According to the Education Trust, a nonprofit research group, about 50 colleges across the country have a six-year graduation rate below 20 percent. Many of the institutions serve low-income and minority students. Such numbers have prompted a fierce debate about who is to blame for the results, whether they are acceptable for nontraditional students, and how universities should be held accountable if the vast majority of students do not graduate. A federal commission that examined the future of American higher education recommended in August that colleges and universities take more responsibility for ensuring that students complete their education. The presidents of Northeastern Illinois and Chicago State, whose graduation rates are 17 and 16 percent respectively, say their universities serve a valuable mission, educating untraditional students who often take a long time to complete course work. Many of their students are the first in their families to attend college, they said. Many come ill prepared. Often the students are older, have children and work full time. "I think the work of this institution should be lauded rather than criticized," said Elnora D. Daniel, the president of Chicago State, where 86 percent of the 7,300 students are African-American. "And I say that for all public institutions nationally that attract and have as part of their mission the education of low-income, disadvantaged minorities." Daniel also said that conventional methods for calculating graduation rates significantly understate how many students actually earn degrees.