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      • 개방형 문제를 이용한 학습에 대한 아동의 태도 연구

        배종수,오은영 한국초등수학교육학회 2005 한국초등수학교육학회지 Vol.9 No.1

        21세기는 수학적 사고 신장뿐만 아니라 수학에 대한 긍정적인 가치 인식이 형성되도록 수학교육이 이루어져야 하지만 교육현장에서는 정의적 영역의 중요성이 간과 되어왔다. 따라서 본 연구는 다양한 방법과 전략을 사용하여 여러 가지 정답을 산출할 수 있는 개방형 문제를 이용한 학습에 대해 아동이 어떠한 태도를 보이는지 연구하였다. 개방형 학습에 대한 아동들의 태도를 관찰과 면담, 설문조사를 통해 분석한 결과 아동들은 수학에 대한 흥미와 자신감이 생기고 성취감을 느껴 수업에 집중하였다. 또한 토의학습을 통해 서로 상대방의 능력을 존중하는 태도를 형성하며 교과서 문제를 변형시킨 개방형 문제에 자신 있게 반응하고 수학을 바라보는 태도에서 발전적인 모습을 보였다. 본 연구 결과 수학에 대한 긍정적이 태도를 형성하기 위해서는 교과서 문제를 개방형 문제로 변형시켜 현장에 적용하려는 노력이 필요하다. The purpose of this study is to transform questions in the 7th curriculum to open-ended problems and exam students' attitude towards open-ended problems. Research questions in this thesis are as follows: First, to transform questions in the 7th curriculum to open-ended problems and apply to a class in the fourth grade D elementary school. Second, to find how students respond to learning mathematics with open-ended problems. As a result of this study, the following are identified. First, the students showed positive reactions towards learning mathematics with open-ended problems. Those experience with open-ended problems make student solve mathematics problems with interest and confidence. Second, both good and bad students in the math class show interest and concentration toward open-ended problem. But a few students show less interest towards those problems. Third, through discussion about problem-solving with open-ended problems, students take part in math class actively and show respect one another. Fourth, especially students show more interest and confidence towards the open-ended problems transformed from mathematics textbook and like the constructive open-ended problems.

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        구 라틴 역과 벌게잇 역에 나타난 막 16:9-20의 진정성

