But that also caused problems in Chicago and another district when Google went looking for teachers to try a new app — effectively bypassing district administrators. In both cases, Google found itself reined in.

Unlike Apple or Microsoft, which make money primarily by selling devices or software services, Google derives most of its revenue from online advertising — much of it targeted through sophisticated use of people’s data. Questions about how Google might use data gleaned from students’ online activities have dogged the company for years.

“Unless we know what is collected, why it is collected, how it is used and a review of it is possible, we can never understand with certainty how this information could be used to help or hurt a kid,” said Bill Fitzgerald of Common Sense Media, a children’s advocacy group, who vets the security and privacy of classroom apps.

Google declined to provide a breakdown of the exact details the company collects from student use of its services. Bram Bout, director of Google’s education unit, pointed to a Google privacy notice listing the categories of information that the company’s education services collect, like location data and “details of how a user used our service.”

Mr. Bout said that student data in Google’s core education services (including Gmail, Calendar and Docs) “is only used to provide the services themselves, so students can do things like communicate using email.” These services do not show ads, he said, and “do not use personal data resulting from use of these services to target ads.”

Some parents, school administrators and privacy advocates believe that’s not enough. They say Google should be more forthcoming about the details it collects about students, why it collects them and how it uses them.

“If my daughter came home and logged on to Google Docs on my computer at home, they’ll know it was now coming from this address,” said Mr. Barsotti, the Chicago-area project manager. “If this is truly for educational purposes, what is their business model and why do they need to collect that?”