PARAMUS, N.J. – Today’s lesson is how to add mixed numbers: 6 ^{2}/_{13 }+ 8 ^{7}/_{26}. “Is anyone still having difficulty finding the least common denominator?” the instructor, Robert Fusco, asks. One student raises her hand and asks for help. “I’ve never seen this before,” she tells Mr. Fusco.

For many students, this is where community college begins – in a remedial arithmetic class, reviewing mathematics concepts they learned, or should have learned, before they graduated from high school.

“I get it quickly, and then I forget it completely,” says Ligia Halvorsen, 46, a student in Mr. Fusco’s class at Bergen Community College. “It’s like it was never explained to me.”

Ms. Halvorsen is determined to work through it. “Even though the material is for little kiddies, as some students in the class have said, I don’t care. I’m getting it,’’ she says.

Her upbeat attitude isn’t shared by thousands of students who enter community college unprepared for college-level work and find math a major stumbling block. As a result, remedial math is also where, for many of them, their community-college experience ends.

Nationally, about 60 percent of all community college students enroll in at least one remedial course in English or math, where they can get stuck studying elementary- and middle-school-level concepts.

Only 31 percent of students placed into remedial math ever move beyond it, according to the Community College Research Center at Columbia University’s Teachers College, meaning the students never even get to college-level work, much less graduate.

The prospects are especially bleak for students who test into the lowest level of a remedial-math course sequence, where they’re asked to add, subtract, multiply, and divide whole numbers, fractions, mixed numbers and decimals.

Remedial math is the biggest obstacle to graduation at a time when President Obama wants community colleges to produce five million more graduates by 2020. Nationally, less than 25 percent of community-college students who take remedial – also known as developmental –courses earn a degree within eight years, and another 14 percent transfer to a four-year college without completing an associate degree or certificate.

By way of comparison, about 40 percent of community-college students who did not enroll in a remedial-education class complete a degree in eight years, and 14 percent transfer without the degree or certificate.

Poor graduation rates are one reason that community colleges nationwide – including Bergen –are rethinking their approach to developmental education, trying a wide variety of strategies to move students more quickly through remedial courses and on to college-level work.

Solutions under way range from using tutors, mentors, and small-group instruction and support groups to new computer labs that offer self-paced diagnostic and practice exams. Some institutions are gearing curricula more specifically to what students need to learn for fields they hope to enter, while others are consolidating courses and moving students more quickly through them.

Students who start at the lowest level of remedial math may otherwise face a long slog through three or even four remedial courses in arithmetic, beginning algebra and intermediate algebra. And that’s before they can even get to the first college-level math course, generally “college algebra” or pre-calculus. Of those students who start three levels below college-level math, only 16 percent complete the sequence within three years.

**Alternate Routes**

That’s why some institutions, like South Texas College in McAllen, Texas, are compressing arithmetic, introductory algebra, and intermediate algebra into two courses instead of three, while also increasing the number of hours spent in class and the computer lab. “We heard from students who said, ‘A three-course sequence is too long. It’s going to take me forever to graduate,’” says Juan E. Mejia, the school’s vice president for academic affairs.

The Carnegie Foundation for the Advancement of Teaching is also helping community colleges develop a shorter, alternative route into statistics for non-STEM (science, technology, engineering, and mathematics) majors, in a push to get students who normally place into elementary algebra to and through a college-level statistics course in a year, instead of having to complete a traditional algebra-oriented sequence. Algebra and arithmetic concepts would be embedded in the statistics course.

“Community colleges are stepping up and saying, If our students aren’t going to be successful here, they aren’t going to be successful, period,” says Kay M. McClenney, director of the Center for Community College Student Engagement at the University of Texas at Austin.

That’s what happened at Bergen Community College, where President G. Jeremiah Ryan identified “fixing” remedial math as his first academic priority when he arrived in 2007.

The overall pass rate in remedial math courses that fall was 52.3 percent. In arithmetic, the lowest-level course, it was just 39.5 percent.

Some faculty members saw the low pass rates as evidence of effective gate-keeping – students would be kept out of college-level classes until they were ready for them. “The math department at the time was totally intransigent and didn’t think anything was wrong,” Mr. Ryan says.

But for the new president, the low pass rates were appalling.

Mr. Ryan moved quickly, splitting math into two separate departments – remedial and college-level math. “We fired the math chair, reorganized the department, then hired [four] new professors and turned the whole thing around,” he says.

The new chair of remedial math, Melanie Walker, helped revamp Bergen’s program and pushed up the school’s pass rates in remedial math by 15 percentage points in two years. The overall remedial-math pass rate this fall was 67.5 percent.

**Too Many Rules**

The old system for teaching remedial math, based on a series of high-stakes tests and a final examination, was particularly rigid and unforgiving, Ms. Walker says. A course had 14 objectives, and each test covered four objectives, with four questions per objective. If students answered three or four questions correctly, they passed the objective; if they got two wrong, they failed.

