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Analysis of the Algebraic Thinking Factors and Search for the Direction of Its Learning and Teaching (대수의 사고 요소 분석 및 학습-지도 방안의 탐색)

  • Woo, Jeong-Ho;Kim, Sung-Joon
    • Journal of Educational Research in Mathematics
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    • v.17 no.4
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    • pp.453-475
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    • 2007
  • School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

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Isolation of an Anticariogenic Compound from Magnoliae Bark (후박피(Magnoliae bark)로부터 항충치활성을 갖는 물질의 분리)

  • Lee, Youn-Soo;Park, Hun-Joo;You, Jae-Sun;Park, Hyung-Hwan;Kwon, Ik-Boo;Lee, Hyeon-Yong
    • Korean Journal of Food Science and Technology
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    • v.30 no.1
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    • pp.230-236
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    • 1998
  • We have screened total 32 herbal drugs to find the highest activity against human cariogenic enzyme, glucosyltransferase (GTase) from the extracts of Magnoliae bark. The extracts were separated into three phases, i. e. water, n-butanol and ethylacetate according to their solvent polarity. Among them, ethylacetate fraction had approximately more than 70% of total activities, and the active principle was further isolated by prep. HPLC following silicagel column chromatography to yield single compound as white powder. The chemical structure of the compound was finally elucidated to be 4,4'-dihydroxy-3,3'-dimethoxylignan from the spectral data of FAB-MS. $^1H-\;and\;^{13}C-NMR$ spectrometries. The compound was also shown to have relatively strong antibacterial activity against ten types of cariogenic oral bacteria and one kind of Actinomyces sp.

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Hybrid MBE Growth of Crack-Free GaN Layers on Si (110) Substrates

  • Park, Cheol-Hyeon;O, Jae-Eung;No, Yeong-Gyun;Lee, Sang-Tae;Kim, Mun-Deok
    • Proceedings of the Korean Vacuum Society Conference
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    • 2013.02a
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    • pp.183-184
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    • 2013
  • Two main MBE growth techniques have been used: plasma-assisted MBE (PA-MBE), which utilizes a rf plasma to supply active nitrogen, and ammonia MBE, in which nitrogen is supplied by pyrolysis of NH3 on the sample surface during growth. PA-MBE is typically performed under metal-rich growth conditions, which results in the formation of gallium droplets on the sample surface and a narrow range of conditions for optimal growth. In contrast, high-quality GaN films can be grown by ammonia MBE under an excess nitrogen flux, which in principle should result in improved device uniformity due to the elimination of droplets and wider range of stable growth conditions. A drawback of ammonia MBE, on the other hand, is a serious memory effect of NH3 condensed on the cryo-panels and the vicinity of heaters, which ruins the control of critical growth stages, i.e. the native oxide desorption and the surface reconstruction, and the accurate control of V/III ratio, especially in the initial stage of seed layer growth. In this paper, we demonstrate that the reliable and reproducible growth of GaN on Si (110) substrates is successfully achieved by combining two MBE growth technologies using rf plasma and ammonia and setting a proper growth protocol. Samples were grown in a MBE system equipped with both a nitrogen rf plasma source (SVT) and an ammonia source. The ammonia gas purity was >99.9999% and further purified by using a getter filter. The custom-made injector designed to focus the ammonia flux onto the substrate was used for the gas delivery, while aluminum and gallium were provided via conventional effusion cells. The growth sequence to minimize the residual ammonia and subsequent memory effects is the following: (1) Native oxides are desorbed at $750^{\circ}C$ (Fig. (a) for [$1^-10$] and [001] azimuth) (2) 40 nm thick AlN is first grown using nitrogen rf plasma source at $900^{\circ}C$ nder the optimized condition to maintain the layer by layer growth of AlN buffer layer and slightly Al-rich condition. (Fig. (b)) (3) After switching to ammonia source, GaN growth is initiated with different V/III ratio and temperature conditions. A streaky RHEED pattern with an appearance of a weak ($2{\times}2$) reconstruction characteristic of Ga-polarity is observed all along the growth of subsequent GaN layer under optimized conditions. (Fig. (c)) The structural properties as well as dislocation densities as a function of growth conditions have been investigated using symmetrical and asymmetrical x-ray rocking curves. The electrical characteristics as a function of buffer and GaN layer growth conditions as well as the growth sequence will be also discussed. Figure: (a) RHEED pattern after oxide desorption (b) after 40 nm thick AlN growth using nitrogen rf plasma source and (c) after 600 nm thick GaN growth using ammonia source for (upper) [110] and (lower) [001] azimuth.

