America’s math problem: Should we get rid of algebra?

Is math holding the United States back?

Last week, a community-college student from Harlem, speaking at a meeting of educators and community activists, told a harrowing story about his battle to get a degree. Raised by a single mother in a neighborhood wracked by violence, he had struggled to make it through high school. Then his mother died of cancer, leaving him to raise his three younger siblings alone. He pressed on in school despite new emotional and financial burdens, but there was a remaining obstacle that sometimes seemed like it would overwhelm him: algebra.

Remedial Math at Bronx Community College in New York City (Photo by Ryan Brenizer)

Like thousands of would-be college graduates in the United States, he had been forced to enroll in remedial math classes in college, and the difficulty of passing it reduced his chances of reaching graduation. Half of community-college students take remedial classes, and only 10 percent of those who do graduate within three years, Business Week reported in May. And a fifth of four-year college students enroll in remediation, of whom only about a third graduate in six years.

Those statistics come from a report on remediation published in April by Complete College America. The report’s numbers suggest that math requirements may be the primary obstacle to graduation for many students: In many states, a larger percentage of students enroll in remedial math courses than in remedial English courses.

But experts and educators are divided on what to do about America’s math problem. Should we scrap algebra altogether, or try instead to better prepare students to understand it? The debate has been particularly heated this summer after a New York Times op-ed by Andrew Hacker asked the question, “Is Algebra Necessary?”

Hacker compiled a list of statistics supporting his argument that it isn’t: “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.”

Hacker is not alone in advocating for the elimination of algebra, at least from the college curriculum. The Complete College America report suggests placing “students in the right math.”

“Most students are placed in algebra pathways when statistics or quantitative math would be most appropriate to prepare them for their chosen programs of study and careers,” the report’s authors argue.

In a report released today by the American Enterprise Institute, Jacob Vigdor calls for a different approach. Although he too is dismayed by American students’ performance in math, he argues that the problem is how algebra is taught, not that it is taught at all. He believes that for many students, an introduction to algebra comes much too soon—in eighth grade—meaning the material must be dumbed down so they can understand it. His evidence includes a program in North Carolina’s Charlotte-Mecklenburg school district aimed at increasing the number of eighth-graders taking algebra; students there who took algebra earlier scored much lower on an end-of-year exam than students who didn’t, he notes.

Pushing algebra down to lower grades also alienates students who are able to grasp the concepts more easily, leaving fewer to be interested in pursuing math, as evidenced by the decline in math majors, according to Vigdor.

“The root of America’s math problem is the conflation of two goals: improving the absolute performance of American students and closing gaps between high and low performers,” Vigdor writes. “Following the failure of a significant initiative to accomplish both goals simultaneously—the ‘new math’ movement of the mid-twentieth century—successive reforms have focused attention on bringing lower-performing students up to standards. In the process, the standards have been lowered, and the advancement of higher-performing students has been allowed to languish. Designers of the nation’s mathematics curriculum, in short, have fallen into an ‘achievement-gap trap,’ raising the relative performance of average students in part by permitting the absolute performance of the best students to decline.”

His solution is not necessarily to do away with algebra for the masses, however, but to do a better job of differentiating how it’s taught to students of various abilities and backgrounds. “American students are heterogeneous, and a rational strategy to improve math performance must begin with that premise,” he concludes.

Getting rid of across-the-board standards in algebra isn’t likely to happen any time soon, however. Schools across the country are gearing up this fall to introduce new common standards, which promise that “students who have completed 7th grade and mastered the content and skills through the 7th grade will be well-prepared for algebra in grade 8” (italics in the original).


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Ed Jones

It’s true we’re squeezing out too many people. It’s also true that too many Black Americans who have the ability are not getting the chance. As a result, Black Americans become civil engineers at 1/4 the rate they should. Same for programming and other STEM jobs. How can they build social capital without the jobs that bring in discretionary income?

The other consideration is that for some students, programming might be an option. Programming teaches much of the discipline algebra does.

Charles R.

Two things:

1. Most Algebra students never mastered pre-Algebra concepts. For example, find the price of an item marked down 25% or find the percent increase of an item that goes up from $50 to $70. Students shouldn’t move on to Algebra if they’re not decent problem solvers going in.

2. The KIPP programs across the country teach Algebra traditionally. They’re successful due to students having twice the time devoted to math than others, as well as multiple teachers in the classroom who can move around and help students who need it while doing guided practice problems.