Students had to pass 11 of the 14 objectives to successfully complete the class. If they failed all four objectives covered on the first test, they failed the class. “I had to teach under the old system,” Ms. Walker says. “It would kill me to tell a student, ‘I’m sorry. You can’t come back.’”

A student also had to pass the final exam to move on to the next level. Ms. Walker says the new system is more flexible and adapted to different students’ needs. The final exam is worth 25 percent of the grade, but other than that, professors have discretion in how they evaluate students. Bergen has also developed a number of different arithmetic classes into which students are sorted based on their placement-test scores.

Students who need remediation and test at the lowest levels may need more time in order to be successful, and for those students, Bergen now offers a four-day-a-week, four-credit remedial course, with supplemental instruction and a skill-building software program.

Students whose scores on the placement test fall in the middle range take a more traditional twice-a-week course. The highest scorers can take a combination beginning-algebra/arithmetic course, allowing them to complete two remedial courses in one semester and accelerate their progress toward a degree.

Skills of students who place into arithmetic, the lowest-level remedial math course, vary widely. Some may not have studied and just missed the cutoff score on the placement test; they drop out because they’re bored and frustrated. “So we’re losing, ironically, the high-end student, and then there’s the really low-end who never mastered how to add whole numbers,” Ms. Walker says. “We realized we would have to do something for both ends of the spectrum.”

Mr. Ryan says the old system had too many rules. “I’m proud of the fact that they’re using student-oriented teaching principles to increase the pass rate, and that wasn’t happening before,” he says.

The president’s approach wasn’t entirely welcome, though. Ruth Feigenbaum, a professor in the college-level mathematics department, told the Faculty Senate in 2008 that in interactions with the math faculty, President Ryan had “created a hostile environment through words, tone, and deeds.”

Ms. Feigenbaum says that under the new system, administrators have emphasized the wrong metric. Pass rates have improved, but she worries whether students passing through the new remedial math sequence are as prepared for college-level courses. “The focus has not been on learning,” says Ms. Feigenbaum, who coordinated the college’s remedial math program before it was a separate department. “The focus has been on the pass rate because that’s what’s reported to the state. And that is a problem. Because the key to going further is, generally, knowledge.”

Under President Obama’s push for more college graduates, however, approaches such as Bergen’s are likely to be seen as an innovative attempt to solve one of the intractable problems plaguing community colleges: low graduation rates.

It’s a problem foundations want to solve, too, including Lumina Foundation for Education and 18 other partners involved in the “Achieving the Dream” initiative, which is helping community colleges use data to target specific remedial intervention strategies.

In April, the Bill & Melinda Gates Foundation pledged $110-million to speed students’ progress through remedial education by replacing weak programs and scaling up those that work.

Community colleges can either “keep doing what you’ve been doing, in which case, you will gradually find yourself able to meet fewer and fewer of your students’ needs, or you can innovate,” Melinda Gates said in a speech at the American Association of Community Colleges convention this year in Seattle.

Thomas Bailey, director of the Community College Research Center at Columbia University’s Teachers College, has long advocated for broad-based reform in how remedial math is taught, and he’s optimistic that solutions are being tried and tested. “As far as what institutions are doing, there’s a lot of innovation in developmental education, but it’s only recently that we’ve started paying much more attention to what actually goes on in the classroom,” he says.

Diversifying course offerings within remedial math is one example. “My big philosophy is, you’ve got to have different methods and modes of delivery for different kinds of students,” says Brad Sullivan, associate professor and program chair of developmental mathematics at the Community College of Denver, where the FastStart option allows students to take two remedial classes in a semester. It also offers a self-paced, computer-based remedial-math class that allows groups of students to work independently in a classroom, with an instructor and one or two tutors present, even if the course takes them more than a semester to complete.

By meeting three requirements – completing at least two tests with scores of 80 percent or higher, getting 25 hours of help in the math lab, and missing no more than 15 percent of classes –students can earn a “satisfactory progress” grade. The grade allows them to pick up the course the next semester where they left off, without an F on their transcript, and without having to pay to retake it.

“These are the students who really never got their math, who never learned it,” Mr. Sullivan says. “It’s certainly better than the alternative you often see, where people fail a class three times in a row.”

South Texas is allowing students to retake the placement test that stymies and discourages so many. “This ability to retest, to exit the developmental sequence whenever they can pass the test – that’s a big deal,” says Richard Getso, interim developmental-math chair. “It seems like it motivates lots of students, especially ones starting at the lowest level.”

At Bergen, Ms. Halvorsen credits her math instructor, Mr. Fusco, with helping her finally master material she has always found difficult. Ms. Halvorsen is determined to get the basic remedial requirements out of the way and earn the degree she’s wanted but put off for years. She even got her first A in math recently. “I’m going to start from the bottom and succeed later on,” Ms. Halvorsen says. “We’ve all got to start somewhere.”

*Elizabeth Redden is a New York-based freelance writer. A version of this story appeared **here** in *The Chronicle of Higher Education *on June 6, 2010.*