If your students are anything like me, then they will have the ability to track their own progress using their phone. I haven't pressed go on it every time but it has let me confirm in de-brief when I had got off track and acted as a memory tool, so I could discuss parts of the flight with my instructor. I've also used it to confirm to myself how far away from the correct circuit I've been in earlier lessons...
To me these things come down to trust. I've really enjoyed the freedom the solo navexes have given me and wouldn't have welcomed "big brother" watching me, but the additional information that I've voluntarily recorded has helped with de-briefs.
To answer the question - you appear to be able to buy a data logger from Amazon for £40 upwards (search for "GPS Data Logger"). They all allow you to export in kml or gpx format, which you can then load into google maps / google earth or another piece of software to view the output.