Sarah Garland

More time to work on math is one of the suggestions that Jacob Vigdor makes; he refers to a study of high schools in Chicago that did that. (Although he also has seemed to suggest that some students just weren’t meant for algebra, see this link: http://bit.ly/RpOARK.) In traditional public schools, would more time spent on math need to come at the expense of other subjects?

Charles R.

Seems to me students need a stronger more intense math background coming into Algebra. If it takes 2 teachers for each math class or more time in middle school (for ex. KIPP) that would go a long ways to making Algebra more palatable for all students. Too many come into high school Algebra these days knowing little to nothing about pre-Algebra. They’re behind from the very start due to many factors (poor middle schools, home environment). It’s little wonder that they struggle and/or give up. I think with a stronger middle school background (based somewhat on the KIPP approach) students have a better fighting chance.

Public schools might have to spend more time in math at the expense of other subjects (unless the school day is somehow extended). They also need a lot more time reading/writing, as those skills are just as bad or worse than their math skills.

America’s math problem — Joanne Jacobs

[...] Algebra for all is a growing trend, notes Sarah Garland on Hechinger Ed. “Schools across the country are gearing up this fall to introduce new common standards, which promise that ‘students who have completed 7th grade and mastered the content and skills through the 7th grade will be well-prepared for algebra in grade 8′.” [...]

Rina

I sympathize with students that struggle with math, who simply (for whatever reason) cannot understand it. That being said, I do not think the solution to all of our problems is to reduce expectations. Rather, we need to regard this as a systems problem. Why is everyone required to take a certain range of courses. If math is not required for their future occupation, it does not make sense to require it for the graduation from a college or university. I fully appreciate the broad background I received as an undergraduate at the University of Kentucky; however, I was a good student for the most part. Truthfully, I believe that broad background has been good for me and helped me to understand other fields of endeavor. Nevertheless, there needs to be a flexibility when making requirements for students. I concede that not everyone is “college material” nor do they have the necessary skills to achieve college work. It is ridiculous to prevent a talented, intelligent, hard-working student from graduating if a subject that is no required for their specific major is an obstacle for them.

Roy Williams

The ability to “do algebra” has a lot to do with one’s level of comfort with numerical calculations “in your head”. If you are totally dependent on a calculator to do such things as “one fourth of sixty” or “ten percent of ninety-five”, then you will not become proficient with algebra. This is because “doing algebra” demands that you be able to visualize the steps “in your head” – just as a chess player must mentally visualize possible future moves.
When I was in elementary school some 60 years ago, we had to take turns standing in front of the class room and answer, without pencil, paper, or chalk, simple arithmetic problems that the teacher would ask us. I don’t see one college freshman in a hundred today that can do simple arithmetic “in their head” as well as we could do as fourth graders; if they can’t do basic arithmetic, they can’t do algebra. We were introduced to some simple algebra concepts in the fifth grade. By the time we were in high school, there were very few students who had any trouble with basic algebra.

Math needs to be taught independently of grade level and the calendar. The youngest students should start with counting, then move to addition and subtraction. The third class would be multiplication and division. The fourth class would be exponents and extraction of roots “by hand”. Some children will move through those classes in a year or two, some might take six. Whenever they are really, really proficient in those skills, they move on to algebra.

It is really obvious that teachers at both the high school level and the university level (at some universities and junior colleges) are being pressured to pass students who do not truly understand the material being taught. I have tutored many, many high school and college students who claim that they got an “A” in “pre calculus”, or even “calculus”, but who cannot do simple algebraic operations. Teachers are very creative in designing tests that give students an “A” just by being able to recognize some patterns – those tests carefully avoid questions that would demand real understanding of the mathematical concepts that are being taught.

The phony grading leads parents and students to believe that “Suzie is good in math” – and are then very surprised and confused when Suzie does below the national average on the SAT test.

We don’t need still another new way to teach math – what was done 60 – 70 years ago worked just fine.

[...] we scrap algebra altogether, or try instead to better prepare students to understand it?”(more)    Comments (0) Return to main news [...]

[...] a rather radical proposal to increase the number of American students who graduate college: dump math. Specifically, the argument is that since many college students, a disproportionately large number [...]

Dr. Dale McMannis

The report from the American Enterprise Institute (AEI) begs an interesting discussion concerning conceptual learning and young children. A comprehensive background in basic mathematics is essential for students to excel at algebra, as algebra is comprised of many more abilities than arithmetic. Algebra requires conceptual thinking and the application of rules in a sequential process. Before students even begin to learn basic mathematics, they must first develop core competencies that will eventually allow them to understand the nature of the questions that advanced math problems ask.

