View source for Mathematics education in the United States

{{short description|Overview of mathematics education in the United States}}
[[File:Math Workshop Portland 7 (9610679810).jpg|thumb|A student solves some math problems with a graphing calculator (2010)|260x260px]]
{{Education in the U.S.}}

'''Mathematics education in the United States''' varies considerably from one state to the next, and even within a single state. However, with the adoption of the [[Common Core]] Standards in most states and the [[District of Columbia]] beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level. The [[SAT]], a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core.<ref>{{cite news |last=Lewin |first=Tamar |date=March 5, 2014 |title=A New SAT Aims to Realign With Schoolwork |newspaper=The New York Times |url=https://www.nytimes.com/2014/03/06/education/major-changes-in-sat-announced-by-college-board.html |url-status=live |access-date=May 14, 2014 |archive-url=https://web.archive.org/web/20140513073917/http://www.nytimes.com/2014/03/06/education/major-changes-in-sat-announced-by-college-board.html |archive-date=May 13, 2014 |quote=He said he also wanted to make the test reflect more closely what students did in high school and, perhaps most important, rein in the intense coaching and tutoring on how to take the test that often gave affluent students an advantage.}}</ref> However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four.<ref>{{Cite news |last=Schwartz |first=Sarah |date=January 17, 2023 |title=Do Students Need Four Years of High School Math? |work=Education Week |url=https://www.edweek.org/teaching-learning/do-students-need-four-years-of-high-school-math/2023/01 |access-date=January 26, 2023 |archive-url=https://archive.today/20230126215104/https://www.edweek.org/teaching-learning/do-students-need-four-years-of-high-school-math/2023/01 |archive-date=January 26, 2023}}</ref> A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs<ref name=":1" /> while many complete high school without passing Calculus or Statistics.<ref name=":3" /><ref name=":47" /> At the other end, counselors at competitive public or private high schools usually encourage talented and ambitious students to take Calculus regardless of future plans in order to increase their chances of getting admitted to a prestigious university<ref name=":16" /> and their parents enroll them in enrichment programs in mathematics.<ref name=":67" /> 

Secondary-school algebra proves to be the turning point of difficulty many students struggle to surmount,<ref name=":27" /><ref name=":28" /><ref name=":19" /><ref name=":20">{{Cite news |last=Schwartz |first=Sarah |date=June 22, 2021 |title=Algebra 1 Is a Turning Point. Here's How to Help Incoming Students |url=https://www.edweek.org/teaching-learning/algebra-1-is-a-turning-point-heres-how-to-help-incoming-students/2021/06 |archive-url=https://archive.today/20230324073225/https://www.edweek.org/teaching-learning/algebra-1-is-a-turning-point-heres-how-to-help-incoming-students/2021/06 |archive-date=March 24, 2023 |access-date=March 24, 2023 |work=Education Week}}</ref> and as such, many students are ill-prepared for collegiate programs in the sciences, technology, engineering, and mathematics ([[Science, technology, engineering, and mathematics|STEM]]),<ref name=":19" /><ref name=":20" /><ref name=":56" /> or future high-skilled careers.<ref name=":26">{{Cite news |last=Cavanagh |first=Sean |date=June 7, 2007 |title=What Kind of Math Matters? |url=https://www.edweek.org/teaching-learning/what-kind-of-math-matters/2007/06 |archive-url=https://web.archive.org/web/20221018083354/https://www.edweek.org/teaching-learning/what-kind-of-math-matters/2007/06 |archive-date=October 18, 2022 |access-date=April 17, 2023 |work=Education Week}}</ref><ref name=":31" /> According to a 1997 report by the [[United States Department of Education|U.S. Department of Education]], passing rigorous high-school mathematics courses predicts successful completion of university programs regardless of major or family income.<ref>{{Cite web |last=U.S. Department of Education |title=Mathematics Equals Opportunity |url=https://files.eric.ed.gov/fulltext/ED415119.pdf}}</ref><ref>{{Cite book |last=Pickover |first=Clifford A. |title=The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics |publisher=Sterling |year=2009 |isbn=978-1-4027-5796-9 |location=New York |pages=10 |author-link=Clifford A. Pickover}}</ref> Meanwhile, the number of eighth-graders enrolled in Algebra I has fallen between the early 2010s and early 2020s.<ref name=":45" /> Across the United States, there is a shortage of qualified mathematics instructors.<ref name=":34">{{Cite news |last=The Editorial Board |date=December 7, 2013 |title=Who Says Math Has to be Boring? |url=https://www.nytimes.com/2013/12/08/opinion/sunday/who-says-math-has-to-be-boring.html |archive-url=https://archive.today/20230430021343/https://www.nytimes.com/2013/12/08/opinion/sunday/who-says-math-has-to-be-boring.html |archive-date=April 30, 2023 |access-date=April 29, 2023 |work=The New York Times}}</ref><ref name=":37">{{Cite news |last=Sparks |first=Sarah D. |date=September 7, 2022 |title=What School Staffing Shortages Look Like Now |url=https://www.edweek.org/leadership/what-school-staffing-shortages-look-like-now/2022/09 |archive-url=https://archive.today/20230425140325/https://www.edweek.org/leadership/what-school-staffing-shortages-look-like-now/2022/09 |archive-date=April 25, 2023 |access-date=April 25, 2023 |work=Education Week}}</ref> Despite their best intentions, parents may transmit their [[mathematical anxiety]] to their children, who may also have school teachers who fear mathematics,<ref name=":35">{{Cite news |last=Sparks |first=Sarah D. |date=May 16, 2011 |title=Researchers probe causes of math anxiety |url=http://www.edweek.org/ew/articles/2011/05/18/31math_ep.h30.html |archive-url=https://archive.today/20230503170352/https://www.edweek.org/leadership/researchers-probe-causes-of-math-anxiety/2011/05 |archive-date=May 3, 2023 |access-date=May 3, 2023 |work=Education Week}}</ref><ref>{{Cite news |last=Hoffman |first=Jan |date=August 24, 2015 |title=Square Root of Kids' Math Anxiety: Their Parents' Help |url=http://well.blogs.nytimes.com/2015/08/24/square-root-of-kids-math-anxiety-their-parents-help/?_r=0 |archive-url=https://archive.today/20150825015754/http://well.blogs.nytimes.com/2015/08/24/square-root-of-kids-math-anxiety-their-parents-help/?_r=0 |archive-date=August 25, 2015 |access-date=April 25, 2023 |work=The New York Times}}</ref> and they overestimate their children's mathematical proficiency.<ref name=":24" /> About one in five American adults are functionally innumerate.<ref name=":34" /> While an overwhelming majority agree that mathematics is important, many, especially the young, are not confident of their own mathematical ability.<ref name=":34" /><ref>{{Cite web |title=In a New Survey, Americans say, "We're Not Good At Math" |url=http://changetheequation.org/press/new-survey-americans-say-%E2%80%9Cwe%E2%80%99re-not-good-math%E2%80%9D |url-status=dead |archive-url=https://web.archive.org/web/20120302082153/http://changetheequation.org/press/new-survey-americans-say-%E2%80%9Cwe%E2%80%99re-not-good-math%E2%80%9D |archive-date=March 2, 2012 |access-date=April 29, 2023 |website=Change the Equation}}</ref> On the other hand, high-performing schools may offer their students accelerated tracks (including the possibility of taking collegiate courses after calculus)<ref name=":2" /> and nourish them for mathematics competitions.<ref name=":48" /><ref name=":49" /> At the tertiary level, student interest in STEM has grown considerably.<ref name=":81" /> However, many students find themselves having to take remedial courses for high-school mathematics<ref name=":50" /><ref name=":17" /> and many drop out of STEM programs due to deficient mathematical skills.<ref name=":56" /><ref name=":67" />

Compared to other developed countries in the Organization for Economic Co-operation and Development ([[OECD]]), the ''average'' level of [[Numeracy|mathematical literacy]] of American students is mediocre.<ref name=":27" /><ref name=":68">{{Cite news |last=Anderson |first=Nick |date=September 3, 2015 |title=SAT scores at lowest level in 10 years, fueling worries about high schools |newspaper=The Washington Post |url=https://www.washingtonpost.com/local/education/sat-scores-at-lowest-level-in-10-years-fueling-worries-about-high-schools/2015/09/02/6b73ec66-5190-11e5-9812-92d5948a40f8_story.html |access-date=September 17, 2020}}</ref><ref name=":23" /><ref name=":0" /><ref name=":8">{{Cite news |last=Hobbs |first=Tawnell D. |date=September 24, 2019 |title=SAT Scores Fall as More Students Take the Test |work=The Wall Street Journal |url=https://www.wsj.com/articles/sat-scores-fall-as-more-students-take-the-test-11569297660 |url-status=live |access-date=February 2, 2021 |archive-url=https://web.archive.org/web/20201128082452/https://www.wsj.com/articles/sat-scores-fall-as-more-students-take-the-test-11569297660 |archive-date=November 28, 2020}}</ref> As in many other countries, math scores dropped during the COVID-19 pandemic.<ref name=":25" /> However, Asian- and European-American students are above the OECD average.<ref name=":03" />  

==Curricular content and standards==
[[File:Status_of_Common_Core_Standards_vector.svg|thumb|350x350px|A map showing states in the U.S. which have either adopted, not adopted, partially adopted, or repealed the Common Core State Standards as of 2016:{{legend|#0066cc|States that have adopted the Standards}} {{legend|#00cccc|States that have partially adopted the Standards}} {{legend|#f9ca68|States that adopted but later repealed the Standards}} {{legend|#bf8040|States that never adopted the Standards}}]]
Each U.S. state sets its own curricular standards, and details are usually set by each local school district. Although there are no federal standards, since 2015 most states have based their curricula on the [[Common Core#Mathematics standards|Common Core State Standards]] in mathematics. The stated goal of the Common Core mathematics standards is to achieve greater focus and coherence in the curriculum.<ref>{{cite web |title=Common Core State Standards for Mathematics |url=http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf |access-date=February 11, 2014 |publisher=Common Core State Standards Initiative |page=3}}</ref> This is largely in response to the criticism that American mathematics curricula are "a mile wide and an inch deep."<ref>{{cite web |title=Mathematics |url=http://www.corestandards.org/math |access-date=January 8, 2014 |publisher=Common Core State Standards Initiative}}</ref><ref name=":5" /> The [[National Council of Teachers of Mathematics]] published educational recommendations in mathematics education in 1989 and 2000 which have been highly influential, describing mathematical knowledge, skills and pedagogical emphases from kindergarten through high school. The 2006 NCTM [http://www.nctm.org/focalpoints/ Curriculum Focal Points] have also been influential for its recommendations of the most important mathematical topics for each grade level through grade 8. However, some states have either abandoned, or never adopted, the Common Core standards, but instead instituted their own. (See [[Common Core implementation by state]].) In fact, there has been considerable disagreement on the style and content of mathematics teaching, including the question of whether or not there should be any national standards at all.<ref name=":3" /><ref name=":18" /><ref name=":5">{{Cite news |last=Schmidt |first=William H. |date=January 5, 2013 |title=The Common Core State Standards in Mathematics |work=Huffington Post |url=https://www.huffpost.com/entry/the-common-core-state-sta_b_2078325 |access-date=March 17, 2023}}</ref> 

In the United States, mathematics [[curriculum]] in elementary and middle school is [[Integrated mathematics|integrated]], while in high school it traditionally has been separated by topic, with each topic usually lasting for the whole school year. However, some districts have integrated curricula, or decided to try integrated curricula after Common Core was adopted.<ref name=":1">{{Cite news |last=Will |first=Madeline |date=November 10, 2014 |title=In Transition to Common Core, Some High Schools Turn to 'Integrated' Math |work=Education Week |url=https://www.edweek.org/teaching-learning/in-transition-to-common-core-some-high-schools-turn-to-integrated-math/2014/11 |access-date=August 31, 2022 |archive-url=https://archive.today/20220831182139/https://www.edweek.org/teaching-learning/in-transition-to-common-core-some-high-schools-turn-to-integrated-math/2014/11 |archive-date=August 31, 2022}}</ref><ref>{{cite web |last=Fensterwald |first=John |title=Districts confirm they're moving ahead with Common Core |url=http://edsource.org/today/2013/districts-confirm-theyre-moving-ahead-with-common-core/40830 |access-date=18 November 2013 |publisher=EdSource}}</ref> Since the days of the ''[[Sputnik crisis|Sputnik]]'' in the 1950s, the sequence of mathematics courses in secondary school has not changed: Pre-algebra, Algebra I, Geometry, Algebra II, Pre-calculus (or Trigonometry), and Calculus. Trigonometry is usually integrated into the other courses. Calculus is only taken by a select few.<ref name=":3" /><ref name=":10">{{cite web |last=Sarikas |first=Christine |date=May 17, 2019 |title=The High School Math Courses You Should Take |url=https://blog.prepscholar.com/the-high-school-math-classes-you-should-take |access-date=August 18, 2023 |website=PrepScholar}}</ref> Some schools teach Algebra II before Geometry.<ref name=":10" /> Success in middle-school mathematics courses is correlated with having an understanding of numbers by the start of first grade.<ref>{{Cite journal |last1=Geary |first1=David |author-link=David C. Geary |last2=Hoard |first2=Mary |last3=Nugent |first3=Lara |last4=Bailey |first4=Drew H. |date=January 30, 2013 |title=Adolescents' Functional Numeracy Is Predicted by Their School Entry Number System Knowledge |journal=PLOS ONE |volume=8 |issue=1 |pages=e54651 |doi=10.1371/journal.pone.0054651 |pmid=23382934 |pmc=3559782 |doi-access=free |bibcode=2013PLoSO...854651G }}</ref> This traditional sequence assumes that students will pursue STEM programs in college, though, in practice, only a minority are willing and able to take this option.<ref name=":3" /> Often a course in Statistics is also offered.<ref name=":34" /> 

While a majority of schoolteachers base their lessons on a core curriculum, they do not necessarily follow them to the letter. Many also take advantage of additional resources not provided to them by their school districts.<ref>{{Cite news |last=Schwartz |first=Sarah |date=May 18, 2023 |title=What Does Math Teaching Look Like in U.S. Schools? 5 Charts Tell the Story |work=Education Week |url=https://www.edweek.org/teaching-learning/what-does-math-teaching-look-like-in-u-s-schools-5-charts-tell-the-story/2023/05 |access-date=May 25, 2023 |archive-url=https://archive.today/20230519153042/https://www.edweek.org/teaching-learning/what-does-math-teaching-look-like-in-u-s-schools-5-charts-tell-the-story/2023/05 |archive-date=May 19, 2023}}</ref>

=== Primary school ===
[[File:Multiplication as scaling integers.gif|center|thumb|400x400px|Multiplication seen as scaling on the number line]]
Primary schoolchildren learn counting, arithmetic and properties of operations, geometry, measurement, statistics and probability. They typically begin studying fractions in third grade.

=== Secondary school ===
[[File:Aa garfield pythag.svg|thumb|[[James A. Garfield|James Garfield]]'s proof of the Pythagorean theorem.]]
'''[[Pre-algebra]]''' can be taken in middle school by seventh or eighth graders. Students typically begin by learning about real numbers and basic number theory ([[prime number]]s, prime factorization, [[fundamental theorem of arithmetic]], ratios, and percentages), topics needed for algebra (powers, roots, graphing, order of operations, variables, expressions, and [[scientific notation]]) and geometry (quadrilaterals, polygons, areas of plane figures, the [[Pythagorean theorem]], distance formula, equations of a line, simple solids, their surface areas, and volumes), and sometimes introductory trigonometry (definitions of the trigonometric functions). Such courses usually then go into simple algebra with solutions of simple linear equations and inequalities.