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RHEOLOGIC STUDY ON THE VISCOELASTIC PROPERTIES OF FLOWABLE AND CONDENSABLE RESIN COMPOSITES (유동성 및 응축성 복합레진의 점탄성에 관한 유변학적 연구)

  • Lee, In-Bog;Cho, Byeong-Hoon;Son, Ho-Hyun;Kwon, Hyuk-Choon;Um, Chung-Moon
    • Restorative Dentistry and Endodontics
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    • v.25 no.3
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    • pp.359-370
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    • 2000
  • The purpose of this investigation was to observe the viscoelastic properties of five commercial flowable(Aeliteflo, Flow it, Revolution, Tetric flow, Compoglass flow), three conventional hybrid(Z-100, Z-250, P-60) and two condensable(Synergy compact, SureFil) resin composites. A dynamic oscillatory shear test was done to evaluate the storage shear modulus (G'), loss shear modulus(G"), loss tangent(tan ${\delta}$) and complex viscosity(${\eta}^*$) of the resin composites as a function of frequency - dynamic frequency sweep test from 0.01 to 100 rad/s at $25^{\circ}C$ - by using Advanced Rheometric Expansion System(ARES). To investigate the effect on the viscosity of resin composites of filler volume fraction, the filler weight % and volume % were measured by means of Archimedes' principle using a pyknometer. The results were as follows 1. The complex viscosity ${\eta}^*$ of flowable resins was lower than that of hybrid resins and significant differences were observed between brands. The complex viscosity ${\eta}^*$ of condensable resins was higher than that of hybrid resins. The order of complex viscosity ${\eta}^*$ at ${\omega}$=10 rad/s was as follows, Surefil, Synergy compact, P-60, Z-250, Z-100, Aeliteflo, Tetric flow, Compoglass flow, Flow it, Revolution. The relative complex viscosity of flowable resins compared to Z-100 was 0.04~0.56 but Surefil was 30.4 times higher than that of Z-100. 2. The storage shear modulus G' and the loss shear modulus G" of flowable resins were lower than those of hybrid resins but those of condensable resins were higher. The patterns of the change of loss tangent, tan ${\delta}$, of resin composites with increasing frequency were significantly different between brands. The phase angles, ${\delta}$, ranged from $30.2{\sim}78.1^{\circ}$ at ${\omega}$=10 rad/s. 3. All composite resins represent pseudoplastic nature with increasing shear rate. 4. The complex shear modulus $G^*$ and the phase angle ${\delta}$ was represented by the frequency domain phasor form, $G^*({\omega})=G^*e^{i{\delta}}=G^*{\angle}{\delta}$. The locus of frequency domain phasor plots in a complex plane was a valuable method that represent the viscoelastic properties of composite resins. 5. There was no direct linear correlationship but a weak positive relation was observed between filler volume % or weight % and the viscosity of the resin composites.

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The effect analysis of birefringence of plastic f$\heta$ Iens on the beam diameter (플라스틱 f$\heta$렌즈의 복굴절이 결상빔경에 미치는 영향분석)

  • 임천석
    • Korean Journal of Optics and Photonics
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    • v.11 no.2
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    • pp.73-79
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    • 2000
  • We measure a beam diameter of scan and sub-scan direction of LSD (Laser Scanning Urnt) which uses $fheta$ lens produced by injecLion molding method as a scanning lens. While the measured beam diameter in scan direction, which is $62muextrm{m}$ to $68\mu\textrm{m}$, shows similar size comparing to the design beam diameter, the sub-scan beam diameter shows sIzable beam diameter deviation as much as 37 11m ranging from $78\mu\textrm{m}$ to $115\mu\textrm{m}$. Injection molding lens has the surface figure error due to the shrinkage III the cooling time and the internal distortion (birefringence) due to the uneven cooling conditIOn so that these bring about wavefront aberration (i.e., the enlargement of beam size), and are eventually expre~sed as the deterioration of the pdnting image. In this paper. we first measure and analyze beam diameter, birefringence (polanzation ratio), and asphedcal figure error of mIens in order to know the principle cause of the beam diameter deviation in sub-scan directIOn. And Lhen. through the analysis of a designed depth of focus and a calculated field curvature (imaging position of the optical axis directIon) using the above figure elTor data, we know Lhat the birefringence IS the main factor of sizable beam diameter deVIation in sub-scan direction. ction.