Research by Susan Landry of The University of Texas System’s Health and Science Center and James Baker III of Rice University details that children begin to fall behind in these skills beginning in the Pre-K years. The shortfalls are highly likely to persist through a child’s entire school career (Effective Early Childhood Programs). If children encounter extensive exposure to patterning, mathematical situations and structures, models of quantitative relationships, and qualitative and quantitative changes during their early childhood, they will later make successful transitions into higher levels of math.

Students feel overwhelmed by advanced math classes like algebra when they have not developed these core competencies. The result is a discouraged outlook on future mathematical endeavors. As students develop aversions to math during their early years, rather than developing the competencies during Pre-K that allow them to excel, fewer students pursue majors related to mathematics. The AEI is correct in their assertion that offering classes like algebra to students before they are equipped to tackle the problems will be detrimental to the student’s confidence in their mathematical abilities; however, the root of the issue is based in helping more children develop core competencies at an early age and not in whether or not 8th graders begin algebra too soon.

Thankfully, educators nationwide are increasingly aware of how critical this time period is to developing conceptual learning skills. Schools are integrating educational technology solutions in early learning classrooms in an effort to bridge learning gaps among students. Early assessment and progress monitoring can identify the areas in which a child may need extra attention.

[...] Report America’s math problem: Should we get rid of algebra?   Experts and educators are divided on what to do about America’s math problem. Should we [...]

Robert Evans

Right on Rina.

Louis Benezet y’all: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/

“Over 70 years ago in Manchester, New Hampshire, children learnt no formal arithmetic until grade 6″

Gaash

The problem with math in america is that there are idiots in this country who actually think eliminating algebra is a good idea.

Nancy Hoyt

I am 50 years old; I want an AS degree in Graphic Design & Communications. The last time I studied Algebra was in 10th grade high school (1978).
I took a placement test in Math and received a depressing 38, which means I have to take (2) Pre-Algebra classes (with zero credits) prior to the actual credit-worthy Algebra class. These two classes are VERY DIFFICULT!
I believe Algebra is important for some degrees programs, but not all. It is certainly impeding my passage to a degree as well because of the difficulty. I’ve been a Graphic Designer for 20 years w/o a degree, and have never used Algebra in practice. I want my AS, and hope colleges modify their math programs to better accommodate the degrees they are associated with.

[...] It seems a little disingenuous to focus so much on teaching first graders to code or third graders about robots while simultaneously shuttering music, art and drama programs. Our expectations of our students when it comes to math, with some suggesting we stop teaching algebra. [...]

Kal

http://en.wikipedia.org/wiki/Dyscalculia
http://www.dyscalculia.org/

We are punishing many people unnecessarily.

Learn math when and if you need it. Learning to think is much more important.

Shawn

If you can’t pass basic math (yes, algebra is basic math), you probably shouldn’t have a degree. They’re not suggesting you solve differential equations or even do trigonometry. “Math is hard” is not a good reason to cut it from curriculum.

Daniel

“Is algebra necessary?” is an intriguing question, although it sounds like it comes from that one guy who only got out of high school because his math teacher didn’t want to look at him anymore.. Obviously if we struck it from the curriculum altogether then we would be worse off than cavemen (the cavemen who first learned math turned into the most powerful civilizations in antiquity: Sumer, the Sanskrit-speakers, China, Egypt). The question really is: why do students have zero interest in it?

Let me tell you, having been put through the ringer myself. By the time the students are able to understand more advanced algebraic concepts, they are so bored with seemingly meaningless mathematical rhetoric that they just don’t give a damn. They want to experience life, not be sitting in a stuffy room doing the same thing over and over. If you want to get students interested: introduce it EARLIER!!!! Teach if a-b=c, then b=a-c, right along with if 2-1=1, then -1=1-2. Then quickly make them realize how this can benefit them in their everyday lives, and each day teach them another way they can manipulate the natural world mathematically. I would have had a masters in mathematics by now if they introduced math with letters and real concepts in grade 4 instead of 8.

Another approach (not saying both approaches should not be incorporated), would be to teach it in a much sneakier way: play games. Today’s parents are so distracted they do not take the time to read to the child, ensure they watch educational tv instead of incessant cartoons, and perhaps most importantly (mathematically speaking) is taking the time for family game night. A youngster might hate straight algebra, but teach ‘em to win money playing poker and they’ll be an extremely proficient mathematician and automatically be more understanding of abstract algebra.

To the point that mathematics should not be forced upon college students who will never use it anyway: YES. Get them out of the classes so those who are trying to push the boundaries of knowledge can do so instead of getting stuck on what you should have learned in high school.

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