View source for New Math

{{Short description|Approach to teaching mathematics in the 1960s}}
{{Other uses}}
[[File:Spines of New Math paperbacks from 1960s.jpg|thumb|right|300px|Paperback introductions to the New Math]]
{{Education in the U.S.}}

'''New Mathematics''' or '''New Math''' was a dramatic but temporary change in the [[mathematics education|way mathematics was taught]] in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s{{ndash}}1970s.

== Overview ==
{{more citations needed|section|date=February 2021}}
In 1957, the U.S. [[National Science Foundation]] funded the development of several new curricula in the sciences, such as the [[Physical Science Study Committee]] high school physics curriculum, [[Biological Sciences Curriculum Study]] in biology, and [https://archive.org/details/CHEMStudy CHEM Study] in chemistry.  Several mathematics curriculum development efforts were also funded as part of the same initiative, such as the [http://library.webster.edu/archives/findingaids/madison/aboutmadisonproject.html Madison Project], [[School Mathematics Study Group]], and [https://archive.org/details/highschoolmathemat01univ/page/6/mode/2up University of Illinois Committee on School Mathematics].

These curricula were quite diverse, yet shared the idea that children's learning of arithmetic algorithms would last past the exam only if memorization and practice were paired with teaching for ''comprehension.''  More specifically, [[elementary school]] arithmetic beyond single digits makes sense only on the basis of understanding [[place-value]].  This goal was the reason for teaching arithmetic in bases other than ten in the New Math, despite critics' derision: In that unfamiliar context, students couldn't just mindlessly follow an algorithm, but had to think why the place value of the "hundreds" digit in base seven is 49.  Keeping track of non-decimal notation also explains the need to distinguish ''numbers'' (values) from the ''numerals'' that represent them.<ref>{{cite web | url =http://web.math.rochester.edu/people/faculty/rarm/beberman.html | title =Chapter 1: Max | last =Raimi | first =Ralph | date =May 6, 2004 | access-date =April 24, 2018}}</ref>

Topics introduced in the New Math include [[set theory]], [[modular arithmetic]], [[inequality (mathematics)|algebraic inequalities]], [[Radix|bases]] other than [[Base 10|10]], [[Matrix (mathematics)|matrices]], [[Mathematical logic|symbolic logic]], [[Boolean algebra]], and [[abstract algebra]].<ref name = Kline>{{cite book | last = Kline | first = Morris | author-link = Morris Kline | title = Why Johnny Can't Add: The Failure of the New Math | publisher = [[St. Martin's Press]] | year = 1973 | location = New York | isbn =  0-394-71981-6| title-link = Why Johnny Can't Add: The Failure of the New Math }}</ref>

All of the New Math projects emphasized some form of [[discovery learning]].<ref>{{Cite web|last=Isbrucker|first=Asher|date=2021-04-21|title=What Happened to 'New Math'?|url=https://medium.com/age-of-awareness/what-happened-to-new-math-eeb8522fc695|access-date=2022-02-10|website=Age of Awareness|language=en}}</ref> Students worked in groups to invent theories about problems posed in the textbooks.  Materials for teachers described the classroom as "noisy."  Part of the job of the teacher was provide [[instructional scaffolding]], that is, to move from table to table assessing the theory that each group of students had developed and "torpedo" wrong theories by providing [[counterexample]]s.  For that style of teaching to be tolerable for students, they had to experience the teacher as a colleague rather than as an adversary or as someone concerned mainly with grading.  New Math workshops for teachers, therefore, spent as much effort on the [[pedagogy]] as on the mathematics.<ref>{{Cite web|title=Whatever Happened To New Math?|url=https://www.americanheritage.com/whatever-happened-new-math-0|access-date=2022-02-10|website=AMERICAN HERITAGE|language=en}}</ref>

== Criticism ==
Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as [[arithmetic]]. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. In an effort to learn the material, many parents attended their children's classes. In the end, it was concluded that the experiment was not working, and New Math fell out of favor before the end of the 1960s, though it continued to be taught for years thereafter in some school districts.{{Citation needed|date=May 2023}}