'''Algebra I''' is the first course students take in algebra. Although some students take it as eighth graders, this class is most commonly taken in ninth or tenth grade,<ref name=":32" /> after the students have taken Pre-algebra. Students learn about real numbers and the [[order of operations]] (PEMDAS), functions, linear equations, graphs, polynomials, the [[factor theorem]], [[Nth root|radicals]], and [[quadratic equation]]s (factoring, [[completing the square]], and the [[quadratic formula]]), and power functions.

This course is considered a gatekeeper for those who want to pursue STEM<ref name=":20" /> because taking Algebra I in eighth grade allows students to eventually take Calculus before graduating from high school.<ref name=":15">{{Cite news |last=Schwartz |first=Sarah |date=March 21, 2023 |title=San Francisco Insisted on Algebra in 9th Grade. Did It Improve Equity? |work=Education Week |url=https://www.edweek.org/teaching-learning/san-francisco-insisted-on-algebra-in-9th-grade-did-it-improve-equity/2023/03 |access-date=March 23, 2023 |archive-url=https://archive.today/20230322053327/https://www.edweek.org/teaching-learning/san-francisco-insisted-on-algebra-in-9th-grade-did-it-improve-equity/2023/03 |archive-date=March 22, 2023}}</ref> As such, tracking students by their aptitude and deciding when they should take Algebra I has become topic of controversy in California<ref name=":43">{{Cite news |last=Schwartz |first=Sarah |date=July 12, 2023 |title=California Adopts Controversial New Math Framework. Here's What's In It |work=Education Week |url=https://www.edweek.org/teaching-learning/california-adopts-controversial-new-math-framework-heres-whats-in-it/2023/07 |access-date=July 21, 2023 |archive-url=https://archive.today/20230714065949/https://www.edweek.org/teaching-learning/california-adopts-controversial-new-math-framework-heres-whats-in-it/2023/07 |archive-date=July 14, 2023}}</ref> and Massachusetts.<ref name=":44">{{Cite news |last=Huffaker |first=Christopher |date=July 14, 2023 |title=Cambridge schools are divided over middle school algebra |work=Boston Globe |url=https://www.bostonglobe.com/2023/07/14/metro/cambridge-schools-divided-over-middle-school-math/ |access-date=July 21, 2023 |archive-url=https://archive.today/20230714170301/https://www.bostonglobe.com/2023/07/14/metro/cambridge-schools-divided-over-middle-school-math/ |archive-date=July 14, 2023}}</ref> Parents of high-performing students are among the most vocal critics of policies discouraging the taking of Algebra I in middle school.<ref name=":43" /><ref name=":44" />

'''Geometry''', usually taken in ninth or tenth grade, introduces students to the notion of [[Rigour#Mathematics|rigor in mathematics]] by way of some basic concepts in mainly [[Euclidean geometry]]. Students learn the rudiments of [[Propositional calculus|propositional logic]], methods of proof ([[Direct proof|direct]] and by [[Proof by contradiction|contradiction]]), [[parallel lines]], triangles ([[Congruence (geometry)|congruence]] and [[Similarity (geometry)|similarity]]), circles ([[Secant line|secants]], tangents, [[Chord (geometry)|chords]], [[central angle]]s, and [[inscribed angle]]s), the Pythagorean theorem, elementary trigonometry (angles of elevation and depression, the [[law of sines]]), basic analytic geometry ([[Linear equation|equations of lines]], point-slope and slope-intercept forms, perpendicular lines, and [[Vector (mathematics and physics)|vectors]]), and geometric probability.<ref name=":11">{{Cite book |title=Geometry |publisher=Prentice Hall |year=2008 |isbn=978-0-133-65948-1}}</ref> Students are traditionally taught to demonstrate simple geometric theorems using [[Mathematical_proof#Two-column_proof|two-column proofs]], a method developed in the early 20th century in the U.S. specifically for this course, though other methods may also be used.<ref name=":51">{{Cite journal |last=National Council of Teachers of Mathematics (NCTM) |date=1912 |title=Final Report of the National Committee of Fifteen on Geometry Syllabus |journal=The Mathematics Teacher |volume=5 |issue=2 |pages=46–131 |doi=10.5951/MT.5.2.0046 |jstor=27949764}}</ref><ref>{{Cite journal |last=Herbst |first=Patricio G. |date=March 2002 |title=Establishing a custom of proving in American school geometry: evolution of the two-column proof in the early twentieth century |url=https://link.springer.com/article/10.1023/A:1020264906740 |journal=Educational Studies in Mathematics |volume=49 |issue=3 |pages=283–312|doi=10.1023/A:1020264906740 |hdl=2027.42/42653 |hdl-access=free }}</ref> Depending on the curriculum and instructor, students may receive orientation towards calculus, for instance with the introduction of the [[method of exhaustion]] and [[Cavalieri's principle]].<ref name=":11" />
[[File:Visual demonstration of the double-angle trigonometric identity for sine.svg|thumb|Visual proof of the double-angle identity for the sine]]

'''Algebra II''' has Algebra I as a prerequisite and is traditionally a high-school-level course. Course contents include [[Inequality (mathematics)|inequalities]], function notation, quadratic equations, power functions, [[exponential function]]s, [[logarithm]]s, systems of linear equations, matrices (including matrix multiplication, <math>2 \times 2</math> matrix [[determinant]]s, [[Cramer's rule]], and the inverse of a <math>2 \times 2</math> matrix), the [[radian]] measure, graphs of trigonometric functions, [[List of trigonometric identities|trigonometric identities]] (Pythagorean identities, the sum-and-difference, double-angle, and half-angle formulas, the laws of sines and [[Law of cosines|cosines]]), [[conic section]]s, among other topics.<ref>{{Cite book |title=Algebra 2 |publisher=Prentice Hall |year=2008 |isbn=978-0-133-19759-4}}</ref>

Requiring Algebra II for high school graduation gained traction across the United States in the early 2010s.<ref>{{Cite news |last=Whoriskey |first=Peter |date=April 3, 2011 |title=Requiring Algebra II in high school gains momentum nationwide |newspaper=The Washington Post |url=https://www.washingtonpost.com/business/economy/requiring-algebra-ii-in-high-school-gains-momentum-nationwide/2011/04/01/AF7FBWXC_story.html |access-date=May 6, 2023 |archive-url=https://archive.today/20230507032655/https://www.washingtonpost.com/business/economy/requiring-algebra-ii-in-high-school-gains-momentum-nationwide/2011/04/01/AF7FBWXC_story.html |archive-date=May 7, 2023}}</ref> The Common Core mathematical standards recognize both the sequential as well as the integrated approach to teaching high-school mathematics, which resulted in increased adoption of integrated math programs for high school. Accordingly, the organizations providing post-secondary education updated their enrollment requirements. For example, the [[University of California]] (UC) system requires three years of "college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry"<ref name="uc-req">{{Cite web|url=http://admission.universityofcalifornia.edu/counselors/freshman/minimum-requirements/subject-requirement/index.html|title=University of California admission subject requirements|access-date=2018-08-24}}</ref> to be admitted. After the [[California Department of Education]] adopted the Common Core, the UC system clarified that "approved integrated math courses may be used to fulfill part or all"<ref name="uc-req" /> of this admission requirement. On the other hand, in a controversial decision, the [[Texas Board of Education]] voted to remove Algebra II as a required course for high school graduation.<ref>{{Cite news |last=Loewus |first=Liana |date=January 31, 2014 |title=Texas Officially Drops Algebra 2 Requirement for Graduation |work=Education Week |url=https://www.edweek.org/teaching-learning/texas-officially-drops-algebra-2-requirement-for-graduation/2014/01 |access-date=May 6, 2023 |archive-url=https://archive.today/20230507032818/https://www.edweek.org/teaching-learning/texas-officially-drops-algebra-2-requirement-for-graduation/2014/01 |archive-date=May 7, 2023}}</ref>

In California, suggestions that Algebra II should be de-emphasized in favor of Data Science (a combination of algebra, statistics, and computer science) has faced severe criticism out of concerns that such a pathway would leave students ill-prepared for collegiate education. In 2023, the faculty of the University of California system voted to end an admissions policy that accepts Data Science in lieu of Algebra II.<ref name=":43" />

Students interested in taking [[AP Computer Science A]]<ref>{{Cite web |title=AP Computer Science A Course and Exam Description, Effective 2020 |url=https://apcentral.collegeboard.org/pdf/ap-computer-science-a-course-and-exam-description.pdf |access-date=September 24, 2020 |website=AP Central |page=7}}</ref> or [[AP Computer Science Principles]]<ref name=":04">{{cite web |date=2020 |title=AP Computer Science Principles: Course and Exam Description |url=https://apcentral.collegeboard.org/pdf/ap-computer-science-principles-course-and-exam-description.pdf?course=ap-computer-science-principles |access-date=9 August 2020 |publisher=College Board |pages=7 |format=PDF}}</ref> must have taken at least one course on algebra in high school. [[AP Chemistry]] specifically requires Algebra II.<ref>{{Cite web |date=Fall 2022 |title=AP Chemistry Course and Exam Description |url=https://apcentral.collegeboard.org/media/pdf/ap-chemistry-course-and-exam-description.pdf |access-date=April 17, 2024 |website=AP Central |page=7}}</ref>[[File:PascalTriangleAnimated2.gif|thumb|Pascal's [[Pascal's triangle|arithmetic triangle]] appears in combinatorics as well as algebra via the binomial theorem.]]'''[[Precalculus]]''' follows from the above, and is usually taken by college-bound students. Pre-calculus combines algebra, analytic geometry, and trigonometry. Topics in algebra include the [[binomial theorem]], [[complex number]]s, the [[Fundamental theorem of algebra|Fundamental Theorem of Algebra]], [[Nth root|root extraction]], [[polynomial long division]], [[partial fraction decomposition]], and [[Matrix (mathematics)|matrix]] operations. In chapters on trigonometry, students learn about [[radian]] angle measure, are shown the [[sine and cosine]] functions as coordinates on the [[unit circle]], relate the six common [[trigonometric functions]] and [[inverse trigonometric functions|their inverses]] and plot their graphs, solve equations involving trigonometric functions, and practice manipulating [[trigonometric identities]]. In the chapters on analytic geometry, students are introduced to [[Polar coordinate system|polar coordinates]] and deepen their knowledge of conic sections. Some courses include the basics of [[Euclidean vector|vector]] geometry, including the [[dot product]] and the [[vector projection|projection]] of one vector onto another. If time and aptitude permit, students might learn [[Heron's formula]] or the [[Cross product|vector cross product]]. Students are introduced to the use of a graphing calculator to help them visualize the plots of equations and to supplement the traditional techniques for finding the roots of a polynomial, such as the [[rational root theorem]] and the [[Descartes' rule of signs|Descartes rule of signs]]. Precalculus ends with an introduction to [[Limit of a function|limits]] of a function. Some instructors might give lectures on [[mathematical induction]] and [[combinatorics]] in this course.<ref>{{Cite book |last1=Demana |first1=Franklin D. |title=Precalculus: Graphical, Numerical, Algebraic |last2=Waits |first2=Bert K. |last3=Foley |first3=Gregory D. |last4=Kennedy |first4=Daniel |publisher=Addison-Wesley |year=2000 |isbn=978-0-321-35693-2 |edition=7th}}</ref><ref>{{Cite book |last=Simmons |first=George |title=Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry |publisher=Wipf & Stock Publishers |year=2003 |isbn=978-1-592-44130-3 |edition=Illustrated |author-link=George F. Simmons}}</ref><ref>{{Cite book |last1=Stewart |first1=James |title=Algebra and Trigonometry |last2=Redlin |first2=Lothar |last3=Watson |first3=Saleem |publisher=Cengage Learning |year=2006 |isbn=978-0-495-01357-0 |edition=2nd |author-link=James Stewart (mathematician)}}</ref> Precalculus is a prerequisite for [[AP Physics 1]] and [[AP Physics 2]] (formerly [[AP Physics B]]).<ref>{{Cite book |last=Giancoli |first=Douglas C. |title=Physics: Principles with Applications |publisher=[[Pearson Education]] |year=2005 |isbn=978-0-130-60620-4 |edition=6th |location=Upper Saddle River, NJ}}</ref><ref>{{Cite book |last1=Serway |first1=Raymond A. |title=College Physics |last2=Vuille |first2=Chris |publisher=Cengage Learning |year=2017 |isbn=978-1-305-95230-0 |edition=11th}}</ref>

AP Precalculus has only three required chapters. polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions and polar curves. Optional materials include parametric equations, implicit functions, conic sections, vectors, and matrix algebra (<math>2 \times 2 </math> matrix inversion, <math>2 \times 2 </math> determinants, and [[Linear map|linear transformations]]).<ref>{{Cite web |date=November 2022 |title=AP Precalculus Course Framework (Preview) |url=https://apcentral.collegeboard.org/pdf/ap-precalculus-proposed-course-framework.pdf |website=AP Central |publisher=College Board}}</ref> According to the College Board, "AP Precalculus may be the last mathematics course of a student's secondary education, the course is structured to provide a coherent capstone experience and is not exclusively focused on preparation for future courses."<ref name="pdf">College Board, "[https://apcentral.collegeboard.org/pdf/ap-precalculus-proposed-course-framework.pdf AP® Precalculus Proposed Course Framework]", 2022. Accessed 26 May 2022.</ref>

Depending on the school district, several courses may be compacted and combined within one school year, either studied sequentially or simultaneously. For example, in California, Algebra II and Precalculus may be taken as a single compressed course.<ref name=":15" /> Without such acceleration, it may be not possible to take more advanced classes like calculus in high school. 

