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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 includes the study of such topics as quantity, structure, space, and change.
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.
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 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 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 (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, 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.
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 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 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.
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.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."
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.
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 1966and 1970 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.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: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.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.
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 ]
Science education is the field concerned with sharing science content and process with individuals not traditionally considered part of the scientific community. The learners may be children, college students, or adults within the general public; the field of science education includes work in science content, science process, some social science, and some teaching pedagogy. The standards for science education provide expectations for the development of understanding for students through the entire course of their K-12 education and beyond. The traditional subjects included in the standards are physical, life, earth, space, and human sciences.
A Bachelor of Education (B.Ed.) is a graduate professional degree which prepares students for work as a teacher in schools, though in some countries additional work must be done in order for the student to be fully qualified to teach.
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 change involved new curriculum topics and teaching practices introduced in the U.S. shortly after the Sputnik crisis, in order to boost science education and mathematical skill in the population, so that the technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.
Richard Kenneth Guy is a British mathematician, professor emeritus in the Department of Mathematics at the University of Calgary. He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory. He is best known for co-authorship of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory. He has also published over 300 papers. Guy proposed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them – thus explaining many coincidences and patterns found among numerous cultures. For this paper he received the MAA Lester R. Ford Award.
The anti-bias curriculum is an activist approach to educational curricula which attempts to challenge prejudices such as racism, sexism, ableism, ageism, homophobia, and other forms of kyriarchy. The approach is favoured by civil rights organisations such as the Anti-Defamation League.
David Harold Blackwell was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and Bayesian statistics. He is one of the eponyms of the Rao–Blackwell theorem. He was the first African American inducted into the National Academy of Sciences, the first black tenured faculty member at UC Berkeley, and the seventh African American to receive a Ph.D. in Mathematics.
Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015.
Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.
Lawrence F. Martinek (Larry) is a Los Angeles-based mathematics educator and creator of the curriculum and educational style that later became known as the Mathnasium Method.
Michael P. Starbird is a Professor of Mathematics and a University of Texas Distinguished Teaching Professor in the Department of Mathematics at the University of Texas at Austin. He received his B.A from Pomona College and his Ph.D. in mathematics from the University of Wisconsin–Madison.
MyMaths is a subscription-based mathematics website based on Adobe Flash which can be used on interactive whiteboards or by students and teachers at home. It is owned and operated by Oxford University Press, who acquired the site in 2011. MyMaths is currently used in over 80% of secondary schools in the UK. As of now MyMaths has over 4 million student users in over 70 countries worldwide, many of whom are in England.
Paul Charles Rosenbloom was an American mathematician.
The Secondary School Mathematics Curriculum Improvement Study (SSMCIS) was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the "New Math" movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College.
Gerald Lee Alexanderson is an American mathematician. He is the Michael & Elizabeth Valeriote Professor of Science at Santa Clara University, and in 1997–1998 was president of the Mathematical Association of America. He was also president of The Fibonacci Association from 1980 to 1984.
Why Johnny Can't Add: The Failure of the New Math is a book written by Morris Kline, first published in 1973. In it, Kline severely criticized the teaching practices characteristic of the "New Math" fashion for school teaching, which were based on Bourbaki's approach to mathematical research, and were being pushed into schools in the United States. Reactions were immediate, and the book became a best seller in its genre and translated into many languages.
Sybilla Beckmann is a 2011 Josiah Meigs Distinguished Teaching Professor of Mathematics at the University of Georgia and is a previous recipient of the Association for Women in Mathematics Louise Hay Award.
Barbara Jean Bestgen Reys is an American mathematics educator known for her research in number sense and mental calculation, for her mathematics textbooks, and for her leadership in developing curriculum standards for elementary school mathematics education. She is Curators Professor Emeritus at the University of Missouri, and a winner of the Lifetime Achievement Award of the National Council of Teachers of Mathematics.
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