151:. He says, "I find objectionable: first, vague generalizations, entirely undocumented, concerning views held by 'modernists', and second, the inferences drawn from what has not been said by the 'modernists'." By 1966, Kline proposed an eight-page high school plan. The rebuttal for this article was by James H. Zant; it asserted that Kline had "a general lack of knowledge of what was going on in schools with reference to textbooks, teaching, and curriculum." Zant criticized Kline's writing for "vagueness, distortion of facts, undocumented statements and overgeneralization."
232:. Pollard conceded, "The society in which learning is admired and pursued for its own sake has disappeared." The Hilton review was more direct: Kline has "placed in the hand of enemies… weapon". Having started in 1956 as an agitator for change in mathematics education, he became a critic of some trends. Skilled expositor that he was, editors frequently felt his expressions were best tempered with rebuttal.
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was titled "Mathematical texts and teachers: a tirade". Calling out teachers who blame students for their failures, he wrote "There is a student problem, but there are also three other factors which are responsible for the present state of mathematical learning, namely, the curricula, the texts, and
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I would urge every teacher to become an actor. His classroom technique must be enlivened by every device used in theatre. He can be and should be dramatic where appropriate. He must not only have facts but fire. He can utilize even eccentricities of behavior to stir up human interest. He should not
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I am wondering whether in point of fact, Professor Kline really likes mathematics I think that he is at heart a physicist, or perhaps a 'natural philosopher', not a mathematician, and that the reason he does not like the proposals for orienting the secondary school college preparatory mathematics
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the teachers." The tirade touched a nerve, and changes started to happen. But then Kline switched to being a critic of some of the changes. In 1958, he wrote "Ancients versus moderns: a new battle of the books". The article was accompanied by a rebuttal by Albert E. Meder Jr. of
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that characterizes good teaching. He lauds scholarship as expressed by expository writing or reviews of original work of others. For scholarship, he expects critical attitudes to topics, materials and methods. Among the rebuttals are those by D.T. Finkbeiner, Harry
Pollard, and
248:'s recommendation to combine science and mathematics at the high school level. But a closer reading shows Kline calling mathematics a "part of man's efforts to understand and master his world", and he sees that role in a broad spectrum of sciences.
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curriculum to the diverse needs of the twentieth century by making use of some concepts developed in mathematics in the last hundred years or so is not that this is bad mathematics, but that it minimizes the importance of physics.
104:. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on
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was being conducted, complaining that often mathematicians, are not willing to become acquainted with the (sometimes deep) context needed to solve applied problems in sciences, prefer to invent
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posed in other fields rather than building structures of interest only to other mathematicians. One can get a sense of Kline's views on teaching from the following:
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in 1952. He taught at New York
University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly
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62:, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate (Ph.D.) in 1936. He continued at NYU as an instructor until 1942.
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Morris Kline, a renowned mathematician, talks about concepts of mathematics, the new math, and God in a vintage interview
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be afraid of humor and should use it freely. Even an irrelevant joke or story perks up the class enormously.
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that occurred in the second half of the twentieth century, a period including the programs of the
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In considering what motivated Morris Kline to protest, consider
Professor Meder's opinion:
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Mathematics: An
Introduction to Its Spirit and Use; readings from Scientific American
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Why the
Professor Can't Teach: Mathematics and the Dilemma of University Education
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489:(2008). "Morris Kline". In Donald J. Albers; Gerald L. Alexanderson (eds.).
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problems that are not necessarily of any consequence. Kline also blamed the
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education; he took on the academic mathematics establishment with his
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626:"Morris Kline, 84, Math Professor And Critic of Math Teaching, Dies"
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M. Kline (1966) "Intellectuals and the schools: a case history" in
262:(ch. XIII: "The Isolation of Mathematics"), Kline deplored the way
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Mathematics in the Modern World; readings from
Scientific American
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Why the
Professor Can't Teach: The Dilemma of University Education
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of instruction as students' intuitions are challenged by the new
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In 1966 and 1970, Kline issued two further criticisms. In 1973,
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Kline resumed his mathematical teaching at NYU, becoming a full
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who sought to unify the subject through its general concepts:
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contributed to the dialogue by publishing Kline's critique,
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Secondary School
Mathematics Curriculum Improvement Study
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was developed. After the war, he continued investigating
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D.T. Finkbeiner, Harry
Pollard, Peter Hilton (May 1979)
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Why Johnny Can't Add: The
Failure of the New Mathematics
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American mathematician, teacher and author (1908–1992)
38:, and also a popularizer of mathematical subjects.