In Oregon, high-school juniors and seniors may choose between three separate tracks, depending on their interests. Those aiming for a career in mathematics, the physical sciences, and engineering can pursue the traditional pathway, taking Algebra II and Precalculus. Those who want to pursue a career in the life sciences, the social sciences, or business can take Statistics and Mathematical Modelling. Students bound for technical training can take Applied Mathematics and Mathematical Modelling.<ref>{{Cite news |last=Gewertz |first=Catherine |date=November 13, 2019 |title=Should High Schools Rethink How They Sequence Math Courses? |work=Education Week |url=https://www.edweek.org/teaching-learning/should-high-schools-rethink-how-they-sequence-math-courses/2019/11 |access-date=May 6, 2023 |archive-url=https://archive.today/20230507025040/https://www.edweek.org/teaching-learning/should-high-schools-rethink-how-they-sequence-math-courses/2019/11 |archive-date=May 7, 2023}}</ref> In Florida, students may also receive lessons on mathematical logic and [[set theory]] at various grade levels in high school following the new 2020 reforms.<ref>{{Cite web |date=2020 |title=Florida B.E.S.T Standards: Mathematics |url=http://www.fldoe.org/core/fileparse.php/18736/urlt/StandardsMathematics.pdf |publisher=Florida Department of Education}}</ref> The new Floridian standards also promote [[financial literacy]] and emphasize how different mathematical topics from different grade levels are connected.<ref name=":41">{{Cite web |date=February 12, 2020 |title=Florida's B.E.S.T.: Here's what's next for the state's new educational standard |url=https://www.clickorlando.com/news/local/2020/02/12/floridas-best-heres-whats-next-for-the-states-new-educational-standard/}}</ref> In Utah, the final required mathematics course in high school incorporates elements of Algebra II, Trigonometry, Precalculus, and Data Science. However, as of 2023, students may opt out of this class with a signed letter from their parents, and about half do.<ref name=":46" />

'''College algebra''' is offered at many community colleges as [[Remedial education|remedial courses]] for students who did not pass courses before Calculus.<ref name="Bailey">{{cite journal |last=Bailey |first=Thomas |author2=Dong Wook Jeong |author3=Sung-Woo Cho |date=Spring 2010 |title=Referral, enrollment and completion in developmental education sequences in community colleges |journal=Economics of Education Review |volume=29 |issue=2 |pages=255–270 |doi=10.1016/j.econedurev.2009.09.002}}</ref> It should not be confused with [[abstract algebra]] and [[linear algebra]], taken by students who major in mathematics and allied fields (such as computer science) in four-year colleges and universities.
[[File:Limes Definition Vektorgrafik.svg|thumb|330x330px|Illustration of the epsilon-delta definition of the limit of a function]]
'''Calculus''' is usually taken by high-school seniors or university freshmen, but can occasionally be taken as early as tenth grade. Unlike many other countries from France to Israel to Singapore, which require high school students aiming for a career in STEM or placed in the track for advanced mathematics to study calculus, the United States generally treats calculus as collegiate mathematics. A successfully completed college-level calculus course like one offered via [[Advanced Placement]] program ([[AP Calculus]] AB and AP Calculus BC) is a transfer-level course—that is, it can be accepted by a college as a credit towards graduation requirements. Prestigious colleges and universities are believed to require successful completion AP courses, including AP Calculus, for admissions.<ref name=":12">{{Cite journal |last=Bressoud |first=David M. |author-link=David Bressoud |date=2021 |title=The Strange Role of Calculus in the United States |url=https://link.springer.com/article/10.1007/s11858-020-01188-0 |journal=ZDM – Mathematics Education |volume=53 |issue=3 |pages=521–533|doi=10.1007/s11858-020-01188-0 |s2cid=225295970 }}</ref><ref name=":13">{{Cite web |last=Bressoud |first=David |date=August 1, 2021 |title=Calculus Around the World |url=https://www.mathvalues.org/masterblog/calculus-around-the-world |access-date=March 18, 2023 |website=Math Values |publisher=[[Mathematical Association of America]]}}</ref> Calculus is a prerequisite or a corequisite for [[AP Physics C: Mechanics]] and [[AP Physics C: Electricity and Magnetism]].<ref>{{Cite book |last1=Serway |first1=Raymond A. |title=Physics for Scientists and Engineers |last2=Jewett |first2=John W. |publisher=[[Thomson Brooks/Cole]] |year=2004 |isbn=978-0-534-40844-2 |edition=6th}}</ref> Since the 1990s, the role of calculus in the high school curriculum has been a topic of controversy.<ref name=":3" />

In this class, students learn about limits and continuity (the [[Intermediate value theorem|intermediate]] and [[mean value theorem]]s), differentiation (the [[Product rule|product]], [[Quotient rule|quotient]], and [[chain rule]]s) and its applications ([[Implicit function|implicit differentiation]], [[logarithmic differentiation]], [[related rates]], [[Mathematical optimization|optimization]], [[Second derivative|concavity]], [[Newton's method]], [[L'Hôpital's rule]]s), integration and the [[Fundamental theorem of calculus|Fundamental Theorem of Calculus]], techniques of integration ([[Integration by substitution|''u''-substitution]], [[Integration by parts|by parts]], [[Trigonometric substitution|trigonometric]] and hyperbolic substitution, and by [[Partial fraction decomposition|partial fractions decomposition]]), further applications of integration (calculating accumulated change, various problems in the sciences and engineering, [[Separation of variables#Ordinary differential equations (ODE)|separable ordinary differential equations]], [[arc length]] of a curve, areas between curves, volumes and surface areas of [[Solid of revolution|solids of revolutions]]), [[improper integrals]], numerical integration (the midpoint rule, the [[Trapezoidal rule|trapezoid rule]], [[Simpson's rule]]), infinite sequences and series and their convergence (the [[Term test|''n''th-term]], [[Direct comparison test|comparison]], [[Ratio test|ratio]], [[Root test|root]], [[Integral test for convergence|integral]],  ''p''-series, and [[alternating series test]]s), [[Taylor's theorem]] (with the Lagrange remainder), [[Binomial series|Newton's generalized binomial theorem]], [[Euler's formula|Euler's complex identity]], polar representation of complex numbers, [[parametric equation]]s, and curves in polar coordinates.<ref name=":7">{{Cite book |last1=Thomas |first1=George B. |title=Thomas's Calculus: Early Transcendentals |last2=Weir |first2=Maurice D. |last3=Hass |first3=Joel |publisher=Addison-Wesley |year=2010 |isbn=978-0-321-58876-0 |edition=12th |author-link=George B. Thomas}}</ref><ref>{{Cite book |last1=Finney |first1=Ross L. |title=Calculus: Graphical, Numerical, Algebraic |last2=Demana |first2=Franklin D. |last3=Waits |first3=Bert K. |last4=Kennedy |first4=Daniel |publisher=Prentice Hall |year=2012 |isbn=978-0-133-17857-9 |edition=4th}}</ref><ref name=":6" /><ref name=":9">{{Cite book |last1=Adams |first1=Robert |title=Calculus: A Complete Course |last2=Essex |first2=Christopher |publisher=Pearson |year=2021 |isbn=978-0-135-73258-8 |edition=10th}}</ref>

Depending on the course and instructor, special topics in introductory calculus might include the classical differential geometry of curves ([[Differentiable curve|arc-length parametrization]], [[curvature]], [[Torsion of a curve|torsion]], and the [[Frenet–Serret formulas]]), the [[Limit of a function#(ε, δ)-definition of limit|epsilon-delta definition]] of the limit, [[Linear differential equation#First-order equation with variable coefficients|first-order linear ordinary differential equations]], [[Bernoulli differential equation]]s.<ref name=":7" /><ref name=":6" /> Some American high schools today also offer multivariable calculus<ref name=":2">{{Cite web |last=Bressoud |first=David |date=July 1, 2022 |title=Thoughts on Advanced Placement Precalculus |url=https://www.mathvalues.org/masterblog/thoughts-on-advanced-placement-precalculus |access-date=September 13, 2022 |website=MAA Blog}}</ref> (partial differentiation, the multivariable chain rule and [[Symmetry of second derivatives|Clairault's theorem]]; constrained optimization, [[Lagrange multiplier]]s and the [[Hessian matrix|Hessian]]; multidimensional integration, [[Fubini's theorem]], change of variables, and [[Jacobian matrix and determinant|Jacobian determinants]]; [[gradient]]s, [[directional derivative]]s, [[divergence]]s, [[Curl (mathematics)|curls]], the fundamental theorem of gradients, [[Green's theorem]], [[Stokes' theorem]], and [[Divergence theorem|Gauss' theorem]]).<ref name=":7" /><ref name=":6">{{Cite book |last=Stewart |first=James |url=https://www.stewartcalculus.com/media/11_home.php |title=Calculus: Early Transcendentals |publisher=Brooks/Cole Cengage Learning |year=2012 |isbn=978-0-538-49790-9 |edition=7th |author-link=James Stewart (mathematician)}}</ref><ref name=":9" />

Other optional mathematics courses may be offered, such as '''statistics''' (including [[AP Statistics]]) or business math. Students learn to use graphical and numerical techniques to analyze distributions of data (including [[univariate]], [[Bivariate data|bivariate]], and [[Categorical data|categorical]] data), the various methods of [[data collection]] and the sorts of conclusions one can draw therefrom, probability, and [[statistical inference]] ([[point estimation]], [[confidence intervals]], and [[significance test]]s).

High school students of exceptional ability may be selected to join a competition, such as the [[United States of America Mathematical Olympiad|USA Mathematical Olympiad]],<ref name="eligibilityUSAMO">{{cite web |year=2006 |title=United States of America Mathematical Olympiad - USAMO |url=http://www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml |archive-url=https://web.archive.org/web/20061106010621/http://www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml |archive-date=November 6, 2006 |access-date=2006-11-29 |publisher=The [[Mathematical Association of America]]}}</ref><ref name=":48">{{cite journal |last=Greitzer |first=S. |date=March 1973 |title=The First U.S.A. Mathematical Olympiad |journal=American Mathematical Monthly |volume=80 |issue=3 |pages=276–281 |doi=10.2307/2318449 |jstor=2318449}}</ref> or the [[International Mathematical Olympiad]].<ref name=":49">{{Cite news |last=Miller |first=Michael E. |date=July 18, 2015 |title=Winning formula: USA tops International Math Olympiad for first time in 21 years |newspaper=The Washington Post |url=https://www.washingtonpost.com/news/morning-mix/wp/2015/07/17/winning-formula-usa-tops-international-math-olympiad-for-first-time-in-21-years/ |access-date=April 27, 2023 |archive-url=https://archive.today/20230423191122/https://www.washingtonpost.com/news/morning-mix/wp/2015/07/17/winning-formula-usa-tops-international-math-olympiad-for-first-time-in-21-years/ |archive-date=April 23, 2023}}</ref><ref>{{Cite news |last=Levy |first=Max G. |date=February 16, 2021 |title=The Coach Who Led the U.S. Math Team Back to the Top |work=Quanta Magazine |url=https://www.quantamagazine.org/po-shen-loh-led-the-u-s-math-team-back-to-first-place-20210216/ |access-date=April 27, 2023}}</ref>

=== Tertiary school ===
{{Excessive citations|section|date=May 2024|details=These citations do not verify the article text. They should be replaced with citations to college and university curricula, or secondary sources.}}
[[File:Curl theorem in EM.svg|thumb|An illustration of Stokes' theorem in vector calculus]]
All students in STEM, especially mathematics, physics, chemistry, computer science, and engineering must take single-variable calculus unless they have Advanced Placement credits (or equivalents, such as [[Ib math hl|IB Math HL]]). Students majoring in mathematics, the physical sciences,<ref>{{Cite book |last=Boas |first=Mary |title=Mathematical Methods in the Physical Sciences |title-link=Mathematical Methods in the Physical Sciences |publisher=Wiley |year=2005 |isbn=978-0-471-19826-0 |edition=3rd |author-link=Mary Boas}}</ref><ref>{{Cite book |last=Hassani |first=Sadri |title=Mathematical Methods: For Students of Physics and Related Fields |publisher=Spring |year=2008 |isbn=978-0-387-09503-5 |edition=2nd}}</ref> and engineering<ref>{{Cite book |last1=Riley |first1=K.F. |title=Mathematical Methods for Physics and Engineering |last2=Hobson |first2=Michael P. |last3=Bence |first3=S.J. |publisher=Cambridge University Press |year=2006 |isbn=978-0-521-67971-8}}</ref> then take multivariable calculus,<ref name=":7" /><ref name=":6" /><ref name=":9" /> linear algebra,<ref>{{Cite book |last=Strang |first=Gilbert |title=Introduction to Linear Algebra |publisher=Wellesley-Cambridge Press |year=2016 |isbn=978-0-980-23277-6 |edition=5th |author-link=Gilbert Strang}}</ref><ref>{{Cite book |last=Axler |first=Sheldon |title=Linear Algebra Done Right |publisher=Springer |year=2014 |isbn=978-3-319-11079-0 |author-link=Sheldon Axler}}</ref><ref>{{Cite book |last=Halmos |first=Paul |title=Finite-Dimensional Vector Spaces |publisher=Dover Publications |year=2017 |isbn=978-0-486-81486-5 |edition=2nd |author-link=Paul Halmos}}</ref> complex variables,<ref>{{Cite book |last1=Spiegel |first1=Murray R. |title=Schaum's Outline of Complex Variables |last2=Lipschutz |first2=Seymour |last3=Schiller |first3=John J. |last4=Spellman |first4=Dennis |publisher=McGraw-Hill Companies |year=2009 |isbn=978-0-071-61569-3 |edition=2nd}}</ref><ref>{{Cite book |last=Kwok |first=Yue Kuen |title=Applied Complex Variables for Scientists and Engineers |publisher=Cambridge University Press |year=2010 |isbn=978-0-521-70138-9 |edition=2nd}}</ref><ref>{{Cite book |last=Krantz |first=Steven G. |title=A Guide to Complex Variables |publisher=[[Mathematical Association of America]] |year=2008 |isbn=978-0-883-85338-2}}</ref> [[Ordinary differential equation|ordinary differential equations]],<ref>{{Cite book |last1=Zill |first1=Dennis G. |title=Differential Equations with Boundary-Value Problems |last2=Wright |first2=Warren S. |publisher=Brooks/Cole Cengage Learning |year=2013 |isbn=978-1-111-82706-9 |edition=8th}}</ref><ref>{{Cite book |last1=Boyce |first1=William E. |title=Elementary Differential Equations and Boundary Value Problems |last2=DiPrima |first2=Richard C. |publisher=Wiley |year=2012 |isbn=978-0-470-45831-0 |edition=10th}}</ref><ref>{{Cite book |last=Arnold |first=Vladimir |title=Ordinary Differential Equations |publisher=The MIT Press |year=1978 |isbn=978-0-262-51018-9 |translator-last=Silverman |translator-first=Richard |author-link=Vladimir Arnold}}</ref> and [[Partial differential equation|partial differential equations]].<ref>{{Cite book |last1=Bleecker |first1=David D. |title=Basic Partial Differential Equations |last2=Csordas |first2=George |publisher=International Press of Boston |year=1997 |isbn=978-1-571-46036-3}}</ref><ref>{{Cite book |last=Asmar |first=Nakhlé H. |title=Partial Differential Equations with Fourier Series and Boundary Value Problems |publisher=Dover Publications |year=2016 |isbn=978-0-486-80737-9 |edition=3rd}}</ref><ref>{{Cite book |last=Strauss |first=Walter A. |title=Partial Differential Equations: An Introduction |publisher=Wiley |year=2007 |isbn=978-0-470-05456-7}}</ref> 

