A TYPICAL American school day finds some six million high
school students and two million college freshmen struggling with algebra. In both
high school and college, all too many students are expected to fail. Why do we
subject American students to this ordeal? I’ve found myself moving toward the
strong view that we shouldn’t.
My question extends beyond algebra and applies more broadly
to the usual mathematics sequence, from geometry through calculus. State
regents and legislators — and much of the public — take it as self-evident that
every young person should be made to master polynomial functions and parametric
equations.
There are many defenses of algebra and the virtue of
learning it. Most of them sound reasonable on first hearing; many of them I
once accepted. But the more I examine them, the clearer it seems that they are
largely or wholly wrong — unsupported by research or evidence, or based on
wishful logic. (I’m not talking about quantitative skills, critical for
informed citizenship and personal finance, but a very different ballgame.)
This debate matters. Making mathematics mandatory prevents
us from discovering and developing young talent. In the interest of maintaining
rigor, we’re actually depleting our pool of brainpower. I say this as a writer
and social scientist whose work relies heavily on the use of numbers. My aim is
not to spare students from a difficult subject, but to call attention to the
real problems we are causing by misdirecting precious resources.
The toll mathematics takes begins early. To our nation’s
shame, one in four ninth graders fail to finish high school. In South Carolina,
34 percent fell away in 2008-9, according to national data released last year;
for Nevada, it was 45 percent. Most of the educators I’ve talked with cite
algebra as the major academic reason.
Shirley Bagwell, a longtime Tennessee teacher, warns that
“to expect all students to master algebra will cause more students to drop
out.” For those who stay in school, there are often “exit exams,” almost all of
which contain an algebra component. In Oklahoma, 33 percent failed to pass last
year, as did 35 percent in West Virginia.
Algebra is an onerous stumbling block for all kinds of
students: disadvantaged and affluent, black and white. In New Mexico, 43
percent of white students fell below “proficient,” along with 39 percent in
Tennessee. Even well-endowed schools have otherwise talented students who are
impeded by algebra, to say nothing of calculus and trigonometry.
California’s two university systems, for instance, consider
applications only from students who have taken three years of mathematics and
in that way exclude many applicants who might excel in fields like art or
history. Community college students face an equally prohibitive mathematics
wall. A study of two-year schools found that fewer than a quarter of their
entrants passed the algebra classes they were required to take.
“There are students taking these courses three, four, five
times,” says Barbara Bonham of Appalachian State University. While some
ultimately pass, she adds, “many drop out.”
Another dropout statistic should cause equal chagrin. Of all
who embark on higher education, only 58 percent end up with bachelor’s degrees.
The main impediment to graduation: freshman math. The City University of New
York, where I have taught since 1971, found that 57 percent of its students
didn’t pass its mandated algebra course. The depressing conclusion of a faculty
report: “failing math at all levels affects retention more than any other
academic factor.” A national sample of transcripts found mathematics had twice
as many F’s and D’s compared as other subjects.
Nor will just passing grades suffice. Many colleges seek to
raise their status by setting a high mathematics bar. Hence, they look for 700
on the math section of the SAT, a height attained in 2009 by only 9 percent of
men and 4 percent of women. And it’s not just Ivy League colleges that do this:
at schools like Vanderbilt, Rice and Washington University in St. Louis,
applicants had best be legacies or athletes if they have scored less than 700
on their math SATs.
It’s true that students in Finland, South Korea and Canada
score better on mathematics tests. But it’s their perseverance, not their
classroom algebra, that fits them for demanding jobs.
Nor is it clear that the math we learn in the classroom has
any relation to the quantitative reasoning we need on the job. John P. Smith
III, an educational psychologist at Michigan State University who has studied
math education, has found that “mathematical reasoning in workplaces differs
markedly from the algorithms taught in school.” Even in jobs that rely on so-called
STEM credentials — science, technology, engineering, math — considerable
training occurs after hiring, including the kinds of computations that will be
required. Toyota, for example, recently chose to locate a plant in a remote
Mississippi county, even though its schools are far from stellar. It works with
a nearby community college, which has tailored classes in “machine tool
mathematics.”
That sort of collaboration has long undergirded German
apprenticeship programs. I fully concur that high-tech knowledge is needed to
sustain an advanced industrial economy. But we’re deluding ourselves if we
believe the solution is largely academic.
A skeptic might argue that, even if our current mathematics
education discourages large numbers of students, math itself isn’t to blame.
Isn’t this discipline a critical part of education, providing quantitative
tools and honing conceptual abilities that are indispensable — especially in
our high tech age? In fact, we hear it argued that we have a shortage of
graduates with STEM credentials.
Of course, people should learn basic numerical skills:
decimals, ratios and estimating, sharpened by a good grounding in arithmetic.
