# Algebra May Not Be Necessary, But Mathematics Is Essential!

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“Is Algebra Necessary?” screamed the front-page headline of The New York Times Sunday Review on July 29, 2012. For almost 2000 words, Andrew Hacker, emeritus professor of political science at Queens College, City University of New York, states his case for eliminating algebra and any other formal mathematics from the requirements for high school graduation, college admission, and graduation from college with a major in anything other than engineering or the physical sciences.

#### Algebra is difficult. So?

Professor Hacker builds his case against algebra and the other formal “math” courses in the public schools on the fact that, “A typical American school day finds some six million high school students and two million college freshmen struggling with algebra.” However, he immediately inserts the disclaimer, “I’m not talking about quantitative skills critical for informed citizenship and personal finance” but then goes on to claim that, “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.”

To support his plea to eliminate “mathematics” as a mandated area of learning in high school and college he cites numerous studies which clearly show that more than half the students in high school and college found difficulty with mathematics and that many in the education system blame the mathematics requirement for high school and college dropouts.

One of the most telling and sad statistics he cites is that, the City University of New York, where he has taught since 1971, “found that 57% of its students didn’t pass its mandated algebra course” and quotes the depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” Unfortunately, Professor Hacker seems to have forgotten the illustrious history of CCNY, as City University used to be known before the war in Southeast Asia forced many public universities to adopt “open admissions” policies and start the race toward the bottom in American public education.

#### Dooming our children to low-wage “service” jobs

Claiming that in the decade ahead a mere 5% of entry-level workers will need to be proficient in algebra or above simply affirms that the children in the American public school system today are doomed to low-wage service jobs no matter how hard they work at their school work because there just will not be any jobs for them that justify their scholastic efforts.

While it is clear that mathematical reasoning and quantitative skills required on the job in the modern workplace may seem markedly different from the math we learned in the classroom, it is not “mathematics” but the curriculum for mathematics developed by the “educrats” in many state education departments that is the root cause of the problem. This is most obvious in the elementary schools where many teachers have had little training in mathematics so that they lack the understanding of where the skills they are trying to teach are supposed to lead and most important why their students should acquire those skills as quickly as possible.

After paying lip service to the oft-repeated opening line in many introductory mathematics courses, “Our civilization would collapse without mathematics.” Professor Hacker goes on to acknowledge that “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.” He also acknowledges that 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” and that “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 *** Mathematics, both pure and applied, is integral to our civilization, whether the realm is aesthetic or electronic.”

His conclusion that “what is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.” cannot be challenged.

#### It is not Mathematics but the public school Mathematics Curriculum

Reluctantly, Professor Hacker finally moves towards understanding that it is not mathematics, but the public school mathematics curriculum and the methods of teaching mathematics that are the root of the problem. He proposes that mathematics teachers at every level create exciting courses in “citizen statistics” which will familiarize students with the kinds of numbers that describe and delineate our personal and public lives. “Such a course 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. He recognizes that researching the reliability of numbers can be demanding and observed that more and more colleges are requiring courses in “quantitative reasoning.” Finally he comes to the conclusion that the teaching of quantitative reasoning should begin in kindergarten.

#### Rethinking The Mathematics Curriculum

The entire mathematics curriculum from kindergarten through college should be “applied” mathematics taught entirely through the solution of “problems” appropriate for the age, experience and culture of the students. The “formal” aspects of mathematics, proofs, rigorous derivations and esoteric computational skills belong in special programs for those students who may need them in the careers they choose or who just enjoy them as many mathematicians do.

Almost all the major advances in the mathematics which make our technological civilization possible originated with a “practical” problem.Teaching mathematics from kindergarten through college as a quest for solutions to practical meaningful problems of great importance to the historical time during which they were solved provides the kind of excitement and stimulus that promotes learning and encourages inquiry among students regardless of their other interests and talents. It also integrates history and the arts with quantitative reasoning and development of computational skills.

The development of perspective in art; the transformation of two dimensional sketches to three-dimensional sculptures; the engineering challenges of architecture; the design and building of ships; navigation on the high seas; the problems of map making; … the list is endless. It is these problems which should be the core of the mathematics curriculum during each year a student attends elementary school, high school and perhaps college.

#### Can No Child Be Left Behind In Mathematics?

Regrettably, the answer to that question is, “No”. While no child should be left behind in any area of learning, we must acknowledge that some children may have inherent limits to the extent they will be able to learn and master particular skills and areas of knowledge. While every child should be helped to reach the maximum level they can attain in every subject, particularly mathematics and quantitative reasoning, the law of diminishing returns must be respected as far as the economics of providing a “free and appropriate public education” to every child in the United States.

We cannot continue to invest increasingly greater percentages of our school budgets in the effort to provide “special” education for students who cannot handle the basic public-school curriculum regardless of the reason. Accommodation for special needs such as physical impairments which require assistive devices or services such as readers for the blind and sign language interpreters for the deaf, wheelchair ramps and elevators, handicapped bathroom facilities, and whatever other help it takes to permit children with these special needs to be included in class with their peers is not the issue.

**The time has come to permit the public school system to exercise the same level of discipline and management that the charter schools and private schools have enjoyed**. Those children who cannot or will not learn and those children whose behavior disrupts the learning efforts of their peers will have to find their education outside of the public school system. They cannot and should not be accommodated.

#### Filtering college applications through the SAT Mathematics test

Professor Hacker questions the college admissions requirements of many schools which insist on SAT scores in mathematics of at least 700 of a possible 800. He claims that such standards unfairly restrict the opportunities of students seeking an education in the arts and humanities at the college or university level. He forgets that most colleges once required Latin and Greek for admission and only reluctantly lowered the requirement to Latin or Greek after World War II. Remember Plato treated mathematics, particularly Geometry, as part of the core curriculum at the *Academy*.

Requiring a score greater than 700 on the SAT mathematics test probably does discriminate against many high school students who have not completed three years of mathematics. That should not be a surprise since the test has been designed to discriminate against those students and restrict their admission to many colleges. However, for those seeking degrees in the arts and humanities there are many colleges which will accept them regardless of their poor preparation in mathematics. There are also specialized vocational education programs at the post secondary school level which do not require demonstrated competence in mathematics.

#### Copllege is not for every child

There is a real problem with the unsupported belief that every American child has a right to go to college whether or not they are prepared for the rigors of a college education. Somehow, since the end of World War II, working in the “trades” no matter how skilled and talented the worker must be has been portrayed as somehow less important and desirable than the “white-collar” work of the college graduate even when the efforts of that college graduate contribute little or nothing to society.

It is the obligation of the American public school system to restore the dignity of working Americans and teach children to respect the efforts of all those who contribute to society whether or not they are college graduates.

It is the obligation of the American public school system to establish alternative paths for students only one of which leads to a four-year liberal arts or technical college education. The path to an Associates degree or Certificate from a community college and a career as a skilled worker has to become a viable alternative for students in our public schools and must be treated with no less respect than the path to a four-year college. The remaining path leads to a place in the workforce which does not require advanced training and where a well-established work ethic, basic skills in reading, writing and arithmetic, honesty and integrity are enough to start a lifetime of substantial gainful employment.

There is, of course, the concomitant obligation on the part of our “Economy” to assure a job for all seeking employment and “a fair day’s pay for a fair day’s work.”