Mathematics majors may take a course offering a rigorous introduction to the concepts of modern mathematics<ref>{{Cite book |last=Eccles |first=Peter J. |title=An Introduction to Mathematical Reasoning: Numbers, Sets and Functions |publisher=Cambridge University Press |year=1998 |isbn=978-0-521-59718-0}}</ref><ref>{{Cite book |last=Hammack |first=Richard |title=Book of Proof |publisher=Lightning Source Inc. |year=2013 |isbn=978-0-989-47210-4 |edition=2nd}}</ref><ref>{{Cite book |last=Hamkins |first=Joel David |title=Proof and the Art of Mathematics |publisher=[[MIT Press]] |year=2020 |isbn=978-0-262-53979-1}}</ref> before they tackle abstract algebra,<ref>{{Cite book |last=Artin |first=Michael |title=Algebra |publisher=Pearson |year=2017 |isbn=978-0-134-68960-9 |edition=2nd |author-link=Michael Artin}}</ref><ref>{{Cite book |last1=Dummit |first1=David S. |title=Abstract Algebra |last2=Foote |first2=Richard M. |publisher=Wiley |year=2003 |isbn=978-0-471-43334-7 |edition=3rd}}</ref><ref>{{Cite book |last=Pinter |first=Charles C. |title=A Book of Abstract Algebra |publisher=Dover Publications |year=2010 |isbn=978-0-486-47417-5 |edition=2nd}}</ref> number theory,<ref>{{Cite book |last1=Scharlau |first1=Winfried |title=From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical Development |last2=Opolka |first2=Hans |publisher=Springer-Verlag |year=2010 |isbn=978-1-441-92821-4}}</ref><ref>{{Cite book |last=Granville |first=Andrew |title=Number Theory Revealed: A Masterclass |publisher=American Mathematical Society |year=2019 |isbn=978-1-4704-6370-0 |location=Rhode Island}}</ref><ref>{{Cite book |last=Dudley |first=Underwood |title=Elementary Number Theory |publisher=Dover Publications |year=2008 |isbn=978-0-486-46931-7 |edition=2nd}}</ref> [[real analysis]],<ref>{{Cite book |last=Mattuck |first=Arthur |title=Introduction to Analysis |publisher=CreateSpace Independent Publishing Platform |year=2013 |isbn=978-1-484-81411-6 |author-link=Arthur Mattuck}}</ref><ref>{{Cite book |last1=Bartle |first1=Robert G. |title=Introduction to Real Analysis |last2=Sherbert |first2=Donald R. |publisher=John Wiley & Sons, Inc. |year=2011 |isbn=978-0-471-43331-6 |edition=4th |author-link=Robert G. Bartle}}</ref><ref>{{Cite book |last=Abbott |first=Stephen |title=Understanding Analysis |publisher=Springer |year=2016 |isbn=978-1-493-92711-1 |edition=2nd}}</ref><ref>{{Cite book |last=Rudin |first=Walter |title=Principles of Mathematical Analysis |publisher=McGraw Hill |year=1976 |isbn=978-0-070-54235-8 |edition=3rd |author-link=Walter Rudin}}</ref> [[Calculus on Euclidean space|advanced calculus]],<ref>{{Cite book |last=Spivak |first=Michael |title=Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus |title-link=Calculus on Manifolds (book) |publisher=CRC Press |year=1965 |isbn=978-0-367-09190-3 |author-link=Michael Spivak}}</ref><ref>{{Cite book |last1=Loomis |first1=Lynn Harold |title=Advanced Calculus |last2=Sternberg |first2=Shlomo Zvi |publisher=World Scientific |year=2014 |isbn=978-9-814-58393-0 |edition=revised |author-link=Lynn Harold Loomis |author-link2=Shlomo Sternberg}}</ref><ref>{{Cite book |last1=Marsden |first1=Jerrold E. |title=Vector Calculus |last2=Tromba |first2=Anthony J. |publisher=W. H. Freeman |year=2011 |isbn=978-1-429-21508-4 |edition=6th |author-link=Jerrold E. Marsden}}</ref> [[complex analysis]],<ref>{{Cite book |last=Ahlfors |first=Lars Valerian |title=Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable |publisher=McGraw-Hill Higher Education |year=1978 |isbn=978-0-070-00657-7 |author-link=Lars Valerian Ahlfors}}</ref><ref>{{Cite book |last=Gamelin |first=Theodore W. |title=Complex Analysis |publisher=Springer |year=2001 |isbn=978-0-387-95069-3 |author-link=Theodore Gamelin}}</ref><ref>{{Cite book |last1=Stein |first1=Elias M. |title=Complex Analysis |last2=Shakarchi |first2=Rami |publisher=Princeton University Press |year=2003 |isbn=978-0-691-11385-2 |author-link=Elias M. Stein}}</ref><ref>{{Cite book |last1=Bak |first1=Joseph |title=Complex Analysis |last2=Newman |first2=Donald J. |publisher=Springer |year=2010 |isbn=978-1-441-97287-3 |edition=3rd |location=New York |author-link2=Donald J. Newman}}</ref> probability theory,<ref>{{Cite book |last1=Anderson |first1=David F. |title=Introduction to Probability |last2=Seppalainen |first2=Timo |last3=Valko |first3=Benedek |publisher=Cambridge University Press |year=2017 |isbn=978-1-108-41585-9}}</ref><ref>{{Cite book |last=Billingsley |first=Patrick |title=Probability and Measure |publisher=Wiley |year=2012 |isbn=978-1-118-12237-2 |edition=Anniversary}}</ref> statistics,<ref>{{Cite book |last1=Wackerly |first1=Dennis D. |title=Mathematical Statistics with Applications |last2=Mendenhall |first2=William |last3=Scheaffer |first3=Richard L. |publisher=Thomson Brooks/Cole |year=2008 |isbn=978-0-495-11081-1 |edition=7th}}</ref><ref>{{Cite book |last=Wasserman |first=Larry |title=All of Statistics: A Concise Course in Statistical Inference |publisher=Springer |year=2003 |isbn=978-0-387-40272-7 |author-link=Larry A. Wasserman}}</ref> and advanced topics, such as set theory and [[mathematical logic]],<ref>{{Cite book |last=Lipschutz |first=Seymour |title=Schaum's Outline of Set Theory and Related Topics |publisher=McGraw-Hill Companies |year=1998 |isbn=978-0-070-38159-9}}</ref><ref>{{Cite book |last=Stoll |first=Robert Roth |title=Set Theory and Logic |publisher=Dover Publications |year=1979 |isbn=978-0-486-63829-4}}</ref><ref>{{Cite book |last=Halmos |first=Paul R. |title=Naive Set Theory |publisher=Springer |year=1968 |isbn=978-0-387-90092-6}}</ref><ref>{{Cite book |last=Rautenberg |first=Wolfgang |title=A Concise Introduction to Mathematical Logic |publisher=Springer |year=2006 |isbn=978-0-387-30294-2}}</ref> [[Stochastic process|stochastic processes]],<ref>{{Cite book |last=Dobrow |first=Robert P. |title=Introduction to Stochastic Processes with R |publisher=Wiley |year=2016 |isbn=978-1-118-74065-1}}</ref> integration and [[Measure (mathematics)|measure theory]],<ref>{{Cite book |last=Bartle |first=Robert G. |title=A Modern Theory of Integration |publisher=[[American Mathematical Society]] |year=2001 |isbn=978-0-821-80845-0 |author-link=Robert G. Bartle}}</ref><ref>{{Cite book |last1=Stein |first1=Elias M. |title=Real Analysis: Measure Theory, Integration, and Hilbert Spaces |last2=Shakarchi |first2=Rami |publisher=Princeton University Press |year=2005 |isbn=978-0-691-11386-9 |author-link=Elias M. Stein}}</ref><ref>{{Cite book |last=Folland |first=Gerald B. |title=Real Analysis: Modern Techniques and Their Applications |publisher=Wiley |year=2007 |isbn=978-0-471-31716-6 |edition=2nd |author-link=Gerald B. Folland}}</ref><ref>{{Cite book |last=Cohn |first=Donald L. |title=Measure Theory |publisher=Birkhäuser |year=2015 |isbn=978-1-489-99762-3 |edition=2nd}}</ref> [[Fourier analysis]],<ref>{{Cite book |last1=Stein |first1=Elias M. |title=Fourier Analysis: An Introduction |last2=Shakarchi |first2=Rami |publisher=Princeton University Press |year=2003 |isbn=978-0-691-11384-5 |author-link=Elias M. Stein}}</ref><ref>{{Cite book |last=Lighthill |first=M.J. |title=An Introduction to Fourier Analysis and Generalised Functions |publisher=Cambridge University Press |year=1958 |isbn=978-0-521-09128-2 |author-link=Michael James Lighthill}}</ref> [[functional analysis]],<ref>{{Cite book |last1=Stein |first1=Elias M. |title=Functional Analysis: Introduction to Further Topics in Analysis |last2=Shakarchi |first2=Rami |publisher=Princeton University Press |year=2009 |isbn=978-0-691-11387-6 |author-link=Elias M. Stein}}</ref> [[differential geometry]],<ref>{{Cite book |last=Sochi |first=Taha |title=Introduction to Differential Geometry of Space Curves and Surfaces |publisher=CreateSpace |year=2017 |isbn=978-1-546-68183-0}}</ref><ref>{{Cite book |last=Do Carmo |first=Manfredo P. |title=Differential Geometry of Curves and Surfaces |publisher=Dover Publications |year=2016 |isbn=978-0-486-80699-0}}</ref><ref>{{Cite book |last=Pressley |first=Andrew |title=Elementary Differential Geometry |publisher=Springer |year=2010 |isbn=978-1-848-82890-2 |edition=2nd}}</ref> and [[topology]].<ref>{{Cite book |last=Munkres |first=James R. |title=Topology |publisher=Pearson |year=2000 |isbn=978-0-131-81629-9 |edition=2nd |author-link=James Munkres}}</ref><ref>{{Cite book |last=Mendelson |first=Bert |title=Introduction to Topology |publisher=Dover Publications |year=1990 |isbn=978-0-486-66352-4 |edition=3rd}}</ref> They may further choose courses in applied mathematics, such as mathematical modelling, [[numerical analysis]],<ref>{{Cite book |last1=Süli |first1=Endre |title=An Introduction to Numerical Analysis |last2=Mayers |first2=David |publisher=Cambridge University Press |year=2003 |isbn=978-0-521-00794-8}}</ref> [[game theory]],<ref>{{Cite book |last1=Osborne |first1=Michael J. |title=A Course in Game Theory |last2=Rubinstein |first2=Ariel |publisher=MIT Press |year=1994 |isbn=978-0-262-65040-3}}</ref><ref>{{Cite book |last=Tadelis |first=Steven |title=Game Theory: An Introduction |publisher=Princeton University Press |year=2013 |isbn=978-0-691-12908-2}}</ref><ref>{{Cite book |last=Gibbons |first=Robert |title=Game Theory for Applied Economists |publisher=Princeton University Press |year=1992 |isbn=978-0-691-00395-5}}</ref> or [[mathematical optimization]]. The [[calculus of variations]],<ref>{{Cite book |last=Kot |first=Mark |title=A First Course on the Calculus of Variations |publisher=American Mathematical Society |year=2014 |isbn=978-1-4704-1495-5}}</ref><ref name=":21">{{Cite book |last=Lanczos |first=Cornelius |title=The Variational Principles of Mechanics |publisher=Dover Publications |year=1986 |isbn=978-0-486-65067-8 |edition=4th |author-link=Cornelius Lanczos}}</ref><ref>{{Cite book |last1=Gelfand |first1=Israel M. |title=Calculus of Variations |last2=Fomin |first2=S.V. |publisher=Dover Publications |year=2000 |isbn=978-0-486-41448-5 |translator-last=Silverman |translator-first=Richard}}</ref> the [[history of mathematics]],<ref>{{Cite book |last=Stillwell |first=John |title=Mathematics and Its History |publisher=Springer |year=2010 |isbn=978-1-441-96052-8 |edition=3rd |author-link=John Stillwell}}</ref><ref>{{Cite book |last=Katz |first=Victor |title=A History of Mathematics: An Introduction |publisher=Addison Wesley Longman |year=2008 |isbn=978-0-321-38700-4 |edition=3rd |author-link=Victor J. Katz}}</ref><ref>{{Cite book |last1=Boyer |first1=Carl B. |title=A History of Mathematics |last2=Merzbach |first2=Uta C. |publisher=Wiley |year=1991 |isbn=978-0-471-54397-8 |author-link=Carl Boyer}}</ref><ref>{{Cite book |last=Kline |first=Morris |title=Mathematical Thought from Ancient to Modern Times |publisher=Oxford University Press |year=1972 |isbn=978-0-195-01496-9 |location=New York |author-link=Morris Kline}}</ref> and topics in theoretical or mathematical physics (such as classical mechanics,<ref>{{Cite book |last=Taylor |first=John R. |title=Classical Mechanics |publisher=University Science Books |year=2005 |isbn=978-1-891-38922-1 |author-link=John R. Taylor}}</ref><ref name=":21" /><ref>{{Cite book |last1=Goldstein |first1=Herbert |title=Classical Mechanics |title-link=Classical Mechanics (Goldstein) |last2=Poole |first2=Charles |last3=Safko |first3=John |publisher=Pearson |year=2001 |isbn=978-0-201-65702-9 |edition=3rd |author-link=Herbert Goldstein}}</ref><ref>{{Cite book |last=Arnold |first=Vladimir |title=Mathematical Methods of Classical Mechanics |publisher=Springer-Verlag |year=1978 |isbn=978-0-387-90314-9 |author-link=Vladimir Arnold}}</ref> electrodynamics,<ref>{{Cite book |last1=Purcell |first1=Edward M. |title=Electricity and Magnetism |title-link=Electricity and Magnetism (book) |last2=Morin |first2=David J. |publisher=Cambridge University Press |year=2013 |isbn=978-1-107-01402-2 |edition=3rd |author-link=Edward M. Purcell}}</ref><ref>{{Cite book |last=Griffiths |first=David J. |title=Introduction to Electrodynamics |title-link=Introduction to Electrodynamics |publisher=Cambridge University Press |year=2017 |isbn=978-1-108-42041-9 |edition=4th |author-link=David J. Griffiths}}</ref> nonlinear dynamics,<ref>{{Cite book |last=Strogatz |first=Steven H. |title=Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering |publisher=CRC Press |year=1994 |isbn=978-0-367-09206-1 |author-link=Steven Strogatz}}</ref> fluid mechanics,<ref>{{Cite book |last=Batchelor |first=G. K. |title=An Introduction to Fluid Dynamics |publisher=Cambridge University Press |year=2000 |isbn=978-0-521-66396-0 |author-link=G. K. Batchelor}}</ref><ref>{{Cite book |last1=Landau |first1=Lev D. |title=Fluid Mechanics |last2=Lifshitz |first2=Evgeny |publisher=Butterworth-Heinemann |year=1987 |isbn=978-0-750-62767-2 |edition=2nd |author-link=Lev Landau |author-link2=Evgeny Lifshitz}}</ref> quantum mechanics,<ref>{{Cite book |last=Townsend |first=John S. |title=A Modern Approach to Quantum Mechanics |publisher=University Science Books |year=2012 |isbn=978-1-891-38978-8 |edition=2nd}}</ref><ref>{{Cite book |last=Shankar |first=Ramamurti |title=Principles of Quantum Mechanics |title-link=Principles of Quantum Mechanics |publisher=Springer-Verlag |year=2012 |isbn=978-1-475-70578-2 |edition=2nd |author-link=Ramamurti Shankar}}</ref><ref>{{Cite book |last1=Sakurai |first1=J. J. |title=Modern Quantum Mechanics |title-link=Modern Quantum Mechanics |last2=Napolitano |first2=Jim |publisher=Cambridge University Press |year=2020 |isbn=978-1-108-47322-4 |edition=3rd |author-link=J. J. Sakurai}}</ref> or general relativity<ref>{{Cite book |last=Hartle |first=James B. |title=Gravity: An Introduction to Einstein's General Relativity |publisher=Pearson |year=2002 |isbn=978-0-805-38662-2 |author-link=James Hartle}}</ref><ref>{{Cite book |last=Carroll |first=Sean |title=Spacetime and Geometry: An Introduction to General Relativity |publisher=Cambridge University Press |year=2019 |isbn=978-1-108-48839-6 |author-link=Sean Carroll (physicist)}}</ref><ref>{{Cite book |last1=Misner |first1=Charles |title=Gravitation |title-link=Gravitation (book) |last2=Thorne |first2=Kip |last3=Wheeler |first3=John |publisher=Princeton University Press |year=2017 |isbn=978-0-691-17779-3 |author-link=Charles W. Misner |author-link2=Kip S. Thorne |author-link3=John Archibald Wheeler}}</ref><ref>{{Cite book |last=Wald |first=Robert |title=General Relativity |title-link=General Relativity (book) |publisher=The University of Chicago Press |year=1984 |isbn=978-0-226-87033-5 |author-link=Robert Wald}}</ref>) may be taken as electives.

