by Ronald A. Wolk

**ASSUMPTION: ***The United States should require all students to take algebra in the 8th grade and higher-order math in high school largely in order to increase the number of scientists and engineers and thus make us more competitive in the global economy.*

The assumption about algebra and higher-order math has become almost an obsession in policymaking arenas today. Who would disagree that every student should master basic math because it is important in meeting the demands of everyday life? But why should everyone be required to study higher-order math?

The reason most often given is that the United States is not producing enough scientists and engineers to compete in a global economy. Policymakers and business leaders are concerned that students flock to the United States from all over the world to study science and engineering in our universities, then return home to compete with us. More and more of our technical work is being outsourced to countries like India and China. This situation is worrisome because our standard of living and, indeed, our national security are undoubtedly linked to our leadership in science and technology.

To strengthen the quality of the U.S. workforce and gird the American economy against foreign competition, Congress approved "competitive legislation" intended to bolster mathematics and science education by providing federal grants for improved teacher recruitment and training and to promote successful classroom practices. But to assume that the United States will produce more scientists and engineers by requiring every student to take algebra in the 8th grade and higher-order math through high school is like assuming that requiring all high school students to take a few courses in painting will make them artists.

Most students who go to college and major in science and engineering are well on their way before they get to high school. Most become hooked on science or math in the early grades and do well in these subjects in elementary and middle school. They come to experience the delicious satisfaction of solving the mystery, of breaking the code. As they move on to more challenging math studies, they see the beautiful symmetry of mathematics and begin to imagine a career in which math is crucial.

Science provokes endless questions in kids—about the stars, animals, snowflakes, fire, space, and on and on. Gifted teachers can nourish that curiosity and encourage these youngsters to be passionate about science. And that passion may well carry over to a passion for mathematics that will lead some of them to become scientists and engineers. But forcing science on kids is a recipe for failure.

A 1997 Chicago Public Schools policy increased the number of college-preparatory science courses that students took and passed. But a recent study by the Consortium on Chicago School Research found that the policy also discouraged students from taking higher-level science courses and did not increase the college-going rate. Researchers also found that the increase in the number of science courses taken did not translate into higher grades. Only 15 percent completed three years of science with a *B* average or higher. A coauthor of the report, Nicholas Montgomery, told *Education Week*, "Before the policy, most students received C's and D's in their classes. If they weren't being successful with one or two years of science, why would we think they would be successful with three years of science, if we don't pay attention to getting the students engaged?" (Aarons, 2010b, "Getting C's & D's," para. 5).

Forcing math on students has the same results. Students who reach the 8th grade ready for algebra and higher-order math should be encouraged (not required) to take it, and, I suspect, many of them would. But some won't because they have neither an interest in math nor a talent for it. These students may do well enough to pass their courses, but they are not likely to excel or remember much of what was taught in higher-order mathematics courses. Worse, of course, is the fact that many reach the 8th grade without having learned to read proficiently or do basic arithmetic.

Unfortunately, the majority of students do not adequately understand or appreciate mathematics by the time they finish middle school. A report by the National Mathematics Advisory Panel concluded that "the delivery system in mathematics education—the system that translates math knowledge into value and ability for the next generation—is broken and must be fixed" (NMAP, 2008, p. 13). It cites the "jumble" of strategies and theories for teaching math through the elementary grades, and it laments the "math wars," compares them to the "reading wars," and calls them "misguided."

Surely it must be clear that if the nation wants more scientists and engineers, then educators must find some way to agree on what to teach in science and mathematics and how to awaken and nourish a passion for those subjects well before the 8th grade. Even if by some miracle that should occur, it would still be unreasonable to insist that every student take two years of algebra and courses in higher-order math. Some kids will have an avid interest in literature, history, or the arts and may not be interested in math or a career in science. Forcing them into advanced math courses is likely to be counterproductive.

When it was first formulating its math standards, California expected all students (not just those who want to be scientists or engineers) to know that a quadratic equation is one "in which one or more of the terms is squared but raised to no higher power, having the general form *ax*^{2} + *bx* + *c* = 0, where *a*, *b*, and *c* are constants." Nobel Prize winner Glenn Seaborg pressed hard for that standard, but how many policymakers understand or use such equations? How many now even remember much of what they were taught in higher-order math courses?

Some would argue that is not the point. A main reason for requiring students to study higher-order math is to help them learn to think and solve problems; after all, math is the language of science and engineering. Mathematics is certainly a way of thinking and reasoning for some people and should be available to all students. But for some, philosophy, literature, and history also serve that purpose quite well.

There is no guarantee that simply taking courses in any subject, including higher-order math, will increase a student's thinking skills. *Science Daily* in 2009 reported on a study of 6,000 college freshmen majoring in science and engineering in the United States and China. The study found that Chinese students know more science facts than Americans, but neither group is particularly skilled in scientific reasoning.

