Students are training their brains and their bodies, thanks to a new initiative that awards free gym memberships to those who hit the books.

The Work2Workout program is the brainchild of Mount Vernon teachers Glen Beram and Demetrios Mihailidis, who pitched the idea as a way to entice students at risk of failing to get on the right track.

It started small – with only three students initially qualifying at Mount Vernon High School – but this year has moved to The Graham School in Hastings, where 30 students and counting are on the roll call.

The ultimate goal is to certify trainers at individual schools and introduce a full training curriculum to be followed in health classes for possible college credit.

“We really wanted an incentive for them to do the right thing and get their grades back up,” Beram said. “These are kids that are bounced from foster home to foster home, and they need that incentive to keep straight.”

Meeting last month at Club @ 1133 in White Plains, students Todd Landers and Reynaldo Reyes of The Graham School worked up a sweat under the watchful eye of personal trainer Brian Denet.

“Pull that leg up!” Denet shouted as the boys warmed up with a stretch. “That’s it! That’s what I’m talking about!”

Making their way around the gym, targeting specific muscles as they went, the students said they had never experienced anything like the program.

It was teaching them the proper way to do things, whether it be stretching or lifting, they said.

But it also had a deeper significance – boosting confidence.

“You get rewarded for your good work,” said Reyes, 17, of the Bronx. “It feels good knowing that you did something.”

Getting into the program isn’t easy, but the stiff requirements are meant to keep students moving in a positive academic direction.

To earn the gym membership, students must first track their school performance on a daily basis for three weeks, with teachers signing off on whether they are showing up to class on time, completing all their assignments and generally behaving well.

Every time the student slips up, a week is added to the time he or she must record his or her performance.

But students are not off the hook once they pass that test.

They still track their progress, with teachers grading their performance every week on a scale of one to five.

If performance slips even slightly, a warning is issued.

Gym memberships can be revoked if the student doesn’t shape up.

“This changes their strength, endurance, pride, behavior and overall morale – just about everything in their life,” said Amy J. Goodman, superintendent of The Graham School.

“Kids are running up to us in the halls, saying, ‘I want to get into Work2Workout,’ ” Graham School Principal Paul R. Tobin said.

Though the program is still new, educators involved said they already have seen positive results.

“Once you get the black and white of seeing the report cards, that’s when you see the impact of the program,” Beram said.

Now the focus is to develop the full training curriculum for schools to use in health classes, with the potential of earning college credit. The curriculum would cover everything from biology to physics to nutrition.

Part of expanding into other schools also would include certifying a trainer for each district. The National Federation of Professional Trainers has offered to cover the cost of these certifications, which typically cost at least $450 each, said Charles DeFrancesco, owner of the personal training program at Club @ 1133.

“The problem I find is that most kids in schools are being trained incorrectly,” DeFrancesco said. “We’re starting here with these underprivileged kids because I want to give them the same advantages that the wealthy kids have. We’re going to expose these kids to the same knowledge that the professional athletes get.”