As Shenandoah University’s chief fundraisers try to grow their donor pool this year, they are targeting a not-so-wealthy population for the first time: students who are about to graduate.

It’s not an easy pitch. The private university in Winchester, Va., charges more than $35,000 a year for tuition and other expenses, and more than 85 percent of a recent graduating class had student loan debt. But like most universities, Shenandoah relies on donations. It wants to train soon-to-be-alumni to give generously.

“It doesn’t have to be a lot,” senior Katie Brown says she frequently tells her classmates as she hits them up for donations. “Just the act of giving helps.”

Despite the national debate over rising tuition and student loan debt, many private and public schools are asking students for donations. In part these solicitations continue the long tradition of senior-class gifts. But the phenomenon appears to be growing, college officials say, and students are giving at what are described as record rates.

Often these campaigns are led by student leaders who contact classmates via e-mail, text message and Facebook, or through old-fashioned, in-person begging.

Fundraisers say they aren’t necessarily seeking large sums. A popular amount to give this year is $20.12. Students are often encouraged to give to a general university fund, scholarship program or a department or student club that was a major part of their education. Sometimes student gifts are matched by more-established donors, administrators or the university president.

The goal is not only to collect extra funds, but to instill in students a sense of obligation and philanthropy that will make them lifelong donors. Of $30.3 billion donated to colleges and universities in 2011, according to the Council for Aid to Education, $7.8 billion came from alumni and the rest from foundations, corporations and other sources.

There were no national figures available for how much students give. But experts say there has been a push of late to teach students the merits of donating.

Small donations can quickly add up. Last year, George Washington University in the District collected more than $90,000 from the class of 2011. At the University of Virginia, the class of 2011 raised nearly half a million dollars before graduation. A decade ago, the U-Va.class of 2001 raised nearly $60,000.

The concept of a class donating an item such as a park bench or a tree is nearly a thing of the past. Schools are asking for cash instead. But most schools set participation goals instead of dollar targets.

Plus, one of the factors in U.S. News and World Report’s ranking of top colleges is the percentage of living alumni who have donated. (Under this formula, school officials say, gifts from seniors can count after graduation.)

While many fundraisers seek to play down the rankings, others use it at the heart of their pitches. At Shenandoah, Brown said she often explains the ranking system to her friends in explaining why they should donate. Shenandoah ranks No. 27 on the U.S. News list of best regional universities in the south.

“The higher the ranking is for the school, the more valuable your degree is,” said Brown, 21, who is majoring in English and mass communications.

The same pitch is used at GWU, which recently broke into the U.S. News national “top 50.” In addition to a YouTube video and social-media campaign, GWU seniors gave their classmates a list of five reasons to give a senior gift, with the No. 1 reason being this: “Give because any gift, regardless of size, counts as alumni participation and elevates GW’s rankings in publications like U.S. News and World Report, raising the value of our degrees.”

Public universities also are hitting up students for donations, driven in part by dwindling state funding. At the University of Maryland, students are asked to donate cash or their leftover dining-hall credits to “Keep Me Maryland,” a hardship fund for students on the brink of dropping out for financial reasons.

At Radford University, a public institution in Virginia, each senior is asked to donate at least $5 (what the school calls “the cost of a Starbucks coffee”) to a general fund.

“The best chance for a gift later in life comes from those who have already given,” said Deborah J. Robinson, Radford’s vice president for university advancement. “We’re state supported, but we’re not 100-percent state funded. And tuition doesn’t cover all of it.”

There is often a reward for donating, beyond the satisfaction of helping future students. Radford donors are entered into a drawing for gift cards to local restaurants. At GWU, names of student donors are published online. At the College of William and Mary, donors are rewarded with a wine-and-cheese social, local restaurant deals and a purple T-shirt.

“They are really popular,” said Elizabeth Keppel, 21, a William and Mary senior who gave $250 and is one of the leaders of this year’s campaign. “Everyone wants one.”