Morris Kline
Encyclopedia
Morris Kline was a Professor of Mathematics
, a writer on the history
, philosophy
, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn
and in Jamaica, Queens
. After graduating from Boys High School
in Brooklyn, he studied mathematics at New York University
, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II
, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey
. Designated a physicist
, he worked in the engineering lab where RADAR
was developed. After the war he continued investigating electromagnetism
, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences
.
Kline resumed his mathematical teaching at NYU, becoming a full professor
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 mathematics teaching. 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 solving problems 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:
Morris Kline was a protagonist in the curriculum
reform in mathematics education that occurred in the second half of the twentieth century, a period including the programs of the new math
. In 1956 Mathematics Teacher magazine published Kline’s "Mathematical texts and teachers: a tirade". Calling out teachers blaming students for 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 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 with a rebuttal by Albert E. Meder Jr. of Rutgers University
. (Mathematics Teacher 51:428 –33). 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 yielded to the pressure to propose something positive with his eight page high school plan (Mathematics Teacher 59:322–330). The rebuttal for this article was by James H. Zant and asserted that Kline had "a general lack of knowledge of what was going on in schools with reference to textbooks, teaching, and curriculum." He criticized Kline’s writing for "vagueness, distortion of facts, undocumented statements and overgeneralization."
Kline continued his critique of mathematical education with his 1966 article "Intellectuals and the schools: a case history" in Harvard Educational Review
(36:505–11). In 1970 he followed with "Logic versus pedagogy" in American Mathematical Monthly
(77:264–82). In 1973 St. Martin’s Press contributed to the dialogue by publishing Kline’s critique, Why Johnny Can’t Add: the Failure of the New Math. Its opening chapter is a parody
of instruction as students’ intuitions are challenged by the new jargon
. The book recapitulates the debates from Mathematics Teacher, with Kline conceding some progress: He cites Howard Fehr of Columbia University
who sought to unify the subject through its general concepts, sets, operations, mappings, relations, and structure.
In 1977 Kline turned to undergraduate university education; he took on the academic mathematics establishment
with his Why the Professor Can’t Teach: the dilemma of university education. Kline argues that requiring original mathematics from professors distracts them too much from the broad knowledge necessary to teach. 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 of May 1979 in American Mathematical Monthly (86:401–12.) by D.T. Finkbeiner, Harry Pollard, and Peter Hilton
, in which Pollard writes, "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…[a] weapon". Though Kline began, in 1956, with a call to action, once the mobilization was in motion he turned critic. Skilled expositor that he was, editors frequently felt his expressions were best tempered with rebuttal.
In considering what motivated Morris Kline to agitate so much we can look back to Professor Meder’s opinion in Mathematics Teacher 51:433:
It might appear so, as Kline recalls E. H. Moore
’s recommendation to combine science and mathematics at the high school level in his Why Johnny Can’t Add (p. 147). But 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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a writer on the history
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
, philosophy
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn
Brooklyn
Brooklyn is the most populous of New York City's five boroughs, with nearly 2.6 million residents, and the second-largest in area. Since 1896, Brooklyn has had the same boundaries as Kings County, which is now the most populous county in New York State and the second-most densely populated...
and in Jamaica, Queens
Jamaica, Queens
Jamaica is a neighborhood in the borough of Queens in New York City, New York, United States. It was settled under Dutch rule in 1656 in New Netherland as Rustdorp. Under British rule, the Village of Jamaica became the center of the "Town of Jamaica"...
. After graduating from Boys High School
Boys High School
Boys High School is an historic and architecturally notable public school building in the Bedford–Stuyvesant, neighborhood of Brooklyn, New York. It is regarded as "one of Brooklyn's finest buildings.-Architecture:...
in Brooklyn, he studied mathematics at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey
Belmar, New Jersey
Belmar is a borough in Monmouth County, New Jersey, United States. As of the 2010 United States Census, the borough population was 5,794. The Borough of Belmar is governed under the Faulkner Act system of municipal government....
. Designated a physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, he worked in the engineering lab where RADAR
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
was developed. After the war he continued investigating electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
.
Kline resumed his mathematical teaching at NYU, becoming a full professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
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 mathematics teaching. 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 solving problems 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:
Mathematics education
Morris Kline was a protagonist in the curriculum
Curriculum
See also Syllabus.In formal education, a curriculum is the set of courses, and their content, offered at a school or university. As an idea, curriculum stems from the Latin word for race course, referring to the course of deeds and experiences through which children grow to become mature adults...
reform in mathematics education that occurred in the second half of the twentieth century, a period including the programs of the new math
New math
New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S...