Forcing students to take four years of higher-order math when they have no interest in math and want to be artists or history teachers or journalists is cruel and unusual punishment. Even if a little rubs off, it is probably a waste of time.

Nonetheless, the pressure continues. State graduation requirements in math have steadily increased over the past decade. Twenty-four states now require students to complete three years of math before graduating from high school, according to the Education Commission of the States. Only two states—Alabama and South Carolina—require four years of math, though 10 other states and the District of Columbia are phasing in that requirement (ECS, n.d.).

Requiring more high school math may be counterproductive, according to the findings of the Consortium on Chicago School Research. Its studies revealed that while enrollment in algebra increased, so did the number of students failing math in the 9th grade. At the same time, the researchers say, the change did not seem to produce significant test-score gains for students in math or lead to sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school. *Education Week* reported that "the Chicago school district was at the forefront of that movement in 1997 when it instituted a mandate for 9th grade algebra as part of an overall effort to ensure that its high school students would be 'college ready' upon graduation" (Viadero, 2009, para. 3). Elaine M. Allensworth, the lead researcher on the study, said in an interview that the trend toward more and earlier algebra "seems to be sweeping the country now, and not a lot of thought is being given to how it really affects schools" (para. 6).

More important, how does it affect students? A Brookings Institution study (Loveless, 2008) offers some answers. *The Misplaced Math Student: Lost in Eighth Grade Algebra* finds that many of the lowest-performing students required to take 8th grade algebra are as far as six grades below grade level in math. Tom Loveless, one of the researchers, argues that efforts to require all students to take introductory algebra, or Algebra 1, in 8th grade are well meaning but ultimately misguided. Policymakers would be better off, he advises, to concentrate on grounding elementary students in the math they need for algebra and intervening with the ones who need extra help. Mr. Loveless told *Education Week* that the issue is even more complex because "no one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year" (Viadero, 2010, "Basic Arithmetic," para. 2).

Nonetheless, the number of 8th graders nationally taking algebra has nearly doubled to 31 percent since 1990. Many of the states with the highest percentages of students enrolled in 8th grade algebra had the lowest average math scores in that grade on the 2007 NAEP. California, for example, enrolls almost 60 percent of its 8th graders in Algebra 1 or another advanced math course but has one of the nation's lowest average scores on NAEP (Cavanagh, 2008). Perhaps that explains why a Sacramento County superior court judge in 2008 issued a temporary restraining order blocking the new mandate that California students be required to take algebra in the 8th grade.

Advocates argue fiercely that to exempt some students from higher-order math is a form of invidious tracking because it would likely prevent them from doing many jobs in the modern workforce. They rightly point out that higher-order math is not only a college admission requirement but also a prerequisite to fully understanding and "doing the work" of science and engineering.

Labor experts, however, say the skills that employers—even those in many high-paying fields—demand don't include the high-level math that policymakers are pushing for. Employers say that fluency in advanced math topics is less crucial than skill in problem solving and in applying math to different tasks. And they contend that creating courses that place a greater emphasis on real-world or "applied" math, as opposed to simply increasing academic requirements, could improve not only students' workforce skills but also their enthusiasm for that subject. In a survey of 51 employers, 35 said they required workers to know relatively basic math, such as how to do simple arithmetic and to add fractions, although some jobs required algebra and trigonometry; but some managers said they had difficulty finding workers with even basic math skills (Cavanagh, 2007).

Michael J. Handel, a professor of sociology at Northeastern University in Boston, surveyed 2,300 employees from a broad range of job backgrounds, including "upper-white-collar" workers, such as managers and technicians; "lower-white-collar" employees, such as salespeople; and a range of blue-collar and service employees, such as factory and food-service workers. Handel found that although 94 percent of workers across those occupations reported using some kind of math on the job, just 22 percent said they used any math more advanced than adding, subtracting, multiplying, or dividing. Only 19 percent said they used skills taught in Algebra 1, and 9 percent used Algebra 2. Most workers said they used more basic math, such as fractions, multiplication, and division. Only 14 percent of higher-level employees, such as managers, said they used Algebra 2 in their work (Cavanagh, 2007).

Stanley Goldstein, founder of the CVS pharmacy chain, once told me, "I have been a successful businessman for 40 years; I founded and ran a Fortune 500 company, and the only math I ever used was addition, subtraction, division, multiplication, and figuring percentages in my head."

If public schools worked as they should, every student would be proficient in math by the 8th grade and many would eagerly study algebra, geometry, trigonometry, and calculus. But if schools don't prepare young people in their first eight years for such courses, how in good conscience can we require them to take four years of higher-order math in high school?

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