In the [[Algebra]] preface of his book, ''Precalculus Mathematics in a Nutshell'', Professor [[George F. Simmons]] wrote that the New Math produced students who had "heard of the [[commutative law]], but did not know the [[multiplication table]]".<ref>{{cite book|title = Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry: Geometry, Algebra, Trigonometry|publisher = [[Wipf and Stock Publishers]]|year = 2003|chapter = Algebra &ndash; Introduction|chapter-url = https://books.google.com/books?id=dN1KAwAAQBAJ&pg=PA33|page = 33|isbn = 9781592441303|author-link = George F. Simmons|first = George F.|last = Simmons}}</ref>

In 1965, physicist [[Richard Feynman]] wrote in the essay, ''New Textbooks for the "New" Mathematics'':

{{blockquote|If we would like to, we can and do say, "The answer is a whole number less than 9 and bigger than 6," but we do not have to say, "The answer is a member of  the set which is the [[Intersection (set theory)|intersection]] of the set of those numbers which are larger than 6 and the set of numbers which are smaller than 9" ... In the "new" mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worthwhile teaching such material.<ref>{{cite journal|author-link = Richard Feynman|first = Richard P.|last = Feynman|url = http://calteches.library.caltech.edu/2362/1/feynman.pdf|title = New Textbooks for the 'New' Mathematics|journal = [[Engineering and Science]]|year = 1965|volume = XXVIII|issue = 6|pages = 9–15|issn = 0013-7812}}</ref>}}

In his book ''[[Why Johnny Can't Add: The Failure of the New Math]]'' (1973), [[Morris Kline]] says that certain advocates of the new topics "ignored completely the fact that mathematics is a cumulative development and that it is practically impossible to learn the newer creations, if one does not know the older ones".<ref name = Kline />{{rp|17}} Furthermore, noting the trend to [[Abstraction (mathematics)|abstraction]] in New Math, Kline says "abstraction is not the first stage, but the last stage, in a mathematical development".<ref name = Kline />{{rp|98}}

As a result of this controversy, and despite the ongoing influence of the New Math, the phrase "new math" was often used to describe any short-lived fad that quickly becomes discredited{{citation needed|date=September 2024}} until around the turn of the millennium<ref>https://books.google.com/ngrams/graph?content=new+math&year_start=1800&year_end=2022&corpus=en&smoothing=3</ref>{{Better source needed|date=September 2024}}, when its use for this purpose was eclipsed by "[[New Coke]]," another short-lived innovation.<ref>https://books.google.com/ngrams/graph?content=New+Math%2CNew+Coke&year_start=1800&year_end=2022&corpus=en&smoothing=3</ref> In 1999, ''[[Time (magazine)|Time]]'' placed New Math on a list of the 100 worst ideas of the 20th century.<ref>{{cite magazine|url=http://content.time.com/time/magazine/article/0,9171,991230,00.html |title=The 100 Worst Ideas Of The Century |date=June 14, 1999 |access-date=April 3, 2020|magazine=[[Time (magazine)|Time]] |first1=Melissa |last1=August |first2=Harriet |last2=Barovick |first3=Michelle |last3=Derrow |first4=Tam |last4=Gray |first5=Daniel S. |last5=Levy |first6=Lina |last6=Lofaro |first7=David |last7=Spitz |first8=Joel |last8=Stein |first9=Chris |last9=Taylor}}{{subscription required}}</ref><ref>[http://www.anvari.org/fun/Political/100_Worst_Ideas_of_the_Century.html "100 Worst Ideas of the Century"], Anvari.org archive of the June 14, 1999, issue of ''[[Time (magazine)|Time]]''.</ref>

