Here’s how Salman Khan thinks schools should work: Students should learn lessons online and do homework and projects in class.

This “flipping” of the traditional classroom is the operating system espoused by Khan and his Khan Academy, a website whose popularity is exploding as millions tune into its free videos, practice exercises and assessment tools.

Khan’s videos provide basic tutorials, mostly in math and science, that students can watch repeatedly in class or at home and pause if they need to — something that can’t happen with a classroom lecture. Teachers are then free to work individually with students and be more creative.

And that, Khan says, enables class time to be “an optimal experience for students and teachers.”

Recently hailed as revolutionary by Bill Gates, Google and some in the media, the concept is gaining traction among educators. Teachers view the site as a useful tool to individualize learning, says Dennis Van Roekel, who taught for 23 years and now is president of the National Education Association.

“Our members see it as something that really does help students,” he said. “Everybody doesn’t learn at the same pace. But once you’ve got it, you’ve got it.”

Karen Cator, director of the Department of Education’s Office of Educational Technology, says Khan automated “something that is so recognizable in our view of education: I have to solve problems, and somebody has to tell me how to do that. . . . It has caught on like wildfire.”

Since Khan first posted math videos on YouTube to tutor his cousins in 2004, the former hedge fund analyst has expanded his video library to 2,400 lessons that include basic addition, advanced calculus, history and science. Users also can access exercises and track their progress.

Based in California’s Silicon Valley, the Khan Academy was established as a nonprofit organization in 2008. Its lessons have been viewed by more than 60 million users, the website says, and are being translated into 10 languages. Khan estimates the website is being used in more than 1,000 classrooms nationwide, including in a pilot math program in two fifth- and seventh-grade classes in Los Altos, Calif., public schools last year. The district plans to expand the pilot program to all fifth- and sixth-grade classes this fall.

Khan, who quit his job in finance in 2009 to serve as the academy’s executive director, views the academy as a stand-alone virtual classroom. “That’s what our mission is: a world-class education for everyone that’s free,” he said.

There’s no doubt that the Khan Academy’s videos, narrated enthusiastically by Khan himself, have struck a chord among students and educators as well as the independent learners who make up the majority of the site’s visitors. Users only hear Khan’s voice; he never appears on screen, and he uses neon colors to write on a computer blackboard.

Microsoft founder Bill Gates is a fan; the Bill and Melinda Gates Foundation made a $1.5 million donation to the academy in 2010. In a video posted on the academy website, Gates says he sees Khan as a pioneer in the movement to use technology to educate people. “It’s the start of a revolution,” Gates says. Google awarded the academy $2 million that year for winning a crowd-sourced contest offering money to organizations with world-changing ideas.

The Khan Academy joins a crowded field of free and for-profit online learning programs, which some tout as the future of education and as options for cash-strapped school districts looking to cut staff.

But educators caution that what Khan offers is just another tool — albeit an effective one — that teachers can use to engage students. The Khan Academy and other online learning sites are no substitute for classroom teachers, they say.

“Technology is not going to replace teachers, but it empowers them to be much more effective with students,” Cator said. “There is an unbelievable opportunity that we have to leverage how people learn through technology.”

Khan acknowledges that his website is not a new idea. “We’re not the first people to put video online,” he said. “What’s different is we started off as a grass-roots, bottom-up thing, reaching students before we started going into the classroom.”

Students in Montgomery County, Md., can tune in to the Math Dude, a series of online math videos by former math teacher Mike DeGraba designed to help middle- and high-school students improve algebra skills. And Stacey Roshan, a math teacher at Bullis School in Potomac, Md., created what she calls a “backwards classroom” by videotaping and posting online her lessons for her Advanced Placement calculus class. She requires students to watch them at home and uses class time to work on homework problems.

“It forces you to try to figure out as much as you can on your own. We’re taking ownership of our learning,” Bullis student Daniel Gray, who graduated in June, said of Roshan’s teaching strategy.

But that’s one of the problems with online learning, educators say. Even sites as sophisticated as the Khan Academy can’t be relied upon to expose everything a student hasn’t learned.

Good teachers listen to students and understand their prior experience to discover where they lack understanding, says Heidi Glidden, assistant director in the education issues department of the American Federation of Teachers.

“To suggest that all kids are able to learn using only one medium wasn’t realistic years ago, and we don’t function that way today,” Glidden said.

Even though the students can earn “badges” as they master Khan Academy exercises, a computer program is no substitute for the motivation that teachers provide, educators say. “A teacher motivates youngsters to aspire to go beyond where they’d go if left alone to their own devices,” said Daniel Domenech, executive director of the American Association of School Administrators.

Still, educators are embracing the technology because it opens doors to new resources and learning techniques. Whereas teachers and students used to rely on books for information, they can now access an infinite world of information with the click of a mouse.

But that world requires vetting. As the Khan Academy ventures beyond basic math and science lessons, and deeper into subjective material such as U.S. history, users will need to navigate lessons with a more critical eye, educators say.

The need to monitor online learning is one example of how technology is changing the teacher’s role. No longer mainly lecturers, teachers are becoming directors of learning who guide students, educators say. “The teacher is not the only one imparting knowledge. The teacher becomes much more of a facilitator of learning,” the NEA’s Van Roekel said.

Khan says he’s had to deal with the misconceptions that using the Khan Academy reduces the need for teachers or that class sizes can increase. Instead, he believes that using the website adds value to the role of a teacher, who becomes a mentor or coach.

“A mentor is much higher up the value chain than a lecturer,” he said. “Someone who designs projects and experiments is higher up the value chain.”

The concept of flipping the classroom is key to the mentoring role: If students are learning the basics through watching videos, then teachers can spend class time on more creative projects instead of practice drills and homework assignments.

Students can work problems at their own pace until they get them right, while the assessment tool tracks progress for teachers, identifying when students need help and how long it takes them to grasp a concept.

“Every teacher will tell you, ‘I wish I had more time with students,’ ” Khan says.