Morris Kline

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Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure, space, and change.

History of mathematics aspect of history

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. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.


Education and career

Kline was born to a Jewish family in Brooklyn and resided 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 (Ph. D) in 1936. He continued at NYU as an instructor until 1942.

Brooklyn Borough in New York City and county in New York state, United States

Brooklyn is the most populous borough of New York City, with an estimated 2,648,771 residents in 2017. Named after the Dutch village of Breukelen, it borders the borough of Queens at the western end of Long Island. Brooklyn has several bridge and tunnel connections to the borough of Manhattan across the East River, and the Verrazzano-Narrows Bridge connects it with Staten Island. Since 1896, Brooklyn has been coterminous with Kings County, the most populous county in the U.S. state of New York and the second-most densely populated county in the United States, after New York County.

Jamaica, Queens Neighborhood of Queens in New York City

Jamaica is a middle-class neighborhood in the New York City borough of Queens. The neighborhood is part of Queens Community Board 12, which also includes Hollis, St. Albans, Springfield Gardens, Baisley Pond Park, Rochdale Village, and South Jamaica. Jamaica is patrolled by the 103rd and 113th Precincts of the New York City Police Department.

New York University private research university in New York, NY, United States

New York University (NYU) is a private research university originally founded in New York City but now with campuses and locations throughout the world. Founded in 1831, NYU's historical campus is in Greenwich Village, New York City. As a global university, students can graduate from its degree-granting campuses in NYU Abu Dhabi and NYU Shanghai, as well as study at its 12 academic centers in Accra, Berlin, Buenos Aires, Florence, London, Los Angeles, Madrid, Paris, Prague, Sydney, Tel Aviv, and Washington, D.C.

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.

World War II 1939–1945 global war

World War II, also known as the Second World War, was a global war that lasted from 1939 to 1945. The vast majority of the world's countries—including all the great powers—eventually formed two opposing military alliances: the Allies and the Axis. A state of total war emerged, directly involving more than 100 million people from over 30 countries. The major participants threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. World War II was the deadliest conflict in human history, marked by 50 to 85 million fatalities, most of whom were civilians in the Soviet Union and China. It included massacres, the genocide of the Holocaust, strategic bombing, premeditated death from starvation and disease, and the only use of nuclear weapons in war.

Signal Corps (United States Army) United States Army division

The United States Army Signal Corps (USASC) is a division of the Department of the Army that creates and manages communications and information systems for the command and control of combined arms forces. It was established in 1860, the brainchild of Major Albert J. Myer, and had an important role in the American Civil War. Over its history, it had the initial responsibility for portfolios and new technologies that were eventually transferred to other U.S. government entities. Such responsibilities included military intelligence, weather forecasting, and aviation.

Belmar, New Jersey Borough in New Jersey

Belmar is a borough in Monmouth County, New Jersey, United States. As of the 2010 United States Census, the borough's population was 5,794, reflecting a decline of 251 (-4.2%) from the 6,045 counted in the 2000 Census, which had in turn increased by 168 (+2.9%) from the 5,877 counted in the 1990 Census.

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 teaching of mathematics. 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:

Professor academic rank at universities and other post-secondary education and research institutions in most countries

Professor is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences, a teacher of the highest rank.

Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems. Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, or medicine are related to mental problem-solving techniques studied in psychology.

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 be afraid of humor and should use it freely. Even an irrelevant joke or story perks up the class enormously. [1]

Critique of mathematics education

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. An article by Kline in 1956 in The Mathematics Teacher, the main journal of the National Council of Teachers of Mathematics, was titled "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. [2] 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. [3] 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."

Curriculum Educational plan

In education, a curriculum is broadly defined as the totality of student experiences that occur in the educational process. The term often refers specifically to a planned sequence of instruction, or to a view of the student's experiences in terms of the educator's or school's instructional goals. In a 2003 study, Reys, Reys, Lapan, Holliday, and Wasman refer to curriculum as a set of learning goals articulated across grades that outline the intended mathematics content and process goals at particular points in time throughout the K–12 school program. Curriculum may incorporate the planned interaction of pupils with instructional content, materials, resources, and processes for evaluating the attainment of educational objectives. Curriculum is split into several categories: the explicit, the implicit, the excluded, and the extracurricular.

Mathematics education mathematics teaching, learning and scholarly research

In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.

The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It provides services concerning mathematics education in the United States and Canada.

In 1966 [4] and 1970 [5] Kline issued two further criticisms. 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 the Secondary School Mathematics Curriculum Improvement Study.

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 onus to conduct research misdirects the scholarly method 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 Peter Hilton. [6] 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…[a] 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.

In considering what motivated Morris Kline to protest, consider Professor Meder’s opinion: [7] 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’s recommendation to combine science and mathematics at the high school level. [8] 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.

Critique of mathematics research

In Mathematics: The Loss of Certainty (ch. XIII: "The Isolation of Mathematics"), Kline deplored the way mathematics research was being conducted, complaining that often mathematicians, not willing to become acquainted with the (sometimes deep) context needed to solve applied problems in sciences, prefer to invent pure mathematics problems that are not necessarily of any consequence. Kline also blamed the publish or perish academic culture for this state of affairs.[ citation needed ]


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  1. Mathematics Teacher 49:171.
  2. Mathematics Teacher 51:428–33
  3. Mathematics Teacher 59:322330
  4. M. Kline (1966) "Intellectuals and the schools: a case history" in Harvard Educational Review 36:50511
  5. M. Kline (1970) "Logic versus pedagogy" in American Mathematical Monthly (77:26482)
  6. D.T. Finkbeiner, Harry Pollard, Peter Hilton (May 1979) American Mathematical Monthly 86:401–412
  7. Mathematics Teacher 51:433
  8. Why Johnny Can’t Add, page 147