732:Courant Institute of Mathematical Sciences faculty
215:. Kline argues that the onus on professors in the
727:Courant Institute of Mathematical Sciences alumni
377:Mathematical Thought From Ancient to Modern Times
161:Why Johnny Can't Add: the Failure of the New Math
22:(May 1, 1908 – June 10, 1992) was a professor of
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742:Institute for Advanced Study visiting scholars
328:Electromagnetic Theory and Geometrical Optics
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767:United States Army personnel of World War II
491:Mathematical People: Profiles and Interviews
336:Calculus, An intuitive and Physical Approach
274:academic culture for this state of affairs.
646:A website having links to two of his books
568:M. Kline (1970) "Logic versus pedagogy" in
291:(with Irvin W. Kay), Houghton Mifflin, 1937
172:. The book recapitulates the debates from
91:Courant Institute of Mathematical Sciences
81:, he worked in the engineering lab where
452:Mathematics and the Search for Knowledge
355:, Addison-Wesley, 1967, (republished as
686:MacTutor History of Mathematics Archive
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207:In 1977, Kline turned to undergraduate
58:in Brooklyn, he studied mathematics at
128:Morris Kline was a protagonist in the
244:It might appear so, as Kline recalls
46:Kline was born to a Jewish family in
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757:Mathematicians from New York (state)
717:20th-century American mathematicians
357:Mathematics for the Nonmathematician
321:Mathematics for the Nonmathematician
297:(ed), Inter-science Publishers, 1951
359:, Dover Publications, Inc., 1985) (
338:, John Wiley and Sons, 1967, 1977,
295:The Theory of Electromagnetic Waves
752:Boys High School (Brooklyn) alumni
737:American historians of mathematics
722:Jewish American military personnel
406:Mathematics: The Loss of Certainty
308:Mathematics and the Physical World
259:Mathematics: The Loss of Certainty
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455:, Oxford University Press, 1985 (
417:); OUP Galaxy Books pb. reprint (
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373:(ed), W. H. Freeman and Co., 1968
140:. An article by Kline in 1956 in
124:Critique of mathematics education
71:Signal Corps (United States Army)
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315:Mathematics, A Cultural Approach
252:Critique of mathematics research
665:A wide-ranging 2016 interview:
656:Pea Soup, Tripe and Mathematics
379:, Oxford University Press, 1972
371:Mathematics in the Modern World
303:, Oxford University Press,1953
301:Mathematics in Western Culture
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652:Why The Professor Can't Teach
583:American Mathematical Monthly
570:American Mathematical Monthly
624:Pace, Eric (June 11, 1992).
393:, St. Martin's Press, 1977 (
353:Mathematics for Liberal Arts
332:, John Wiley and Sons, 1965
289:Introduction to Mathematics
164:. Its opening chapter is a
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762:20th-century American Jews
557:Harvard Educational Review
387:, St. Martin's Press, 1973
323:, Dover Publications, 1967
69:, Kline was posted to the
497:, Ltd. pp. 173–183.
311:, T. Y. Crowell Co., 1959
54:. After graduating from
691:University of St Andrews
531:The Mathematics Teacher
143:The Mathematics Teacher
102:teaching of mathematics
36:teaching of mathematics
440:The Language of Shapes
317:, Addison-Wesley, 1962
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648:Why Johnny Can't Add?
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134:mathematics education
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607:Why Johnny Can’t Add
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42:Education and career
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654:, a lecture titled
595:Mathematics Teacher
544:Mathematics Teacher
518:Mathematics Teacher
487:Alexanderson, G. L.
330:(with Irvin W. Kay)
178:Columbia University
174:Mathematics Teacher
60:New York University
631:The New York Times
445:Abraham Wolf Crown
340:Dover Publications
156:St. Martin's Press
149:Rutgers University
77:. Designated as a
75:Belmar, New Jersey
26:, a writer on the
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712:1992 deaths
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246:E. H. Moore
219:to conduct
24:mathematics
701:Categories
609:, page 147
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495:A K Peters
468:References
209:university
198:structures
186:operations
132:reform in
130:curriculum
32:philosophy
658:, and an
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473:Citations
194:relations
98:professor
79:physicist
660:obituary
221:research
190:mappings
138:new math
48:Brooklyn
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65:During
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