If the issue is purely about whether the school can determine what equipment you use for schoolwork, then the school will usually have reasonable discretion about that.
If the issue is about the manner of the screen monitoring, then you may be on strong ground in insisting that the monitoring is done openly and on similar terms to how a school operating healthily would monitor the contents of paper workbooks.
In other words, a teacher might pace the classroom and look over shoulders when people are working, or they may ask to see the contents of workbooks.
But you wouldn't expect there to be casino-style gantries in the ceiling so that teachers can spy into workbooks unseen, or other kinds of routine hidden snooping or rifling. That would usually be considered highly inappropriate behaviour for a teacher - at least when I went to school. It would have been considered an inappropriate mentality in the way it relates to students and seeks to supervise them.
Even if a school can ultimately override privacy without the consent of the student, and there are perfectly legitimate reasons why they may on occasion, doesn't mean that the override itself shouldn't occur openly.
If this is the root of the issue about the Classwize software on the school-issued device, that it doesn't embed appropriate boundaries in its workings, then you may want to make that argument as justification for retaining a personal device.
Ultimately you may have to persuade and gain consent on the point, rather than insist on any particular rights.