Schoolkids have an uncanny ability to cause minor hair disasters. How to handle three common ones, from Sandra Holland of the National Cosmetology Association:
Spray some detangler or apply a dollop of conditioner, then use a wide-tooth comb, starting from the bottom of the hair and gradually working up to the knot. (To prevent knots' landing, comb hair twice a day and put curly or long hair in a ponytail or braid for sleeping.)
Work about a teaspoon or two of peanut butter into the wad. It's messy, but most of the gum will dissolve in a few minutes. Shampoo afterward to remove the peanut butter. Or use an ice cube to freeze the gum, then pick it out.
If your child did her own trimming, you'll probably need to either live with it or have a professional feather the damaged portion. (Clips and head-bands can help hide the problem while the hair grows out.)