If the stitch you used will not roll (stockinette does roll), I would just do a few rows of garter stitch at either end. Manly, LOL.

If you're in the mood to knit another scarf for your son (or for anyone else, for that matter), do a Google search for "palindrome scarf." One of the first hits to come up in the search will be http://www.cometosilver.com/patterns/ she has a pattern for a scarf and a matching hat that have reversible cables, so there is no "wrong side." A great scarf pattern for men and women. You don't need to worry about doing anything to the ends. You cast on, knit the scarf, and then bind off. And, because of the pattern, it doesn't roll in on itself.