. In 1956 Mathematics Teacher magazine published Kline’s "Mathematical texts and teachers: a tirade". Calling out teachers blaming students for 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 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 with a rebuttal by Albert E. Meder Jr. of Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
. (Mathematics Teacher 51:428 –33). 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 yielded to the pressure to propose something positive with his eight page high school plan (Mathematics Teacher 59:322–330). The rebuttal for this article was by James H. Zant and asserted that Kline had "a general lack of knowledge of what was going on in schools with reference to textbooks, teaching, and curriculum." He criticized Kline’s writing for "vagueness, distortion of facts, undocumented statements and overgeneralization."
Kline continued his critique of mathematical education with his 1966 article "Intellectuals and the schools: a case history" in Harvard Educational Review
Harvard Educational Review
The Harvard Educational Review is a peer-reviewed academic journal of opinion and research dealing with education, associated with the Harvard Graduate School of Education, and published by the Harvard Education Publishing Group. The journal was established in 1930.Since 1945, editorial decisions...
(36:505–11). In 1970 he followed with "Logic versus pedagogy" in American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
(77:264–82). In 1973 St. Martin’s Press contributed to the dialogue by publishing Kline’s critique, Why Johnny Can’t Add: the Failure of the New Math. Its opening chapter is a parody
Parody
A parody , in current usage, is an imitative work created to mock, comment on, or trivialise an original work, its subject, author, style, or some other target, by means of humorous, satiric or ironic imitation...
of instruction as students’ intuitions are challenged by the new jargon
Jargon
Jargon is terminology which is especially defined in relationship to a specific activity, profession, group, or event. The philosophe Condillac observed in 1782 that "Every science requires a special language because every science has its own ideas." As a rationalist member of the Enlightenment he...
. The book recapitulates the debates from Mathematics Teacher, with Kline conceding some progress: He cites Howard Fehr of Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
who sought to unify the subject through its general concepts, sets, operations, mappings, relations, and structure.
In 1977 Kline turned to undergraduate university education; he took on the academic mathematics establishment
Academia
Academia is the community of students and scholars engaged in higher education and research.-Etymology:The word comes from the akademeia in ancient Greece. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning...
with his Why the Professor Can’t Teach: the dilemma of university education. Kline argues that requiring original mathematics from professors distracts them too much from the broad knowledge necessary to teach. 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 of May 1979 in American Mathematical Monthly (86:401–12.) by D.T. Finkbeiner, Harry Pollard, and Peter Hilton
Peter Hilton
Peter John Hilton was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War.-Life:Hilton was born in London, and educated at St Paul's School...
, in which Pollard writes, "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…[a] weapon". Though Kline began, in 1956, with a call to action, once the mobilization was in motion he turned critic. Skilled expositor that he was, editors frequently felt his expressions were best tempered with rebuttal.
In considering what motivated Morris Kline to agitate so much we can look back to Professor Meder’s opinion in Mathematics Teacher 51:433:
-
- 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 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.
It might appear so, as Kline recalls E. H. Moore
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
’s recommendation to combine science and mathematics at the high school level in his Why Johnny Can’t Add (p. 147). But 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.
Books
- Introduction to Mathematics (with Irvin W. Kay), Houghton Mifflin, 1937
- The Theory of Electromagnetic Waves (ed), Inter-science Publishers, 1951
- Mathematics in Western Culture, Oxford University Press,1953
- Mathematics and the Physical World, T. Y. Crowell Co., 1959
- Mathematics, A Cultural Approach, Addison-Wesley, 1962
- Electromagnetic Theory and Geometrical Optics (with Irvin W. Kay), John Wiley and Sons, 1965
- Calculus, An intuitive and Physical Approach, John Wiley and Sons, 1967, 1977, Dover Publications 1998 reprint ISBN 0-486-40453-6
- Mathematics for Liberal Arts, Addison-Wesley, 1967, (republished as Mathematics for the Nonmathematician, Dover Publications, Inc., 1985) (ISBN 0-486-24823-2)
- Mathematics in the Modern World (ed), W. H. Freeman and Co., 1968
- Mathematical Thought From Ancient to Modern Times, Oxford University Press, 1972
- Why Johnny Can't Add: The Failure of the New Mathematics, St. Martin's Press, 1973
- Why the professor can't teach: Mathematics and the dilemma of university education, St. Martin's Press, 1977 (ISBN 0-312-87867-2)
- Mathematics: The Loss of CertaintyMathematics: The Loss of CertaintyMathematics: The Loss of Certainty is a book by Morris Kline on the developing perspectives within mathematical cultures throughout the centuries....
, Oxford University Press, 1980 (ISBN 0-19-502754-X); OUP Galaxy Books pb. reprint (ISBN 0-19-503085-0) - Mathematics: An Introduction to Its Spirit and Use; readings from Scientific American
- Mathematics in the Modern World; readings from Scientific American
- The Language of Shapes (with Abraham Wolf Crown)
- Mathematics and the Search for Knowledge