Computer science majors must study [[discrete mathematics]]<ref>{{Cite book |last1=Graham |first1=Ronald L. |title=Concrete Mathematics: A Foundation for Computer Science |title-link=Concrete Mathematics |last2=Knuth |first2=Donald |author-link2=Donald Knuth |last3=Patashnik |first3=Oren |publisher=Addison-Wesley Professional |year=1994 |isbn=978-0-201-55802-9 |edition=2nd}}</ref><ref>{{Cite book |last=Rosen |first=Kenneth H. |title=Discrete Mathematics and Its Applications |publisher=McGraw-Hill |year=2018 |isbn=978-1-259-67651-2 |edition=8th}}</ref> (such as combinatorics and [[graph theory]]), [[information theory]],<ref>{{Cite book |last1=Cover |first1=Thomas M. |title=Elements of Information Theory |last2=Thomas |first2=Joy A. |publisher=Wiley-Interscience |year=2006 |isbn=978-0-471-24195-9 |edition=2nd}}</ref> the [[theory of computation]],<ref>{{Cite book |last=Sipser |first=Michael |title=Introduction to the Theory of Computation |publisher=Cengage Learning |year=1996 |isbn=978-1-133-18779-0 |edition=3rd}}</ref><ref>{{Cite book |last1=Cormen |first1=Thomas H. |title=Introduction to Algorithms |last2=Leiserson |first2=Charles E. |last3=Rivest |first3=Ronald L. |last4=Stein |first4=Clifford |publisher=The MIT Press |year=2009 |isbn=978-0-262-03384-8 |edition=3rd}}</ref> and [[cryptography]]. Students in computer science and economics might have the option of taking [[algorithmic game theory]].<ref>{{Cite book |last=Roughgarden |first=Tim |title=Twenty Lectures on Algorithmic Game Theory |publisher=Cambridge University Press |year=2016 |isbn=978-1-107-17266-1}}</ref>

Those who study biomedical and social sciences have to study elementary probability<ref>{{Cite book |last1=Gross |first1=Benedict |title=Fat Chance: Probability from 0 to 1 |last2=Harris |first2=Joseph |last3=Riehl |first3=Emily |publisher=Cambridge University Press |year=2019 |isbn=978-1-108-72818-8 |author-link=Benedict Gross |author-link2=Joe Harris (mathematician) |author-link3=Emily Riehl}}</ref> and statistics.<ref>{{Cite book |last1=Johnson |first1=Robert |title=Just the Essentials of Elementary Statistics |last2=Kuby |first2=Patricia |publisher=Thomson Brooks/Cole |year=2003 |isbn=0-534-38472-2 |edition=3rd}}</ref> Students in the physical sciences and engineering need to understand [[Error analysis (mathematics)|error analysis]] for their laboratory sessions and courses.<ref>{{Cite book |last=Taylor |first=John R. |title=Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements |publisher=University Science Books |year=1996 |isbn=978-0-93570-275-0 |edition=2nd |author-link=John R. Taylor}}</ref><ref>{{Cite book |last1=Hughes |first1=Ifan G. |title=Measurements and their Uncertainties: A Practical Guide to Modern Error Analysis |last2=Hase |first2=Thomas P. A. |publisher=Oxford University Press |year=2013 |isbn=978-0-19-956633-4 |location=Oxford}}</ref> Advanced undergraduates and beginning graduate students in physics may take a course on advanced mathematical methods for physics, which may cover [[contour integration]], the theory of distributions ([[Generalized function|generalized functions]]), Fourier analysis, [[Green's function]]s, [[special functions]] (especially Euler's [[Gamma function|gamma]] and [[beta function]]s; [[Bessel function]]s; [[Legendre polynomials]]; [[Hermite polynomials]]; [[Laguerre polynomials]]; and the [[Hypergeometric function|hypergeometric series]]), [[Asymptotic expansion|asymptotic series expansions]], the calculus of variations, [[tensor]]s, and [[Group (mathematics)|group]] theory.<ref>{{Cite book |last1=Weber |first1=Hans J. |title=Mathematical Methods for Physicists |last2=Harris |first2=Frank E. |last3=Arfken |first3=George B. |publisher=Elsevier Science & Technology |year=2012 |isbn=978-9-381-26955-8 |edition=7th |author-link3=George B. Arfken}}</ref><ref>{{Cite book |last=Hassani |first=Sadri |title=Mathematical Physics: A Modern Introduction to Its Foundations |publisher=Springer |year=2013 |isbn=978-3-319-01194-3 |edition=2nd}}</ref><ref>{{Cite book |last=Neuenschwander |first=Dwight E. |title=Tensor Calculus for Physics: A Concise Guide |publisher=Johns Hopkins University Press |year=2014 |isbn=978-1-421-41565-9}}</ref><ref>{{Cite book |last=Jeevanjee |first=Nadir |title=An Introduction to Tensors and Group Theory for Physicists |publisher=Birkhäuser |year=2015 |isbn=978-3-319-14793-2 |edition=2nd |location=Boston}}</ref><ref>{{Cite book |last=Zee |first=Anthony |title=Group Theory in a Nutshell for Physicists |publisher=Princeton University Press |year=2016 |isbn=978-0-691-16269-0 |edition=Illustrated |author-link=Anthony Zee}}</ref><ref>{{Cite book |last1=Bender |first1=Carl |title=Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory |last2=Orszag |first2=Steven A. |publisher=Springer |year=2010 |isbn=978-1-441-93187-0}}</ref> Exact requirements and available courses will depend on the institution in question.

At many colleges and universities, confident students may compete in the [[Integration Bee]].<ref name=":02">{{Cite news |last=Baker |first=Billy |date=January 20, 2012 |title=An integral part of MIT life |work=Boston Globe |url=http://archive.boston.com/news/local/massachusetts/articles/2012/01/20/mit_math_competition_creates_bmoc/ |access-date=February 6, 2021}}</ref><ref name=":210">{{Cite web |last= |first= |date=2018 |title=Integration Bee |url=https://ams.math.uconn.edu/bee/ |access-date=February 6, 2021 |website= |publisher=AMS Student Chapter, University of Connecticut}}</ref><ref name=":73">{{Cite web |date=2023 |title=WVU Integration Bee Competition |url=https://mathanddata.wvu.edu/news-and-events/other-recurring-events/integration-bee |access-date=May 4, 2023 |publisher=School of Mathematical and Data Sciences, West Virginia University}}</ref><ref name=":36">{{Cite web |last= |first= |date= |title=Integration Bee |url=https://sps.berkeley.edu/events/int_bee |access-date=February 6, 2021 |website=Berkeley SPS |publisher=University of California, Berkeley}}</ref> Exceptional undergraduates may participate in the annual [[William Lowell Putnam Mathematical Competition]].<ref name=":33">{{Cite news |last=Miller |first=Sandi |date=March 3, 2020 |title=MIT students dominate annual Putnam Mathematical Competition |work=MIT News |url=https://news.mit.edu/2020/mit-students-dominate-putnam-mathematical-competition-0303 |access-date=April 27, 2023}}</ref><ref>{{Cite news |last=Jiang |first=Georgia |date=February 27, 2023 |title=UMD Students Win Fourth Place in Putnam Mathematical Competition |work=Maryland Today |publisher=University of Maryland |url=https://today.umd.edu/umd-students-win-fourth-place-in-putnam-mathematical-competition |access-date=April 27, 2023}}</ref> Many successful competitors have gone on to fruitful research careers in mathematics. Although doing well on the Putnam is not a requirement for becoming a mathematician, it encourages students to develop skills and hone [[Logical intuition|intuitions]] that could help them become successful researchers.<ref name=":33" /><ref>{{Cite news |last=Shelton |first=Jim |date=March 29, 2023 |title=Yale team excels at Putnam student mathematics competition |work=Yale Daily News |url=https://news.yale.edu/2023/03/29/yale-team-excels-putnam-student-mathematics-competition |access-date=May 7, 2023}}</ref> Besides the monetary prize, the winners are virtually guaranteed acceptance to a prestigious graduate school.<ref>{{Cite book |last=Nasar |first=Sylvia |title=A Beautiful Mind |publisher=Simon & Schuster |year=1998 |isbn=0-7432-2457-4 |location=New York |pages=43–44 |chapter=2: Carnegie Institute of Technology}}</ref> Such competitions are one way for mathematical talents to stand out.<ref>{{Cite news |last=Miller |first=Sandi |date=March 27, 2019 |title=Solving for fun (and sometimes prizes) |work=MIT News |url=https://news.mit.edu/2019/solving-fun-danielle-wang-mit-math-0327 |access-date=May 6, 2023}}</ref>

==Attendance and completion rates==
[[File:Algebra I by Sex or Race (2015-16).png|thumb|500x500px|Significant race or sex differences exist in the completion of Algebra I.<ref name=":39" />]]
For many students, passing algebra is often a Herculean challenge,<ref name=":27">{{Cite news |last=Hacker |first=Andrew |date=July 28, 2012 |title=Is Algebra Necessary? |work=The New York Times |url=https://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html |access-date=April 24, 2023 |archive-url=https://archive.today/20210706191923/https://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html |archive-date=July 6, 2021}}</ref><ref name=":19" /><ref name=":20" /> so much so that many students have dropped out of high school because of it.<ref name=":27" /> The greatest obstacle for excelling in algebra is fluency with fractions, something many Americans do not have.<ref name=":28">{{Cite news |last=Lewin |first=Tamar |date=March 14, 2008 |title=Report Urges Changes in Teaching Math |work=The New York Times |url=https://www.nytimes.com/2008/03/14/education/14math.html |access-date=April 24, 2023 |archive-url=https://archive.today/20230424033439/https://www.nytimes.com/2008/03/14/education/14math.html |archive-date=April 24, 2023}}</ref> Without mastery of high-school algebra—Algebra I and II—students will not be able to pursue collegiate STEM courses.<ref name=":20" /><ref name=":19" /><ref name=":39">{{Cite web |date=November 2018 |title=A Leak in the STEM Pipeline: Taking Algebra Early |url=https://www2.ed.gov/datastory/stem/algebra/index.html |access-date=May 13, 2023 |website= |publisher=U.S. Department of Education |language=en}}</ref> In fact, the lack of adequate preparation in mathematics is part of the reason why the rate of attrition in STEM is so high.<ref name=":56" /> From 1986 to 2012, though more students were completing Algebra II, their average performance has fallen. Indeed, students who had passed high-school courses, including those labeled "honors" courses, might still fail collegiate placement exams and had to take remedial courses.<ref name=":50">{{Cite news |last=Robelen |first=Erik W. |date=September 4, 2013 |title=Algebra 2: Not the Same Credential It Used to Be? |work=Education Week |url=https://www.edweek.org/teaching-learning/algebra-2-not-the-same-credential-it-used-to-be/2013/09 |access-date=May 6, 2023 |archive-url=https://archive.today/20230507031855/https://www.edweek.org/teaching-learning/algebra-2-not-the-same-credential-it-used-to-be/2013/09 |archive-date=May 7, 2023}}</ref> As for Algebra I, the number of 13-year-olds enrolled fell from 34% in 2012 to 24% in 2023.<ref name=":45">{{Cite news |last=Rubin |first=April |date=June 21, 2023 |title=Middle schoolers' reading and math scores plummet |work=Axios |url=https://www.axios.com/2023/06/21/schools-students-reading-math-test-scores-decline |access-date=August 7, 2023}}</ref>

Longitudinal analysis shows that the number of students completing high-school courses on calculus and statistics, including AP courses, have declined ''before'' 2019.<ref name=":47">{{Cite web |last=Bressoud |first=David |date=September 1, 2022 |title=The Decline of High School Calculus |url=https://www.mathvalues.org/masterblog/the-decline-in-high-school-calculus |access-date=March 18, 2023 |website=Math Values |publisher=[[Mathematical Association of America]]}}</ref><ref>{{Cite web |date=2019 |title=AP Exam Volume Change (2009-2019) |url=https://reports.collegeboard.org/media/pdf/2019-Exam-Volume-Change_1.pdf |website=AP Data Archive |publisher=College Board}}</ref> Data taken from students' transcripts (<math>N = 15,188</math>) from the late 2000s to the mid-2010s reveals that majorities of students had completed Algebra I (96%), Geometry (76%), and Algebra II (62%). But not that many took Precalculus (34%), Trigonometry (16%), Calculus (19%), or Statistics (11%) and only an absolute minority took Integrated Mathematics (7%). Overall, female students were more likely to complete all mathematics courses, except Statistics and Calculus. Asian Americans were the most likely to take Precalculus (55%), Statistics (22%), and Calculus (47%) while African Americans were the least likely to complete Calculus (8%) but most likely to take Integrated Mathematics (10%) in high school.<ref name=":14" /> Among students identified as mathematically proficient by the [[PSAT/NMSQT|PSAT]], Asians are much more likely than blacks to attend an honors or Advanced Placement course in mathematics.<ref>{{Cite news |last=Quinton |first=Sophie |date=December 11, 2014 |title=The Race Gap in High School Honors Classes |work=The Atlantic |url=https://www.theatlantic.com/politics/archive/2014/12/the-race-gap-in-high-school-honors-classes/431751/ |access-date=May 17, 2023 |archive-url=https://archive.today/20210402014907/https://www.theatlantic.com/politics/archive/2014/12/the-race-gap-in-high-school-honors-classes/431751/ |archive-date=April 2, 2021}}</ref> Asians are also the most likely to have scored at least a 3 on the AP Calculus exams.<ref name=":12" /> Students of lower socioeconomic status were less likely to pass Precalculus, Calculus, and Statistics.<ref name=":14">{{Cite book |last1=Champion |first1=Joe |url=https://www.maa.org/sites/default/files/RoleOfCalc_rev.pdf |title=The Role of Calculus in the Transition from High School to College Mathematics |last2=Mesa |first2=Vilma |publisher=MAA and NCTM |year=2017 |editor-last=Bressoud |editor-first=David |location=Washington, D.C. |pages=9–25 |chapter=Factors Affecting Calculus Completion among U.S. High School Students}}</ref> While boys and girls are equally likely to take AP Statistics and AP Calculus AB, boys are the majority in AP Calculus BC (59%), as well as some other highly mathematical subjects, such as [[AP Computer Science A]] (80%), [[AP Physics C: Mechanics]] (74%) and [[AP Physics C: Electricity and Magnetism]] (77%).<ref>{{Cite news |last=Robelen |first=Erik W. |date=February 15, 2012 |title=Girls Like Biology, Boys Like Physics? AP Data Hint at Preferences |work=Education Week |url=https://www.edweek.org/teaching-learning/girls-like-biology-boys-like-physics-ap-data-hint-at-preferences/2012/02 |access-date=April 30, 2023 |archive-url=https://archive.today/20230430041749/https://www.edweek.org/teaching-learning/girls-like-biology-boys-like-physics-ap-data-hint-at-preferences/2012/02 |archive-date=April 30, 2023}}</ref> Although undergraduate men and women score the same grades in Calculus I (in college) on average, women are more likely than men to drop out because of mathematical anxiety.<ref>{{Cite news |last=Loewus |first=Liana |date=August 3, 2016 |title=What's Keeping Women Out of Science, Math Careers? Calculus and Confidence |work=Education Week |url=https://www.edweek.org/teaching-learning/whats-keeping-women-out-of-science-math-careers-calculus-and-confidence/2016/08 |access-date=April 30, 2023 |archive-url=https://archive.today/20230430041020/https://www.edweek.org/teaching-learning/whats-keeping-women-out-of-science-math-careers-calculus-and-confidence/2016/08 |archive-date=April 30, 2023}}</ref> Perceptions and stereotypes of girls being less mathematically able than boys begin as early as second grade, and they affect [[Self-fulfilling prophecy|how girls actually perform]] in class or in a competition, such as the International Mathematical Olympiad.<ref>{{Cite news |last=Whitney |first=A.K. |date=April 18, 2016 |title=Math for Girls, Math for Boys |work=The Atlantic |url=https://www.theatlantic.com/education/archive/2016/04/girls-math-international-competiton/478533/ |access-date=May 2, 2023 |archive-url=https://archive.today/20210404225815/https://www.theatlantic.com/education/archive/2016/04/girls-math-international-competiton/478533/ |archive-date=April 4, 2021}}</ref> Among university students who have taken calculus, engineering disciplines are the most popular among men and biology among women.<ref name=":12" />

