In the Fairfax County, Va., school district, technology experts have conducted their own security reviews of several hundred digital learning products, and failed a few of the most popular ones. In Houston, one of the largest districts in the country, administrators are testing their own rating system for digital learning products and developing a set of district-approved apps for teachers.

And in Raytown, Mo., Melissa Tebbenkamp, the school district’s director of instructional technology, vets every app that teachers want to try before allowing it to be used with students. Among other things, she checks to make sure those services do not exploit students’ email addresses to push products on them or share students’ details with third parties.

“We have a problem with sites targeting our teachers and not being responsible with our data,” Ms. Tebbenkamp said. For school technology directors around the country, she added, “it is a can of worms.”

The new tools are being pushed by a rapidly expanding education technology industry. Some educators, entrepreneurs and philanthropists are particularly enthusiastic about adaptive learning products because they aim to tailor lessons to the individual abilities of each student.

“If Suzy is good at long division but has trouble with division by zero, the software will show her more problems about division by zero,” said Umang Gupta, an entrepreneur who has invested in Front Row Education, an adaptive math start-up, and other educational technology ventures.

To get such products into classrooms quickly, many start-ups offer their basic products free to individual teachers, but charge for extra features or districtwide use — a “freemium” business model.