== In other countries ==
In the broader context, reform of school mathematics curricula was also pursued in European countries, such as the [[United Kingdom]] (particularly by the [[School Mathematics Project]]), and [[France]] due to concerns that mathematics as taught in schools was becoming too disconnected from mathematics research, in particular that of the [[Nicolas Bourbaki|Bourbaki group]].<ref>{{Cite web|date=2017-07-15|title=L'enseignement des mathématiques au XXe siècle|url=http://culturemath.ens.fr/histoire%20des%20maths/htm/Gispert08-reformes/Gispert08.htm |lang=fr |access-date=2020-09-01|archive-url=https://web.archive.org/web/20170715164210/http://culturemath.ens.fr/histoire%20des%20maths/htm/Gispert08-reformes/Gispert08.htm|archive-date=2017-07-15}}</ref> In [[West Germany]] the changes were seen as part of a larger process of ''[[Education reform|Bildungsreform]]''. Beyond the use of set theory and different approach to [[arithmetic]], characteristic changes were [[transformation geometry]] in place of the [[Natural deduction|traditional deductive]] [[Euclidean geometry]], and an approach to [[calculus]] that was based on greater insight, rather than emphasis on facility.{{clarify|date=February 2011}}{{citation needed|date=February 2011}}

Again, the changes were met with a mixed reception, but for different reasons. For example, the end-users of mathematics studies were at that time mostly in the [[physical science]]s and [[engineering]], and they expected manipulative skill in calculus rather than more abstract ideas. Some compromises have since been required, given that [[discrete mathematics]] is the basic language of [[computing]].{{citation needed|date=February 2011}}

Teaching in the [[Soviet Union|USSR]] did not experience such extreme upheavals, while being kept in tune, both with the applications and academic trends:

{{blockquote|Under [[Andrey Kolmogorov|A. N. Kolmogorov]], the mathematics committee declared a reform of the curricula of grades 4–10, at the time when the school system consisted of 10 grades. The committee found the type of reform in progress in Western countries to be unacceptable; for example, no special topic for sets was accepted for inclusion in school textbooks. [[Transformation geometry|Transformation approaches]] were accepted in teaching geometry, but not to such sophisticated level {{sic}} presented in the textbook produced by [[Vladimir Boltyansky]] and [[Isaak Yaglom]].<ref name="textbook">{{cite conference|chapter = The Third World Mathematics Education is a Hope for the World Mathematics Education Development in the 21st Century|first = George|last =  Malaty|chapter-url = http://math.unipa.it/~grim/EMALATY231-240.PDF |archive-url=https://web.archive.org/web/20050214093107/http://math.unipa.it/~grim/EMALATY231-240.PDF | archive-date= 14 February 2005 |url-status=dead |year = 1999|title = Proceedings of the International Conference Mathematics Education into the 21st Century: Societal Challenges, Issues and Approaches|pages = 231–240|location = Cairo, Egypt|conference = Mathematics Education into the 21st Century: Societal Challenges, Issues and Approaches}}</ref>}}

In [[Japanese mathematics|Japan]], New Math was supported by the [[Ministry of Education, Culture, Sports, Science and Technology]] (MEXT), but not without encountering problems, leading to [[Student-centred learning|student-centred]] approaches.<ref>{{cite web |url=https://www.researchgate.net/publication/37261895 |title=第二次大戦後のわが国における数学教育の発展について― 「科学化運動」から「生きる数学」への飛翔 ― |lang=ja |website=www.researchgate.net}}</ref>