During the 1970s and 1980s, the number of students taking remedial courses in college rose substantially, partly due to the de-emphasis of calculus in high school, leading to less exposure to pre-calculus topics.<ref name=":3" /> In the twenty-first century, American community colleges require 60% of their students to pass at least one course in mathematics, depending on the program.<ref name=":17" /> But around 80% fail to meet this requirement,<ref name=":17">{{Cite news |last1=Lattimore |first1=Kayla |last2=Depenbrock |first2=Julie |date=July 19, 2017 |title=Say Goodbye To X+Y: Should Community Colleges Abolish Algebra? |work=NPR |url=https://www.npr.org/2017/07/19/538092649/say-goodbye-to-x-y-should-community-colleges-abolish-algebra |access-date=April 9, 2023}}</ref> and 60% require remedial courses.<ref name=":19">{{Cite news |last=Hanford |first=Emily |date=February 3, 2017 |title=Trying to Solve a Bigger Math Problem |work=The New York Times |url=https://www.nytimes.com/2017/02/03/education/edlife/accuplacer-placement-test-math-algebra.html |access-date=April 9, 2023}}</ref> Many students at these schools drop out after failing even in remedial courses, such as (the equivalent of) Algebra II.<ref>{{Cite news |last=Quinton |first=Sophie |date=October 29, 2013 |title=Algebra Doesn't Have to Be Scary |work=The Atlantic |url=https://www.theatlantic.com/education/archive/2013/10/algebra-doesnt-have-to-be-scary/280931/ |access-date=May 2, 2023 |archive-url=https://archive.today/20220708101534/https://www.theatlantic.com/education/archive/2013/10/algebra-doesnt-have-to-be-scary/280931/ |archive-date=July 8, 2022}}</ref> On the other hand, four-year institutions have seen increased student interest in STEM programs, including mathematics and statistics.<ref name=":81">{{Cite news |last=Dutt-Ballerstadt |first=Reshmi |date=March 1, 2019 |title=Academic Prioritization or Killing the Liberal Arts? |url=https://www.insidehighered.com/advice/2019/03/01/shrinking-liberal-arts-programs-raise-alarm-bells-among-faculty |access-date=March 1, 2021 |work=Inside Higher Ed}}</ref>

[[File:U.S._college_major_change_between_2011_and_2018.png|center|thumb|700x700px|Healthcare and [[Science, technology, engineering, and mathematics|STEM]] subjects, including mathematics and statistics, have grown in popularity while the liberal arts and social studies, especially history, have declined due to market forces.<ref name=":81" /><ref name=":132">{{Cite news |date=April 3, 2023 |title=Was your degree really worth it? |url=https://www.economist.com/international/2023/04/03/was-your-degree-really-worth-it |archive-url=https://archive.today/20230408160109/https://www.economist.com/international/2023/04/03/was-your-degree-really-worth-it |archive-date=April 8, 2023 |access-date=April 14, 2023 |newspaper=The Economist}}</ref>]]

==Controversies and issues==
[[File:Boy in school, 1961 (52338002867).jpg|left|thumb|A schoolboy in Seattle (1961). The contents of mathematical education has been a topic of debate for decades.]]
Mathematics education has been a topic of debate among academics, parents, as well as educators.<ref name=":3" /><ref name=":28" /><ref name="Banchero">{{cite news |author=Stephanie Banchero |date=May 8, 2012 |title=School-standards pushback |work=[[The Wall Street Journal]] |url=https://www.wsj.com/articles/SB10001424052702303630404577390431072241906 |access-date=March 23, 2013}}</ref><ref name=":5" /> Majorities agree that mathematics is crucial, but there has been many divergent opinions on what kind of mathematics should be taught and whether relevance to the "real world" or rigor should be emphasized.<ref name=":15" /><ref name=":26" /> Another source of contention is the decentralized nature of American education, making it difficult to introduce standard curriculum implemented nationwide, despite the benefits of such a program as seen from the experience of other countries, such as Italy.<ref name=":40" /> In the early 2020s, the decision by some educators to include the topics of race and sexuality into the mathematical curriculum has also met with stiff resistance.<ref>{{Cite news |last=Blad |first=Evie |date=April 17, 2023 |title=Parents, Teachers Agree: Math Matters, But Schools Must Make It Relevant |work=Education Week |url=https://www.edweek.org/teaching-learning/parents-teachers-agree-math-matters-but-schools-must-make-it-relevant/2023/04 |access-date=April 17, 2023 |archive-url=https://web.archive.org/web/20230417192359/https://www.edweek.org/teaching-learning/parents-teachers-agree-math-matters-but-schools-must-make-it-relevant/2023/04 |archive-date=April 17, 2023}}</ref>

=== Progressive education ===
During the first half of the twentieth century, there was a movement aimed at systematically reforming American public education along more "[[Progressive education|progressive]]" grounds. [[William Heard Kilpatrick]], one of the most vocal proponents of progressive education, advocated for the de-emphasis of intellectual "luxuries" such as algebra, geometry, and trigonometry, calling them "harmful rather than helpful to the kind of thinking necessary for ordinary living." He recommended that more advanced topics in mathematics should only be taught to the select few. Indeed, prior to the Second World War, it was common for educationists to argue against the teaching of academic subjects and in favor of more utilitarian concerns of "home, shop, store, citizenship, and health," presuming that a majority of high school students could not embark on a path towards higher education but were instead, destined to become unskilled laborers or their wives.<ref name=":3">{{Cite web |last=Klein |first=David |date=2003 |title=A Brief History of American K-12 Mathematics Education in the 20th Century |url=http://www.csun.edu/~vcmth00m/AHistory.html |access-date=March 16, 2023 |publisher=California State University, Northridge}}</ref>

By the 1940s, however, the deficiency in mathematical skills among military recruits became a public scandal. Admiral [[Chester W. Nimitz|Chester Nimitz]] himself complained about the lack of skills that should have been taught in public schools among officers in training and volunteers. In order to address this issue, the military had to open courses to teach basic skills such as arithmetic for bookkeeping or gunnery.<ref name=":3" />

Indeed, many parents opposed the progressive reforms, criticizing the lack of contents. By mid-century, technological marvels, such as [[radar]], [[Nuclear power|nuclear energy]], and the [[jet engine]], made progressive education untenable.<ref name=":3" />

=== New Math ===
[[File:Navajo students studying mathematics at day school - NARA - 295155.jpg|thumb|Navajo students learning arithmetic (c. 1940). By the late 1950s, mathematics education had become more rigorous.]]
Under the '[[New Math]]' initiative, created after the successful launch of the Soviet satellite ''[[Sputnik 1|Sputnik]]'' in 1957, conceptual [[Abstraction (mathematics)|abstraction]] rather than calculation gained a central role in mathematics education.<ref name=":18" /> The educational status quo was severely criticized as a source of national humiliation and reforms were demanded, prompting Congress to introduce the [[National Defense Education Act]] of 1958.<ref name=":3" /> The U.S. federal government under President [[Dwight D. Eisenhower]] realized it needed thousands of scientists and engineers to match the might of its ideological rival the Soviet Union and started pouring enormous sums of money into research and development as well as education.<ref name="Garraty-1991">{{Cite book |last=Garraty |first=John A. |title=The American Nation: A History of the United States |publisher=Harper Collins |year=1991 |isbn=978-0-06-042312-4 |location=United States of America |pages=896–7 |chapter=Chapter XXXII Society in Flux, 1945-1980. Rethinking Public Education}}</ref><ref>{{Cite book |last=Farmelo |first=Graham |title=The Strangest Man: the Hidden Life of Paul Dirac, Mystic of the Atom |publisher=Basic Books |year=2009 |isbn=978-0-465-02210-6 |pages=363 |chapter=Twenty-six: 1958-1962}}</ref> Conceived in response to the lack of emphasis on content of the progressive education<ref name=":3" /> and the technological advances of World War II,<ref name=":4">{{Cite news |last=Gandel |first=Stephen |date=May 30, 2015 |title=This 1958 Fortune article introduced the world to John Nash and his math |work=Fortune |url=https://fortune.com/2015/05/30/john-nash-fortune-1958/ |access-date=March 16, 2023}}</ref> New Math was part of an international movement influenced by the [[Nicolas Bourbaki|Nicholas Bourbaki]] school in France, attempting to bring the mathematics taught in schools closer to what research mathematicians actually use. Students received lessons in [[set theory]], which is what mathematicians actually use to construct the set of real numbers, normally taught to advanced undergraduates in [[real analysis]] (see [[Dedekind cut]]s and [[Cauchy sequence]]s). Arithmetic with bases other than ten was also taught (see [[Binary number|binary arithmetic]] and [[modular arithmetic]]).<ref name=":22">{{Cite web |last=Gispert |first=Hélène |title=L'enseignement des mathématiques au XXe siècle dans le contexte français |url=http://culturemath.ens.fr/histoiredesmaths/htm/Gispert08-reformes/Gispert08.htm |url-status=live |archive-url=https://web.archive.org/web/20170715164210/http://culturemath.ens.fr/histoire%20des%20maths/htm/Gispert08-reformes/Gispert08.htm |archive-date=July 15, 2017 |access-date=November 4, 2020 |website=CultureMATH |language=FR}}</ref> Other topics included [[number theory]], [[probability theory]], and analytic geometry.<ref name=":4" /> 

However, this educational initiative soon faced strong opposition, not just from teachers, who struggled to understand the new material, let alone teach it, but also from parents, who had problems helping their children with homework.<ref name=":18">{{Cite news |last=Knudson |first=Kevin |date=2015 |title=The Common Core is today's New Math – which is actually a good thing |work=The Conversation |url=https://theconversation.com/the-common-core-is-todays-new-math-which-is-actually-a-good-thing-46585 |access-date=September 9, 2015}}</ref> It was criticized by experts, too. In a 1965 essay, physicist [[Richard Feynman]] argued, "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 |last=Feynman |first=Richard P. |year=1965 |title=New Textbooks for the 'New' Mathematics |url=http://calteches.library.caltech.edu/2362/1/feynman.pdf |journal=Engineering and Science |volume=XXVIII |issue=6 |pages=9–15 |issn=0013-7812}}</ref> In his 1973 book, ''[[Why Johnny Can't Add: the Failure of the New Math]]'', mathematician and historian of mathematics [[Morris Kline]] observed that it was "practically impossible" to learn new mathematical creations without first understanding the old ones, and that "abstraction is not the first stage, but the last stage, in a mathematical development."<ref name="Kline2">{{cite book |last=Kline |first=Morris |title=Why Johnny Can't Add: The Failure of the New Math |publisher=[[St. Martin's Press]] |year=1973 |isbn=0-394-71981-6 |location=New York |pages=17, 98}}</ref> Kline criticized the authors of the 'New Math' textbooks, not for their mathematical faculty, but rather their narrow approach to mathematics, and their limited understanding of pedagogy and educational psychology.<ref>{{Cite journal |last=Gillman |first=Leonard |date=May 1974 |title=Review of ''Why Johnny Can't Add'' |journal=American Mathematical Monthly |volume=81 |issue=5 |pages=531–2 |jstor=2318615}}</ref> Mathematician [[George F. Simmons]] wrote in the algebra section of his book ''Precalculus Mathematics in a Nutshell'' (1981) that the New Math produced students who had "heard of the [[commutative law]], but did not know the [[multiplication table]]."<ref>{{cite book |last=Simmons |first=George F. |title=Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry: Geometry, Algebra, Trigonometry |publisher=[[Wipf and Stock Publishers]] |year=2003 |isbn=9781592441303 |page=33 |chapter=Algebra – Introduction |chapter-url=https://books.google.com/books?id=dN1KAwAAQBAJ&pg=PA33}}</ref>

By the early 1970s, this movement was defeated. Nevertheless, some of the ideas it promoted still lived on. One of the key contributions of the New Math initiative was the teaching of calculus in high school.<ref name=":3" />

=== Standards-based reforms and the NCTM ===
{{main | Math wars | NCTM }}
From the late twentieth century to the early twenty-first, there has been a fierce debate over how mathematics should be taught. On one hand, some campaign for a more traditional teacher-led curriculum, featuring algorithms and some memorization. On the other hand, some prefer a conceptual approach, with a focus on problem-solving and the sense of numbers.<ref>{{Cite news |date=November 6, 2021 |title=America's Maths Wars |newspaper=The Economist |url=https://www.economist.com/united-states/2021/11/06/americas-maths-wars |access-date=August 23, 2022 |archive-url=https://archive.today/20211104165730/https://www.economist.com/united-states/2021/11/06/americas-maths-wars |archive-date=November 4, 2021}}</ref> However, as mathematician Hung-Hsi Wu explained, the apparent dichotomy between basic skills and understanding of mathematical concepts is a delusion.<ref>{{Cite journal |last=Wu |first=Hung-Hsi |date=Fall 1999 |title=Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education |url=https://math.berkeley.edu/~wu/wu1999.pdf |journal=American Educator |publisher=American Federation of Teachers}}</ref> 

In 1989 the National Council for Teachers of Mathematics (NCTM) produced the [[National Council of Teachers of Mathematics#1989 Curriculum and Evaluation Standards for School Mathematics|Curriculum and Evaluation Standards for School Mathematics]]. Widespread adoption of the new standards notwithstanding, the pedagogical practice changed little in the United States during the 1990s.<ref>{{Cite journal |last=Hiebert |first=James |author2=Stigler, James W. |date=September 2000 |title=A proposal for improving classroom teaching: Lessons from the TIMSS video study |journal=The Elementary School Journal |volume=101 |issue=1 |pages=3–20 |doi=10.1086/499656|s2cid=144020162 }}</ref> In fact, mathematics education became a hotly debated subject in the 1990s and early 2000s. This debate pitted mathematicians (like [[University of California, Berkeley|UC Berkeley]] mathematician Hung-Hsi Wu) and parents, many of whom with substantial knowledge of mathematics (such as the [[Institute for Advanced Study]] physicist [[Chiara Nappi|Chiara R. Nappi]]), who opposed the NCTM's reforms against educational professionals, who wanted to emphasized what they called "conceptual understanding." In many cases, however, educational professionals did not understand mathematics as well as their critics. This became apparent with the publication of the book ''Knowing and Teaching Elementary Mathematics'' (1999) by Liping Ma. The author gave evidence that even though most Chinese teachers had only 11 or 12 years of formal education, they understood basic mathematics better than did their U.S. counterparts, many of whom were working on their master's degrees.<ref name=":3" />