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An Analysis of Students' Mathematical Communication Competency focused on Fraction Division (분수의 나눗셈에 대한 초등학생의 수학적 의사소통 능력 분석)

  • Pang, Jeong Suk;Kim, Yoon Young;Sunwoo, Jin
    • Education of Primary School Mathematics
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    • v.25 no.2
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    • pp.179-195
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    • 2022
  • Mathematical communication competency, one of the six mathematical competencies emphasized in the latest mathematics curriculum, plays an important role both as a means and as a goal for students to learn mathematics. Therefore, it is meaningful to find instructional methods to improve students' mathematical communication competency and analyze their communication competency in detail. Given this background, this study analyzed 64 sixth graders' mathematical communication competency after they participated in the lessons of fraction division emphasizing mathematical communication. A written assessment for this study was developed with a focus on the four sub-elements of mathematical communication (i.e., understanding mathematical representations, developing and transforming mathematical representations, representing one's ideas, and understanding others' ideas). The results of this study showed that students could understand and represent the principle of fraction division in various mathematical representations. The students were more proficient in representing their ideas with mathematical expressions and solving them than doing with visual models. They could use appropriate mathematical terms and symbols in representing their ideas and understanding others' ideas. This paper closes with some implications on how to foster students' mathematical communication competency while teaching elementary mathematics.

Effects of Iterative Reconstruction Algorithm, Automatic Exposure Control on Image Quality, and Radiation Dose: Phantom Experiments with Coronary CT Angiography Protocols (반복적 재구성 알고리즘과 관전류 자동 노출 조정 기법의 CT 영상 화질과 선량에 미치는 영향: 관상동맥 CT 조영 영상 프로토콜 기반의 팬텀 실험)

  • Ha, Seongmin;Jung, Sunghee;Chang, Hyuk-Jae;Park, Eun-Ah;Shim, Hackjoon
    • Progress in Medical Physics
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    • v.26 no.1
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    • pp.28-35
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    • 2015
  • In this study, we investigated the effects of an iterative reconstruction algorithm and an automatic exposure control (AEC) technique on image quality and radiation dose through phantom experiments with coronary computed tomography (CT) angiography protocols. We scanned the AAPM CT performance phantom using 320 multi-detector-row CT. At the tube voltages of 80, 100, and 120 kVp, the scanning was repeated with two settings of the AEC technique, i.e., with the target standard deviations (SD) values of 33 (the higher tube current) and 44 (the lower tube current). The scanned projection data were reconstructed also in two ways, with the filtered back projection (FBP) and with the iterative reconstruction technique (AIDR-3D). The image quality was evaluated quantitatively with the noise standard deviation, modulation transfer function, and the contrast to noise ratio (CNR). More specifically, we analyzed the influences of selection of a tube voltage and a reconstruction algorithm on tube current modulation and consequently on radiation dose. Reduction of image noise by the iterative reconstruction algorithm compared with the FBP was revealed eminently, especially with the lower tube current protocols, i.e., it was decreased by 46% and 38%, when the AEC was established with the lower dose (the target SD=44) and the higher dose (the target SD=33), respectively. As a side effect of iterative reconstruction, the spatial resolution was decreased by a degree that could not mar the remarkable gains in terms of noise reduction. Consequently, if coronary CT angiogprahy is scanned and reconstructed using both the automatic exposure control and iterative reconstruction techniques, it is anticipated that, in comparison with a conventional acquisition method, image noise can be reduced significantly with slight decrease in spatial resolution, implying clinical advantages of radiation dose reduction, still being faithful to the ALARA principle.

