Contributed by William Walter Kay BA JD © 2022
Professor Emeritus (Poli-Sci) at Queens College, Andrew Hacker (b.1929), received his PhD from Princeton and later worked at Oxford. While not a mathematician, Hacker has taught university-level math and stats. He’s authored 10 books and written for the New York Times and New York Review of Books. His forte includes the popularization of statistics and the politicization of education.
Hacker had been compiling notes and conducting interviews regarding mathematics instruction for 15 years before the New York Times solicited an Op-ed on the topic. His Is Algebra Necessary? (2012) generated near record responses, spurring him to write The Math Myth (2016).
Most “Mandarins” are tenured Math profs at universities renowned for grad studies and research. Other Mandarins haunt lesser campuses but sit on scholastic and education committees. Mandarins are Math’s power elite – a self-perpetuating priesthood awed as sages blessed with higher orders of intellect. This unaccountable caste dictates how an entire realm of knowledge is taught, from kindergarten to postdoc.
Mandarins deride those not sharing their proclivity for abstract mathematical thought. They believe their intellects license them to dominate all education – an agenda founded on the supposition that mathematics unveils the mind at its finest. Mathematics is their ideology; their Theology.
Having imposed mandatory ‘Math 101’ onto universities, Mandarins command commodious budgets. Math 101 instructors are low-waged, overworked, cubicle-dwelling adjunct profs or grad students. To Mandarins “academic freedom” means freedom from teaching; a chore beneath their talents.
Mandarins while away the hours on research, sabbaticals, conferences, and paper publishing. Esoterica within these papers is terra incognita even to adults with reputable educations. SUNY’s Math Department concedes: “information with which a mathematics research project deals is usually inaccessible to undergraduates.”
Stanford’s Keith Devlin surmises Math: “has reached a stage of such abstraction that many of its frontier problems cannot be understood even by experts.”
Mandarins can’t communicate with each other. Hilbert spaces, Reimann zeta functions, Calabi-Yau manifolds etc exemplify “academic” in its pejorative sense.
Illusions surrounding the powers of mathematics constitute a defining mythology of our times.
In 1957 Sputnik launched the spectre of an America falling behind in STEM (Science, Technology, Engineering, Math). Mandarins, claiming computational education inadequate, demanded students learn mathematical theory. Thus begat “New Math” which, according to Suzanne Wilson (Michigan State U), “failed because it was led by mathematicians not by math teachers.”
Modern Mandarin fronts include: National Council of Teachers of Mathematics, National Math and Science Initiative, American Association of Universities, Achieve Inc. et al.
Achieve Inc.’s Math Works (2008) spouts spurious stats about alleged multitudes of jobs requiring advanced math. Achieve Inc. lobbied the National Governors Association and the Council of Chief State School Officers. Bill Gates kicked-down $200 ml.
Also in 2008, a 20-member panel selected by the US Education Department issued its 857-page Foundations for Success (F4S) to address K-12 shortcomings. Fifteen panelists were profs from universities emphasizing doctoral studies. A lone teacher tokenized the panel. F4S recommended prepping students for advanced algebra starting in Grade 6. F4S precipitated Common Core, with its universal math hurdles.
Common Core architect, Achieve Inc., demands:
“All students – those attending a four-year college, those planning to earn a two-year degree, or get some post-secondary training, and those seeking to enter the job market right away – need to have comparable preparation in high school.”
Common Core’s high-denominator, one-size-fits-all requirements sets up many students for disaster. Inflicting “Math for Harvard” on everyone is like demanding everyone play concerto violin.
The research-oriented American Association of Universities (AAU) sent copies of Standards for Success (S4S) to 20,000 high-schools. S4S warns students are often shocked by the math skills universities expect. S4S lists 68 skills (quadratic functions, trigonometric shifts) all students must master, even Art majors.
The agenda is radical. Every student must conquer advanced algebra. Between 1982 and 2016 the percentage of high-schools demanding 2 years of algebra rose from 55% to 76%. College administrators prove their rigor by piling on algebra. Most now use SATs which presume 3 years of advanced math.
Meanwhile, students flee this once leading discipline. Between 1970 and 2013 annual awards of Math BAs fell from 27,135 to 17,408 (from 3.4% to 1% of all BAs). Awards of Math MAs fell 5,145 to 1,809 (2.5% to 0.3%). Math PhDs fell from 1,052 to 730 (3.5% to 0.5%). As Princeton entrants must hit sky-high SAT Math scores, this cohort should teem with algebra-philes. 3% major in Math.
