Measure 1 cup of the berries; mash.
Slice remaining berries.
In chafing dish or medium saucepan stir together brown sugar and cornstarch.
Gradually stir in the mashed strawberries and lime or lemon juice.
Cook and stir over medium heat till mixture is bubbly.
Cook and stir 1 minute more.
Add the sliced strawberries, stirring gently, and heat through.
Heat the rum in a small saucepan or ladle till almost simmering.
Flame and pour over fruit.
Stir gently till flame dies.
Serve over scoops of ice cream.