The educational activities of Donam Seowon (돈암서원의 강학 활동)

  • Kim, Moon Joon
    • The Journal of Korean Philosophical History
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    • no.58
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    • pp.161-199
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    • 2018
  • The contents and method of education of all Korean scholars are similar to the contents and method of education provided by Zhu Xi(朱熹), but they operated in a somewhat different way according to schools. Those who served as the first directors of Donam Seowon were Kim Gip(金集, 1574~1656), Song Joon-gil(宋浚吉, 1606~1672) and Song Si-yeol(宋時烈, 1607~1689), who were the writers of Kim Jang-saeng(金長生, 1548~1631). Donam Seowon is supposed to have weakened the status of scholarship and the activities of lectures as HwaYang Seowon and Seoksil Seowon, which principals were all the Noron(老論) scholars, grew to be the center of education institution of the Noron. Donam Seowon have not preserved the school regulations. But the way of operating system of Donam Seowon can be guessed through the letter of Song Joon-gil, who was the headmaster of the late 17th century on the whole operation of Donam Seowon. From this letter, it is assumed that the school of Donam Seowon is similar to the 'Unbyoung-Jungsa regulations' written by Lee Yi(李珥). The headmasters of Donam Seowon was the Noron scholars. And scholars of the Kim Chang-hyeop(金昌協, 1651~1708) school became headmasters more than the scholars of Kwon Sang-ha(權尙夏, 1641~1721) school. Headmasters of the Donam Seowon had served as the headmasters of HwaYang Seowon and Seoksil Seowon also. In the early days of the establishment of the Donam Seowon, the lecture activities conducted in Donam Seowon were preceded by the textbooks of Kim Jang-saeng/Song Si-yeol's teaching curriculum and neo-confucian books[i.e Sohak (小學)${\rightarrow}$Family Ritual(家禮)${\rightarrow}$Simkyong(心經)${\rightarrow}$Keunsarok(近思錄). It is assumed that the scholars of Seoksil Seowon, who was a Noron Nak-ron(洛論) scholars, gradually adopted Lee Yi's teaching curriculum[i.e, Sohak(小學)${\rightarrow}$Sasoe(四書)${\rightarrow}$Okyoung(五經)]. This lecture contents and procedure was contents and procedure of the Seoksil Seowon, established and operated by the scholars of the Kim Chang-hyeop school. Entrance qualification of Donam Seowon's did not place importance on the social status, but on scholarship and personality. The examination for a high-ranking government official was not allowed. Although the principle, students had to participate in the lecture and study(講學), they were living in Seowon, while the financial and operating of the Seowon became increasingly difficult, the students were changed to participate in the conference(講會) held twice a month while studying at their homes.

