I only wanted a border on the ends of the scarf, and the whole thing is trying to curl. What can I do?
See this thread for some ideas. You can knit a border on the scarf as you go along, or pick up sts to knit or crochet one when you're done. Stockinette is going to curl and you'll have to have an edging border.
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Unfortunately that is the nature of the beast for stockinette. You'll either have to pick up stitches and knit a border or do it as you knit in the first place.