        배종수 서울신학대학교 2005 神學과 宣敎 Vol.31 No.-

        I have proved that Mark had written Mk 16:9-20. The treatises are "A Positive Reconsideration on Mark 16:9-20: centering around its Terms, Styles, and Contents)," Theology and Mission. vol. 28(Seoul Theological University, 2003): 73-105: "Can Mark as a Book End with 'Yap'?-A Criticism on Quotations of Ancient Greek Literature," A Collection of Treatises, Vol. 14(STU, 2003): 287-322: "Genuineness of Mark 16:9-20 in the Church Fathers' Writings," Theology and Mission. vol. 30(STU, 2004): 155-89: "A Study on the Loss of Mark 16:9-20)," A Collection of Treatises, vol. 15(STU, 2004): 43-64: "Possibilities of Some Scribes of Alexandrian school's Omission of Mark 16:9-20 from // and B in the Eusebian Scriptorium.)," A Collection of Treatises. vol. 16(STU, 2004): 243-282. I tried to confirm the genuinenss of Mk 16:9-20 in the paper, studying that it existed originally in manuscripts a, k, b and the Vulgate. Metzger and Willker rejected Mark's authenticity of the long ending through quotation of the "calculation of space" of C. H. Turner(JTS, 29, 1927-28, 16-18). But I pointed out the errors of his "calculation of space" in the thesis. I proved that mark of the manuscript a originally had its long ending, pointing to his mistakes of the "calculation" and their misunderstanding about it through the "re-calculations of space" made by the present writer. Wieland Willker quotes: "C H Turner(JTS 29, 1927-28, 16-18) analyzed codex a(codex Vercellensis, 4th CE) and found the following evidence: The text of the MS ends on f632b with Mk 15:5(sic. Pilatus autem), then four pages are torn away, after that one page has been added(f633) with the Vulgate text of Mk 16:7-20 added by a later hand. Turner now concluded that on the torn away pages the text of Mk 15:5(sic.)-16:7 was originally present. Then the last page got lost and had been replaced by the Vulgate text. If only one more page was originally present after the four torn away pages then one must conclude that either no ending or the short ending was present originally. The one last page is not sufficient to take the long ending."(quotes from www.bautz.de/bbk1/t/turner_c_h.shtml(2005, 1, 20. pp.1-18). But I pointed out in the paper that their points have no basis, because the four torn-away pages can not be sufficient to take Mk 15:15-16:7. And I proved that the "one last page" is sufficient to take the long ending, with the other "one more page" because these two pages can afford Mk 16:7-20, if St. Eusebius, Bishop of Vercelli would write some more letters in only some lines. If codex a and the Vulgate had almost equal letters in equal verses, for examples, John 16:23-30 of the former and the same verses of the latter(actually the Vulgate has 18 more letters), and if every line with letters less than 11 has 11 letters, or every line with letters less than 12 has 12 letters, he could write Mk 16:7-20 in the last two pages(see the appendix and footnote 11. average letters of 48 lines of Jn 16:23-30 in codex a are 10.42; total letters 500.), through the "re-calculations of space" made by me. letters in Mk 16:7-20 of the Vulgate are 1084. The total of the former are 551 letters and the total of the latter are 584. 1084 divided by 551 is 1.967 pages. Then 1084 letters would need 1 page and 47 lines, and leave one line, if 551 per page was written. 1084 divided by 584 equals 1.86 pages. these would need one page and 42 liens, and leave 6 lines. According to the re-calculations of the present writer, we must conclude that 16:7-20 was present originally in the last two pages. Metzger contends according to C. H. Turner: "The last four leaves of the codex(after Mark xv. 15) have been cut out. and then follows a single leaf containing Mark xvi. 7(from the word Galileam) to 20 in a later hand and in the Vulgate text. According to calculation of space made by C. H. Turner, the four excised leaves(maybe 8 pages-the present writer's note) probably did not contain the long ending of Mark. 'unless both very drastic methods of compression were employed in the text itself, and also there was a complete absence of colophon or subscription....[The manuscript] must have had either the shorter ending or none at all."(Metzger, The Early Versions of the New Testament.(1977)312-13). It seems to me that there is a big problem in Turner's "calculation of space" and Metzger's quotation of it and contention. This is what Metzger and Turner explain that the four excised leaves probably did not contain the long ending of Mark. "unless both very drastic methods of compression were employed in the text itself, and also there was a complete absence of colophon of subscription....[The manuscript] must have had either the shorter ending or none at all." I do not agree with them. My re-calculation of space agrees to contain Mk 15:15-16:20 in the four cut leaves. The methods of my recalculation of space are: 1) the number of letter of a page(Jn 16:23-30 in p. 21) of codex Vercellensis(cod. a) is about 500 and the number of letters of same page of the Vulgate 518. The one is 18 letters less than the other. The number on letters in Mk 15:15-16:20 of the Vulgate is 4074. 4074 letters divided by 518 is 7.86 pages. Then 8 pages can be sufficient to take Mk 15:15-16:20 of the Vulgate. The letters of Mark 15:15(after "Pilatus autem")-16:20 are 4074. If its number of letters is on an average 18 letters less than that of the Vulgate per page, the number of letters of Mk 15:15-16:20 in codex Vercellensis is about 3930 letters, because of 4074 letters-(18 x 8 pages)=3930 letters. 3930 letters devided by 500 letters(in page) are 7.86 pages. In other words, 7.86 pages are 7 pages and 42 lines. As methods like above, if every line with letters less than 10 has 10 letters, the total of Jn 16:23-30 are 523. 4074 divided by 523 is 7.79 pages. If 11 letters 7.39 pages, and if 12 letters. 6.98 pages. Therefore our re-calculations prove that St. Eusebius has written Mk 15:15-16:20 of codex a in the four excised leaves, or 8 pages, and that Mk 16:9-20 is originally present at the last 8 pages in codex Vercellensis(a). The text of the extant codex k is 150 years after that of St. Cyprian(d. 200-258). The bishop of Thibaris, Vincentius, gave a word to the 87 African bishops who were present at the seventh synod in Carthage(A.D. 256), convened by Cyprian, quoting and fusing Mk 16:15, 17, and 18. According to the local texts of Streeter, Vincentius, Cyprian, and most of the 87 African bishops must have used the acient versions of the extant k. Most of them did not oppose Cyprian and Vincentius. Maybe, that is why most of the bishops had the same texts which was like k, including Mk 16:9-20. Metzger and Higgins(including Klijn) said that Turtullian of Carthage who also quoted Mk 16:19 two times, used a African text. Therefore they must have used k manuscripts, including Mk 16:9-20 and the Markan ending of the extant k must have revised in history of 150 years between Cyprian and A.D. 400. Jerome included the long ending in his revised edition, the Vulgate. Judging from his principles revising the current Latin version(codex b) in the preface to the four gospels, I think that Mark 16:9-20 was present originally in codex Veronensis (b) and the many Greek manuscripts "apparently belonged to the Alexandrian type of text"(Kenyon and Metzger), used as the bases for the revised Vulgate. Jerome emphasizes it through his expressions in the preface, for examples, "...you[Pope Damasus-the present writer's note] would have me decide which of them agree with the Greek original," "If...we are to glean the truth from a comparison of many. why not go back to the original Greek and correct the mistakes introduced by inaccurate translators, and the blundering alterations of confident but ignorant critics, and further, all that has been inserted or changed by copyists more asleep than awake?" "Matthew, Mark, Luke. John. as they have been revised by a comparison of the Greek manuscripts." "...While I have corrected only such passages as seemed to convey a different meaning. I have allowed the rest to remain as they are." His conservatism to keep correct meaning of the codex b and desire for revising incorrect meanings according to "apparently belonged to the Alexandrian type of text"(Kenyon and Metzger) demonstrate that the Markan longer ending existed in the codex b and the Greek original.

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