==In popular culture==
{{Listen|type=music|image=none|help=no
|filename=3-10_New_Math.mp3
|title="New Math" (1965)
|description=Musician and mathematician [[Tom Lehrer]] satirised New Math through song.}}
* Musician and university mathematics lecturer [[Tom Lehrer]] wrote a [[Satire|satirical]] song named "[[New Math (song)|New Math]]" (from his 1965 album ''[[That Was the Year That Was]]''), which revolved around the process of subtracting 173 from 342 in decimal and [[octal]]. The song is in the style of a lecture about the general concept of subtraction with [[positional notation]] in an arbitrary base, illustrated by two simple calculations, and highlights the New Math's emphasis on insight and abstract concepts – as Lehrer sardonically put it, "In the new approach ... the important thing is to understand what you're doing, rather than to get the right answer." At one point in the song, he notes that "you've got thirteen and you take away seven, and that leaves five... well, six, actually, but the idea is the important thing." The chorus pokes fun at parents' frustration and confusion over the entire method: "Hooray for New Math, New Math / It won't do you a bit of good to review math / It's so simple, so very simple / That only a child can do it."<ref>{{cite web|first = Tom|last = Lehrer|author-link = Tom Lehrer|url = https://genius.com/Tom-lehrer-new-math-lyrics|title = New Math Lyrics|year = 2019|publisher = [[Genius (website)|Genius Media Group]]|access-date = May 19, 2019}}</ref>
* In 1965, cartoonist [[Charles Schulz]] authored a series of ''[[Peanuts]]'' strips, which detailed kindergartener Sally's frustrations with New Math. In the first strip, she is depicted puzzling over "sets, one-to-one matching, equivalent sets, non-equivalent sets, sets of one, sets of two, renaming two, [[subset]]s, joining sets, number sentences, placeholders." Eventually, she bursts into tears and exclaims, "All I want to know is, how much is two and two?"<ref name="gocomics">{{cite web|url = http://www.gocomics.com/peanuts/2012/10/02|title = Peanuts by Charles Schulz for October 02, 2012|date = October 2, 1965|access-date = May 19, 2019|website = [[GoComics]]|publisher = [[Universal Uclick]]|author-link = Charles Schulz|first = Charles|last = Schulz}}</ref> This series of strips was later adapted for the 1973 ''Peanuts'' animated special ''[[There's No Time for Love, Charlie Brown]]''.  Schulz also drew a one-panel illustration of Charlie Brown at his school desk exclaiming, "How can you do 'New Math' problems with an 'Old Math' mind?"<ref>{{cite web|author-link = Charles Schulz|first = Charles|last = Schulz|url = https://www.chisholm-poster.com/posters/CL68406.html|title = Charlie Brown Poster (1970s) &ndash; Peanuts &ndash; How Can You do "New Math" Problems with an "Old Math" Mind?|via = Chisholm Larsson Gallery|access-date = May 19, 2019}}</ref>
* In the 1966 ''[[Hazel (TV series)|Hazel]]'' episode "A Little Bit of Genius", the show tackles the division that the introduction of New Math wrought between families, friends, and neighbors, as well as its impact on the then ever-widening generation gap.<ref>{{Citation |last=Russell |first=William D. |title=A Little Bit of Genius |date=1966-04-04 |url=https://www.imdb.com/title/tt1368938/ |series=Hazel |access-date=2022-04-10}}</ref>

==See also==
{{Portal|Education|Mathematics}}
* [[Chicago movement]]
* [[Common core]]
* [[Comprehensive School Mathematics Program]] (CSMP)
* [[André Lichnerowicz]] &ndash; Created 1967 French Lichnerowicz Commission
* [[List of abandoned education methods]]
* [[Math wars|New New Math]] – a satirical term for the Math Wars of the 1990s
* [[School Mathematics Project]]: UK version in use 1960s–1980s
* [[School Mathematics Study Group]] (SMSG)
* [[Secondary School Mathematics Curriculum Improvement Study]] (SSMCIS)

==References==
{{Reflist|30em}}

==Further reading==
* {{cite book|author-link = Irving Adler|last = Adler|first = Irving|title = The New Mathematics|location = New York|publisher = [[John Day Company]]|year = 1972|edition = revised|isbn = 0-381-98002-2}}
* {{cite book|first = Maurice|last =  Mashaal|year = 2006|title = Bourbaki: A Secret Society of Mathematicians|publisher = [[American Mathematical Society]]|isbn = 9780821839676|chapter = New Math in the Classroom|chapter-url = https://books.google.com/books?id=-CXn6y_1nJ8C&pg=PA134|pages = 134&ndash;145}} This work was originally published as ''Bourbaki: une société secrète de mathématiciens'' (2002, {{isbn|2842450469}}, in French) and the 2006 English-language version was translated by Anna Pierrehumbert.
* {{cite book|last = Phillips|first = Christopher J.|title = The New Math: A Political History|year = 2014|publisher = [[University of Chicago Press]]|isbn = 9780226185019}}
* Raimi, Ralph A. (1995). [https://web.math.rochester.edu/people/faculty/rarm/smsg.html ''Whatever Happened to the New Math?'']

==External links==
* [http://old.nationalcurvebank.org/newmath/newmath.htm Tom Lehrer Deposit #10]

{{Mathematics education}}
{{Authority control}}

[[Category:Education reform]]
[[Category:Mathematics education]]