This article is an online extra from the December/January issue of MAA FOCUS.
Andrew Hacker, a retired political science professor from Queens College of the City University of New York, wrote an article "Is Algebra Necessary?" that appeared in the New York Times on July 29, 2012. His thesis is that for most people, algebra is not necessary and, for many, it is an obstacle to graduation from high school or from college. After the article appeared, I, as a longterm mathematician, was asked to write a commentary on the subject of the necessity of studying algebra. However, I should add that my father was an English professor and my mother was an established weaver. Their specialties were definitely in the humanities. As a result, I don’t wish to respond yes or no to whether algebra should be required for all students. Rather, I will address reasons for studying algebra and then will focus on negative aspects of studying algebra that are mentioned in Hacker’s article.
10 Reasons Why Studying Algebra Could Be Considered Prudent

Algebra is likely the first subject in which students develop logical thinking. It is also a place where students are exposed to abstract reasoning, and make decisions based on given information.

Algebra is likely the first subject in which students develop their problemsolving skills, which can involve extrapolation and stepbystep analysis.

Algebra can help students prepare to transfer abstract thinking to other disciplines. Transferring knowledge from one discipline to another is neither easy nor obvious. Thus, any help that can be given to students so that they will be able to make such connections, whether it be as a scientist or as a modern global citizen, is important.

Algebra is a prerequisite for study in college science courses, such as physics, chemistry, and biology, as well as computer science and engineering. In addition, a usable understanding of algebra is assumed for college statistics courses, such as Statistical Methods in Psychology, which are required for majors outside of science and mathematics.

Algebra is a prerequisite for virtually all collegelevel mathematics courses, such as precalculus, calculus, linear algebra, statistics and probability, and more advanced mathematics courses. An understanding of algebra is also assumed in geometry and trigonometry courses.

Relevant to the preceding reason, algebra can serve to solidify and firm up the arithmetic skills that are already learned in school. Without revisiting skills learned in arithmetic, students will forget them and are likely to then become uncomfortable with anything related to number sense.

Algebra is one aspect in the education of students that will allow them to communicate better with people who use mathematical ideas.

Algebra can serve to enhance one’s comfort with technical issues, from welding to art design to analysis of stock market issues.

Algebra is one ingredient in opening the doors to study in a variety of disciplines, and in attaining successful careers.

Finally, if we decide that algebra is not for everyone, then that automatically leads to a lowering of academic standards. That has consequences for our nation as it competes in the global economy.
Many people have enunciated these reasons since the appearance of Hacker’s article. They have been communicated by people of all ages, from high school to retirees, and by people who use mathematics on a daily basis to those who don’t need to use mathematics but who profess the usefulness of their study of algebra in their lives.
Hacker’s Five Points
Now I turn to addressing five claims by Hacker supporting his contention that algebra should not be required of all students.

Claim: Untold numbers of students fail algebra, and they may need to take algebra several times before passing it.
Response: A halfcentury ago in the USA, and currently in most civilized nations, algebra did not have that reputation. What is the case now in many parts of our country is that because of political pressure (from state officials, school districts, school officials), coursework in grade school and high school is accelerated, and students are promoted without understanding the material necessary for the next course. (I am told that this is true in English as well as mathematics.) This is a recipe for student failures.

Claim: Requiring algebra tends to make many students hate mathematics.
Response: People tend to dislike what they don’t understand. If students are not prepared well enough for algebra, and are rushed through the various topics in the course, then, again, this is a recipe for the students to hate mathematics.

Claim: Algebra prevents the United States from finding and developing young talent.
Response: Same argument about being prepared for the courses.

Claim (I quote): "A definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entrylevel workers will need to be proficient in algebra or above."
Response: It would be astonishing to think that nearly everyone in the teaching profession and nearly everyone in STEM (i.e., science, technology, engineering, and mathematics) fields will need no proficiency in algebra. The innuendo is that people would not need any kind of logical thinking skills.

Claim: What would be a reasonable alternative to algebra would be a course in "citizen statistics," a course which could "teach students how the Consumer Price Index is computed."
Response: Analysis of the Consumer Price Index would be reasonable, but without any algebra base I doubt that the students would get longterm value out of it. What would be my advice? I believe that courses in algebra, and other mathematics courses, would generally be successful if students were prepared for them. Thus I would suggest that state education officials, local school district officials, and school officials make sure that students are ready for the next mathematics course in each grade in K12 before the students take them. And what would it mean for a student to be ready? My suggestion: "A student is ready for the next mathematics course in K12 if the student has a firm command of the prerequisite knowledge for that next course and is ready to use this knowledge in addressing concepts and problems to arise in that next course."
Finally, we need to make sure that the teachers at all levels of K12 have a substantive understanding of mathematics, including algebra. —Denny Gulick
Denny Gulick is a professor of mathematics at the University of Maryland College Park.