Rebellious students and security-minded parents are not the only ones defying Mayor Bloomberg’s cell phone ban: The school system’s own technology department offers teachers classes on how to incorporate cell phones into lesson plans.

One such class, a four-hour session on how to use the Google Web site to enhance education, will happen Friday afternoon.

During one part of the class, teachers learn how students can use text-messaging to look up the definitions of words, search currency exchange rates, and find countries on a map. Among the suggested reading is an essay titled, “What Can You Learn From A Cell Phone? – Almost Anything!”

The creator of the class, Lisa Nielsen, who manages professional development at the Department of Education’s Office of Instructional Technology, said she is not trying to encourage teachers and principals to flout Mr. Bloomberg’s cell phone ban.

She does not support the ban, though, saying school leaders should be able to determine cell phone policies on their own. “I think that we should respect their views and let them lead the school the way they feel is most effective,” she said.

Ms. Nielsen’s view is that cell phones are “brain extenders” that students should be taught to harness productively. If she ran a school, she said, she would first make sure teachers were comfortable with the educational uses of cell phones, and then incorporate them into the regular curriculum, allowing students to use them as supplementary tools for learning.

The Department of Education’s ban was the subject of an unsuccessful lawsuit by parents who said they were concerned about safety.

It came under scrutiny again when the department launched a test project to motivate students to score well on tests by giving them free cell phones. That program involves after-school hours, a Department of Education spokesman, David Cantor, said.

Mr. Cantor defended the ban on phones during school hours. Although the technology is exciting, he said, “We also need to keep our schools free from disruption — free from telephone calls, texting, surfing the Web, taking pictures, playing games — all the things that cell phones bring into schools. The instructional potential of phones should be explored outside of the classroom.”

The idea that schools should embrace, not shun, technologies including cell phones, Internet video, social networking, and e-mail is part of a growing movement taking root — where else? — on the Internet.

The movement is centered on Web logs, such as Ms. Nielsen’s ( theinnovativeeducator.blogspot.com), and on special social-networking sites set up for teachers and principals.

Ms. Nielsen also protested against the Department of Education last week, when she used her blog to publicize a new policy prohibiting staffers from including their blog URLs with their e-mail signatures.

The online community is partly a reaction to all-out bans such as that on cell phones in New York City’s public schools, as well as to programs used by school systems to block students’ access to certain Web sites. Computers at the city’s public schools block MySpace.com, according to educators.

Mr. Cantor said which Web sites are blocked is a matter of principal discretion.

“If we don’t teach how banned and filtered technologies can be used,” Ms. Nielsen wrote in one blog post, “then we are not empowering students to operate in safe, appropriate, and acceptable ways with or without technology whether inside or outside school walls.”

An educational consultant who speaks regularly to New York City public school teachers about technology in education, Will Richardson, said navigating how to treat new technologies is a difficult problem for schools. He said bans are the wrong answer.

“Right now the policy simply is no; we’re not going to talk about it. We’re not even going to discuss it. We’re just pretending that these things don’t even exist,” Mr. Richardson said. “That’s just bad. Because then I think we cannot be shocked when we hear of all the bad things that happen with cell phones. Who’s teaching the kids? Who’s teaching them what they should and shouldn’t be doing with cell phones?”

Mr. Richardson said he favors teaching students about the “context” of technologies: how they can be used for ill, as well as for good.

He said he recently visited a Manhattan high school and spoke to a class about cell phones, showing students how phones can be research tools (he looked up the population of Spain by texting “Spain population” to Google).

The students were wowed, but they had to rely on Mr. Richardson’s phone to do the trick. Because of the ban, they told him, all their phones were at a bodega down the street, where the students were paying $3 a day to store them.