In 1989, the more radical NCTM reforms were eliminated. Instead, greater emphasis was put on substantive mathematics.<ref name=":3" /> In some large school districts, this came to mean requiring some algebra of all students by ninth grade, compared to the tradition of tracking only the college-bound and the most advanced junior high school students to take algebra. A challenge with implementing the Curriculum and Evaluation Standards was that no curricular materials at the time were designed to meet the intent of the Standards. In the 1990s, the National Science Foundation funded the development of curricula such as the [[Core-Plus Mathematics Project]]. In the late 1990s and early 2000s, the so-called [[math wars]] erupted in communities that were opposed to some of the more radical changes to mathematics instruction. Some students complained that their new math courses placed them into remedial math in college.<ref name="Christian Science Monitor">[http://www.csmonitor.com/sections/learning/mathmelt/p-2story052300.html Christian Science Monitor] {{webarchive|url=https://web.archive.org/web/20080509105739/http://www.csmonitor.com/sections/learning/mathmelt/p-2story052300.html |date=2008-05-09 }}</ref> However, data provided by the [[University of Michigan]] registrar at this same time indicate that in collegiate mathematics courses at the University of Michigan, graduates of Core-Plus did as well as or better than graduates of a traditional mathematics curriculum, and students taking traditional courses were also placed in remedial mathematics courses.<ref>{{Cite web |url=http://www.wmich.edu/cpmp/cpmpfaq.html#questioncollege |title=Frequently Asked Questions About the Core-Plus Mathematics Project |access-date=2009-10-26 |archive-url=https://web.archive.org/web/20100821131145/http://www.wmich.edu/cpmp/cpmpfaq.html#questioncollege |archive-date=2010-08-21 |url-status=dead }}</ref> Mathematics instructor [[Jaime Escalante]] dismissed the NCTM standards as something written by a PE teacher.<ref name=":3" />

In 2001 and 2009, NCTM released the [[Principles and Standards for School Mathematics]] (PSSM) and the [[Principles and Standards for School Mathematics#Curriculum Focal Points|Curriculum Focal Points]] which expanded on the work of the previous standards documents. Particularly, the PSSM reiterated the 1989 standards, but in a more balanced way, while the Focal Points suggested three areas of emphasis for each grade level. Refuting reports and editorials<ref>Wall Street Journal, New York Times, Chicago Sun Times</ref> that it was repudiating the earlier standards, the NCTM claimed that the Focal Points were largely re-emphasizing the need for instruction that builds skills and deepens student mathematical understanding. These documents repeated the criticism that American mathematics curricula are a "mile wide and an inch deep" in comparison to the mathematics of most other nations, a finding from the Second and Third International Mathematics and Science Studies.

=== Integrated mathematics ===
[[File:Inverse Curves Parabola Cardioid.svg|thumb|Some geometric curves expressed algebraically in polar coordinates]]
As previously stated, American children usually follow a unique sequence of mathematics courses in secondary school (grades 6 to 12), learning one subject at a time. They take two years of Algebra punctuated by a year of Geometry. Geometry, hitherto a collegiate course, was introduced into high schools in the nineteenth century. In Europe, schools followed [[Felix Klein]]'s call for Geometry to be integrated with other math subjects. In 1892 the American [[Committee of Ten]] recommended the same strategy for the United States, but American teachers had already been developing the habit of teaching Geometry has a separate course. The American high-school geometry curriculum was eventually codified in 1912 and developed a distinctive American style of geometric demonstration for such courses, known as "two-column" proofs.<ref name=":51" /> This remains largely true today, with Geometry as a proof-based high-school math class. On the other hand, many countries around the world from Israel to Italy teach mathematics according to what Americans call an [[Integrated mathematics|integrated curriculum]], familiarizing students with various aspects of calculus and prerequisites throughout secondary school.<ref name=":12" /><ref name=":13" /> In fact, many topics in Algebra and Geometry that Americans typically learn in high school are taught in middle school in Europe,<ref name=":40">{{cite journal |last=Nappi |first=Chiara |author-link=Chiara Nappi |date=May 1990 |title=On Mathematics and Science Education in the US and Europe |journal=[[Physics Today]] |volume=43 |issue=5 |page=77 |bibcode=1990PhT....43e..77N |doi=10.1063/1.2810564}}</ref> making it possible for European countries to require and to teach Calculus in high school. In France and Germany, calculus was brought into the secondary-school curriculum thanks to the advocacy of famous mathematicians, such as [[Henri Poincaré]] and Felix Klein, respectively.<ref name=":12" /><ref name=":13" /> However, as the Singaporean case demonstrates, early exposure to the concepts of calculus does not necessarily translates to actual understanding among high school students.<ref>{{Cite journal |last=Toh |first=Tin Lam |date=2021 |title=School calculus curriculum and the Singapore mathematics curriculum framework |url=https://link.springer.com/article/10.1007/s11858-021-01225-6 |journal=ZDM – Mathematics Education |volume=53 |issue=3 |pages=535–547|doi=10.1007/s11858-021-01225-6 |s2cid=233904989 }}</ref><ref name=":13" /> In the U.S., this is reflected in the concerns voiced by many university professors, according to whom their students lack sufficient preparation in pre-calculus mathematics.<ref name=":12" /> Proponents of teaching the integrated curriculum believe that students would better understand the connections between the different branches of mathematics. On the other hand, critics—including parents and teachers—prefer the traditional American approach both because of their familiarity with it and because of their concern that certain key topics might be omitted, leaving the student ill-prepared for college.<ref name=":1" /> As mentioned above, only 7% of American high school students take Integrated Mathematics.<ref name=":14" />

=== Preparation for college ===
Beginning in 2011, most states have adopted the Common Core Standards for mathematics, which were partially based on NCTM's previous work. Controversy still continues as critics point out that Common Core standards do not fully prepare students for college and as some parents continue to complain that they do not understand the mathematics their children are learning. Indeed, even though they may have expressed an interest in pursuing science, technology, engineering, and mathematics ([[Science, technology, engineering, and mathematics|STEM]]) in high school, many university students find themselves ill-equipped for rigorous STEM education in part because of their inadequate preparation in mathematics.<ref name=":56">{{Cite news |last=Drew |first=Christopher |date=November 4, 2011 |title=Why Science Majors Change Their Minds (It's Just So Darn Hard) |work=The New York Times |department=Education Life |url=https://www.nytimes.com/2011/11/06/education/edlife/why-science-majors-change-their-mind-its-just-so-darn-hard.html |url-status=live |url-access=subscription |access-date=October 28, 2019 |archive-url=https://web.archive.org/web/20111104171721/http://www.nytimes.com/2011/11/06/education/edlife/why-science-majors-change-their-mind-its-just-so-darn-hard.html |archive-date=2011-11-04}}</ref><ref name=":67">{{Cite news |last=Tyre |first=Peg |date=February 8, 2016 |title=The Math Revolution |work=The Atlantic |url=https://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/ |url-status=live |access-date=February 4, 2021 |archive-url=https://web.archive.org/web/20200628224704/https://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/ |archive-date=June 28, 2020}}</ref> Meanwhile, Chinese, Indian, and Singaporean students are exposed to high-level mathematics and science at a young age.<ref name=":56" /> About half of STEM students in the U.S. dropped out of their programs between 2003 and 2009.<ref name=":67" /> On top of that, many mathematics schoolteachers were not as well-versed in their subjects as they should be, and might well be uncomfortable with mathematics themselves.<ref name=":35" /><ref name=":67" /><ref name=":38">{{Cite news |last=Sparks |first=Sarah D. |date=January 7, 2020 |title=The Myth Fueling Math Anxiety |work=Education Week |url=https://www.edweek.org/teaching-learning/the-myth-fueling-math-anxiety/2020/01 |access-date=August 31, 2022 |archive-url=https://archive.today/20220831184139/https://www.edweek.org/teaching-learning/the-myth-fueling-math-anxiety/2020/01 |archive-date=August 31, 2022}}</ref> An emphasis on speed and rote memorization gives as many as one-third of students aged five and over [[mathematical anxiety]].<ref name=":0" />

Parents and high school counselors consider it crucial that students pass Calculus if they aim to be admitted to a competitive university. Private school counselors are especially likely to make this recommendation while admissions officers are generally less inclined to consider it a requirement.<ref name=":15" /> Moreover, there has been a movement to de-emphasize the traditional pathway with Calculus as the final mathematics class in high school in favor of Statistics and Data Science for those not planning to major in a STEM subject in college.<ref name=":16">{{Cite news |last=Schwartz |first=Sarah |date=September 7, 2022 |title=Why Elite College Admissions May Play an Outsized Role in K-12 Math Programs |work=Education Week |url=https://www.edweek.org/teaching-learning/why-elite-college-admissions-may-play-an-outsized-role-in-k-12-math-programs/2022/09 |archive-url=https://archive.today/20220910172042/https://www.edweek.org/teaching-learning/why-elite-college-admissions-may-play-an-outsized-role-in-k-12-math-programs/2022/09 |archive-date=September 10, 2022}}</ref> Nevertheless, Calculus remains the most recommended course for ambitious students.<ref name=":16" /> But in the case of Utah, as of 2023, students may skip the final required course for high-school graduation—one that combines elements of Algebra II, Trigonometry, Precalculus, and Statistics—if they submit a letter signed by their parents acknowledging that this decision could jeopardize their chances of university matriculation.<ref name=":46">{{Cite news |last=Sparks |first=Sarah D. |date=July 31, 2023 |title=Are Students Getting All the Math They Need to Succeed? |url=https://www.edweek.org/teaching-learning/are-students-getting-all-the-math-they-need-to-succeed/2023/07 |archive-url=https://archive.today/20230731194857/https://www.edweek.org/teaching-learning/are-students-getting-all-the-math-they-need-to-succeed/2023/07 |archive-date=July 31, 2023 |access-date=January 5, 2024 |work=Education Week}}</ref>

By the mid-2010s, only a quarter of American high school seniors are able to do grade-level math,<ref>{{Cite news |last=Gonser |first=Sarah |date=April 12, 2018 |title=Students are being prepared for jobs that no longer exist. Here's how that could change. |work=NBC News |department=Culture Matters |url=https://www.nbcnews.com/news/us-news/students-are-being-prepared-jobs-no-longer-exist-here-s-n865096 |access-date=October 25, 2019}}</ref> yet about half graduate from high school as A students, prompting concerns of [[grade inflation]].<ref>{{Cite news |last=Wang |first=Amy X. |date=July 19, 2017 |title=No wonder young Americans feel so important, when half of them finish high school as A students |work=Quartz |url=https://qz.com/1032183/no-wonder-young-americans-feel-so-important-when-half-of-them-finish-high-school-as-a-students/ |archive-url=https://archive.today/20210619224958/https://qz.com/1032183/no-wonder-young-americans-feel-so-important-when-half-of-them-finish-high-school-as-a-students/ |archive-date=June 19, 2021}}</ref> Strong performance in Algebra I, Geometry, and Algebra II predict good grades in university-level Calculus even better than taking Calculus in high school.<ref name=":32">{{Cite news |last=Sparks |first=Sarah D. |date=June 28, 2021 |title=Doubling Down on Algebra Can Pay Off in College, But Who Your Peers Are Matters, Too |work=Education Week |url=https://www.edweek.org/teaching-learning/doubling-down-on-algebra-can-pay-off-in-college-but-who-your-peers-are-matters-too/2021/06 |access-date=April 25, 2023 |archive-url=https://archive.today/20230425145608/https://www.edweek.org/teaching-learning/doubling-down-on-algebra-can-pay-off-in-college-but-who-your-peers-are-matters-too/2021/06 |archive-date=April 25, 2023}}</ref>

Another issue with mathematics education has been integration with science education. This is difficult for public schools to do because science and math are taught independently.  The value of the integration is that science can provide authentic contexts for the math concepts being taught and further, if mathematics is taught in synchrony with science, then the students benefit from this correlation.<ref>Furner, Joseph M., and Kumar, David D. [http://www.ejmste.com/v3n3/EJMSTE_v3n3_Furner&Kumar.pdf], "The Mathematics and Science Integration Argument:
A Stand for Teacher Education," Eurasia Journal of Mathematics, Science & Technology Education,  Vol. 3, Num. 3, August, 2007, accessed on 15 December 2013</ref>

=== Enrichment programs and accelerated tracks ===
[[File:Math Club at Lakehill Preparatory.jpg|thumb|A math club at a preparatory school in Texas (2018)]]
Growing numbers of parents have opted to send their children to enrichment and accelerated learning after-school or summer programs in mathematics, leading to friction with school officials who are concerned that their primary beneficiaries are affluent white and Asian families, prompting parents to pick private institutions or [[math circle]]s. Some public schools serving low-income neighborhoods even denied the existence of mathematically [[Intellectual giftedness|gifted]] students.<ref name=":67" /> In fact, American educators tend to focus on poorly performing students rather than those at the top, unlike their Asian counterparts.<ref name=":412">{{Cite journal |last=Clynes |first=Tom |date=September 7, 2016 |title=How to raise a genius: lessons from a 45-year study of super-smart children |journal=Nature |volume=537 |issue=7619 |pages=152–155 |bibcode=2016Natur.537..152C |doi=10.1038/537152a |pmid=27604932 |s2cid=4459557 |doi-access=free}}</ref> Parents' proposal for an accelerated track for their children are oftentimes met with hostility by school administrators.<ref>{{Cite news |last=Matthews |first=Jay |date=September 10, 2022 |title=Middle schools shun challenges, such as teaching your kid algebra |newspaper=The Washington Post |url=https://www.washingtonpost.com/education/2022/09/10/algebra-in-eighth-grade/ |access-date=April 29, 2023 |archive-url=https://archive.today/20220912132643/https://www.washingtonpost.com/education/2022/09/10/algebra-in-eighth-grade/ |archive-date=September 12, 2022}}</ref> Conversely, initiatives aimed at de-emphasizing certain core subjects, such as Algebra I, triggered strong backlash from parents and university faculty members.<ref name=":43" /><ref name=":44" /> Students identified by the [[Study of Mathematically Precocious Youth]] as top scorers on the mathematics (and later, verbal) sections of the SAT often became highly successful in their fields.<ref>{{Cite journal |last=Clynes |first=Tom |date=January 2017 |title=Nurturing Genius |url=https://www.scientificamerican.com/article/nurturing-genius/ |journal=Scientific American |archive-url=https://web.archive.org/web/20161223172352/https://www.scientificamerican.com/article/nurturing-genius/ |archive-date=December 23, 2016}}</ref> By the mid-2010s, some public schools have begun offering enrichment programs to their students.<ref name=":67" />

Similarly, while some school districts have proposed to stop separating students by mathematical ability in order to ensure they begin high school at the same level, parents of gifted children have pushed back against this initiative, fearing that it would jeopardize their children's future college admissions prospects, especially in the STEM fields.<ref name=":15" /><ref name=":16" /> In San Francisco, for example, such a plan was dropped due to a combination of mixed results and public backlash.<ref name=":15" />