Mandarins fail spectacularly in transmitting their love of Math to students. They blame Math’s unpopularity on pampered students, fearful of difficult subjects.
Math-dense SAT and Common Core exams raise insurmountable barriers for students whose aptitudes lie elsewhere. In many states 60+% of students fail Common Core math.
Most students fail high-school Algebra; although most eventually squeak through. First-try failure rates at Algebra in Los Angeles high-schools is 65%. In Arizona its 64%; in Washington: 61%. These are senior-year students!
20% of high-school students drop-out. Math is the chief academic culprit. Math is also the main barrier to entering college.
Mandatory algebra can be a nightmare of enigmatic abstractions that turn kids off Math… and off education.
Listen to Math teachers:
“I will have close to 200 students who now believe they are failures because they did not meet excessive math standards.”
“In my 40 years as a math educator, I have seen too many capable people crippled by this algebra curse. We are losing too many students to the gatekeepers who push algebra as some kind of miracle drug for success.”
The National Center on Education and Economy complains:
“…many community college students are denied a certificate or diploma, because they have failed in a mathematics course irrelevant to the work these students plan to do or the courses they need to take….(algebra) is being used much as Latin was used a century ago, as a screen to keep the unwanted out of college.”
Algebra and Calculus anguish rich and poor. Expensive tutoring, however, helps privileged kids succeed. Corporations like Kaplan and Princeton Review rake in billions for tutoring. Additional billions go to freelancers – mostly for Math prep. Tutors teach test-taking techniques i.e., back-solving exam questions. With shrewd tutoring students with scant Math knowhow fetch decent SAT scores.
Parental ability to pay tutors segregates students. Affluent and impoverished districts exhibit gaping Math disparities.
Failure rates for university Math are over twice that of any other discipline. City University’s mandatory Algebra 101 inflicts a 57% failure rate. Math is the principal academic reason why 45% of university entrants leave without degrees.
Few attend Math 101 voluntarily. Most end up in Remedial Math. Huge class sizes deprive students of one-on-one explanations.
Mandarins feel no obligation to help struggling students or to make Math appealing. Math is designed for failure. Mandarins love abstract algebra because many students can’t do it. They brag about weeding-out weaklings. Mandarins can afford such behaviour because each autumn yields a fresh crop of involuntary pupils. Screening students based on algebra ability dumps millions into the career landfill.
Hacker tells of an aspiring veterinary technician, with a knack for animal care, who had her hopes crushed by algebra. No veterinarian Hacker interviewed recalled any need for algebra. Numbers figure in prescriptions and treatments, but determining such quanta requires only arithmetic.
Harvard’s Tony Wagner studies what businesses want from employees. Even at high-tech firms: “knowledge of mathematics did not make the top-ten list of the skills employers found important.”
Mandarins claim Math degrees equal higher earnings. Any degree equals higher earnings. Reading Dickens equals higher earnings.
According to Rutgers’ Math prof Joseph Rosenstein:
“It is hard to make the case that topics like complex numbers, rational exponents, systems of linear equality and inverse functions are needed by all students.”
Rosenstein asks policy wonks: “When was the last time you needed to factor trinomials?”
Mathematician Lynn Steen adds:
“…mathematics teachers simply do not know enough about how mathematics is used by people other than mathematicians… What current and prospective employees lack is not calculus or college algebra, but a plethora of more basic quantitative skills that could be taught in high school…”
Manufacturing scholar, John Smith, argues:
“Mathematical reasoning in workplaces differs markedly from school mathematics… the algorithms taught in school are often not the computational methods of choice for workers… few teachers have any idea what goes on in the work world.”
Two skills experts echo Smith:
“Higher levels of abstract mathematics are required for access to certain professions even when high-level mathematical procedures are unnecessary in the day-to-day work of those professions.”
The ‘E’ in STEM, Engineers, are shrinking in numbers relative to other professions. Universities graduate more Engineers than the economy needs. Graduates often work in sales or management. Moreover, experts estimate only 15% of practising Engineers use advanced math. N.Y. Polytechnic’s Dean of Mechanical & Aerospace Engineering reckons 10% of his fields’ tasks require advanced math.
