seas and Mountains differs from Kim Hong-do's paintings of his official trips and other painting albums he influenced. This album is a siginificant artwork in that it broadens the understanding of the art world of Kim Eung-hwan and illustrates another layer of real scenery landscape paintings in the late eighteenth century.