A group of local and national organizations on Monday announced a $2 million grant competition meant to spur the creation of District schools that combine online and face-to-face instruction.

The Breakthrough Schools: D.C. competition is open to traditional and charter schools that want to redesign their instruction. Also eligible are groups seeking to open new schools in the District.

The aim is to encourage the use of technology to reach each student at his or her own level, a personalized approach that has gained momentum around the country. Funders see it as a powerful way to lift achievement quickly.

“We want something more than incremental improvement, which our schools have now proven we can do in D.C.,” Katherine Bradley, president of the local CityBridge Foundation, said in an e-mail. “We are road-mapping much faster pathways to the creation of transformational schools, schools that will really tap the full potential we know our kids have.”

Schools will be able to apply for one of up to six $100,000 planning grants. Those recipients will then be eligible to win as much as $450,000 to open their new or newly designed schools in the fall of 2015.

CityBridge is funding the effort along with the Eli and Edythe Broad Foundation, which has invested hundreds of millions of dollars to shape the direction of public education around the country.

The targeted grants for the District and Chicago are part of the national Next Generation Learning Challenges, which the Bill and Melinda Gates Foundation started in 2010 and has since donated more than $20 million to help launch about 60 schools around the country.

One of those national grants went to Ingenuity Prep, which opened this school year as the District’s first charter organized around blended-learning principles, according to Don Soifer, a member of the D.C. Public Charter School Board. The board has approved an additional blended-learning operator — Rocketship Education — to open two schools in 2015.

Although blended learning has engendered optimism in some quarters, it also has its share of skeptics. Some schools have made impressive gains with a blended approach, but there is scant research showing that it is more effective than traditional teaching.

In the District, school system leaders credited an online mathematics program with helping some schools raise their math test scores this year. But at Hart Middle School in Southeast, math scores fell after the school implemented “Teach to One,” an approach that puts a computer algorithm in charge of figuring out what each child needs to learn and do each day.

CityBridge is responsible for drumming up interest in the grants and helping applicants flesh out their ideas. Foundation officials said they hope to draw some applicants from a pool of 12 D.C. teachers who have been participating in a year-long CityBridge fellowship meant to introduce blended-learning strategies.

One fellow, Valyncia Hawkins, a fifth-grade teacher at Anne Beers Elementary in Southeast, said that she and others at the school are interested in applying for a grant to help redesign instruction schoolwide.

Hawkins said she has designed her math lessons this year so that students rotate through stations, spending part of their time learning online and part of their time working with her in small groups.

“Through blended learning, that may be a way we can truly personalize instruction for our students,” Hawkins said. “We know that as a school, we want to do something different where we’re actually reaching all of our students, not just a minority of our students.”