Editing New Math (section)

== 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>