Arizona State U Engineering’s Dean, Mitzi Montoya, complains students lack functional numeracy not advanced algebra. Montoya:
“…go out and look at what engineers use, it’s not calculus or differential equations. Even if you go into a big company that’s building sophisticated rockets, you will still find only a very small percentage doing mathematical analysis.”
She speaks of students who did exciting robot-building in high-school yet flunked Calculus. She fears losing incipient Edisons. The inventors who hitherto became industrialists couldn’t pass through schools today with their mind-numbing algebra and calculus obsessions.
Another Engineering prof regularly asks alumni what math they use. Their main response: “addition, subtraction, multiplication, division” (i.e., arithmetic). Such revelations find support from the field:
“Many of the peers I work with are very good engineers, but have retained very little mathematics… because they do not need to use it.”
“I have been an engineer for all of my adult life. Algebra? Calculus? Differential equations? I have forgotten most of this stuff from lack of use.”
“I have worked in a technical capacity at Texas Instruments and Honeywell and have been awarded two patents. I have never had to solve a calculus problem or a quadratic equation.”
The ‘T’ in STEM, Technicians, are ordinary people doing ordinary jobs like: “pump system gauger,” “gynecological sonographer,” “avionic equipment mechanic,” or “cryptanalysis keyer.” Techs need agility with numbers as applied to specific processes or equipment. Most have only high-school, or community college, diplomas. Techs get on-the-job quantitative instruction. German and Japanese carmakers locate uber-modern plants in states populated with high-school dropouts.
Computer techs are mostly coders. Beneath each creative designer crouch hundreds of coders who must get every symbol, letter and integer precisely right. This is spelling not math.
University of Georgia’s Dave Edwards teaches “Math for Computer Science.” He asked recruiters from a software developer what math they used. They responded: “none.” They used Math BAs to filter jobseekers. (Edwards contends most Engineers use eighth-grade arithmetic.)
Hacker audited an “Algorithmic Problem Solving” class. No mathematic equations were mentioned. The class taught logical sequencing of a symbolic language.
One software designer quips that he only uses math to calculate his restaurant tips.
Media drumbeats about tech shortages recall complaints about farm-labor shortages. It’s about lowering wages. (An article about a fabricating firm lacking technicians neglected to mention the jobs paid $10 an hour.) Boston Consulting jibes: “trying to hire high-skilled workers at rock-bottom prices is not a skills gap.” While Microsoft and Honeywell cry for computer grads, the American Association of Professional Coders complains half its members make under $41,000 a year.
The Association of American Medical Colleges asked 14,240 medical students to rate the usefulness of pre-med courses. Biology and Bio-chem topped the list. Calculus came in distant last.
The Admissions Dean at Mount Sanai Medical School believes: “only arithmetic is needed in patient care.” Another Physician opines:
“For medical school, one big hurdle was always calculus, a thoroughly irrelevant course. Any honest physician will tell you the last time he/she used calculus was on a final exam in the subject.”
Actuaries endure exams comparable to Princeton’s Math PhD program. An actuary for a multi-billion dollar pension fund confides: “the test covers mathematics that people will never need in their jobs.” He has seconders:
“I am a retired finance type of guy with an MBA. In my forty years of work, I never had to solve or use quadratic equations. The times tables and long division usually sufficed.”
Famed Biologist, E. O. Wilson, reminds that Darwin lacked mathematical talent; adding:
“Many of the most successful scientists in the world today are mathematically no more than semiliterate.”
Math requirements: “deprive science of an immeasurable amount of sorely needed talent.”
Nobel-winning Physicist, Carl Wieman, says real Physicists use: “sophisticated mathematics less and less.”
70% of working Americans lack degrees. They somehow drive UPS trucks and manage Safeway’s without advanced algebraic training – which isn’t to say they don’t use algebra. Elementary algebra is ubiquitous. Right-sizing a recipe requires algebra.
One researcher studied carpet-layers. Pros conserve carpet and minimize seams by deploying: coordinate geometry, tangency points and computational algorithms. They evince intricate algebraic competence sans high-school diplomas.
A study of odds-beating racetrack handicappers found astonishing abilities to combine variables (i.e., algebra). Handicappers were drop-outs who performed poorly on math tests. Scholars concluded academic tests are: “unrelated to real-world forms of cognitive complexity.”
The National Council of Teachers of Mathematics contends: “a person who has studied mathematics should be able to live more intelligently than one who has not.” Renowned mathematician, Morris Kline doubts this, as does colleague Peter Johnson:
“There appears to be no research whatever that would indicate that the kind of reasoning skills a student is expected to gain from learning algebra would transfer to other domains of thinking…”
A DePauw Mathematician adds:
“To assert that mathematical training strengthens the mind is as impossible to prove as the proposition that music and art broaden and enrich the soul.”
