New Math

{{Short description|Approach to teaching mathematics in the 1960s}}

File:Spines of New Math paperbacks from 1960s.jpg

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

Overview

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.{{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}}

Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra.{{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 }}

All of the New Math projects emphasized some form of discovery learning.{{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}} 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 counterexamples. 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.{{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}}

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".{{cite book|title = Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry: Geometry, Algebra, Trigonometry|publisher = Wipf and Stock Publishers|year = 2003|chapter = Algebra – 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}}

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 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.{{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}}}}

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".{{rp|17}} Furthermore, noting the trend to abstraction in New Math, Kline says "abstraction is not the first stage, but the last stage, in a mathematical development".{{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 millenniumhttps://books.google.com/ngrams/graph?content=new+math&year_start=1800&year_end=2022&corpus=en&smoothing=3{{Better source needed|date=September 2024}}, when its use for this purpose was eclipsed by "New Coke," another short-lived innovation.https://books.google.com/ngrams/graph?content=New+Math%2CNew+Coke&year_start=1800&year_end=2022&corpus=en&smoothing=3 In 1999, Time placed New Math on a list of the 100 worst ideas of the 20th century.{{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 |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}}[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.

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 Bourbaki group.{{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}} In West Germany the changes were seen as part of a larger process of Bildungsreform. Beyond the use of set theory and different approach to arithmetic, characteristic changes were transformation geometry in place of the 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 sciences 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 USSR did not experience such extreme upheavals, while being kept in tune, both with the applications and academic trends:

{{blockquote|Under 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 approaches were accepted in teaching geometry, but not to such sophisticated level {{sic}} presented in the textbook produced by Vladimir Boltyansky and Isaak Yaglom.{{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}}}}

In 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 approaches.{{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}}

In popular culture

Musician and university mathematics lecturer Tom Lehrer wrote a satirical song named "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."{{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 Media Group|access-date = May 19, 2019}}
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, subsets, joining sets, number sentences, placeholders." Eventually, she bursts into tears and exclaims, "All I want to know is, how much is two and two?"{{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}} 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?"{{cite web|author-link = Charles Schulz|first = Charles|last = Schulz|url = https://www.chisholm-poster.com/posters/CL68406.html|title = Charlie Brown Poster (1970s) – Peanuts – How Can You do "New Math" Problems with an "Old Math" Mind?|via = Chisholm Larsson Gallery|access-date = May 19, 2019}}
In the 1966 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.{{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}}

References

External links

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

Category:Education reform

Category:Mathematics education