The older Schwinns commonly had 21.1 mm (7/8") quill stems. A few other brands used them at times as well.

I just bought a 21.1 mm quill to 1 1/8" adapter for $10 US on ebay. It was totally worth it. Fussing with 7/8 stems is a pain in the butt. If the stem on the bike works well for you, leave it alone. If' you need a different stem, I'd get an adapter. Mine was under the brand "Kruzer Kitz". The only other good option for ditching the 7/8 stem is to get a new fork and headset locknut that are 22.2 mm.