From what I can tell your GPS is a Magellan eXplorist 100, which does NOT have an electronic compass, though I really like the orange case AND the fact that you're out with your kids.

GPS's without an electronic compass rely only on movement to determine direction. The faster the movement, the better its ability to determine direction, though I've found even at a walking pace they do surprisingly well. Once you stop, the GPS's compass is dumb - it either stops displaying the compass altogether or only shows the most recent direction observed.

The Geko 301 mentioned by someone else has a +/- 2 degree accuracy, which is pretty good - close to many (most?) magnetic compasses.

Keep having fun out there!