Although I do want the ability to block and filter web and search on my teens' monitored devices, on the other hand I do not want histories reported to me. Obviously, I can just ignore the histories, but I don't feel that's good enough. (I can understand why some parents may view histories as a feature; but I view it as a mistake.)
I don't see a way to disable the history. For example, in my parental panel under Web, I can View Activity History, then under the settings-wheel (Web Supervision), my options are On/Off, Supervision: Monitor, Warn, or Block, then I have controls over categories and manual website lists. Search Supervision is similar.
So, have I missed an option to turn off activity histories?