=== Shortage of instructors ===
A shortage of qualified mathematics schoolteachers has been a serious problem in the United States for many years.<ref name=":34" /><ref name=":37" /> In order to rectify this problem, the amount of instructional hours dedicated towards mathematical contents has been increased in undergraduate programs aimed at training elementary teachers.<ref>{{Cite news |last=Will |first=Madaline |date=May 18, 2022 |title=Are Aspiring Elementary Teachers Learning Enough Math? |work=Education Week |url=https://www.edweek.org/teaching-learning/are-aspiring-elementary-teachers-learning-enough-math/2022/05 |access-date=May 10, 2023 |archive-url=https://archive.today/20220831183308/https://www.edweek.org/teaching-learning/are-aspiring-elementary-teachers-learning-enough-math/2022/05 |archive-date=August 31, 2022}}</ref> Teachers oftentimes unknowingly transmit their own negative attitude towards mathematics to their students, damaging the quality of instruction.<ref name=":38" />
== Standardized tests ==
<gallery mode="packed" heights="250">
File:PISA average Mathematics scores 2018.png|[[Programme for International Student Assessment|PISA]] average mathematics scores (2018)
File:TIMSS 4th grade average Mathematics scores 2019.png|[[Trends in International Mathematics and Science Study|TIMSS]] 4th grade average mathematics scores (2019)
</gallery>The [[Programme for International Student Assessment|Program for International Student Assessment]] (PISA) is held every three years for 15-year-old students worldwide.<ref>{{Cite news|url=https://www.economist.com/international/2016/12/10/what-the-world-can-learn-from-the-latest-pisa-test-results|title=What the world can learn from the latest PISA test results|newspaper=The Economist|access-date=2018-07-25|language=en}}</ref> In 2012, the United States earned average scores in science and reading. It performed better than other progressive nations in mathematics, ranking 36 out of 65 other countries. The PISA assessment examined the students’ understanding of mathematics as well as their approach to this subject and their responses. These indicated three approaches to learning. Some of the students depended mainly on memorization. Others were more reflective on newer concepts. Another group concentrated more on principles that they have not yet studied. The U.S. had a high proportion of memorizers compared to other developed countries.<ref name=":0">{{Cite journal |last1=Boaler |first1=Jo |last2=Zoido |first2=Pablo |date=2016-10-13 |title=Why Math Education in the U.S. Doesn't Add Up |url=https://www.scientificamerican.com/article/why-math-education-in-the-u-s-doesn-t-add-up/ |journal=Scientific American Mind |language=en |volume=27 |issue=6 |pages=18–19 |doi=10.1038/scientificamericanmind1116-18 |issn=1555-2284 |archive-url=https://archive.today/20220823231901/https://www.scientificamerican.com/article/why-math-education-in-the-u-s-doesn-t-add-up/ |archive-date=August 23, 2022}}</ref> During the 2015 testing, the United States failed to make it to the top 10 in all categories including mathematics. More than 540,000 teens from 72 countries took the exam. American students' average score in mathematics declined by 11 points compared to the previous testing.<ref name=":23">{{Cite news |last1=Jackson |first1=Abby |last2=Kiersz |first2=Andy |date=December 6, 2016 |title=The latest ranking of top countries in math, reading, and science is out — and the US didn't crack the top 10 |work=Business Insider |url=https://www.businessinsider.com/pisa-worldwide-ranking-of-math-science-reading-skills-2016-12 |access-date=July 25, 2016}}</ref> The 2022 PISA test showed that U.S. national average in mathematics remained behind those of other industrialized nations and remained below the OECD average.<ref>{{Cite news |last=Saric |first=Ivana |date=December 5, 2023 |title=U.S. students' math scores plunge in global education assessment |url=https://www.axios.com/2023/12/05/us-students-pisa-global-assessment |access-date=January 7, 2024 |work=Axios}}</ref> Furthermore, one third of American students did not meet the requirements for basic proficiency in mathematics.<ref>{{Cite news |last=Mervosh |first=Sarah |date=December 5, 2023 |title=Math Scores Dropped Globally, but the U.S. Still Trails Other Countries |url=https://www.nytimes.com/2023/12/05/us/math-scores-pandemic-pisa.html |archive-url=https://archive.today/20231205110953/https://www.nytimes.com/2023/12/05/us/math-scores-pandemic-pisa.html |archive-date=December 5, 2023 |access-date=January 7, 2024 |work=The New York Times}}</ref>

However, European- and especially Asian-American students perform above the OECD average. See chart below.<ref name=":03">{{Cite web |title=Highlights of U.S. PISA 2018 Results Web Report |url=https://nces.ed.gov/surveys/pisa/pisa2018/pdf/PISA2018_compiled.pdf}}</ref>
[[File:PISA Math Scores (2018).png|center]]
According to a 2021 report by the [[National Science Foundation]] (NSF), American students' [[Numeracy|mathematical literacy]] ranks 25th out of 37 nations of the Organization for Economic Cooperation and Development ([[OECD]]).<ref>{{Cite web |last1=Rotermund |first1=Susan |last2=Burke |first2=Amy |date=July 8, 2021 |title=Elementary and Secondary STEM Education - Executive Summary |url=https://ncses.nsf.gov/pubs/nsb20211/executive-summary |access-date=January 27, 2023 |website=National Science Foundation}}</ref>

During the 2000s  and 2010s, as more and more college-bound students take the SAT, scores have gone down.<ref name=":29">{{Cite news |last=Finder |first=Alan |date=August 28, 2007 |title=Math and Reading SAT Scores Drop |work=The New York Times |url=https://www.nytimes.com/2007/08/28/education/28cnd-sat.html |access-date=April 24, 2023 |archive-url=https://archive.today/20230424033620/https://www.nytimes.com/2007/08/28/education/28cnd-sat.html |archive-date=April 24, 2023}}</ref><ref name=":8" /><ref name=":68" /> (See chart below.) This is in part because some states have required all high school students to take the SAT, regardless of whether or not they were going to college.<ref name=":29" />
[[File:Historical Average SAT Scores (Vector).svg|center|thumb|680x680px|Historical average SAT math scores reached a nadir in 1980, declined between 2005 and 2016 and after the 2016 re-scaling.]]
In 2015, educational psychologist Jonathan Wai of Duke University analyzed average test scores from the [[Army General Classification Test]] in 1946 (10,000 students), the Selective Service College Qualification Test in 1952 (38,420), [[Project Talent]] in the early 1970s (400,000), the [[Graduate Record Examinations|Graduate Record Examination]] between 2002 and 2005 (over 1.2 million), and the SAT Math and Verbal in 2014 (1.6 million). Wai identified one consistent pattern: those with the highest test scores tended to pick mathematics and statistics, the natural and social sciences, and engineering as their majors while those with the lowest were more likely to choose healthcare, education, and agriculture. (See the two charts below.)<ref name="Wai-2015">{{Cite news |last=Wai |first=Jonathan |date=February 3, 2015 |title=Your college major is a pretty good indication of how smart you are |work=Quartz |url=http://qz.com/334926/your-college-major-is-a-pretty-good-indication-of-how-smart-you-are/ |url-status=live |access-date=January 30, 2021 |archive-url=https://web.archive.org/web/20200116221413/http://qz.com/334926/your-college-major-is-a-pretty-good-indication-of-how-smart-you-are/ |archive-date=January 16, 2020}}</ref><ref>{{Cite news |last=Crew |first=Bec |date=February 16, 2015 |title=Your College Major Can Be a Pretty Good Indication of How Smart You Are |work=Science Magazine |department=Humans |url=https://www.sciencealert.com/your-college-major-can-be-a-pretty-good-indication-of-how-smart-you-are |access-date=January 30, 2021}}</ref>
[[File:Uni_Major_and_SAT_Averages.png|center]]
[[File:Graduate Majors and GRE Averages.png|center]]
Results from the [[National Assessment of Educational Progress]] (NAEP) test show that scores in mathematics have been leveling off in the 2010s, but with a growing gap between the top and bottom students. The COVID-19 pandemic, which forced schools to shut down and lessons to be given online, further widened the divide, as the best students lost fewer points compared to the worst and therefore could catch up more quickly.<ref name=":25">{{Cite news |last=Mervosh |first=Sarah |date=September 1, 2022 |title=The Pandemic Erased Two Decades of Progress in Math and Reading |work=The New York Times |url=https://www.nytimes.com/2022/09/01/us/national-test-scores-math-reading-pandemic.html |access-date=September 1, 2022 |archive-url=https://archive.today/20220901124205/https://www.nytimes.com/2022/09/01/us/national-test-scores-math-reading-pandemic.html |archive-date=September 1, 2022}}</ref> While students' scores fell for all subjects, mathematics was the hardest hit, with a drop of eight points,<ref>{{Cite news |last=Binkey |first=Collin |date=October 24, 2022 |title=Test scores show how COVID set kids back across the U.S. |work=PBS Newshour |url=https://www.pbs.org/newshour/education/test-scores-show-how-covid-set-kids-back-across-the-u-s |access-date=December 31, 2022}}</ref> the steepest decline in 50 years.<ref name=":45" /> Scores dropped for students of all races, sexes, socioeconomic classes, types of schools, and states with very few exceptions.<ref name=":30">{{Cite news |last=Sparks |first=Sarah D. |date=October 24, 2022 |title=Explaining That Steep Drop in Math Scores on NAEP: 5 Takeaways |work=Education Week |url=https://www.edweek.org/teaching-learning/explaining-that-steep-drop-in-math-scores-on-naep-5-takeaways/2022/10 |access-date=April 25, 2023 |archive-url=https://archive.today/20230320173042/https://www.edweek.org/teaching-learning/explaining-that-steep-drop-in-math-scores-on-naep-5-takeaways/2022/10 |archive-date=March 20, 2023}}</ref><ref name=":42">{{Cite news |last=Chapman |first=Ben |date=October 24, 2022 |title=Math Scores Dropped in Every State During Pandemic, Report Card Shows |work=The Wall Street Journal |url=https://www.wsj.com/amp/articles/math-scores-dropped-in-every-state-during-pandemic-report-card-shows-11666584062 |access-date=May 18, 2023 |archive-url=https://archive.today/20221024123306/https://www.wsj.com/amp/articles/math-scores-dropped-in-every-state-during-pandemic-report-card-shows-11666584062 |archive-date=October 24, 2022}}</ref> This might be because mathematics education is more dependent upon the classroom experience than reading,<ref name=":42" /> as students who were allowed to return to in-person classes generally did better, more so in mathematics than in reading.<ref>{{Cite news |last=Lasarte |first=Diego |date=May 3, 2023 |title=US eighth graders' history test scores hit lowest levels on record |work=Quartz |url=https://qz.com/stock-ownership-in-america-is-still-less-common-than-it-1850377788 |access-date=May 18, 2023 |archive-url=https://archive.today/20230519001618/https://qz.com/stock-ownership-in-america-is-still-less-common-than-it-1850377788 |archive-date=May 19, 2023}}</ref> However, on the topics of statistics and probability, student performance had already declined before the pandemic.<ref name=":31">{{Cite news |last=Schwartz |first=Sarah |date=February 24, 2023 |title=Students' Data Literacy Is Slipping, Even as Jobs Demand the Skill |work=Education Week |url=https://www.edweek.org/teaching-learning/students-data-literacy-is-slipping-even-as-jobs-demand-the-skill/2023/02 |access-date=April 25, 2023 |archive-url=https://archive.today/20230425141548/https://www.edweek.org/teaching-learning/students-data-literacy-is-slipping-even-as-jobs-demand-the-skill/2023/02 |archive-date=April 25, 2023}}</ref> As consequence, the entire cohort of college students in the 2022-23 academic year have lower average grades and mathematical standards.<ref>{{Cite news |last=Fawcett |first=Eliza |date=November 1, 2022 |title=The Pandemic Generation Goes to College. It Has Not Been Easy. |work=The New York Times |url=https://www.nytimes.com/2022/11/01/us/covid-college-students.html |access-date=May 25, 2023 |archive-url=https://archive.today/20221101154830/https://www.nytimes.com/2022/11/01/us/covid-college-students.html |archive-date=November 1, 2022}}</ref>

A 2023 comparison between parents' views and standardized test scores revealed a significant gap; most parents overestimated their children's academic aptitude. In mathematics, only 26% were proficient, even though 90% of the parents asked thought their children met grade standards.<ref name=":24">{{Cite news |last1=Nawaz |first1=Amna |last2=Cuevas |first2=Karina |date=April 6, 2023 |title=Study shows parents overestimate their student's academic progress |work=PBS Newshour |url=https://www.pbs.org/newshour/show/study-shows-parents-overestimate-their-students-academic-progress |access-date=April 9, 2023}}</ref> Having a higher NAEP math score in eighth grade is correlated with high academic standing, higher income, lower rates of [[Teenage pregnancy in the United States|adolescent parenthood]], and lower chances of criminality.<ref>{{Cite journal |last1=Doty |first1=Elena |last2=Kane |first2=Thomas J. |last3=Patterson |first3=Tyler |last4=Staiger |first4=Douglas O. |date=December 2022 |title=What Do Changes in State Test Scores Imply for Later Life Outcomes? |url=https://www.nber.org/papers/w30701 |journal=NBER Working Papers |series=Working Paper Series |publisher=National Bureau of Economic Research |doi=10.3386/w30701|doi-access=free }}</ref>

==Advanced Placement Mathematics==
There was considerable debate about whether or not calculus should be included when the [[Advanced Placement]] (AP) Mathematics course was first proposed in the early 1950s. AP Mathematics has eventually developed into AP Calculus thanks to physicists and engineers, who convinced mathematicians of the need to expose students in these subjects to calculus early on in their collegiate programs.<ref name=":2" />

In the early 21st century, there has been a demand for the creation of AP Multivariable Calculus and indeed, a number of American high schools have begun to offer this class, giving colleges trouble in placing incoming students.<ref name=":2" />

As of 2021, [[AP Precalculus]] was under development by the College Board, though there were concerns that universities and colleges would not grant credit for such a course, given that students had previously been expected to know this material prior to matriculation.<ref name=":2" /> AP Precalculus launched in Fall 2023.<ref>{{Cite news |last=Najarro |first=Ileana |date=May 19, 2022 |title=A New AP Precalculus Course Aims to Diversify the Math Pipeline |work=Education Week |url=https://www.edweek.org/teaching-learning/a-new-ap-precalculus-course-aims-to-diversify-the-math-pipeline/2022/05 |archive-url=https://archive.today/20230324081354/https://www.edweek.org/teaching-learning/a-new-ap-precalculus-course-aims-to-diversify-the-math-pipeline/2022/05 |archive-date=March 24, 2023}}</ref>

==Conferences==
Mathematics education research and practitioner conferences include: [[National Council of Teachers of Mathematics|NCTM]]'s [http://www.nctm.org/conferences ''Regional Conference and Exposition'' and ''Annual Meeting and Exposition'']; The Psychology of Mathematics Education's North American Chapter [http://www.pmena.org annual conference]; and numerous smaller regional conferences.

==See also==
{{Portal|Education|Mathematics|United States}}
* [[Mathematics education]]
* [[Embodied design (mathematics education)]]
* [[Graduate science education in the United States]]
* [[Mathematics education in New York]]
* [[National Museum of Mathematics]]
* ''[[Stand and Deliver]]'' (1988 film)
* [[Math 55]] at Harvard University
* [[Financial literacy curriculum]]
* [[Chicago movement]]

== References ==
{{reflist}}

== Further reading ==
* {{Cite book |last1=Garelick |first1=Barry |title=Traditional Math: An effective strategy that teachers feel guilty using |last2=Wilson |first2=JR |publisher=John Catt Educational |year=2022 |isbn=978-1-91526-154-0}}
== External links ==
* [https://mathisyourfuture.com/articles/1 Math courses with “Math Is Your Future”]; an article about studying math with the use of Internet technologies
* [https://www.youtube.com/watch?v=l9byN0skNKY Math is amazing and we have to start treating it that way], [[Eugenia Cheng]] for the PBS ''Newshour''.

{{Mathematics education}}
{{American mathematics}}
[[Category:Mathematics education in the United States| ]]
[[Category:Curricula]]