Seems pretty sketchy. Unless they make their intention very clear from the beginning, this is inappropriate. Maybe if they make it VERY clear from the beginning, like say hey, were going to be looking at everything you do a google search on.
For context, this is the next part of the article (which I couldn't paste due to character limits)
Caldeira said she did not monitor student activities on her own initiative. With the onset of virtual learning, Buena Vista Middle School began using GoGuardian, a software that is usually installed on school-provided devices and allows teachers to see what students are doing on their computers while they are in class. The software is designed to flag words or behaviors identifying children at risk of harming themselves or others. According to its website, GoGuardian is used in 30,000 schools with over 22 million K-12 students, helping teachers communicate with students and keep them on task. Caldeira said her school uses the software for suicide and violence prevention as well, but that individual teachers do not have access to that information. The district declined to answer questions about its use of GoGuardian. Caldeira said she didnt intend to track her students activities online My theory is: If you were off task, the consequence is a poor grade, she said but that one day, as she used the software to chat with students, she noticed one student on a website about Transgender Day of Visibility. I see a site thats emblazoned with rainbows, she said. How am I not going to notice that? After class, she said, she made a mental note to invite the student to the UBU club. Baraki had a similar experience, Caldeira said, once noticing a student on an LGBTQ website. She said the two shared these anecdotes at the conference, But that was it. As for the we totally stalked what they were doing on Google comment, Caldeira said, It was tongue in cheek. She said teachers do not have access to students private social posts, messages and emails. If the schools investigation finds that Caldeira and Baraki had taken action based on students online activity during class through GoGuardian, there is likely no law preventing what they did, privacy experts said. Amelia Vance, vice president of youth and education at the Future of Privacy Forum, explained that, legally speaking, an educator seeing something a student is doing through GoGuardian is not any different than a teacher walking around a classroom and noticing students behavior or what they had visible on their screens.