A university-level Biologist is adamant:
“We are told that if we could think logically about triangles, we could think logically about all sorts of things. What nonsense!”
Proving Math theorems means securing Mandarin consensus. Proofs run to hundreds of pages of argumentation detached from earthly experience. Conversely, legal and scientific proofs involve more than pondering. They involve evidence. Legal proofs apply trying standards of doubting and balancing evidence. Scientific verdicts are more tentative than Math verdicts. Harvard’s
Astrophysics Chair asserts:
“In physics, you are required to base what you do on proven facts. In mathematics, you are allowed to go in all directions that have no connections with reality.”
Students with high Math scores aren’t any better at, say, History. High SAT Math scores don’t correlate with high scores across the board. (High literacy scores do.)
Are math-nurds the most reasonable, well-informed people you’ve met?
International competitions correlate math proficiency with authoritarianism. China and Iran shine; as do authoritarian cultures like South Korea where tutoring is universal; tonnes of homework the norm; and where kids suffer sleep deprivation and commit suicide.
Children from aspiring immigrant families excel at Math because they arrive with unquestioning willingness to jump through arbitrary hoops. One educator describes Math instruction as “teaching how to spell without knowing what the words mean.”
Math instruction opposes: subjectivity, creativity and curiosity. Mandarins are suspicious of classes students enjoy. They disdain entertaining instructors. They want students seated in grid rows, working alone toward the one correct answer. They extol Math’s compatibility with standardized machine testing.
Denunciations of Hacker’s New York Times article fulminated with bellicose superiority about the perseverance needed to conquer algebra and calculus. None spoke of their utility or beauty. Pointless Math drills were a rite of passage they’d endured.
Math favors acquiescent drudges.
Academic luminaries confess: “little is know about what effective teachers do to generate greater gains in student learning.”
Debates centre around “Discovery” versus “Drilling.” Discovery instills love of learning. Discovery students analyse problems and create solutions as communities of learners. Teams explore concrete problems encountered by students. In Japan, Math assignments are done together in class – not home alone. Whizzes help strugglers.
In 1999, after the US Education Secretary endorsed a panel report praising Discovery, 200 Math profs signed a letter complaining about the panel’s dearth of “research mathematicians.” They demanded elementary schools prepare students for the Math encountered in grad studies. Every first-graders was reckoned a budding research mathematician.
Hacker wants higher education to teach: adult arithmetic; functional numeracy; quantitative reasoning.
Beacons of hope include Toyota’s collaboration with a Mississippi community college on a “Machine Tool Math” course which ditches abstract algebra in favour of equations essential for machinists.
Berkeley Biologist, John Matsui, created a Biology-oriented Math course. Matsui contends that science disciplines: “need a mathematics course tailored to their discipline, which few mathematics faculties are willing, let alone able, to teach.”
Bemoaning 50% drop-out rates among Science and Engineering students, the Council of Advisors on Science and Technology recommended Math be taught by professors from outside Math departments. The American Mathematical Society erupted in outrage, insisting only possessors of advanced Math degrees teach introductory and vocational Math.
The Carnegie Foundation commissioned a public stats course as an alternative to algebra. Mandarins loaded it with “chi-square homogeneity” and “least square regressions.” Failure rates persisted.
When Harvard showcased “quantitative reasoning,” 92 of its 94 Math profs boycotted.
Arizona State U Engineering designed an in-house “Math for Engineers” course. The Math faculty killed it!
We each arrive with sufficient intelligence and imagination to excel at some endeavour. Some possess aptitudes for abstract algebra. Some can dance. Speak not of more or less intelligence. Speak of multiple intelligences. Imposing so prolonged a sequence on algebra suppresses opportunities, stifles creativity, and denies society a wealth of diverse talents. Mandarins impose abstruse mathematics on every student even though basic arithmetic is all that is needed for 99.9% of careers. Students are sacrificed to advance the Mandarins’ agenda.
The above article is not a work of original writing or research. All facts, quotes and insights are taken from:
Hacker, Andrew. Is Algebra Necessary; New York Times, July 28, 2012.
Hacker, Andrew. The Math Myth and other STEM Delusions; The New Press, New York, 2016.