We tried a few different techniques for cleaning our stove top that I think would work well for you too! https://www.charlestoncrafted.com/three-ways-clean-glass-electric-stove/
This should help, Lori:
I use Bon Ami or Bartender's Friend.
If you use baking soda and water along with a pot scrubber you should be able to remove the burn marks.
Bar keepers friend, or glass stove top cleaner with a scrubbie.