A New Item Recommendation Procedure Using Preference Boundary

  • Kim, Hyea-Kyeong;Jang, Moon-Kyoung;Kim, Jae-Kyeong;Cho, Yoon-Ho
    • Asia pacific journal of information systems
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    • v.20 no.1
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    • pp.81-99
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    • 2010
  • Lately, in consumers' markets the number of new items is rapidly increasing at an overwhelming rate while consumers have limited access to information about those new products in making a sensible, well-informed purchase. Therefore, item providers and customers need a system which recommends right items to right customers. Also, whenever new items are released, for instance, the recommender system specializing in new items can help item providers locate and identify potential customers. Currently, new items are being added to an existing system without being specially noted to consumers, making it difficult for consumers to identify and evaluate new products introduced in the markets. Most of previous approaches for recommender systems have to rely on the usage history of customers. For new items, this content-based (CB) approach is simply not available for the system to recommend those new items to potential consumers. Although collaborative filtering (CF) approach is not directly applicable to solve the new item problem, it would be a good idea to use the basic principle of CF which identifies similar customers, i,e. neighbors, and recommend items to those customers who have liked the similar items in the past. This research aims to suggest a hybrid recommendation procedure based on the preference boundary of target customer. We suggest the hybrid recommendation procedure using the preference boundary in the feature space for recommending new items only. The basic principle is that if a new item belongs within the preference boundary of a target customer, then it is evaluated to be preferred by the customer. Customers' preferences and characteristics of items including new items are represented in a feature space, and the scope or boundary of the target customer's preference is extended to those of neighbors'. The new item recommendation procedure consists of three steps. The first step is analyzing the profile of items, which are represented as k-dimensional feature values. The second step is to determine the representative point of the target customer's preference boundary, the centroid, based on a personal information set. To determine the centroid of preference boundary of a target customer, three algorithms are developed in this research: one is using the centroid of a target customer only (TC), the other is using centroid of a (dummy) big target customer that is composed of a target customer and his/her neighbors (BC), and another is using centroids of a target customer and his/her neighbors (NC). The third step is to determine the range of the preference boundary, the radius. The suggested algorithm Is using the average distance (AD) between the centroid and all purchased items. We test whether the CF-based approach to determine the centroid of the preference boundary improves the recommendation quality or not. For this purpose, we develop two hybrid algorithms, BC and NC, which use neighbors when deciding centroid of the preference boundary. To test the validity of hybrid algorithms, BC and NC, we developed CB-algorithm, TC, which uses target customers only. We measured effectiveness scores of suggested algorithms and compared them through a series of experiments with a set of real mobile image transaction data. We spilt the period between 1st June 2004 and 31st July and the period between 1st August and 31st August 2004 as a training set and a test set, respectively. The training set Is used to make the preference boundary, and the test set is used to evaluate the performance of the suggested hybrid recommendation procedure. The main aim of this research Is to compare the hybrid recommendation algorithm with the CB algorithm. To evaluate the performance of each algorithm, we compare the purchased new item list in test period with the recommended item list which is recommended by suggested algorithms. So we employ the evaluation metric to hit the ratio for evaluating our algorithms. The hit ratio is defined as the ratio of the hit set size to the recommended set size. The hit set size means the number of success of recommendations in our experiment, and the test set size means the number of purchased items during the test period. Experimental test result shows the hit ratio of BC and NC is bigger than that of TC. This means using neighbors Is more effective to recommend new items. That is hybrid algorithm using CF is more effective when recommending to consumers new items than the algorithm using only CB. The reason of the smaller hit ratio of BC than that of NC is that BC is defined as a dummy or virtual customer who purchased all items of target customers' and neighbors'. That is centroid of BC often shifts from that of TC, so it tends to reflect skewed characters of target customer. So the recommendation algorithm using NC shows the best hit ratio, because NC has sufficient information about target customers and their neighbors without damaging the information about the target customers.

A Jungian Perspective on 'Spiritual Exercises' of St. Ignatius (이냐시오 '영신수련'에 대한 분석심리학적 고찰)

  • Jung Taek Kim
    • Sim-seong Yeon-gu
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    • v.25 no.1
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    • pp.27-64
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    • 2010
  • The main focus of this article investigates Jung's analytic implications of the Spiritual Exercises by St. Ignatius of Loyola. The Exercises is referred to not only as the tool for transformation that transformed Ignatius from a soldier of the world into a soldier of God and led him to a completely changed life but also as a tool which galvanizes self-realization, i.e., individuation process, in which a faithful experiences the presence of God in his life and is in search for himself in a new way. The interest in the Exercises regarded as a Western version of Yoga of the East which is a tool for transformation led Jung to give a series of 20 lectures on the Exercises in a seminar held in Zurich from 1939 to 1940. Curiosity about Jung's understanding on the Exercises provokes my desire to step into this research. The Exercises is a book for spiritual exercises that prepare and dispose one's soul to rid itself of all disordered attachments and to order one's life. The Exercises is made up of four Weeks. The First begins with 'Principle and Foundation' which illustrates what human beings are created for. It leads retreatants to rid themselves of disordered attachments and to have a new perspective on life by the consideration and contemplation of sins as the subversion of the Principle and Foundation. The Second is the period in which retreatants accept Christ as the Master of their lives through the meditation and contemplation of the life of Christ. In the Third, retreatants take part in the salvation history of Christ not only by actively participating in the Passion of Christ but also by incorporating the Passion into their lives. The Fourth aids retreatants to undergo their transformation and experience it deeply in order to participate in the new life of Christ who by His resurrection overcame death. In conclusion, Jung viewed the Exercises as a Western tool which plays the similar role of Yoga of the East which engenders inner transformation. The four-week-long retreat helps retreatants to meditate on God who unifies everything and is Himself/Herself the perfect union or the unity so that imperfect retreatants are given opportunities to undergo complete metamorphosis into the immortal, indivisible, and impeccable God. Jung understood that this metamorphosis leads human beings to the totality, that is, the genuine self as the image of God. The author interprets that it is the transformation that the Exercises tries to attain, which resonates with individuation, the key element of analytic psychology.