But a definitive analysis by the Georgetown Center on Education and the
Workforce forecasts that in the decade ahead a mere 5 percent of entry-level
workers will need to be proficient in algebra or above. And if there is a
shortage of STEM graduates, an equally crucial issue is how many available
positions there are for men and women with these skills. A January 2012
analysis from the Georgetown center found 7.5 percent unemployment for
engineering graduates and 8.2 percent among computer scientists.
Peter Braunfeld of the University of Illinois tells his
students, “Our civilization would collapse without mathematics.” He’s
absolutely right.
Algebraic algorithms underpin animated movies, investment
strategies and airline ticket prices. And we need people to understand how
those things work and to advance our frontiers.
Quantitative literacy clearly is useful in weighing all
manner of public policies, from the Affordable Care Act, to the costs and
benefits of environmental regulation, to the impact of climate change. Being
able to detect and identify ideology at work behind the numbers is of obvious
use. Ours is fast becoming a statistical age, which raises the bar for informed
citizenship. What is needed is not textbook formulas but greater understanding
of where various numbers come from, and what they actually convey.
What of the claim that mathematics sharpens our minds and
makes us more intellectually adept as individuals and a citizen body? It’s true
that mathematics requires mental exertion. But there’s no evidence that being
able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political
opinions or social analysis.
Many of those who struggled through a traditional math
regimen feel that doing so annealed their character. This may or may not speak
to the fact that institutions and occupations often install prerequisites just
to look rigorous — hardly a rational justification for maintaining so many
mathematics mandates. Certification programs for veterinary technicians require
algebra, although none of the graduates I’ve met have ever used it in
diagnosing or treating their patients. Medical schools like Harvard and Johns
Hopkins demand calculus of all their applicants, even if it doesn’t figure in
the clinical curriculum, let alone in subsequent practice. Mathematics is used
as a hoop, a badge, a totem to impress outsiders and elevate a profession’s
status.
It’s not hard to understand why Caltech and M.I.T. want
everyone to be proficient in mathematics. But it’s not easy to see why
potential poets and philosophers face a lofty mathematics bar. Demanding
algebra across the board actually skews a student body, not necessarily for the
better.
I WANT to end on a positive note. Mathematics, both pure and
applied, is integral to our civilization, whether the realm is aesthetic or
electronic. But for most adults, it is more feared or revered than understood.
It’s clear that requiring algebra for everyone has not increased our
appreciation of a calling someone once called “the poetry of the universe.”
(How many college graduates remember what Fermat’s dilemma was all about?)
Instead of investing so much of our academic energy in a
subject that blocks further attainment for much of our population, I propose
that we start thinking about alternatives. Thus mathematics teachers at every
level could create exciting courses in what I call “citizen statistics.” This
would not be a backdoor version of algebra, as in the Advanced Placement
syllabus. Nor would it focus on equations used by scholars when they write for
one another. Instead, it would familiarize students with the kinds of numbers
that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price
Index is computed, what is included and how each item in the index is weighted
— and include discussion about which items should be included and what weights
they should be given.
This need not involve dumbing down. Researching the
reliability of numbers can be as demanding as geometry. More and more colleges
are requiring courses in “quantitative reasoning.” In fact, we should be
starting that in kindergarten.
I hope that mathematics departments can also create courses
in the history and philosophy of their discipline, as well as its applications
in early cultures. Why not mathematics in art and music — even poetry — along
with its role in assorted sciences? The aim would be to treat mathematics as a
liberal art, making it as accessible and welcoming as sculpture or ballet. If
we rethink how the discipline is conceived, word will get around and math
enrollments are bound to rise. It can only help. Of the 1.7 million bachelor’s
degrees awarded in 2010, only 15,396 — less than 1 percent — were in
mathematics.
I’ve observed a host of high school and college classes,
from Michigan to Mississippi, and have been impressed by conscientious teaching
and dutiful students. I’ll grant that with an outpouring of resources, we could
reclaim many dropouts and help them get through quadratic equations. But that
would misuse teaching talent and student effort. It would be far better to
reduce, not expand, the mathematics we ask young people to imbibe. (That said,
I do not advocate vocational tracks for students considered, almost always
unfairly, as less studious.)
Yes, young people should learn to read and write and do long
division, whether they want to or not. But there is no reason to force them to
grasp vectorial angles and discontinuous functions. Think of math as a huge
boulder we make everyone pull, without assessing what all this pain achieves.
So why require it, without alternatives or exceptions? Thus far I haven’t found
a compelling answer.
Andrew Hacker is an emeritus professor of political science
at Queens College, City University of New York, and a co-author of “Higher
Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What
We Can Do About It.”
Source: http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?_r=2&pagewanted=all
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